CFD CALIBRATED THERMAL NETWORK MODELLING FOR OIL-COOLED POWER TRANSFORMERS

Transcription

1 CFD CALIBRATED THERMAL NETWORK MODELLING FOR OIL-COOLED POWER TRANSFORMERS A thesis submitted to The University of Manchester for the degree of PhD in the Faculty of Engineering and Physical Sciences 2011 WEI WU School of Electrical and Electronic Engineering

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3 Table of Contents List of Figures... 6 List of Tables... 8 Nomenclature... 9 Vocabulary Abstract Declaration Copyright statement Acknowledgements Chapter 1 Introduction Background Statement of the problem Research objective and scope Original contribution and outline of the thesis Chapter 2 Literature review Transformer end-of-life Transformer life and transformer ageing Cellulose thermal ageing Thermal ageing mechanisms Thermal performance

4 2.2.1 Transformer losses Transformer cooling Thermal diagram Heat run test Direct measurement of the hot-spot temperature Dynamic loading and overloading Thermal modelling CFD/FEM methods Experimental validation Network modeling Introduction Equations Prediction on oil flow and temperature distributions Review of the methodology Summary Chapter 3 Network modelling and assumptions Paper Paper Chapter 4 CFD calibration for network modelling Paper Paper

5 Chapter 5 Comparison between network model and CFD predictions Paper Chapter 6 Optimisation of transformer thermal design Paper Chapter 7 Conclusions References Appendix I Reference [19] Appendix II Reference [40] Appendix III List of publications The final word count, including footnotes and endnotes, is 47,590. 5

6 List of Figures Figure 1.1 A 410/120 kv, 400 MVA power transformer [5] Figure 1.2 Transformer thermal diagram in IEC loading guide [9] Figure 1.3 Predicted end-of-life from DP versus IEC thermal model [16] Figure 1.4 The objectives of thermal network modelling work Figure 1.5 Overall research scope related to network modelling Figure 1.6 Calibration and application of network modelling Figure 2.1 Research theme framework covered by literature review Figure 2.2 Representative of paper insulation ageing to transformer ageing Figure 2.3 Relative transformer insulation life per unit life [49] Figure 2.4 Representation of DP and TS to cellulose chain scissions η for Kraft paper [8,7] Figure 2.5 Derivation of DP after a thermal ageing period Figure 2.6 Transformer losses classification [56] Figure 2.7 Three geometry models for winding eddy current loss simulation [57].. 40 Figure 2.8 Magnetic leakage flux results from three geometry models in Figure 2.7 [56] Figure 2.9 Large eddy current loss at winding top and uniform DC loss distribution [57] Figure 2.10 Transformer cooling oil circuit (non-directed mode) Figure 2.11 Transformer cooling oil circuit (directed mode)

7 Figure 2.12 Analytical derivation of hot-spot factor (2.12) Figure 2.13 Inverse accumulated distribution of hot-spot factors H [48] Figure 2.14 Themes relevant to transformer heat run test Figure 2.15 Arrangement of thermal sensors in [70] Figure 2.16 Examples of fixation slots for optic-fibres inside windings [8] Figure 2.17 Principle sketch of thermal circuit analogy [77] Figure 2.18 General procedure for CFD/FEM simulations Figure D model and mesh for calculating [37] Figure 2.20 Streamline results for the simulation case in [36] Figure 2.21 Hierarchy of network modelling equations Figure 2.22 Hydraulic and thermal networks Figure 2.23 Flow chart for solving network models Figure 2.24 Calculated disc temperatures with directed oil washers [26] Figure 2.25 Calculated oil velocities of horizontal ducts with directed oil washers [26]

8 List of Tables Table 2-1 Normal insulation life of a well-dried, oxygen-free thermally upgraded insulation system at the reference temperature of 110 o C Table 2-2 Environmental factor and activation energy for oxidation and hydrolysis of Kraft paper [8] Table 2-3 Analogy to electric circuit principles [87] Table 2-4 Categorised literatures list Table 2-5 Categorised literatures related to CFD/FEM simulations Table 2-6 Categorised literatures related to experimental validation Table 2-7 Network modelling equations Table 2-8 Equations for Nusselt number at various conditions [30]

9 Nomenclature θ Temperature Θ Temperature in Kelvin (= θ ) θ h θ a Δθ hr Δθ h Δθ or Δθ o Δθ br Δθ om,w g r g H K R R x y k 11 k 21 k 22 t τ o τ w η k F AA A E A f l A c D u ΔP Hot-spot temperature Ambient temperature Hot-spot-to-top-oil temperature rise at rated load Hot-spot-to-top-oil temperature rise Top-oil temperature rise at rated load Top-oil temperature rise Bottom-oil temperature rise at rated load Average oil temperature at winding Winding-to-oil temperature gradient at rated load Winding-to-oil temperature gradient Hot-spot factor Load factor Ratio of load losses at rated load to no-load losses Molar gas constant, J/(K mol) Oil exponent Winding exponent Thermal model constant Thermal model constant Thermal model constant Time Oil time constant Winding time constant Chain scissions of insulating paper Ageing rate of insulation Relative ageing acceleration rate Chemical environment pre-exponent Activation energy Friction coefficient at fluid flow ducts Length of oil duct Cross-sectional area of oil duct Hydraulic diameter of oil duct (= 4A c =wetted perimeter) Average flow velocity at oil duct Pressure drop from upstream to downstream of oil duct 9

10 ρ μ μ c μ w C k Re Nu Pr Gr Ra Density of oil Dynamic viscosity of oil The dynamic viscosity at oil duct centre The dynamic viscosity at oil duct wall Specific heat capacity of oil Thermal conductivity of oil Reynolds number Nusselt number Prandtl number Grashof number Raleigh number 10

11 Vocabulary LV Low voltage HV High voltage HSR Hot-spot temperature rise MWR Mean winding temperature rise TOR Top oil temperature rise BOR Bottom oil temperature rise MOR Mean oil temperature rise ONAN Oil-Natural-Air-Natural cooling mode ONAF Oil-Natural-Air-Forced cooling mode OFAF Oil-Forced-Air-Forced cooling mode ODAF Oil-Directed-Air-Forced cooling mode DP Degree of Polymerisation of insulating paper TS Tensile strength of insulating paper LTC Load tap changer 1-D One Dimensional 2-D Two Dimensional 3-D Three Dimensional CFD Computational Fluid Dynamics N-S Navier-Stokes Equation FEM Finite Element Method FVM Finite Volume Method JPL Junction pressure loss in network models HWA Hot Wire Anemometry TNM Thermal Network Modelling TMDS Transformer Monitoring and Diagnosis System GUI Graphic User Interface 11

12 Abstract Power transformers are key components of electric system networks; their performance inevitably influences the reliability of electricity transmission and distribution systems. To comprehend the thermal ageing of transformers, hot-spot prediction becomes of significance. As the current method to estimate the hot-spot temperature is based on empirical hot-spot factor and is over-simplified, thermal network modelling has been developed due to its well balance between computation speed and approximation details. The application of Computational Fluid Dynamics (CFD) on transformer thermal analysis could investigate detailed and fundamental phenomena of cooling oil flow, and the principle of this PhD thesis is then to develop more accurate and reliable network modelling tools by utilising CFD. In this PhD thesis the empirical equations employed in network model for Nusselt number (Nu), friction coefficient and junction pressure losses (JPL) are calibrated for a wide range of winding dimensions used by power transformer designs from 22 kv to 500 kv, 20 MVA to 500 MVA, by conducting large sets of CFD simulations. The newly calibrated Nu equation predicts a winding temperature increase as the consequence of on average 15% lower Nu values along horizontal oil ducts. The new friction coefficient equation predicts a slightly more uniform oil flow rate distribution across the ducts, and also calculates a higher pressure drop over the entire winding. The new constant values for the JPL equations shows much better match to experimental results than the currently used off-the-shelf constants and also reveals that more oil will tend to flow through the upper half of a pass if at a high inlet oil flow rate. Based on a test winding model in the laboratory, the CFD calibrated network model s calculation results are compared to both CFD and experimental results. It is concluded that the deviation between the oil pressure drop over the pass calculated by the network model and the CFD and the measured values is acceptably low. It proves that network modelling could deliver quick and reliable calculation results of the oil pressure drop over windings and thereby assist to choose capable oil pumps at the thermal design stage. However the flow distribution predicted by network model deviates from the one by CFD; this is particularly obvious for the cases with high flow rates probably due to the entry eddy circulation phenomena observed in CFD. As no experiment validation has been conducted, further investigation is necessary. The CFD calibrated network model is also applied to conduct a set of sensitivity studies on various thermal design parameters as well as loads. Because the studies are on a directed oil cooling winding case, an oil pump model is incorporated. From the studies recommendations are given for optimising thermal design, e.g. narrowed horizontal ducts will reduce average winding and hot-spot temperatures, and narrowed vertical ducts will however increase the temperatures. Doubled oil block washers are found to be able to significantly reduce the disc temperatures, although there is a slight reduction of the total oil flow rate, due to the increase of winding hydraulic impedance. The impact of different loadings, 50%~150% of rated load, upon the forced oil flow rate is limited, relative change below 5%. The correlations between the average winding and hot-spot temperatures versus the load factors follow parabolic trends. 12

13 Declaration No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. 13

14 Copyright statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the Intellectual Property ) and any reproductions of copyright works in the thesis, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see and in The University s policy on Presentation of Theses. 14

15 Acknowledgements I would like to express my sincere gratitude to my supervisor Professor Zhongdong Wang for her invaluable guidance and great support throughout the research project. Her perpetual enthusiasm in research has motivated everyone including me, and without her knowledgeable supervision and patient assistance, it would be impossible for this thesis to be prepared. I would like to thank National Grid and the Engineering and Physical Sciences Research Council (EPSRC) Dorothy Hodgkin Postgraduate Award (DHPA) for providing the PhD scholarship at The University of Manchester. I would like to express my gratitude to Paul Jarman of National Grid, John Lapworth of Doble PowerTest, Edward Simonson of Southampton Dielectric Consultants Ltd and Dr Alistair Revell and Professor Hector Iacovides from School of Mechanical, Aerospace and Civil Engineering, University of Manchester for their precious technical advices. Due appreciation should also be given to the colleagues of CIGRE WG A2.38 for inspiring discussions. To the colleagues of the Power Systems Research Centre, I would like to extend my sincere gratitude. I would like to specially thank my colleagues and friends for their support along the way, which makes my stay here such a tremendous experience. Last and not least, I would like to thank my family for their support. I would like to thank my parents for their encouragement and constant blessings. I would like to thank my wife, Ting Dong, for her deep love and constant support to me and my work, especially when I was facing difficulties. 15

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17 Chapter 1 Introduction 1.1 Background Power transformers include the transformers connecting generation stations and distribution networks as well as generator transformers, and their power ratings are commonly larger than 500 kva [1,2]. An onsite 400 MVA power transformer is shown in Figure 1.1. Power transformers are key, and one of the most expensive components of electric system networks. Their performance and reliability inevitably influence the reliability of electricity transmission and distribution systems, especially when a significant fraction of the transformer fleet has been in operation for more than their designed life, 50 years [3,4]; for instance, in the UK network, by 2010 almost half of the in-service transformer population have approached or exceeded their designed life. Figure 1.1 A 410/120 kv, 400 MVA power transformer [5]. Although a transformer failure can originate from different components, such as tapchangers, windings, bushings and tanks etc, and can be triggered from various events from the network such as short circuits and lightning, thermal degradation of the insulating paper is regarded as an important and ultimate factor for the deleterious changes to the serviceability of transformers. The thermal degradation is a function 17

18 of temperature [6,7,8], and as such the hot-spot temperature θ h defined as the highest temperature of transformer windings [9] becomes significant since the insulation at the hot-spot will undergo the worst degradation. In consequence, it is of paramount interest for transformer users, including electricity network operators, to predict and constrain the magnitude of the hot-spot temperature, in order to limit the insulation ageing rate and to manage the assets lifetime. The overall demand for energy in the UK is expected to increase by 1% per annum over the period from 2007 to 2023 [10]. This increasing demand as well as the increasing financial constraints placed on electricity utility companies by the Office of Gas and Electricity Markets (OFGEM) force the companies to be more strategic with the maintenance and replacement of their transformer assets. The real load of a transformer varies with time due to the different usage of electricity at different periods, so daily, weekly and yearly loading may vary with time (being dynamic) and follow a certain pattern. The thermal overshoot phenomena caused by dynamic loading may cause severe transformer life depletion. Thermal overshoot means the hot-spot temperature rise over top-oil temperature Δθ h may be higher at a step increase of load than the fully established steady state value [11,12]. In the period of high electricity usage, the transformer may work with load exceeding its rated load; in this scenario the transformer is overloaded. The impact of overloading upon hot-spot and thermal ageing needs to be better understood before overloading a transformer, especially the aged ones [13,14]. At the same time, manufacturers are also under increasing pressures from their customers to produce transformers with better thermal performance, namely lower mean winding temperature rise, hot-spot rise and top oil rise above ambient [8]. In the factory heat run test, the mean winding and top oil temperature rises can be measured, but hot-spot cannot be measured directly since its location is unknown. Prediction of hot-spot location is challenging because the coolant oil distributions flowing through the array of winding discs are complex and often inhomogeneous. So far, there have been 3 CIGRE working groups (WG) assembled to carry out studies which are relevant to transformer thermal performance, WG Thermal aspects of transformers in 1986, WG A2.24 Thermal performance of transformers 18

19 in 2003 and WG A2.38 Transformer thermal modelling in Particularly the initiation of the on-going working group A2.38 emphasized the importance of numerical thermal modelling tools to predict the hot-spot and to update the manufacturers thermal design tools. 1.2 Statement of the problem The present ageing status of the in-service transformers in the electrical power network prompts the examination of thermal design tools. Consequently the problem studied in this PhD thesis is related to how to accurately predict hot-spot temperature and its location. When considering hot-spot [15], firstly manufacturers need to design oil cooling systems to restrain the hot-spot temperature, including suitable oil driving methods, i.e. naturally by buoyancy or forced by pumps, as well as sufficient oil duct dimensions and block washer arrangement if necessary. Secondly winding-to-oil temperature gradient g r and top-oil temperature rise Δθ or of the manufactured transformer is measured during heat run test and both values can then be used to roughly estimate the hot-spot temperature with the standard thermal diagram. The standard thermal diagram, Figure 1.2, in the IEC loading guide [9] is used to predict the approximate hot-spot temperature. Hot-spot temperature θ h is regarded to be higher than top winding temperature and an empirical hot-spot factor H is defined as the ratio of hot-spot-to-top-oil temperature gradient Δθ hr to winding-to-oil temperature gradient g r for estimating hot-spot θ h. 19

20 Component Height Top of the winding Hot spot temperature θ hr = 98 ºC Top Winding Rise = 72 K TOR Δθ or = 52 K T-B = 14 K 6 K Δθ hr = Hg r = 26 K Hot spot temperature Winding Height g r = 20 K Bottom of the winding 20 ºC Ambient θ a MOR = 45 K MWR = 65 K Temperature Figure 1.2 Transformer thermal diagram in IEC loading guide [9]. The methods currently used by transformer manufacturers to predict hot-spot temperature rely on a general empirical hot-spot factor, which in truth, heavily depends on individual designs and is also affected by the non-uniformity of winding losses, local heat transfer coefficient over the winding height. The approximate hot-spot factor values recommended from IEC are 1.1 for distribution transformers, 1.3 for power transformers; the larger the transformer, the greater the value should be used [9]. These recommended values may under-estimate hot-spot temperatures; this impression is based on the mis-match between the predicted transformer lifetimes from measured Degree of Polymerisation (DP) values and from the IEC thermal model with the recommended hot-spot factors [16]. DP values of paper at various locations are available from scrapping transformers, the lowest DP of paper in a transformer can be used for estimating the worst insulation ageing rate which can be converted into the transformer s lifetime. On the other hand the worst ageing rate of paper in a transformer can be derived from the hot-spot temperature, which is calculated with IEC thermal model, heat run test data, 20

21 Thermal end-of-life (Year) CFD Calibrated Thermal Network Modelling for Oil-cooled Power Transformers recommended hot-spot factors, load profile and ambient temperature. Figure 1.3 uses the hot-spot factor of 1.3 and shows that for the 12 scrapped power transformers, IEC thermal model predicted lifetimes are much longer than the lowest DP predicted ones with only one exception. In the IEC thermal model predicted lifetimes, additional factors such as the switch between natural and forced dual-cooling modes and the different dominating ageing mechanisms in different applicable temperature ranges, i.e. oxidation and hydrolysis, are all considered [16]; therefore the lifetime deviation indicates that the general hot-spot factor 1.3 may be underestimated. Predicted end-of-life from DP vs IEC thermal model up to Scrapped transformer number Lowest DP predicted life IEC thermal model predicted life Figure 1.3 Predicted end-of-life from DP versus IEC thermal model [16]. Overall, to obtain the precise hot-spot factor requires accurate understanding of the temperature distributions along the windings and costly detailed measurement validations [17]. As a matter of fact, along with the development of computation technologies, numerical modelling has been applied for predicting the temperature distributions for over 40 years [18]. Due to the complexity of the transformer thermal phenomena, approximations of different discretisation levels were made to deliver the calculation targets including oil flow and temperature distributions and hot-spot temperature. So far the numerical tools that have gained widespread usage can generally be categorised as either 21

22 lumped parameter network modelling [19-33] or the methods which incorporate a degree of Computational Fluid Dynamics (CFD) [13,34-44]. Generally as methods of the highest spatial resolution, CFD simulations can be expected to provide more detailed results but also with a tremendous increase in the required computational effort. In comparison to CFD, lumped parameter network models cannot be expected to exhibit the detailed flow pattern at a junction point or inside a duct region, but they are regarded as a quick and simple numerical approximation and are convenient for industry use, as a large range of design parameters can be trialed for a relatively low computational effort. Network models are well balanced between its calculation speed and approximation details. The primary principle of this thesis is therefore on network modeling and the main objective of this PhD work is to develop more accurate and reliable network modelling tools for industry. Network models incorporate significant assumptions about the flow and subsequently empirical equations to describe physical properties of the fluid, and these approximations and empirical equations are to be calibrated by using CFD simulations within a well-defined range of transformer design parameters, such as oil duct dimensions. 1.3 Research objective and scope The ultimate purposes of the research are to develop accurate and reliable thermal design tools and to aid transformers lifetime assessment by using these thermal modelling tools to calculate the hot-spot temperature. This is briefly summarised in Figure 1.4. The overall research scope is shown in Figure 1.5. A complete thermal network model comprises a network model for coping with multi-winding, an external radiator model and a model for describing oil pumps, which will be present if the transformer has a forced oil cooling mode. The latter two models can determine the inlet oil flow rate and the temperature of oil supplied into the winding model. The three parts are coupled together to model the complete coolant oil circulation from the windings to the external radiators. 22

23 Thermal network modelling Examine the hot-spot temperature Thermal design tool for manufacturers Transformer end-oflife assessment Figure 1.4 The objectives of thermal network modelling work. Network modelling scope External radiator model Pump model CFD calibration Multi-winding network model Application on transformer cases Parametric studies Experimental validation Figure 1.5 Overall research scope related to network modelling. (The dash line parts are future work beyond this thesis scope.) The winding network model was firstly calibrated by using CFD simulations for a wide range of winding dimensions used by power transformer designs from 22 kv to 500 kv, 20 MVA to 500 MVA. The fully calibrated network model was then applied to several winding cases, and parametric studies were also completed on oil duct dimensions etc for suggesting optimal thermal design practice. Both the external radiator model and experimental verification belong to the future work beyond this thesis scope. In particular, the CFD calibration minimized the calculation error of network models by using CFD results as a baseline; however in 23

24 order to validate the models, experimental measurements are required. In the work of [21-23,37,40,45-47] different test and measurement approaches, such as thermocouples, hot wire anemometry (HWA) and Laser-Doppler velocimetry etc, were used to valid the numerical model they had developed. In detail, Figure 1.6 describes the items relevant to calibrating the network model with CFD simulations. The CFD calibration work was conducted upon the three sets of empirical equations on Nusselt number, friction coefficient at oil ducts and junction pressure losses (JPL) respectively. The parametric studies using the calibrated network model are classified into forced and natural oil cooling modes. For the force oil cooling mode, the inlet oil flow rate is determined by oil pumps, and as such the study incorporated pump models. For the natural oil cooling mode, the inlet oil flow is driven by buoyancy, and a proper external radiator model is required. Oil pump model External radiator model Forced oil cooling mode Natural oil cooling mode Parametric study Calibrated network modelling Nusselt number (Nu) Friction coefficient Junction pressure losses (JPL) Calibration Computational Fluid Dynamics (CFD) simulations Figure 1.6 Calibration and application of network modelling. (The dash line parts are future work beyond this thesis scope.) 24

25 1.4 Original contribution and outline of the thesis In summary, this PhD thesis focuses on network modelling techniques and the possible improvement when being calibrated by the CFD. This is achieved by 1. An analytical study conducted to prove that 2D channel flow approximation is sufficient for modelling horizontal oil ducts in disc-type windings. 2. A mathematical model developed to predict the detailed temperature distribution at a winding disc. The model was then used to verify the assumption in network models that oil temperature is linearly increasing along disc surfaces and thus the highest temperature is located at the downstream end of oil duct. 3. Large sets of CFD simulations produced for calibration of the empirical expressions employed in network modelling, including Nusselt number, friction coefficient and junction pressure loss (JPL) equations. 4. A network modelling prediction on both oil flow and winding temperature distributions compared with the corresponding CFD predictions as well as the available hydraulic-only experimental results. 5. A set of parametric studies, by using the CFD calibrated network model, upon different design parameters including oil duct dimensions and block washer arrangement etc. Recommendations on thermal design were concluded from the study finally. The remainder of this thesis is organized as follows: Chapter 2: Literature review This chapter presents a literature survey on the transformer thermal related issues, including knowledge of insulation cellulose ageing, thermal end-of-life and numerical thermal modelling. The latest meaningful work relative to the transformer thermal modelling and applications are particularly mentioned. Chapter 3: Network modelling and assumptions This chapter comprises two papers, Natural convection cooling ducts in transformer network modelling, published in Proceedings of the International Symposium on High Voltage Engineering (ISH) 2009, and Heat transfer in transformer winding conductors and surrounding insulating paper, published in Proceedings of the 25

26 International Conference on Electrical Engineering (ICEE) The first author of the two papers is this thesis author who did the work, and the other two authors are this thesis author s supervisor and advisor. Chapter 4: CFD calibration for network modelling This chapter comprises two papers, CFD calibration for network modelling of transformer cooling oil flows Part I heat transfer in oil ducts, accepted by IET Electric Power Applications, and CFD calibration for network modelling of transformer cooling flows Part II pressure loss at junction nodes, accepted by IET Electric Power Applications. The first author of the two papers is this thesis author who did the work. The second and the third authors are this thesis author s supervisor and advisor respectively. The fourth author of the first paper is a professor in School of Mechanical, Aerospace and Civil Engineering (MACE), University of Manchester, who contributed through technical discussions. The last author is the transformer specialist of the sponsoring company, who gave technical advices through discussions. Chapter 5: Comparison between network modelling and CFD calculation results This chapter comprises one paper, Prediction of the oil flow distribution in oilimmersed transformer windings by network modelling and CFD, provisionally accepted by IET Electric Power Applications. This paper was produced from the collaboration work with Universität Stuttgart and the second author is this thesis author who did 50% of the work. The first author is a PhD student in Institut für Energieübertragung und Hochspannungstechnik (IEH), Universität Stuttgart, who did the other half of the work, and the third author is his supervisor, the professor of IEH, Universität Stuttgart. The last author is this thesis author s supervisor. Chapter 6: Optimisation of transformer thermal design This chapter comprises one paper, Optimisation of transformer directed oil cooling design using network modelling, submitted to IET Generation, Transmission & Distribution. The first author of the paper is this thesis author who did the work. The second author is this thesis author s supervisor and the third author is the transformer specialist of the sponsoring company, who gave technical advices through discussions. 26

27 Chapter 7: Conclusions This chapter summarises conclusions of the PhD research and recommendations for further study. This thesis is structured in an alternative format due to the sufficient number of the publications produced during the three years PhD research. The publication list is in Appendix III. 27

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29 Chapter 2 Literature review In this chapter a literature survey is made on the background knowledge of insulation cellulose ageing, thermal end-of-life and numerical modelling methods. The latest worldwide worth-noting work relevant to transformer thermal performance, thermal design optimization and thermal modelling are particularly mentioned. A framework of the research themes covered by the literature review is shown in Figure 2.1 to guide the readers. IEC model IEEE model Other variations Life depletion Insulation ageing (Arrhenius equation) Thermal performance Thermal modelling Thermo-circuit analogy Network models Lumped parameter models CFD FVM / FEM Heat run test Optic-fibre Simulation of total losses Short-circuit method Open-circuit method Measurement devices Install recommendations Fluorescent optic-fibre Figure 2.1 Research theme framework covered by literature review. Poor thermal performance, i.e. high operational temperatures, is the major underlying reason for transformer life depletion. Thermal performance is assessed in three ways: numerically by (1) thermal modelling and experimentally by (2) heat run test or (3) optic-fibre temperature measurements where hot-spot temperature is always the most desirable parameter to identify. Thermal modelling techniques can be split into three major categories, two of which are lumped parameter models, i.e. the thermo-circuit analogy and network models; and the third one, CFD, which is based on highly discretised finite volume method (FVM) or finite element method (FEM) methods. Thermal modelling is particularly 29

30 useful when prediction of a hot-spot temperature becomes necessary during design stage or for new operational loading scenarios. Heat run test is based on the principle of total loss simulation, and according to the simulation approaches, is categorised into short-circuit (simulated by copper loss, for large transformers) and open-circuit (simulated by iron loss, for small transformers including distribution transformers) methods. The shortcoming of heat run test is that it can only be used to assess the global temperature parameters of a transformer such as top-oil temperature and average winding temperature rise. This prompts the necessity to install the opticfibres for local temperature measurement. 2.1 Transformer end-of-life Transformer life and transformer ageing Lifetime evaluation of any equipment is related to its ageing process. Particularly for transformers, the term ageing could refer to either the transformer or its insulating material. The ageing terms can be described as in [48] Ageing of transformers: irreversible deleterious changes to the serviceability of the transformers. Ageing of material: an irreversible negative change in a pertinent property of the insulation s mechanical strength. The difference between them is that transformers have functions to perform in a sense that a material does not. Assuming that the insulation ageing can represent the transformer ageing, the life duration of transformer can be described almost exclusively by the insulation ageing, or more specifically, the thermal degradation of the mechanical strength of the paper insulation between the winding turns. The ultimate life duration of a transformer is assumed to be the life duration of its paper insulation, thus one-to-one correspondence exists between the transformer remaining life and the value of a pertinent property under consideration. The pertinent property can be either degree of polymerization (DP) or tensile strength (TS). Then the correlation from transformer life to DP and TS is shown by the framework in Figure

31 Transformer lifetime Transformer ageing (functional) equivalent Thermal degradation of paper insulation reflect Pertinent properties DP TS Figure 2.2 Representative of paper insulation ageing to transformer ageing. The irreversible ageing or deterioration of paper insulation strongly depends on temperature as well as moisture, acidity and oxygen etc. For sealed transformers, the modern oil preservation systems minimise the moisture and oxygen contributions, leaving temperature as the governing parameter accounting for the insulation ageing [49]. For free breathing transformers, the ageing is equally affected by the moisture and oxygen. The word life in the loading guides means calculated insulation life rather than actual transformer life. As addressed in the IEC and IEEE loading guides [9,49], many factors can influence the ageing process and it is difficult to use only one straight-forward end-of-life criterion to contain all of these factors. Arrhenius s Law of the thermal degradation at absolute temperature Θ, (2.1), is commonly applied to express the insulating material ageing process. Due to the temperature non-uniformity in a transformer winding, the part operating with hotspot temperature will undergo the worst degradation, and transformer end-of-life would be estimated by (2.1) with the substitution of hot-spot temperature into the temperature variable. / R k Ae E A (2.1) k = Ageing rate of insulation A = Chemical environment pre-exponent E A = Activation energy R = Molar gas constant, J/(K mol) Θ = Temperature in Kelvin 31

32 IEC loading guide As IEC loading guide [9] proposed, the ageing rate of non-thermally upgraded paper, Kraft paper, would be doubled for each temperature increase of 6 o C [50,51], and this rate suits for the temperature range from 90 o C to 110 o C [15]. A relative ageing rate V can therefore be represented by (2.2), based on 98 o C reference temperature. For thermally upgraded paper the ageing rate is relatively lower than that of Kraft paper and (2.3) was suggested, in which 110 o C reference was used instead. Equation (2.3) is referred from the ageing acceleration factor F AA equation in IEEE loading guide [49]. V ageing rate at h o ageing rate at 98 C 2 h 98 6 (2.2) V ageing rate at h ageing rate at 110 o C exp h 273 (2.3) For thermally upgraded paper, IEC Loading Guide also suggests four end-of-life criteria at the reference temperature 110 o C, as in Table 2-1. Depending on the different criteria, lifetime varies from 65,000 to 180,000 hours. The criterion of 200 retained DP value, equivalent to 20% retained TS, is commonly accepted and DP is relatively easier to measure than TS in practice. With the reference lifetime and the relative ageing rate V, lifetime at a given temperature can be estimated. Table 2-1 Normal insulation life of a well-dried, oxygen-free thermally upgraded insulation system at the reference temperature of 110 o C. Basis Normal insulation life Hours Years 50 % retained tensile strength of insulation ,42 25 % retained tensile strength of insulation , retained degree of polymerization in insulation ,12 Interpretation of distribution transformer functional life test data ,55 32

33 IEEE loading guide IEEE loading guide [49] defines a relative per unit life and an ageing acceleration factor F AA which has the same definition with the relative ageing rate V in IEC loading guide. The per unit life is based on a reference temperature 110 o C and is defined as per unit life ,000 exp h 273 (2.4) where θ h is the hot-spot temperature in o C. Apparently per unit life is equal to 1 when θ h = 110 o C, and it is more than 1 for temperature θ h below 110 o C whereas it is less than 1 for θ h above 110 o C. The correlation of per unit life to hot-spot temperature, in line with (2.4), is shown in Figure 2.3. Figure 2.3 Relative transformer insulation life per unit life [49]. The F AA equation for thermally upgraded paper is the same as (2.3). F AA is more than 1 for hot-spot θ h above the reference 110 o C, and otherwise it is less than 1. By integral of F AA, the equivalent life consumed in a specific time duration can be estimated. 33

34 All in all, the relative ageing rate and lifetime equations (2.2) to (2.4) indicate that the insulation ageing and lifetime are sensitive to temperatures. The hot-spot temperature θ h then corresponds to the transformer s lifetime. This is the reason why the prediction on hot-spot temperature is of primary interests for transformer thermal design. When concerning the lifetime management of an entire transformer fleet, statistical tools such as normal or Weibull distribution models need to be applied using the individual transformer ageing or lifetime as a sample [52]. Various operation conditions, including loading profiles, ambient temperatures etc and various thermal designs, should add variability to the population and therefore ageing and lifetime prediction is a statistical matter for the entire fleet [53] Cellulose thermal ageing As previously discussed, transformer ageing can be reflected by a pertinent property of the insulating paper. From a chemical viewpoint, the ageing of insulation materials is a reflection of the molecular cellulose chains breaking, and thus the chain scissions (η) can be used as an ageing factor. However because of the difficulty in directly measuring η, equivalent quantities can be considered in practice to be a measurement. Due to the cellulose chains breaking, the chain length and degree of polymerization (DP) value of the cellulose reduce at the same time. Therefore DP can be chosen as a measurable property to describe the chain scissions and for limited ageing, chain scissions η is proportional with 1/DP [8]. DP of new Kraft paper is in the range of 1000 ~ After going through the factory drying process, the paper in transformers will have a DP of ~1000 [7]. Along with the material ageing the DP value reduces gradually. By experiments, a good correlation between the reduction of mechanical strength and of DP has been shown [54]. On the other hand, while DP values are above 200, chain scissions η is proportional to tensile strength (TS) as well; TS can also be selected to reflect the chain scissions. The relationships between cellulose chain scissions, DP and TS are described in Figure

35 = DP 0 =DP t 1 Material chain scissions η = 0:06 (110 TS) DP TS Figure 2.4 Representation of DP and TS to cellulose chain scissions η for Kraft paper [8,7]. It is found that 1/DP correlates linearly with thermal ageing time duration, t, i.e. (2.5), and the thermal ageing rate, k, is also in Arrhenius equation, (2.1). (2.1) and (2.5) can then be combined to obtain the DP equation in Figure DP t 1 DP 0 kt (2.5) 35

36 Linear reduction of DP with time 1 DP t 1 DP 0 Arrhenius equation = kt k = A e E A=R } DP( ; t) = DP 0 : Initial value of DP DP DP 0 At e E A=R R: Molar gas constant Θ: Absolute temperature A: Chemical environment parameter t: Time duration E A : Activation energy Life span is the time duration for DP value decreasing from 1000 down to 200. Figure 2.5 Derivation of DP after a thermal ageing period. As a matter of fact, with the help of the equation, the DP reduction in a time duration t, from DP 0 to DP t, can be calculated if the hot-spot temperature θ h in the duration is known and substituted into Θ. In practice, θ h varies with transformer loading; thereby the operation time of a transformer can be discretised into a series of consecutive time steps which are small enough that for each step, θ h can be assumed as a constant. In this way the equation in Figure 2.5 can be utilised to calculate the DP reduction of each time step, and starting from the initial DP of 1000, the accumulation of all the time steps for the DP value to continuously reduce to 200 is then the total lifespan of the transformer insulation Thermal ageing mechanisms Latest studies in [6,7,8] have identified the main ageing mechanisms of insulation paper in an in-service transformer to be oxidation or hydrolysis. Oxidation dominates at paper temperature within 60 C and hydrolysis at higher range up to 150 C. The third mechanism, pyrolysis, requires much higher activation energy than oxidation and hydrolysis and usually governs at temperatures higher than 150 o C, so it is not of interest in this thesis. While (2.1) is applied for calculating the insulation ageing rate k, A and E A are socalled environmental parameter and activation energy respectively. Different ageing mechanisms have different sets of A and E A values, and the values for Kraft paper are listed in Table

37 Table 2-2 Environmental factor and activation energy for oxidation and hydrolysis of Kraft paper [8]. A (hour -1 ) E A (kj/mol) Oxidation (dry) Hydrolysis (1.5% moisture content) Besides ageing mechanisms, the activation energy E A also depends on experimental conditions. For example, in some experiments for oxidation in which copper dusts were added to facilitate radical formation more easily, i.e. accelerating the ageing rate [55], lower E A values around 50 kj/mol was even found [8]. 2.2 Thermal performance Transformer thermal performance is reflected by the temperature rises of windings and oil; the lower the temperature rises, the better the thermal performance is. The temperature rises are the results from transformer losses, namely the heat source, and the oil cooling circulation. According to IEC standard, the thermal performance is assessed with factory heat run test, in which the global temperatures such as the top oil and the average winding temperature rises are measured. However the hot-spot temperature that reflects the worst insulation ageing and the transformer s end-of-life is not directly measured in a normal heat run test. While the hot-spot temperature estimation with the standard thermal diagram and the recommended hot-spot factor is recognised to be oversimplified, the direct temperature measurement on the localised hot-spot using opticfibres then becomes a necessity Transformer losses The preparation step prior to performing thermal modelling on a winding comprises the determination of the amplitude and the distribution profile of electromagnetic losses. The losses behave as the heat source and they are commonly classified as in Figure

38 Total losses No-load loss Load loss DC loss Stray losses Winding eddy loss Structural parts Figure 2.6 Transformer losses classification [56]. Total losses comprise load loss and no-load loss. Load loss is measured from short circuit tests, whereas no-load loss from open circuit tests. Load losses comprise DC loss and stray losses. In no-load conditions, magnetic leakage flux is very small and therefore stray losses on winding conductors and structural parts can be neglected [56]. The DC loss, also called Joule loss or Ohmic loss, is due to the Joule heating of the current in winding conductors and other current carrying parts. The stray losses, also called eddy current losses, are induced by stray flux in winding conductors and other metallic structural parts. The stray losses depend on the distribution of stray flux, which is affected by the current distribution over all the windings [31]. Load loss determination is necessary for winding thermal modelling. While DC loss can be calculated by the Joule s law and is uniformly distributed in a winding, eddy current loss in winding conductors is non-uniformly distributed. [57] discovered that with a uniform loss distribution, network modelling prediction on hot-spot matched CFD predictions acceptably, but with a non-uniform distribution of loss, deviation between these two approaches occurred, because in the top pass, where the hot-spot located, hot streak is strengthened by the intensive eddy current loss at the winding top and considerably affected the oil flow distribution. The phenomena of hot streaks can only be captured by CFD; it will be further discussed in Section

39 For the other metallic structural parts apart from windings, [58] used 3D finite element method (FEM) simulations to model the eddy current loss at the clamp plates and the un-shield transformer tank. [59] developed a new way to avoid expensive electromagnetic computation by performing detailed simulations only on the localized eddy current domain, such as bushing adapters and the tank part nearby the bushing adapters. In the two simulation examples in [59], the time and effort for eddy current calculation was reduced to 11% and 37% respectively. This section concentrates on the methods to calculate the eddy current loss on copper conductors Analytical equation A winding comprises many conductors. The eddy current loss in one conductor can be estimated by (2.6) [60], showing that eddy current loss is greater when the frequency is higher; for high frequency transformers, it is therefore significant to model eddy current loss accurately when investigating hot-spot [61,62]. P c eddy Bi hi r A c (2.6) c P eddy = Eddy current loss produced in the conductor by the magnetic leakage flux, in W ω = Angular frequency, 2πf, in s -1 B i = i component of the peak value of the magnetic leakage flux density, i = x, y, in V s m -2 h i = The conductor dimension perpendicular to the direction of the leakage flux density component B i, in m ρ = Electrical resistivity of the conductor, in Ω m r = The distance from the conductor centre to the core axial, in m A c = The cross-sectional area of the conductor, in m Finite element simulations Besides equation (2.6), finite element method (FEM) is commonly applied to calculate eddy current loss. Due to the axisymmetric geometry of the winding, 2D 39

40 axisymmetric modelling is often used for simplification. The 2D geometry can be approximated into different models; for example, the LV winding in [57] could be approximated into: (a) 1x1 single section neglecting the structure of discs and conductors, shown in Figure 2.7 (a). (b) 78x1 sections to model the 78 individual discs, in Figure 2.7 (b). (c) 78x18 sections to model all the individual conductors, in Figure 2.7 (c). (a) 1x1 section for both LV and HV windings. (b) 78x1 sections for LV winding. (c) 78x18 sections for LV winding. Figure 2.7 Three geometry models for winding eddy current loss simulation [57]. Magnetic leakage flux can then be calculated based on the three geometry models by using FEM simulations; the results are shown in Figure 2.8 respectively. 40

41 (a) 1x1 section for both windings. (b) 78x1 sections for LV winding. (c) 78x18 sections for LV winding. Figure 2.8 Magnetic leakage flux results from three geometry models in Figure 2.7 [56]. The geometry model (c) has the most detailed winding structure and can be used as a baseline for evaluating the other two models. By comparing the loss calculation results from the three models, [56] concluded: The total DC loss result of the most simplified model (a) is only 0.8% lower than that of the model (c). It means that the approximation of (a) is sufficient for DC loss calculation. The total eddy current loss result of the mode (a) is 6% lower than that of (c), and (b) is 5% higher than (c). The errors mean that the most detailed (c) is required to calculate eddy current loss with a good accuracy. A FEM prediction on the loss distribution of this LV winding is shown in Figure 2.9. The large increase at the winding top is due to the considerably large contribution of eddy current loss resulted from the leakage flux radial component at the end of the winding. 41

42 Figure 2.9 Large eddy current loss at winding top and uniform DC loss distribution [57]. The highest eddy current loss at the top disc predicted from the most simplified model, Figure 2.7 (a), is 15% higher than that from the most detailed model (c) [57] Transformer cooling The cooling system of a transformer is designed to dissipate the heat generated due to the losses. The primary purpose is to constrain the hot-spot temperature within a requested threshold; in IEC loading guide [9] the hot-spot limit for oil-immersed transformers under overloading conditions is 140 o C. Based on coolant oil circulation, the oil absorbs heat from winding conductors across insulating paper, cores and other active heating parts and then transports and dissipates the heat out to ambient atmosphere by equipped external radiator facilities. Figure 2.10, referring to [63], illustrates the oil circulation. The oil circuit comprises the routes inside the transformer, through the tank, the core and the windings, and the outside paths, including the pipework, pumps and external radiators. Arrows in the figure show the oil flow directions along the routes and the colour shows oil temperature; blue is cool and red warm. 42

43 Figure 2.10 Transformer cooling oil circuit (non-directed mode). Figure 2.10 shows a typical disc-type winding. In the oil routine the part inside the winding is the most complex one. In details, there are two vertical oil ducts at the left and right sides of the winding and they are cross-linked with an array of horizontal channels. All the ducts compose a network to maximize the oil-to-paper contacting surface for optimizing heat absorption of the oil flow. In this way while oil flows it becomes warmer and warmer and will merge at the winding top. Thereby, one might expect that the maximum temperature is at the winding top but this is generally found not to be true due to the effect of the non-uniform oil flow distribution across the horizontal channels [64]. In order to drive the oil into the winding, additional oil pumps can be used, or if no pump, the oil is driven only by buoyancy, so-called thermal driving force. Additional cooling fans facilitated for external radiators can improve the radiator cooling efficiency to enhance the thermal driving force. Pumps and fans are optional and therefore drawn with dash lines in the figure. If there are oil pumps, the transformer is in forced oil (OF) cooling mode, otherwise it is in natural oil (ON) mode. Similarly, if there are cooling fans present, it is forced air (AF) mode, otherwise natural air (AN) mode. 43

44 Another worthy point to discuss for the design of Figure 2.10 is that the oil flow is free to distribute between the different routes inside the transformer, i.e. not directed. This design is a non-directed cooling mode. Direction facilities such as oil guiding and restriction washers can be arranged to direct more oil to major heating parts such as windings and cores, in order to optimise the cooling oil distribution. The design with direction facilities is then called directed oil (OD) cooling mode. As an example of OD mode, Figure 2.11 shows the direction facilities. Compared to Figure 2.10, the facilities have been arranged at the bottom oil inlet to direct more oil into the active heating windings, and oil washers are also arranged inside the windings to force the oil flow into horizontal channels. Figure 2.11 Transformer cooling oil circuit (directed mode). Overall, different cooling modes are designed for transformers in order to meet the thermal criteria specified by the customers. The transformer cooling modes can be summarised into the three categories: 44

45 1. Natural oil (ON) mode: oil is elevated through the windings due to the thermal expansion and density reduction of oil. In another word, buoyancy is the only driving force for oil flow. 2. Non-directed forced oil (OF) mode: pumps are applied to force the oil through the windings and the radiators. The driving force is from the pumps which also dominate the oil flow rate. OF mode often has a higher cooling performance than ON mode but auxiliary power is also consumed by the pumps. 3. Directed forced oil (OD) mode: based on OF mode, additional direction facilities are then equipped to optimize the oil flow distribution among the active heating parts such as windings, and it becomes OD mode. In practice, oil block washers are often used in OD mode to achieve more uniform flow distribution across horizontal channels, and zig-zag like flow directions are then formed Thermal diagram The standard thermal diagram is shown in Figure 1.2. Windings are heating parts and the heat dissipation requires a temperature gradient to the surrounding coolant oil. Therefore in the thermal diagram the winding temperature is higher than the oil temperature by a winding-to-oil gradient g r ; the subscript r indicates rated load. Besides, the diagram applies the assumptions as follows The increase of the winding and oil temperatures from the bottom to the top of the winding is linear; The winding-to-oil temperature gradient g r remains the same at all height levels of the winding; Hot-spot temperature is assumed to be at the winding top but higher than the top winding temperature. The empirical hot-spot factor H is defined accordingly to (2.7). H g hr (2.7) r With hot-spot factor H, equation (2.8) is used to calculate the hot-spot temperature. Theoretically the top oil temperature inside the winding should be used for the Δθ or instead of the top oil temperature in the tank [11]; the top oil in the tank is mixed 45

46 with the oil from all the bottom-to-top channels and its temperature may not be equal to the top oil temperature inside the winding. Equation (2.9) is then believed to be more reliable, since it uses the bottom oil temperature Δθ br as the reference temperature instead of Δθ or, and the bottom oil in the tank has the same temperature with the bottom oil inside the winding [65,66]. Hg (2.8) hr a or r 2 (, ) Hg (2.9) hr a br om w br r θ hr = Hot-spot temperature at rated load θ a = Ambient temperature Δθ or = Top-oil temperature rise at rated load Δθ br = Bottom-oil temperature rise at rated load Δθ om,w = Average oil temperature along the winding at rated load H = Hot-spot factor g r = Winding-to-oil temperature gradient at rated load Here lies the necessity to determine the hot-spot factor H. Generally, if the hot-spot temperature is exactly the top-winding temperature, referring to the thermal diagram Figure 1.2, hot-spot factor is 1.0, but this value overlooks the intensified eddy current loss at the winding top and the non-uniformity of oil flow distribution across horizontal ducts, both of which cause that the temperature increase along the winding height is not linear. Hot-spot factor represents the non-linearity. 1.0 is the lowest limit of the hot-spot factor. IEC standard [67] recommended hot-spot factors greater than 1.1, varying from transformer design to design, in general H = 1.1 for distribution transformers; H = 1.3 for medium size power transformers; Regarding large power transformers, there are considerable variations on H depending on different designs. The manufacturers should be consulted for a proper value, unless real measurements are carried out [67]. 46

47 In practice, these recommended H values are however controversial, and transformer customers should consult the manufacturers for appropriate values of their transformers [68] Determination of hot-spot factor A task force was set up in CIGRE working group (WG) to attempt to recommend simple formula for the hot-spot factor H calculation. The WG concluded that the hot-spot factor ranges from 1.1 to 2.2 and suggested that 1.3 can be used for power transformers below 100 MVA and that 1.5 for higher ratings. Analytical determinations All members of CIGRE WG were asked to propose a formula for calculating the hot-spot factor H, and the collected formulae include [48] ˆ 1) h B H k 1 k2 (2.10) J 2 h = strand height in axial direction without insulation, in mm Bˆ = peak value of radial magnetic flux density, in T J = rms (root-mean-square) value of current density, in A/mm 2 k 1 = constant depending on transformer design k 2 = constant depending on cooling mode In this format no value was suggested for k 1 or k 2. k2 1 2) H 1 k h Bˆ 2 (2.11) The variable denotation follows (2.10). In this format no value was recommended for k 1, but k 2 = 0.6 was suggested for ON or OF cooling modes and 1.0 for OD. 2 max. EL 3) H 1 ksf khtf (2.12) avg. EL k 47

48 max.el = maximum per unit eddy current loss at the hot-spot avg.el = average per unit eddy current loss, corresponding to average winding temperature rise k 2 = constant depending on cooling mode. 0.8 for ON and OF; 1.0 for OD k SF = Surface factor = cooling suface at hot -spot average - winding cooling surface k HTF = Heat transfer factor = heat transfer coefficient at hot - spot average- winding heat transfer coefficient k2 k 2 This final equation has the most complex format and all the relative quantities are explained in an intuitive way as in Figure The hot-spot factor is calculated by synthesizing the effect from the localised loss, the cooling surface area and the heat transfer efficiency at the hot-spot. }Cooling mode factor 0.8 for ON and OF 1.0 for OD H = ³ losses at hot-spot average losses k 0 SF k0 HTF k2 Loss ratio Cooling surface ratio Heat transfer coefficient ratio Figure 2.12 Analytical derivation of hot-spot factor (2.12). Equation (2.12) still relies on other empirical constants. The complexity of the equation format implies the difficulty to propose a practically usable analytical hotspot factor expression. Finally CIGRE WG did not recommend any one of the three formats [48]. 48

49 Probability CFD Calibrated Thermal Network Modelling for Oil-cooled Power Transformers Experimental determinations In order to examine hot-spot factor from experimental tests, CIGRE WG collected hot-spot factor measurement samples from 7 countries: Australia, Austria, Canada, Finland, France, Sweden and the USA, and the samples correspond to 60 different load tests upon 34 transformers [48]. The distribution of the H samples is shown in Figure The H dispersal leads to the recommendation that no generalized formula or a constant can be used for the hot-spot factor, like what has been recommended in IEC 354 [69]. 100% 90% 80% 70% Inverse accumulated distribution of hot-spot factor 60% 50% 40% 30% 20% 10% 0% Hot-spot factor H Figure 2.13 Inverse accumulated distribution of hot-spot factors H [48]. Basic conclusions from Figure 2.13 are 1. The measure H values range from 0.51 to 2.06 and show no obvious trend toward a concentration around a specific value. The values below 1.0 are not reliable and may be caused by measurement at a wrong location other than hot-spot. 2. Statistical analysis of this data set showed that the H value is distributed almost linearly from 1 to 1.5, with a 65% probability of occurrence and with a mean probable value of

50 3. The dispersal proves that it is difficult to establish feasible correlations between the hot-spot factor and the transformer design, size or rating etc. 4. There is no observable effect upon hot-spot factor from the different cooling modes, ONAN, ON, OF or OD, though IEC 354 suggests 1.1 for ONAN and 1.3 for the others. In consequence, a utility company that has no overload rules and wants to utilise the load ability of its new transformers has two choices [48]: 1. Measure the hot-spot directly with sensors and, in the case of several similar transformer designs, develop a thermal model for the hot-spot; 2. Use the manufacturer s calculated value deduced from previous knowledge of his design Heat run test Heat run test is performed in factory to measure the temperature rises, including average winding and top and bottom oil temperature rises etc, of transformers under rated load and overload. A typical heat run test procedure can follow IEC and IEEE standards [9,69,49,68] and any other special requirements both customers and manufacturers have agreed. The purposes of heat run test is to check whether the thermal design meets the requirement of the guaranteed temperature rise values, including bottom and top oil temperature rises and mean winding temperature rise. The principle of heat run test is the simulation of the total losses, i.e. the sum of noload and load losses. The loss simulation is achieved by short-circuit or open-circuit test methods, as in Figure

51 Temperature rises Hot-spot temperature Heat run test } Short circuit test Open circuit test Principle: simulation of total losses. Verify design Figure 2.14 Themes relevant to transformer heat run test. The typical sequence of the temperature rise test is 1. Measurement of winding resistance from the cold start condition, i.e. the winding temperature is equal to ambient temperature; 2. Simulation of the total losses at required loadings by doing short-circuit or opencircuit tests until the stabilization of the oil temperature rise. The stabilization state means that the temperature rise does not vary more than 2.5% or 1 K, whichever is greater, per hour over 3 consecutive hours [68]. In general a temperature rise test lasts from 6 to 15 hours Short circuit test Short-circuit test is often applied for large power transformers. The principle of short-circuit test is that the total losses are simulated by copper loss. Copper loss depends on temperature, at the commencement of the test, i.e. the cold start, the current supply should be [15] s µiron loss + hot copper loss normal current cold copper loss (2.13) and at the end of the test the current should be normal current s µ 1 + iron loss hot copper loss (2.14) 51

52 Open-circuit test A transformer possessing a ratio of copper loss to iron loss lower than two would not be suitable for short-circuit test, and open-circuit test will then be used instead. Open-circuit test is mainly for small transformers, such as distribution transformers. Assuming that the iron loss varies with the voltage square, the voltage supply required for an open-circuit test is given by [15] normal voltage s µ 1 + 1:2 cold copper loss normal iron loss (2.15) Direct measurement of the hot-spot temperature As only global temperatures, such as top oil and average winding temperatures etc, are measured in the heat run test, detailed temperature distribution along the winding height cannot be obtained directly. Direct temperature measurement by optic-fibres has been proposed as a more profound approach for verifying thermal design. Many attempts have been made to develop reliable measuring devices, e.g. optic-fibres, and also guidance for how to install the sensors, the sensor number and installation positions. In brief, the major incentives which promotes direct hot-spot measurement include (in the order of importance) 1. To test the overloading capacity of a transformer; 2. To check and optimize the thermal design; 3. To have better load and overload monitoring and control in operational time. The topics related to optic-fibre measurement are discussed in this section Measurement devices The principle of the devices for direct temperature measurement is based on either the wavelength change of visible or ultraviolet (UV) light in a crystal sensor or the variation in phosphor fluorescent decay time with temperatures. The light is transmitted via optical fibres and as such the devices are often called optic-fibres. Experiences so far indicate no interference with electromagnetic fields for most popular optic-fibre devices used nowadays. 52

53 The specification and performance of the optic-fibre devices include [48] Accuracy: ±1 C is a normal value; Permissible temperature: 90 o C for continuous measurements for long periods, typically years, 140 o C for several days and 200 o C for hours. The operation time can be longer if without mechanical load; Long-time stability: when oil temperature ranges o C, the optical properties of the devices do not have any detectable degradation; Calibration: calibrated in factory; Mechanical durability: optical fibres are highly vulnerable to physical damage and careful installation is required Sensor number and locations For a transformer, 2 ~ 8 sensors are adequate for placing in the winding where a localised high temperature is predicted. For prototype transformers, 20 ~ 30 sensors should be sufficient [48]. The sensor positions should be very well supported by sufficient thermal modelling work to guarantee the real hot-spot at windings is being monitored [57]. It is recommended to place the sensors on the uppermost disc or turn, between the conductors or embedded into spacers, also with circumferential position varied. On a three-phase unit, the highest temperature is likely to occur near the top of the central coil. In particular, when the transformer is equipped with a load tap changer (LTC), it is recommended that the sensors are placed to minimize the interference between the fibers and the LTC leads. It is also recommended the fibres to be located away from the current transformer leads. In brief, the two precautions when locating sensors are 1. The sensors should be located in one or more positions that previous experiences or numerical thermal analysis have indicated to be the hot-spots of the transformer; 2. Sensors and fibres should be arranged such that they are isolated from any potential sources of physical damage. 53

54 A complete example from [70] would be helpful to illustrate on how to arrange multiple sensors. In this case a 20.5/0.71 kv distribution transformer having LV winding that consists of 18 Al-foil layers with an axial duct between layer 9 and 10. HV winding that consists of 15 layers, each layer containing 66 conductors except one containing only 21. Two axial ducts, one between layer 15 and 16 and the other 10 and 11. was facilitated with in total 28 sensors as follows [70] Nine at the LV winding top, including 2 predicted hot-spot locations, shown in Figure 2.15 (a). The sensors were inserted into adjacent foils with depth of 5 mm to measure conductor temperatures. Six at the HV winding top, including 1 predicted hot-spot location, shown in Figure 2.15 (a). Two in oil pockets at each side of the tank, ~30 mm from the tank wall, shown as T 2 in Figure 2.15 (b). Two on the outside surface of the tank, B 2 at the bottom and T 3 at the top in Figure 2.15 (b). Two under the tank cover by 50 mm, T 1 in Figure 2.15 (b). Two in the mixed bottom oil, located on the center line and between two adjacent phases, B 1 in Figure 2.15 (b). Four at both the oil duct inlet, B 3, and the outlet, T 4, of the HV winding and 1 at the duct outlet, T 4, of the LV at different phases, shown in Figure 2.15 (a) and (b). The basic conclusion from [70] s measurement results is that the top oil temperatures measured from different locations vary too much. They follow the magnitude order: T 4 at the winding outlet > T 1 under tank cover > T 3 at tank surface > T 2 at oil pocket. For example, for the rated load, the temperatures at the 4 locations are 84.8 o C > 82.1 o C > 77.1 o C > 72.9 o C respectively. Thermal overshoot of hot-spot-to-top-oil gradient was observed for the top oil measured under the cover T 1, but not found for the top oil at winding duct outlet T 4. From a pure scientific viewpoint, the top oil at the winding should be selected as the reference oil rather than the top oil at the tank, but in a regular heat run test the top-oil at winding is not often present due to the measurement difficulty [11]. 54

55 (a) Position of sensors for phase C; top view. (b) Position of sensors in tank, cross-sectional view; dimensions are in mm. Figure 2.15 Arrangement of thermal sensors in [70]. 55

56 The bottom oil temperatures also depend on locations, i.e. the temperature B 1 at the mixed bottom oil is greater than the B 2 at tank surface by 25 K. Another example in [17] is an ONAN transformer of 630 kva, 10/6 kv, equipped with 112 sensors (102 placed in the central positioned 10 kv winding). This paper also noted that the top oil temperature measurement strongly depends on sensor locations and therefore recommended to use bottom oil temperatures, as no thermal overshoot was observed for bottom oil. As more relevant publications, [71] built a 468 kva, 22 kv transformer in laboratory which is equipped with 16 optic-fibres for measuring winding temperatures and 24 thermocouples for measuring the temperatures at the core, the tank and the external radiator. [72] also presented some examples of using optic-fibres to measure hot-spot temperatures with different cooling designs Installation Fibres are often placed in an S-shaped slot inside the spacers and inserted into windings. The slot must be arranged to position the fibre sensor tip at the measurement location, allow the spacer to enter the winding radially but should also protect the fibre from being pulled out. Examples of the slots are in Figure Figure 2.16 Examples of fixation slots for optic-fibres inside windings [8]. As a recommended practice, a spacer which contains an optic-fibre will be installed by replacing an existing spacer after the coil has been completed. 56

57 2.2.6 Dynamic loading and overloading As mentioned in Section 1.1, it is of significance for electricity network operators to comprehend the temperature responses to dynamic loading and overloading. Thermal overshoot may be caused by dynamic loading and risks are associated with operating transformers beyond their nameplate ratings, i.e. overloading transformers. Because of economic reasons or the responsibility to ensure continuous power supply, overloading a transformer may be required in practice. In order to reduce the insulation ageing and to avoid severe damage associated with overloading cycles, it is necessary to perform temperature rise tests at loads higher than the rated load [68,73,74] Steady state temperature rises As for steady state calculations, the temperature rise equations recommended in IEC standard [9] include 1. Top oil temperature rise 2 x 1 R K o or (2.16) 1 R x is oil exponent. When the load factor K > 1, (2.16) is for an overloading condition. IEEE C [68] has recommended loads of approximately 70%, 100% and 125% of the maximum nameplate rating should be used in tests to produce losses approximately equal to total losses of 50%, 100% and 150% of that at rated load. Additional values may also be chosen, yet the differences among these 3 losses is sufficient to determine the oil and winding exponents x and y. With the 3 measured temperature Δθ o, the exponent x can be derived by curve fitting the 3 data pairs of K and Δθ o. 2. Hot-spot-to-top-oil temperature gradient y h Hg r K (2.17) y is winding exponent and may be determined from the line that best fits the 3 data pairs of winding-to-oil gradient g r against K on log-log coordinates [68]. 57

58 In the equations (2.16) and (2.17) the parameter R is the ratio of load loss at rated load to no-load loss; it can be determined from transformer short-circuit and opencircuit tests. g r is the winding-to-oil temperature gradient at rated load and can be obtained from heat run test. H is hot-spot factor recommended in the loading guides. If the hot-spot temperature has been measured by optic-fibres, H can be calculated by (2.7) [70] Temperature rises at dynamic loading Two solutions are proposed in IEC standard [9] to describe the temperature rises as functions of time, for varying load and overload conditions: 1. Exponential equations, suitable for a load variation according to a step function. 2. Difference equations, suitable for arbitrarily time-varying load factor K and timevarying ambient temperature θ a. The two solutions are mathematically equivalent and as such this section will only present the approach with exponential equations. Exponential equations (2.18) to (2.21) are given to describe the unsteady temperature responses to a step increase of load to a load factor K, including 1. Top oil temperature rise ( K ) f ( ) ( t ) t 1 (2.18) o f oi 1( 11 o o oi t) 1 exp[ t /( k )] (2.19) f 1 (t) describes the relative increase of the top-oil temperature rise according to the unit of the steady-state value. 2. Hot-spot-to-top-oil temperature gradient ( K ) f ( ) ( t ) t 2 (2.20) h hi h 1 exp[ t /( k )] ( k 1) 1 exp[ t /( / )] f 2 ( t) k21 22 w 21 o k22 (2.21) f 2 (t) describes the relative increase of the hot-spot-to-top-oil gradient according to the unit of the steady-state value. Thermal overshoot may occur for the hot-spot-to-topoil gradient according to the f 2 (t) [9]; thermal overshoot means that the temperature hi 58

59 difference in transient procedures jumps up to a higher value than the stabilised value at the same load level [17]. Otherwise for a step decrease of load to the factor K: ( K ) f ( ) ( t ) ( K ) t 3 (2.22) o f o oi 3( 11 o o t) exp[ t /( k )] (2.23) f 3 (t) describes the relative decrease of the top-oil-to-ambient gradient according to the unit of the total decrease. Time constant The winding and oil time constants of the temperature variations can be calculated by using the method in IEC Annex A [9]. The winding time constant at the load considered is m C g w m w (2.24) 60 Pw m w C m g P w The mass of the winding, in kg The specific heat of the conductor material, in J/(kg K) (390 for Cu and 890 for Al) The winding-to-oil gradient at the load considered, in K The winding loss at the load considered, in W The oil time constant at the load considered is given by C om 60 o (2.25) P Δθ om C P The average oil temperature rise above ambient temperature at the load considered, in K The thermal capacity of oil cooling system, in J/K The supplied losses at the load considered, in W 59

60 The thermal capacity of the oil cooling system, C, depends on different cooling mode and is determined by empirical equations. For example C for ON cooling mode can be estimated by C m m m (2.26) A T O m A m T m O The mass of core and coil assembly, in kg The mass of tank and fittings (only the portions that are in contact with heated oil shall be considered), in kg The mass of oil, in kg On the other hand, the time constants can also be measured during heat run test with load step changes [68]. The oil time constant is equal to the time required for the oil temperature to change by 63% of the ultimate temperature change. The winding time constant may be calculated from the measured data of the average winding temperature rise over the average oil temperature versus time. The time constant is equal to the time required for the average winding temperature rise over average oil temperature to decay to 37% of its initial value [68]. Load cycles In addition, it is recommended to perform a temperature rise test with a specific sequence of loads and overloads, so as to demonstrate the potential of the transformer to be loaded with practical load profiles. Preferably, a typical load profile can be suggested, with the minimum time interval being one hour, except for high overloading durations a shorter interval can be used. For the intervals longer than one hour, the root-mean-square (RMS) load is used for the period. Otherwise for the intervals of one hour or less, loads can be the arithmetic average over time [68] Model validation In order to evaluate the thermal models on transformers overloading capability, Reference [11] compared measurement results with the IEC model calculated responses, and found that the IEC model yields temperatures which are either conservative or with a reasonable accuracy at a step increase of load. References [11] and [65] compared measurement results with the calculation results from the model 60

61 in IEEE standard C57 [68] Annex G and then concluded that the IEEE model yielded a good accuracy. However, Reference [5] noted that the IEC and IEEE models give significantly low hot-spot temperatures in the case of short-time emergency loadings. Short-time emergency loading is a unusual heavy loading with less than 30 minutes, due to the occurrence of one or more system events that severely disturb the normal loading [9]. In Reference [5] a short-time overload of 2.5 per unit load, following a preload of 0.3 per unit, lasted for 20 minutes and the hot-spot temperature reached 156 o C at the end of the overload period, which is dramatically higher than the values predicted by the IEC and IEEE models, 83 o C and 95 o C respectively. Besides, transformers overloading capability is also affected by ambient temperature variations [75]. The thermal model in ANSI standard C57.92 [76] for overloading is only valid for ambient temperature > 0 o C, so that Reference [66] presents a study, which considers the high oil viscosity at temperatures below 0 o C, in order to extend the thermal model down to ambient temperature of -40 o C. At such low temperatures, the newly developed model calculated more reliable hot-spot temperatures than the ANSI standard model. At a normal ambient temperature ranging from 0 o C to 40 o C, results from both models are equivalent. The model in IEEE standard C57.91 [49] suits for ambient temperature down to -30 o C Thermo-circuit analogy Due to the significance of dynamic loading and overloading, the suitability of the IEC and IEEE thermal models are increasingly questioned and based on fundamental heat transfer principles, a new category of thermal models, named thermal-circuit analogy, have been developed for calculating the temperature variation responding to dynamic loading and overloading [17,70,77-86]. By comparing the governing equations, Fourier theory for heat transfer and Ohm s law for electric circuit, the physical quantities and equations for both fields are analogous; the quantities are summarized into Table 2-3. Hydraulic quantities are also listed for analogy but without a storage element. 61

62 Table 2-3 Analogy to electric circuit principles [87]. Electric Thermal Hydraulic Through variable Current I Amps Heat transfer rate q Watts Mass flow rate Q kg/s Across variable Voltage V Volts Temperature θ Degree C Pressure P Pascal Dissipation element Electrical resistance R el Ohms Thermal resistance R th Degree C/Watt Hydraulic impedance R p Storage element Electrical capacitance C el Farads Thermal capacitance C th Joules/Degree C Based on the analogy between thermal and electric theories, Swift and Molinski et al [77,78] presented the principle to use equivalent thermal circuits, Figure 2.17, to describe the thermal energy transportation in oil-immersed transformers. The cooling system is separated into different components: the active heating parts such as cores and windings, and the coolant media such as oil and ambient air. The heat conduction and convection are simulated by thermal resistances (R hs for hot-spot and R oil for oil) to the heat flows (q fe and q cu ) from cores and windings to oil and from oil to ambient air [80]. The analogy method models the two heat flows to the two circuits in Figure 2.17; C hs and C oil are the thermal capacity for hot-spot and oil respectively and the oil temperature, θ o, is the common quantity coupled between both circuits. In practice, it is not necessary to be aware of the values of these R and C, because in the differential equation derivation for θ o and θ h, R and C will be combined together to be a time constant, for example, oil time constant τ o = R oil C oil. 62

63 Figure 2.17 Principle sketch of thermal circuit analogy [77]. In the thermal circuit, the non-linearity of the convective heat transfer in cooling oil or air is presented by a general non-linear model, (2.27). n Rth q (2.27) The exponent n in (2.27) depends on the cooling mode of the transformer [85]. For natural cooling mode typically n = 0.8, and for forced cooling n = 1.0, because the convection efficiency at a high flow speed becomes independent of temperature [77]. Because n is empirical, in order to determine its value [80] utilized a genetic algorithm (GA) as a search approach to identify the non-linear thermal parameters. The differential equation to calculate the top oil temperature θ o was deduced from the oil-to-air thermal circuit in Figure 2.17, with oil time constant τ o = R oil C oil, as [77] 1 1 R d dt 2 R K 1/ n o 1/ n or o o a (2.28) In (2.28) the load loss at rated load to no-load loss ratio, R, the top oil temperature rise at rated load, Δθ or, and the oil time constant τ o are all from heat run test, and the top oil temperature θ o at the given load factor K and ambient temperature θ a can then be solved. The equation is used to predict the oil temperature variation responding to the load and ambient temperature conditions which were not included at the factory heat run test. 63

64 Same is the derivation for the hot-spot temperature θ h in the hot-spot-to-oil thermal circuit in Figure Note that θ h is a localised temperature and as such it is actually not related to the total loss q fe + q cu ; however it is still valid to use the total loss in the circuit by adjusting the R hs and C hs values to compensate [77]. Unfortunately in [77] it is not clearly stated how to derive the R hs and C hs values nor how to adjust. Because thermal-circuit models are lightweight calculation methods and consume significantly less computational time than the detailed modelling approaches such as network modelling and CFD, they are used to calculate the temperature response, as a function of time, to dynamic conditions. For example, the thermal-circuit proposed in [88] was applied to predict the real-time temperature response to the variations of load and weather conditions, including ambient temperature, solar radiation and wind velocity. It was concluded that the winding and oil temperatures were most affected by the load, and that the tank temperature was more affected by the thermal radiation from the sun. The wind velocity, 10 mph (14.7 m/s), could considerably reduce the temperatures compared to the no wind condition, but the tripled wind velocity, 30 mph, only resulted in a small temperature reduction compared to the condition with 10 mph. 2.3 Thermal modelling In Section 2.2.3, it was concluded that the standard thermal diagram is oversimplified and it is difficult or impossible to determine a reasonable and general hotspot factor for transformers with different designs. Since the appearance of computers, numerical analysis becomes possible and the numerical tools on transformer thermal analysis were initiated at least 40 years ago [21]. As mentioned in Chapter 1, the existing numerical solutions can be categorized into two categories, network modelling and CFD/FEM simulations. Table 2-4 follows as a brief summary of the literatures on the three categories as well as their experimental validations. 64

65 Table 2-4 Categorised literatures list. Network modelling Oliver (1980) [19] Simonson & Lapworth (1995) [20] Allen & Szpiro et al (1981) [21] Yamaguchi & Kumasaka et al (1981) [22] Yamazaki & Takagi et al (1992) [23] Declercq & Van der Veken (1998) [24] Declercq & Van der Veken (1999) [25] Vecchio & Feghali (1999) [26] Vecchio & Poulin et al (2001) [27] Zhang & Li (2004) [28,29] Joshi & Deshmukh (2004) [30] Buchgraber & Scala et al (2005) [31] Radakovic & Sorgic (2010) [32] CIGRE WG A2.38 (2011) [33] CFD/FEM simulation Mufuta & Van den Bulck (2000) [35] Shih (2001) [36] Oh & Song et al (2003) [37] Takami & Gholnejad et al (2007) [38] Kranenborg & Olsson et al (2008) [39] Weinläder & Tenbohlen (2009) [40] Torriano & Chaaban et al (2010) [41] Tenbohlen & Weinläder et al (2010) [42] Lee et al (2010) [43] CIGRE WG A2.38 (2011) [44] Experimental validation Allen & Szpiro et al (1981) [21] Yamaguchi & Kumasaka et al (1981) [22] Yamazaki & Takagi et al (1992) [23] Wang & Zhang et al (2000) [45] Oh & Song et al (2003) [37] Rahimpour & Barati et al (2007) [46] Zhang & Li et al (2008) [47] Weinläder & Tenbohlen (2009) [40] 65

66 These publications will be reviewed in detail in the following sub-sections, except that the ones relevant to network modelling will be discussed in Section 2.4 more profoundly, because the thesis concentrates on network models CFD/FEM methods Generally speaking, a simulation with Computational Fluid Dynamics (CFD) or Finite Element Method (FEM) comprises several steps, as listed in Figure Defining the geometry Meshing the geometry Defining material properties and boundary conditions Choosing dominating physical laws and equations Solving Post-processing and visualising the results Figure 2.18 General procedure for CFD/FEM simulations. Although the geometry modelling and meshing for a transformer could ideally be 3D to model a complete structure, the geometry is often symmetrical and can be reduced to some extent for saving computational resources. For example, [37] modelled a single phase 400 kva natural cooling transformer with layer type windings, and due to the geometrical symmetry, only a quarter of the transformer was modelled in 3D. The geometry model and the corresponding mesh are shown in Figure 2.19, and the number of the mesh elements is around 600,000. A commercial CFD code was then used to solve the model. In order to validate the CFD results, thermocouples were installed into the windings, 4 sensors for each oil duct from the bottom to the top. The calculated temperatures showed a good agreement with the measured values, which means that the geometry approximation and the mesh elements were sufficient for calculation accuracy. 66

67 Figure D model and mesh for calculating [37]. Upon the meshed domain required for solution, material properties such as density, viscosity (only for fluid), thermal conductivity and specific heat should be defined; the density and the viscosity of transformer oil are applied as temperature dependent. On the other hand, boundary conditions such as inlet oil flow rate and temperature and heat flux at winding disc surfaces etc need be prescribed at the boundaries of the domain. No-slip boundary conditions are applied at all solid-fluid interfaces. Finally, physical laws, such as conservation of mass, energy and momentum etc, expressed in a set of mathematical equations, i.e. Navier-Stokes equations, can be solved with the mesh. The Navier-Stokes equations can be presented by using compact vector notation as D u 0 Dt (2.29) Du Dt p g (2.30) D C Dt Cu k 0 (2.31) In the equations, ρ, C and k are the density, specific heat and thermal conductivity of the fluid respectively. t is the time, p is the pressure, τ is the viscous shear stress tensor and g is the gravity vector. u and Θ are the fluid velocity and temperature 67

68 Software Transformer/model details Mufuta & Van den Bulck (2000) [35] Shih (2001) [36] Oh & Song et al (2003) [37] Takami & Gholnejad et al (2007) [38] Kranenborg & Olsson et al (2008) [39] and both are unknown variables to be solved. The equations can be discretised via finite volume method to produce a set of algebraic equations at each location, which can subsequently be solved iteratively. From the solution the distributions of oil velocity and temperature can be obtained. It is worth noting that numerical errors are associated with the discretisation and in order to restrain the errors to be acceptable, the control volumes need to be small enough which then means the geometry domain should be meshed into a sufficiently large number of control volumes. Various commercial and open-source software can be chosen for the CFD/FEM modelling. Table 2-5 summarises the simulation software and the model cases from literatures. For example, Shih used commercial CFD package, STAR-CD, and an unstructured mesh. STAR-CD is the acronym of Simulation of Turbulent flow in Arbitrary Regions Computational Dynamics [36]. Kranenborg and Olsson et al used Fluent, another commercial CFD code, to investigate the effects of buoyancy and the phenomena of hot streaks [39]. Other software packages such as ANSYS- CFX and COMSOL (FEMLAB) etc were used as well in the literatures [38,40,41,42]. Table 2-5 Categorised literatures related to CFD/FEM simulations. 2D Navier- Stokes equations STAR-CD A commercial CFD code FEMLAB Fluent 400 kva 6600/220 V Grid number: 600, MVA OFAF/ONAN/OFAN OF/ON/OD No gravity and with gravity 68

69 Weinläder & Tenbohlen (2009) [40] Torriano & Chaaban et al (2010) [41] Tenbohlen & Weinläder et al (2010) [42] Lee et al (2010) [43] CIGRE WG A2.38 (2011) [44] ANSYS-CFX ANSYS-CFX ANSYS-CFX UNIFLOW Fluent Fluent etc Axial symmetric model Axial symmetric model Axial symmetric model 66 MVA, 26.4/225 kv ONAF Shih [36] chose unstructured mesh for simulations, and the geometry model of the study comprised half a core and two arrays of rectangular heating winding discs that are separated with three vertical oil ducts, shown in Figure From the simulation results, it was found that there is more turbulence in the top oil domain than in the bottom; the oil flow in the bottom is almost stagnant. This phenomenon is also shown in the figure, where Ψ denotes stream function value. The contour of Ψ presents streamlines, i.e. lines whose tangent is everywhere parallel to the local flow velocity vector. Takami and Gholnejad et al [38] considered the transformer winding structure to be thermally anisotropic and used a 2D laminar flow model; the fluid was assumed to be incompressible. The density and viscosity of oil were considered to be temperature dependent and the loss at each conductor was calculated based on the temperature dependent electric resistivity of copper. Steady state simulations were firstly done with FEMLAB and MATLAB packages and showed that the maximum temperature occurred in the neighbourhood of 80~90% of the axial and 50% of the radial directions of the winding. The steady state model was then developed into an unsteady one to predict the temperature response to a changing loss with time. With the unsteady study, winding time constant was found to be around 4.5~5 min. 69

70 Figure 2.20 Streamline results for the simulation case in [36]. Mufuta and Van den Bulck [35] used finite volume method (FVM) on a geometry that includes three vertical oil channels enclosing and between two arrays of winding discs, similar to the structure of Figure Assumptions include constant and homogeneous heat flux at conductor surfaces, and uniform oil velocity at inlet. Fluctuation of oil flow rate along the central vertical duct was found and the factor affecting the fluctuation was then identified to be the interaction between inertia and buoyancy forces. A quantity Re=Gr 1 2 could be used to express the interaction; Gr is Grashof number which approximates the ratio of the buoyancy to viscous force acting on a fluid. In a recent work, Kranenborg and Olsson et al [39] used 2D CFD model to recognize the significant effects of buoyancy term and hot oil streak formations, the latter of which could more or less worsen downstream oil temperatures. A hot oil streak is formed from a streak of oil that flows along the disc surface, absorbs heat from the disc, becomes hotter and hotter and can persist its temperature for a long distance, due to the high Prandtl number of oil (~200), and subsequently rise the oil 70

71 temperature in the downstream. They noted that a very fine discretisation mesh is required to capture this effect. Torriano and Chaaban et al [41] presented a detailed CFD study on a single pass of the 26.4 kv LV winding of a natural oil cooling 66 MVA transformer. It was concluded that buoyancy is important to include and that the approximation of solid domain, i.e. the winding discs, as homogenous copper blocks is sufficient for calculation accuracy Experimental validation The numerical thermal modelling requires experimental tests to validate. Table 2-6 summarises the literatures to classify their measurement parameters and the used devices. Basically most works measured oil velocities or temperatures or both. Table 2-6 Categorised literatures related to experimental validation. Allen & Szpiro et al (1981) [21] Yamaguchi & Kumasaka et al (1981) [22] Wang & Zhang et al (2000) [45] Oh & Song et al (2008) [37] Measured parameters Oil velocity Oil velocity Disc temperature Oil temperature Measurement method / facilities Hot wire anemometry Laser-Doppler velocimeter Copper-constantan thermocouples Small-sized thermocouples Rahimpour & Barati et al (2007) [46] Local temperature on discs PT100 sensors temperature Zhang & Li et al (2008) [47] Weinläder & Tenbohlen (2009) [40] Oil and disc temperatures Oil pressure over winding Flow meter, OMEGA Model No. FL-6102A Thermocouples error ±0.2 o C Oil pressure sensors with 71

72 Various devices were used to measure oil flow velocity, basically including hot wire anemometry (HWA) and laser-doppler velocimeter. A laser-doppler velocimeter was used by Yamaguchi and Kumasaka et al [22] to measure the inlet oil velocity of a self-cooled (ONAN) winding model. Their network model predictions agreed with the experimental results within relative error of 15%, and they drew the conclusion that the oil flow rate increases almost proportionally to the square root of the heat amount produced in the winding. Doppler equipments are often expensive and complex to adjust the coordinates of measurement locations. Cheaper devices like HWA can be used instead. Besides the cost reason, HWA was considered the best by Allen and Szpiro et al [21] because they were measuring oil velocity inside windings in their laboratory. In a metal tank the measuring points inside the windings are not accessible to a laser beam but the probes of HWA are tiny enough to be inserted into thin oil ducts. In principle, a HWA uses a fine wire, for which tungsten is popularly chosen, while the wire is heated up to a temperature. Because the fluid flowing past the wire causes a cooling effect, and the cooled down wire temperature can be related to its electric resistivity, a correlation between the wire resistivity and the flow velocity can be obtained beforehand which can then be utilized for determining flow velocities from measuring electric resistivity. Therefore another advantage of the HWA is that it can be used as a resistivity based thermometer at the same time for measuring local oil temperature. An alternative way to validate the numerical modelling from a hydraulic viewpoint is to measure oil pressures instead of oil velocities. With CFD analysis [40] noted that only the global oil pressure measurement over an entire winding pass is reliable for modelling validation, and that the pressure measurement at other places rather than at the oil inlet and outlet will contain unacceptable uncertainties. With respect to temperature measurement, thermocouples were used in both [45] and [37]. Electrical insulation should be taken care of when using thermocouples, since the thermocouples are at earth potential. Thermocouple leads are often molded with epoxy and then shielded with Kepton film to guarantee a good thermal conductivity and insulation property at the same time [37]. 72

73 By embedding thermocouples onto a natural oil cooled winding that is equipped with oil block washers, [45] found that the block washers could considerably reduce the winding temperature rise and that the reduction is proportional to the number of the washers. However, the effect on the hot-spot temperature is not so straight-forward because hot-spot is synthetically affected by a range of factors including the number of block washers, pass sizes, horizontal duct dimensions and oil flow directions etc. 2.4 Network modeling Introduction Network modelling is initiated from the process of reducing the complex pattern of cooling oil passages in a transformer down to a matrix of hydraulic oil flow duct approximations, which are interconnected by junction points or nodes. Because of the axisymmetric winding geometry, 2D axisymmetric models can be used [40,41]. Moreover, since the circumferential width of an oil duct is significantly longer than the duct s radial length, 2D flow duct models between infinite parallel plates can be applied as a sufficient approximation of the oil ducts [19,28,38]. As one of the pioneering papers, Oliver [19] completely introduced the network model developed at the Central Electricity Research Board (CEGB) in the 1980s. He presented a network model which predicts hot-spot temperature and location. A computer program, named TEFLOW version 1, was also developed to implement iterative solutions for the equations. By taking a particular LV winding design as an example, calculation results were presented and showed that the hot-spot occurs on the middle disc of the topmost pass of the winding. Following from the work of TEFLOW 1, TEFLOW 2 was developed for incorporating capacity of modelling varying load cycles [20]. References [19,27] presented complete sets of the mathematical equations for network modelling, and in the appendix of [19] a detailed solving procedure was summarised. Both works focused on only single windings, and the empirical equations employed were from general fluid dynamics and heat transfer handbooks and had not been fully calibrated for transformer oil and oil ducts. In order to model an entire transformer, [25,24] proposed a global model for multiple windings and an internal network model for an individual winding respectively. In 73

74 the global model, the windings of a transformer are approximated as parallel connected hydraulic impedances and thus oil flow rate distribution between them can be calculated based on hydraulic piping principles. On the other hand the internal model is a traditional network model for an individual winding, in which the inlet oil flow rate is from the global model prediction. This internal model is to calculate the oil temperature and velocity distributions inside each winding, and then contributed to the global model by handing over the winding s new hydraulic impedance. In this way the two models are coupled and with iterations they could achieve convergence simultaneously. In [25] the algorithm was implemented into a software tool with user friendly Graphic User Interface (GUI). In the work of [30] a transformer was also modelled as a whole to develop a more complete and accurate network model than the conventional single winding model; even heat radiation of external coolers was included in this complete model Equations The input parameters a single winding network model requires include 1. The structural design of the winding, including the disc number, disc and oil duct dimensions and oil block washer arrangement. 2. Load current and the mass flow rate and temperature of the oil supplied from the bottom inlet. 3. Oil and insulating paper properties, i.e. density, viscosity, thermal conductivity and specific heat. From these input data, network model employs a set of assumptions and equations to calculate the oil flow rate and temperature distributions across the winding oil ducts in order to identify the hot-spot. The physical assumptions of network modelling are outlined as 1. Oil flow inside ducts is assumed to be entirely laminar due to the low Reynolds number (Re = 25 ~ 100 [28]). 2. Oil ducts are approximated by a pair of infinite parallel flat plates; i.e. oil flow inside ducts is approximated by 2D channel flow. As oil is viscous fluid, there is frictional pressure loss along with the oil flow. 74

75 3. Oil temperature is assumed to rise linearly as the oil flows along a duct and picks up heat from adjacent discs, i.e. the heat source. Moreover, because vertical ducts are much shorter, only the heat flux into horizontal ducts is considered and it is assumed that the oil temperature along vertical ducts remains constant. 4. Oil flow is completely mixed at nodes in terms of both hydraulic and thermal aspects; i.e. the flow velocity and temperature profiles become uniform upon departure from the junctions. The equations of network modelling can be categorised into two coupled networks: hydraulic and thermal networks. Both networks are based on a suite of mathematic equations which are often analogously understood with the help of Kirchhoff s law. The equation hierarchy is illustrated in Figure 2.21 and the equations are then listed in Table 2-7. The details of these equations application in network modelling will be introduced in the following paragraphs. Network modelling Hydraulic network Thermal network Mass conservation Darcy equation (pressure drop equation) Thermal energy conservation Heat transfer equations Conduction equation Convection equation Figure 2.21 Hierarchy of network modelling equations. 75

76 Table 2-7 Network modelling equations. Illustrations i u i;i+1 u i;i+n+1 u i 1;i Equations Mass conservation X ½ i;j A i;j u i;j = _m j Thermal energy conservation X C½ i;j A i;j u i;j µ i;j + 12 A s(i;j) _q i;j = C _mµ i j µ 2 ; P 2 Darcy-Weisbach equation (pressure drop equation) D; A u _q A s l P = 4fL 1 D 2 ½u2 Temperature increase equation A s _q = C½uA µ µ 1 ; P 1 m Junction pressure loss (JPL) equations for combining and dividing junctions (a) (b) 2 1 A combining junction. 1 2 m A dividing junction. P P im mi K K im mi u 2 u 2 2 i 2 i in which i = 1,2, K is JPL coefficient, K K K K 1m 2m m1 m2 u u 72 Re 2 u u 276 Re 2 1 m 1 m u u 1 m u u Convective heat transfer equation _q = Nu k D (µ w µ b ) Conductive heat transfer equation _q = krµ 1 m Re Re 1 76

77 A small size network model example which only includes 3 winding discs is used to illustrate how to apply the equations, as shown in Figure In the example there are 10 oil ducts and 8 duct junction nodes; the nodes are numbered in the figure and the ducts are then denoted by a pair of numbers which are their start and end nodes. The oil flow rates and oil temperatures of the 10 ducts are unknowns and they will be solved from the hydraulic and thermal network respectively. In the hydraulic network, as marked in Figure 2.22 (a), mass conservation is applied at the 7 redly circled nodes to obtain 7 node equations and along the 3 closed loops, indicated by the 3 blue arrows, the pressure drop summation is zero and thus 3 loop equations can be written. In this way 10 independent equations in total can be given for solving the 10 unknown duct flow rates. In a generalised scenario, for N discs there are 2N + 2 nodes and 3N + 1 ducts. Node equation, (2.32), can be applied at all the 2N + 2 nodes, i.e. i = 0,,2N + 1, but only 2N + 1 of them are independent. 2N+1 X j=0 i;j ½ i;j A i;j u i;j = _m (2.32) in which α i,j is the connection factor (α i,j = 1 if nodes i and j are connected by a duct and i > j, α i,j = -1 if nodes i and j are connected and i < j and α i,j = 0 otherwise), ρ is the fluid density, A i,j is the cross-sectional area of duct (i, j), u i,j is the flow velocity from node i to j. On the right hand side, _m is the imposed mass flow insertion at node i; _m = Q, i.e. the total oil mass flow rate, if i = 0, (node i is the inlet), _m = -Q if node i is the outlet and _m = 0 otherwise. 77

78 3 2,3 2 1,2 1 0, ,7 2,6 1,5 0,4 7 6,7 6 5,6 5 4,5 4 (a) Nodes and loops in hydraulic network. 3 2,3 2 1,2 1 0, ,7 2,6 1,5 0,4 7 6,7 6 5,6 5 4,5 4 (b) Nodes and temperature development paths in thermal network. Figure 2.22 Hydraulic and thermal networks. In the loop equations, Darcy-Weisbach equation, (2.33), is employed to describe the frictional pressure losses along the oil ducts which compose the closed loops. Darcy- Weisbach equation describes the correlation between the pressure drop, ΔP, and the flow velocity, u, at a viscous channel flow. 78

79 4 f l D P u (2.33) ΔP = Pressure drop from the upstream to the downstream of oil duct, in Pa f = Friction coefficient at oil duct, dimensionless l = Length of oil duct, in m D = Hydraulic diameter of oil duct, in m ρ = Density of oil, in kg/m 3 u = Average flow velocity at oil duct, in m/s Oil ducts can be sufficiently approximated by 2D channel flow between infinite parallel plates. For 2D channel flow, friction coefficient f = 24/Re; Re is dimensionless Reynolds number. In [26] friction coefficient f correlation from Olson [89], (2.34), is used. The equation is however for ducts with rectangular cross-section and with two sides a and b (a < b). (2.34) As shown in Figure 2.22 (a), the closed loops are composed, in general, by 4 ducts (i, i + 1), (i + 1, i + N + 2), (i + N + 2, i + N + 1) and (i + N + 1, i), i = 0,,N - 1. Denote the set of these 4 ducts subscripts as Ω, and the general format of a loop equation is then f = K(a=b) µ Re D = ½uD Re D ¹ K(a=b) = 56: :31 e 3:5a=b 0:0302 ( i, j) 4 fi, j li Di, j, j K i, j 1 2,,, 1 1, 2 0 i jui j i i in in g lv (2.35) 2 The first term of (2.35) includes both the frictional and junction pressure losses; K i,j is the junction pressure loss (JPL) coefficient applied at duct (i, j) and its format is listed in Table 2-7, depending on whether duct (i, j) bears the straight-through or the branch direction of a combining or dividing junction. The second term considers the gravity effect; l v is the length of the vertical ducts. The equation, (2.35), is nonlinear, so when solving it iteratively, it needs to be linearised by the factorisation u 2 i,j = u i,j 79

80 u i,j ; in the first iterative step u i,j is the initialised value and in the following steps u i,j is the result of the previous step. All in all, in the hydraulic network, with the 2N + 1 node equations, (2.32), and the N loop equations, (2.35), the 3N + 1 duct flow velocities can be solved. On the other hand, in the thermal network, as marked in Figure 2.22 (b), thermal energy conservation is applied at the 7 nodes for 7 independent node equations. In addition, temperature development equations along the blue paths due to the heat flux from the discs are then used. For example, ducts (0, 1) and (0, 4) both originates from the same node 0 and their temperatures can be correlated; in particular, while neglecting the heat flux into the vertical duct (0, 1), the temperature increase from duct (0, 1) to (0, 4) is due to the heat flux into the horizontal duct (0, 4). Finally 10 equations in total can be given for solving the oil temperatures at the 10 ducts. For the node 0 to 2N, the general format of the node equations in the thermal network is 2N+1 X j=0 i;j C½ i;j A i;j u i;j µ i;j + 12 A s(i;j) _q i;j = C _mµ i (2.36) C is the fluid specific heat, θ i,j is the average oil temperature at duct (i, j) and A s(i,j) is the total wall area of duct (i, j). θ i is the temperature of the imposed flow insertion at node i; θ i is the bottom oil temperature if i = 0, (node i is the inlet), θ i is the top oil temperature if node i is the outlet and θ i = 0 otherwise. _q i;j is the heat flux into duct (i, j) and depends on the power loss at winding discs. In practice the power loss at a disc comprises both DC and eddy current losses, as discussed in Section Here as a simplified case, the constant heat flux _q i;j boundary condition is prescribed at the disc surfaces. As shown in Figure 2.22 (b), the temperature increase along the ducts (i, i + N + 1), i = 0,,N - 1, is µ i;i+1 µ i;i+n A s;(i;j) _q i;i+n+1 C½ i;j A i;j u i;i+n+1 = 0 (2.37) 80

81 Thus in the thermal network, with the 2N + 1 node equations, (2.36), and the N temperature development equations, (2.37), the 3N + 1 duct oil temperatures, i.e. oil bulk temperatures, can be solved. After the oil bulk temperatures are obtained, not only the temperature dependent oil properties such as oil density and viscosity can be updated for the next iterative step, but also the oil temperature at duct surfaces, namely wall temperatures θ w(i,j), can be derived with (2.38). As the heat transfer in the ducts is convective, Nusselt number is employed to correlate the heat flux _q i;j to the temperature drop from the duct wall to the bulk. Secondly, the heat conduction from the copper conductors to the duct walls is described by Fourier s law, and the temperature of the conductor adjacent to duct (i, j) θ c(i,j) is then calculated with (2.39). µ w(i;j) = µ i;j + _q i;j D i;j Nu k (2.38) in which D i,j is the equivalent hydraulic diameter of duct (i, j). µ c(i;j) = µ w(i;j) + _q i;j d p 1 2 A s(i;j) k (2.39) in which d p is the thickness of insulating paper. The complete set of network model equations can also be found in [19] and Chapter 5. The equations require iterative approaches to solve, because both of the hydraulic and thermal networks are coupled via the temperature dependent oil properties such as viscosity and density. The solving procedure of network modelling is summarised in Figure Starting with the initialisation of oil velocities and temperatures, the algorithm updates the oil properties and calculates the new oil velocities with the hydraulic network. Based on the newly obtained oil velocities, the oil temperatures at ducts are calculated with the thermal network. The new temperatures together with the new velocities are used to update the oil properties anew for the next iteration step. Until the relative changes on oil velocities and temperatures between two consecutive iteration steps fall in a tolerance range, the convergence is regarded to be reached. Finally the wall temperatures and winding disc temperatures can be derived according to the oil bulk temperatures and the heat transfer equations. 81

82 Initialise oil velocities and bulk temperatures at ducts Update temperatures dependent oil properties at ducts Calculate oil velocities at ducts Hydraulic network Calculate bulk temperatures at ducts Thermal network Checking step errors on oil velocities and bulk temperatures error >= tolerance error < tolerance Calculate wall temperatures at ducts Calculate disc temperatures Quit Figure 2.23 Flow chart for solving network models. With respect to the fluid properties, transformer oil viscosity is measured to be highly temperature dependent and, for example, the expression format (2.40) can be used for an estimation, in which B and C are constants that are different for different types of fluid [90]; [12] used B = , C = respectively. Otherwise [26] borrowed the equation (2.41) for oil viscosity from Kreith and Black (1980) [91]. C /( T273) Be (2.40) ( T 50) (2.41) Oil density also depends on temperature, although the variation with temperature is slight, i.e. the thermal expansion coefficient is K -1. Thermal conductivity and specific heat can be constant values 0.13 W/m/K and J/kg/K respectively [19]. 82

83 The empirical equations for Nusselt number and junction pressure losses (JPL) will be discussed in detail in Chapter Equation calibrations Empirical expressions are also applied in network models and they are Convective heat transfer related expressions for Nusselt number and the temperature correction of friction coefficient at oil ducts. Junction pressure loss (JPL) related expressions used to estimate pressure losses due to oil flow mixing at duct junctions. In [14,19,27,30,92-94] different formats and parameters for Nusselt number, friction coefficient and JPL expressions have been proposed from general fluid dynamics and heat transfer handbooks but, to the author s best knowledge, their suitability for transformer oil and oil duct dimensions has never been fully explored. It is then necessary to evaluate them in order to improve the accuracy of network modelling. Chapter 4 will show the principle work of this PhD thesis on empirical equation evaluation, and this section briefly reviews the equations. Nusselt number Joshi and Deshmukh [30] borrowed five equations, (2.42) to (2.46), from [95] to calculate the Nusselt number for various conditions, listed in Table 2-8. Table 2-8 Equations for Nusselt number at various conditions [30]. Equation Applicable condition (2.42) Ra < 10 9 For heat transfer at vertical isothermal surfaces, e.g. tank walls and radiator fin surfaces. (2.43) Ra > 10 9 (2.44) For heat transfer at colder fluid over horizontal plate or hotter fluid below horizontal plate. (2.44) was used for the top cooling surface of winding discs. (2.45) For heat transfer at colder fluid below horizontal plate or hotter fluid over horizontal plate. (2.45) was used for the bottom cooling surface of winding discs. (2.46) If there is a fan and the air flow over radiator fins is laminar flow at the beginning (Re < ) but followed by turbulence, for the rest of the entire fin, (2.46) can be applied. 83

84 0:67 Ra 0:25 Nu = 0: Ã! 1 0: A Pr 0 0:387 Ra 1=6 Nu = 0: Ã! 1 0: A Pr 4=9 8=27 1 C A 2 (2.42) (2.43) Nu = 0:54Ra 0:25 Nu = 0:15Ra 0:25 Nu = 0:036 Re 0:8 836 Pr 1=3 (2.44) (2.45) (2.46) Besides, [94] proposed Nusselt number expressions (2.47) to (2.49) for the heat transfer at horizontal oil duct bottom and top surfaces and vertical ducts respectively. Nu Nu h l h l Re Re h c Nu 1.9 Re Pr l w Pr Pr GrPr GrPr Gr Pr (2.47) (2.48) (2.49) h = Height of oil duct, in m l = Length of oil duct, in m Re = Reynolds number at oil duct, dimensionless Pr = Prandtl number at oil duct, dimensionless Gr = Grashoff number at oil duct, dimensionless 84

85 μ c = The dynamic viscosity at oil duct centre, in Pa s μ w = The dynamic viscosity at oil duct wall, in Pa s Junction pressure losses Junction pressure losses (JPL) are often associated with the flow turning at bends or mixing at branches, and the losses are due to the energy loss with sudden or gradual changes in flow directions. [28] noted that, although JPL is conventionally regarded as minor losses, they can actually play a predominant influence on oil flow distributions. Joshi and Deshmukh [30] used (2.50) and (2.51) to determine pressure drops at right angle bends and Tee junctions respectively. P bend = 7000 ½u 2 Re 2 P tee = 4200 ½u 2 Re 2 (2.50) (2.51) The equations for Nusselt number, friction coefficient and JPL will be calibrated by using large sets of CFD simulations in Chapter Prediction on oil flow and temperature distributions By using network modelling, [19] predicted that oil flow and disc temperature distributions follow patterns with a series of peaks and valleys; the number of the peaks (or valleys) corresponds to the number of the passes in the winding. This is the same pattern with the profiles in Figure 2.24 and Figure 2.25 [26]. In the figures, it is interesting to see that there are additional special patterns at the disc number 40 and 100, because the discs arranged there were thinner and the oil ducts were therefore widened. Although [26] did not present more details about the winding design, the special patterns illustrate that localised high temperatures could be due to specific designs. 85

86 Figure 2.24 Calculated disc temperatures with directed oil washers [26]. Figure 2.25 Calculated oil velocities of horizontal ducts with directed oil washers [26]. It is necessary to mention that the results of [26] did not include junction pressure losses which has been addressed to be significant for predicting oil flow distributions in [28]. 86

87 2.4.4 Review of the methodology In order to validate the network modeling, [57] conducted both network and CFD modelling on the LV winding of a transmission transformer, 66 MVA, 225/26.4 kv, ON cooling mode, and concluded that for uniform loss distribution, the network model predictions on hot-spot temperature and location matched the CFD predictions very well, even if network model could not capture details such as hot streaks, which were previously noted in [39]. However, for non-uniform loss distributions, the deviation between network model and CFD became greater [57]. Reference [30] used network modelling and concluded that: 1. If there are a large number of discs in one pass, say 20 or more, possibly oil flows in horizontal ducts do not follow the same directions. 2. If the ratio of disc width to duct height exceeded 35, in case of ONAN, and 50, in case of ONAF and OFAF, insufficient oil could reach up to the middle of the disc width so that the measured winding temperature rise would be higher than the modelling predicted value. It was then recommended that numerical approaches can be particularly improved to include this effect. Reference [29] conducted sensitivity studies using a network model, in which effects of various winding design parameters such as oil duct dimensions and pass sizes etc were investigated and summarised. In the studies both the oil flow rate and temperature at the bottom inlet are set as constants, but in reality the modification of winding design may modify the hydraulic impedance of the winding and as such, if the original external radiator and pump is kept, (pump is only for forced oil cooling mode), the inlet oil flow rate and temperature may also vary. Reference [31] developed a network model and applied it into a Transformer Monitoring and Diagnosis System (TMDS). The model is intended to provide information about heat generation and oil flow distribution in the transformers being monitored. Because of the integration with the TMDS, the thermal model can gather input parameters directly from the available measurement sensors and the 87

88 transformer database. This application of network modeling can be a compensation for the on-line monitoring systems of transformer thermal fault [96,97]. 2.5 Summary In this chapter, a literature review on transformer insulation ageing, end-of-life, thermal performance, thermal modelling and its experimental validation has been made. The basic conclusions from the literatures include 1. A transformer s lifetime is evaluated by its insulation ageing rate and the ageing rate is strongly related to temperature. The insulation at the hot-spot undergoes the worst ageing scenario and its lifetime therefore represents the transformer s end-of-life. 2. Better thermal performance means lower top oil, average winding and hot-spot temperatures. The traditional assessment of a transformer s thermal performance relies on the factory heat run test; however only the global temperatures can be measured in a heat run test and the hot-spot temperature is roughly estimated by the empirical hot-spot factor. This prompts the necessity to directly measure the hot-spot by using optic-fibres. In order to guide the optic-fibre installation, numerical modelling approaches are used to predict the hot-spot location. 3. Among the thermal modelling approaches, network modelling offers a good balance between calculation speed and approximation detail. Compared with network modelling, the thermal-circuit analogy methods are faster but approximate the oil cooling system into only several integral components and cannot predict the details of oil flow and temperature distributions. CFD simulations require significantly more computational efforts than network modelling but with better representations of details and sometimes CFD can reveal some fundamental fluid dynamics phenomena, which network modelling cannot represent. 4. The assumptions and empirical equations employed in network modelling for describing Nusselt number, friction coefficient and junction pressure losses (JPL) were from general fluid dynamics and heat transfer handbooks. Their suitability for transformer oil and oil duct dimensions may require a full calibration. 5. Numerical modelling requires experimental validation to check its calculation accuracy and network modelling is no exception. Various measurement devices 88

89 such as optic-fibres, hot wire anemometry (HWA), Laser-Doppler velocimetry and oil pressure sensors etc can be applied for the experimental validation. 89

90 90

91 Chapter 3 Network modelling and assumptions 3.1 Paper 1 Natural convection cooling ducts in transformer network modelling W. Wu, Z.D. Wang and A. Revell 2009 The 16th International Symposium on High Voltage Engineering (ISH) 91

92 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg NATURAL CONVECTION COOLING DUCTS IN TRANSFORMER NETWORK MODELLING W. Wu 1, Z.D. Wang 1 and A. Revell 2 1 School of Electrical and Electronic Engineering, 2 School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M60 1QD, UK zhongdong.wang@manchester.ac.uk Abstract: In the context of transformer thermal performance and end-of-life criteria, the accurate prediction of the magnitude and location of the maximum temperature or Hotspot inside a transformer is of great importance. In the attempt to accurately represent the characteristics of this hot-spot, various thermal modelling approaches have been developed, one of which can be generally classified as network models such as TEFLOW developed in the UK in the late 1980 s. Of the two flow cooling modes employed in a transformer: forced oil flow cooling (OF) and natural oil flow cooling (ON), the latter is ordinarily accepted to be the more challenging of the two to model. As such it comes as little surprise that network models like TEFLOW are believed and observed to be able to better cope with OF conditions. This paper begins by reviewing the physical background and theory used to describe coolant oil flow with natural convection inside the cooling ducts of power transformers. Furthermore, it highlights aspects of ongoing research which are anticipated to enable enhancements in the TEFLOW code, specifically for the modelling of flow in the natural convection cooling mode. In particular, the pressure drop network model is redevised to consider the effect of a non-uniform cross-sectional area. LIST OF SYMBOLS H = height of the fluid duct L = length of the fluid duct W 1 = inner width of the fluid duct W 2 = outer width of the fluid duct W = average width of the fluid duct P 1 = pressure at inner side of the fluid duct P 2 = pressure at outer side of the fluid duct P = pressure drop between inner and outer sides of the fluid duct U 1 = inner velocity of the fluid duct U 2 = outer velocity of the fluid duct Ū = average velocity of the fluid duct ρ = average density of fluid µ = average dynamic viscosity of fluid µ w = dynamic viscosity of fluid at the wall temperature µ b = dynamic viscosity of fluid at the bulk temperature f = average dimensionless friction coefficient of the fluid duct Re = Reynolds number ρu H/µ windings are generally cooled by oil flowing from the bottom to the top of the winding through an extensive network of crossover ducts and passages. However, the hot spot is generally found not to be located at the top winding disc as one might expect, due to the effect of a non-uniform oil flow [1]. Numerical modelling has been used for thermal analysis of power transfomers for at least 40 years, see Allen & Finn (1969) [2], and Network Modelling is one of the numerical tools that has gained widespread usage. Network Modelling is a process of reducing the complex pattern of passages down to a matrix of simple hydraulic duct approximations, which are interconnected by junction points or nodes. In the transformer cooling system, oil flows through numerous horizontal ducts between heat generating winding discs, thereby extract the heat away from the source. Horizontal ducts join up to a single vertical duct which carries the oil up and across to next section of the winding. The crosspoint linking a horizontal duct and a vertical duct is regarded as a node in the network model. 1. INTRODUCTION Power transformers are core components of electric system networks, and inevitably the reliability of electricity transmission and distribution systems is ultimately influenced by the performance of transformers. Prediction of the magnitude and location of the maximum temperature or Hot-spot inside a transformer winding is of importance for power system asset management. In large power transformers, Figure 1 shows the process by which the geometry for a 2D network model is approximated from a disctype transformer winding. Due to axial symmetry, a 3D segment between two adjacent spacers is first taken, and a 2D slice of this segment is then reproduced to represent the network of oil flow ducts. In this 2D model, we define a single pass as the section between two adjacent block washers (as labelled in Figure 1). The Network modelling methodology can be best de- Pg. 1 Paper F-32

93 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg disc nodes ducts pass Figure 1: Derivation of geometry for a 2D network model from a disc-type transformer winding. scribed as a lumped-parameter model, which implies that it is based upon the assumption that coolant oil is well mixed at each node of the flow junctions so that physical characters, such as temperature and velocity, can be reasonably represented by a single mean value. It is not therefore possible to examine the detailed flow pattern at a node location or inside a duct when using network models, although this would be possible by employing other numerical methods of higher spatial resolution such as Computational Fluid Dynamics (CFD) [3]. In Network Modelling, the mechanics are separated into two aspects: the hydraulic network and the thermal network. The hydraulic network is a mass transfer system, in which the conservation of mass can be applied to the pressure drop equation. On the other hand, the thermal network is an energy transfer system, in which energy is conserved and heat transfer equations are employed. Oliver (1980) [1] derived a set of detailed mathematical equations, developed an algorithm for iterative calculations, and also implemented them into the network modelling software called TEFLOW version 1. Following on from this work, TEFLOW 2 introduced by Simonson & Lapworth (1996) [4], was developed to incorporate a modelling capability of transient loading, so that the program can be used to predict the temporal variation of load on a transformer. In a later review paper of Network Modelling by Zhang & Li (2004) [5], the inability to account for a non-uniform cross-sectional area of horizontal cooling ducts was identified as over-simplistic, and it was stated that a more detailed geometric analysis should be incorporated into the model, although they did not undertake this development. As such, this paper begins by presenting the hydraulic network model in its original form, and then provides examination and analysis of the geometry of the non-uniform horizontal cooling ducts. 2. COOLING DUCTS EQUATION The horizontal cooling ducts represent the primary path of heat transfer from winding discs to coolant oil and as such are of great significance. Figure 2 shows both a cross-sectional view and a top view of a horizontal cooling duct between two winding discs. The equation used to describe balance of forces for the oil flow in the cooling duct is P = P 1 P 2 = f L ρu 2 H 2 (1) Equation (1) is so-called Darcy-Weisbach Equation, which is widely used in hydraulics and describes relationship between pressure loss P and the average velocity U. Here, duct length L and height H are both known, but the friction coefficient f must be determined. For ducts with rectangular cross-section of sides a and b, and with a < b, the friction coefficient may be approximated following the equation given in Vecchio and Poulin et al (2001) [6]: f = ( e 3.5a/b ) 4Re (2) In Oliver (1980) [1] and Declercq (1999) [7], Equation (3) is adopted to calculate f for transformer cooling ducts. f = 24 (3) Re Pg. 2 Paper F-32

94 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg Flow direction ¹ du dr r p 1 p 2 l H = 2R Figure 2: Winding cooling duct (top view and cross-sectional view). Figure 3: Control volume inside the fluid flow region between two infinite parallel plates. From Figure 2 it is clear that the inner and outer sides of the duct are not of equal width, although the above equations intrinsically assume an infinite span. Zhang & Li (2004) [5] notes that non-uniform crosssectional area in the radial direction of the flow has a significant influence on flow distribution within cooling ducts and should not be neglected. It is therefore the task of the following section to derive an equation with consideration of this non-uniform cross-section, so as to improve approximation of the flow friction coefficient f. To represent heat transfer effects and the temperature distribution across the duct, a simple modification is made to Equation (3) to account for the variation of molecular viscosity between the near wall flow, µ w, and the bulk flow, µ b (Oliver, 1980 [1]). f = 24 Re ( ) 0.58 µw In the following section of analysis, this thermal modification is omitted for clarity. µ b (sufficiently far from the walls) for analysis, which is shown in Figure 3. For this control volume, using lowercase letters, height is defined as 2r, length l and pressure drop p = p 1 p 2. Considering only the pressure drop and shear stress due to viscosity, the balance of forces should be 2lµ du dr = 2r p, to which the no-slip boundary condition u(r) = 0 is applied and the resulting differential equation solved to obtain u(r) = p ( R 2 r 2). 2µl The mean velocity across the duct is obtained by integration of velocity u, as follows: U = R 0 u dr R = 1 p 3 µl R2. (4) 3. ANALYTIC DERIVATION Due to the low Reynolds number of the flow in cooling ducts [1, 5], the oil motion may confidently be treated as laminar flow, such that the shear stress caused by viscosity is the primary source of frictional force acting to resist the driving pressure force. Since the width of the cooling duct is generally much greater than its height; W H. The following analysis starts by considering fluid flow between two parallel plates of infinite width, or 2- dimensional flow before deriving a modification to account for the width expansion effect INFINITE WIDTH DUCT FLOW For convenience, we define half of the height between the two infinite parallel plates as R = D/2, and select an infinitessimal control volume from the flow This is then used to provide an expression for the pressure drop as: p = 12µlU H 2 = P = 24 L Re H ρu2 2, (5) where finally, it has been assumed that the duct is sufficiently long to ensure that the flow is fully developed along the entire length of the duct; i.e. p and l may be replaced by P and L respectively. We thus arrive at the friction coefficient approximation currently employed in TEFLOW (given in Equation (3)) RADIAL EXPANSION OF THE DUCT The infinite span duct flow approximation assumes a constant averaged velocity U throughout the fluid flow, although in the case considered here there would clearly be a velocity drop in the direction of Pg. 3 Paper F-32

95 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg W U 1 U ¹ U 2 1 W 2 x L dx Figure 4: Schematic of the cooling duct: top view. the width expansion due to the conservation of mass flow rate, as shown in Figure 4. Therefore we have to consider the velocity variation with width of duct segment, which can be expressed by U(x) = U 1 W 1 w = U 1 W 1 W 1 + x L (W 2 W 1 ) (6) where w is the duct width at location x. From now on U is a function of location x. The average velocity along the duct is given by Ū = 0.5 (U 1 + U 2 ). Substitution of Equation (6) into Equation (5) gives dp = 12µ H 2 U 1 W 1 W 1 + x L (W 2 W 1 ) dx in the limit α 1 the equation returns β = 1 and so collapses to the original model f = f, P = P : 1 α + 1 β(1) = lim α 1 2 α 1 ln α = 1 4. ANALYSIS AND FUTURE WORK Figure 5 displays the variation of β against different α values. It is interesting to note from that β 1 and so f f and P P. For transformers, the ratio α is commonly found to lie in the range 0.5 2; as given by Zhang & Li (2004) [5]. From the above analysis it may then be shown that the estimated difference between f and f, (f f) /f = β 1, is no more than 5%. Using typical geometric parameters for transformer ducts presented in Zhang & Li (2004) [5] and the newly derived form of the pressure network model (Equation (10)) within TEFLOW code, calculations were made to investigate the predicted impact of different values of α, α = 1.00, 1.18, 1.43, 1.82 (corresponding to R I O = 1.00, 0.85, 0.70, 0.55 in Zhang & Li (2004) [5]), as shown in Figure 6. At the extreme condition, α = 1.82, the mass flow rate is increased (or decreased) by 12.6%, i.e. less than the 33.7% change predicted by Zhang & Li (2004) [5]. Then with integration of pressure along the duct, a modified pressure drop, P is obtained P = L 0 dp = 12µ H 2 U L 1W 1 ln W 2 (7) W 2 W 1 W 1 It is convenient to define a width expansion coefficient, α = W 2 /W 1, so that Equation (7) may be expressed as P = 1 α + 1 ln α12µlū 2 α 1 H 2 (8) Furthermore, by comparing Equation (8) with Equation (5), a pressure loss factor, β is defined: such that β = 1 α + 1 ln α (9) 2 α 1 P = β 12µLŪ H 2 = β P and f = β 24 Re = βf (10) The pressure loss factor, β, has thus been introduced to account for the variation of fluid velocity in the flow direction due to the width expansion. As W 2 W 1, i.e. as the cross-sectional area of the fluid duct becomes uniform, α 1. It can easily be shown that The ongoing work on cooling ducts will incorporate natural convection heat transfer effects. A two dimensional CFD investigation of this flow is also underway as an alternative method to Network Modelling; as illustrated in Figure 7, the mesh used for CFD simulation is much finer than the domain discretisation used in Network Modelling. While CFD offers a drastically increased resolution of flow physics, this is accompanied by a significant increase in cost, both in terms of the required computational processing power and computation time. As such, this approach is not expected to become a widespread practical alternative to Network Modelling in the near future. The initial aim of the CFD study will be to provide verification of the Network Modelling code, beyond which it is anticipated that predicted CFD results would be analysed with a view to enhancing approximations in the existing models used in Network Modelling codes such as TEFLOW. 5. ACKNOWLEDGEMENTS Financial support is gracefully received from the Engineering and Physical Sciences Research Council (EPSRC) and National Grid Company. The authors appreciate the technical support given by Paul Jarman from National Grid, John Lapworth from Doble PowerTest and Edward Simonson from Southampton Dielectric Consultants Ltd. Mr. Wei Wu would also like to thank EPSRC-National Grid Dorothy Hodgkin Postgraduate Award (DHPA) for partially Pg. 4 Paper F-32

96 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg β α Figure 5: Relationship between factors β and α. Figure 6: Comparison between different mass flow rate distributions on varied α values. Figure 7: Comparison of the domain discretisation used in Network Modelling and CFD (where mesh density is much higher). providing the PhD scholarship at The University of Manchester. REFERENCES [1] A. J. Oliver. Estimation of transformer winding temperatures and coolant flows using a general network method. IEE PROC., vol. 127, no. 6, pp , [2] P. H. G. Allen and A. H. Finn. Transformer winding thermal design by computer. IEE Conf. Publ., vol. 51, pp , [3] E. J. Kranenborg, C. O. Olsson, B. R. Samuelsson, L.-A. Lundin, and R. M. Missing. NUMERI- CAL STUDY ON MIXED CONVECTION AND THERMAL STREAKING IN POWER TRANS- FORMER WINDINGS. 5th European Thermal- Sciences Conference, The Netherlands, [4] E. Simonson and J. Lapworth. Thermal capability assessment for transformers. Reliability of Transmission and Distribution Equipment, 1995., Second International Conference on the, pp , Mar [5] J. Zhang and X. Li. Coolant flow distribution and pressure loss in ONAN transformer windings. Part I: Theory and model development. Power Delivery, IEEE Transactions on, vol. 19, no. 1, pp , Jan [6] R. M. D. Vecchio, B. Poulin, P. T. Feghali, D. M. Shah, and R. Ahuja. TRANSFORMER DESIGN PRINCIPLES : With Applications to Core-Form Power Transformers. The Netherlands: Gordon and Breach Science Publishers, [7] J. Declercq and W. van der Veken. Accurate hot spot modeling in a power transformer leading to improved design and performance. Transmission and Distribution Conference, 1999 IEEE, vol. 2, pp vol.2, Apr Pg. 5 Paper F-32

97 3.2 Paper 2 Heat Transfer in Transformer Winding Conductors and Surrounding Insulating Paper W. Wu, A. Revell and Z.D. Wang 2009 The International Conference on Electrical Engineering (ICEE) 93

98 The International Conference on Electrical Engineering Heat Transfer in Transformer Winding Conductors and Surrounding Insulating Paper W. Wu, A. Revell and Z.D. Wang, Member, IEEE Abstract--The accurate prediction of magnitude and location of the maximum temperature or hot-spot of transformer windings is of great importance for evaluating transformer thermal performance. In the attempt to accurately represent characteristics of this hot-spot, various thermal modelling methodologies have been developed, including methods which employed forms of Computational Fluid Dynamics (CFD). In the simplified scenario where eddy loss is ignored, the ohmic power generated by winding conductors is the only heat source to be extracted by the coolant oil flow, and a winding disc of multiple cable elements is modelled as a uniformly distributed volumetric heat source at the duct surface boundary. In CFD such an assumption reduces the complexity of modelling process; however it limits the predictive accuracy. This paper considers the heat transfer phenomena inside winding discs comprising copper conductors and surrounding insulating paper, and proposes a non-uniform temperature distribution among conductors. It is envisaged that this would help improve boundary conditions used for the CFD modelling of transformer coolant oil circulation. Index Terms--Power Transformer, Thermal Modelling, Heat Transfer, Hydraulic, CFD I. NOMENCLATURE = thickness of insulating paper layer = width of copper conductors = height of copper conductors = temperature of node = temperature of node = temperature of boundary node = distance between nodes and = height of the contacting surface area between nodes and = length of the winding conductors = thermal conductivity of insulating paper = thermal conductivity of copper conductors = heat generated at a source node of heat = heat flux from nodes to This work is funded by the Engineering and Physical Sciences Research Council (EPSRC), National Grid, Dorothy Hodgkin Postgraduate Award (DHPA) in the UK. W. Wu is a PhD student in the School of Electrical and Electronic Engineering at University of Manchester. A. Revell is a Lecturer in the School of Mechanical, Aerospace and Civil Engineering at University of Manchester. Z.D. Wang is a Senior Lecturer in the School of Electrical and Electronic Engineering at University of Manchester ( zhongdong.wang@manchester.ac.uk). P Subscripts = heat flux from node to boundary node = total number of nodes = total number of boundary nodes = connection matrix for the nodes network: 1 if and nodes and are connected 0 if or nodes and are not connected = connection matrix between the nodes network and the boundary nodes: 1 if node and boundary node are connected 0 if node and boundary node are not connected = coefficients defined for the matrix solution Refers to node Refers to node Refers to boundary node Refers to connection linking nodes and Refers to connection linking node and boundary node II. INTRODUCTION OWER transformers are core components of electric system networks, and as such thermal performance of transformers directly influences reliability of electricity transmission and distribution. In order to evaluate transformer thermal ageing, the accurate prediction of magnitude and location of maximum temperature or hot-spot inside a transformer winding is of great importance. In the attempt to accurately represent characteristics of hot-spot, various thermal modelling methodologies have been developed over the past tens of years, see network model by Allen & Finn [1] and the model by Kranenborg, Olsson, Samuelsson, Lundin & Missing which incorporates some forms of Computational Fluid Dynamics (CFD) [2]. The process by which a 2D CFD model is obtained for a disc-type winding is described as follows (where refer to labels in Fig. 1): (a) Starting from part of a disc-type transformer winding 1, due to axial symmetry, a 3D segment between two adjacent spacers may be extracted, shown as 2 ; (b) A 2D slice of the segment 2 is then reproduced to represent the geometry of oil flow ducts, shown as 3. In 3, note that the hot winding discs are heat sources,

99 2 while the oil ducts could be classified as either horizontal ducts which are the primary cooling paths, or vertical ducts which carries the oil up and across to the next section of the transformer winding; (c) In particular, the geometry of oil ducts 3 is meshed for CFD modelling, shown as 4 (a sub-region was specified for example). However, heat flux from winding discs must be provided as boundary conditions for the CFD model 4. The inner structure of a winding disc 5 is composed of multiple copper conductors covered by insulating paper. Neglecting eddy loss, the ohmic power generated by current passing through transformer winding conductors is the sole source of heat which must be extracted away from the source by cooling oil circulation. Each winding disc is treated as a single homogenous heat source so that a uniform heat boundary condition may be applied for the CFD simulation; i.e. effects due to different heat transfer rates through different materials are ignored. This is a working assumption to reduce the complexity of modelling; however it limits the predictive accuracy. In reality, conductors will accumulate and dissipate heat at differing rates based on their locations; depending on geometry and layout of the conductor and its insulating paper of the disc. For instance, a centrally located conductor has smaller heat-dissipating surface area than the one located at the sides of the disc. In order to more accurately represent the heat flux boundary conditions for CFD modelling, it becomes necessary to consider both of the paper and the individual conductors, and also to account for the downstream accumulation of heat due to the raised temperature of the oil fluid as it moves down the duct. This paper reports the initial results from an in-house code, TEDISC when it is applied to the heat transfer cross a single winding disc composed of copper conductors and surrounding insulating paper. III. THE NUMERICAL MODEL Fig. 1. Derivation of 2D CFD model of a disc-type transformer winding. A. Assumptions and Discretisation The inner structure of the winding disc is shown as part 5 of Fig. 1, and this is where the heat transfer between conductors and insulating paper occurs. It is possible to use a collection of interconnected copper conductor and insulating paper elements to discretise the thermal field inside this region, as shown in Fig. 2. For each element, an average temperature value is assumed to represent the temperature property of the whole element region, while a node is defined to be at the centre of this element. Following these definitions, the following implicit assumptions are stated: 1) The thermal conductivity of copper ( ~380 Wm -1 K -1 [3]) is much higher than that of insulating paper, ( ~0.2 Wm -1 K -1 [3]); so the temperature gradient inside the conductor is assumed to be negligible; 2) The thickness of the insulating paper is relatively thin (less than a few mm), i.e. ; so temperature variation across the paper thickness may be ignored. Temperatures at the outer boundaries of the insulating paper (this paper layer surface boundary can also be described as oil duct surface boundary or winding disc surface boundary, depending on the context in the paper) have been applied from previous calculations.

100 3 Fig. 3. Heat flux geometry between two adjacent nodes and. Fig. 2. Nodes representation of the winding disc. Fig. 2 illustrates a network of these nodes, including unknown temperature nodes inside the winding disc as well as the known temperature nodes at the boundaries. Each component block of one conductor and its surrounding insulating paper has been represented by nine nodes in total. Therefore, for a winding disc containing conductors, the total number of unknown nodes will be, and the total number of boundary nodes will be. B. Equations Employed The physical model is composed of the following: 1) Heat transfer equation applied between adjacent nodes or applied between a node and a neighboring boundary node; 2) Thermal energy conservation applied to each node. The first of these can be summarized as two contacting nodes and, as shown in Fig. 3, or between one node and a boundary node next to it. Condition (A) in Fig. 3 represents the heat transfer across a homogenous material, while condition (B) is used for heat transfer across two different materials. In the real scenario, condition (A) may be used for heat transfer between two adjacent insulating paper nodes, as well as between a paper node and a neighboring boundary node (use instead of in Fig. 3 for this situation); on the other hand, condition (B) will be adopted to cope with heat flux between a copper conductor node and a paper node adjoining to it. According to Fourier s law, the thermal heat flux through a surface is proportional to the negative temperature gradient across the surface, and the ratio between them is defined as the thermal conductivity. Fourier s law can be expressed by Using discretised form of Fourier s law, for condition (A) in Fig. 3, heat flux from nodes to is where and are the height and width of the contacting surface area respectively, and is the distance between nodes and, as labeled in Fig. 3. For condition (B), heat flux from nodes to is where. are used to express subdistance and thermal conductivity in the segments belonging to nodes and respectively. An equivalent thermal conductivity can be defined to incorporate (2) into (1), as given by (3). Thereby, it is possible to only use (1) for expression of heat flux from now on. Conservation of thermal energy for each node gives The first sum term is the total thermal energy diffused from node to any existing neighboring nodes. The second sum term is the total thermal energy flowing to existing adjacent boundary nodes. Both of heat flux term and in (4) can be calculated according to (1). Further substitution of (1) into (4) gives the primary matrix equation, which must then be solved. C. Solution Procedure Substitute (1) into (4) and obtain (1) (2) (3) (4) (5)

101 4 Denote are. Then (5) can be rewritten into Equation (6) is a set of linear simultaneous equations. In the equations, and can be determined by the geometric parameters of the disc, and and depending on the layout of the inner structure. With respect to determined as the following: (6), it could be 1) If node is located at insulating paper layer, ; 2) If node belongs to a copper conductor, is the ohmic loss generated per unit length of that winding conductor. In conclusion, there are linear equations corresponding to unknown node temperatures, in (6), and it is sufficient to solve for using the Gaussian elimination method. MATLAB was chosen as the development platform of TEDISC since it has a good matrix manipulation library. Fig. 4. Dimensions definition for the calculation results presentation. The calculation results for temperatures at y = 0 and y = d are shown in Fig. 5. Due to symmetry of the boundary conditions set as Table I, the temperatures at is distributed as the same way with y = d. Plateau-like temperature distribution patterns can be seen from Fig. 5, and the saw-teeth shape temperature distribution for paper layer is probably due to the limited number of discretised elements and different lengthes represented by nodes. IV. AN ILLUSTRATIVE TEST CASE Using the transformer winding disc geometry presented in Oliver (1980) [3] and the newly developed TEDISC code, calculations were made to investigate temperature distribution inside a winding disc. In this winding disc, there are 22 conductors; i.e. the size of the matrix to be solved will be 198 by 198. A. Case I: uniform temperature Initially, a uniform temperature values is applied at all boundaries, as shown in Table I. TABLE I UNIFORMLY DISTRIBUTED BOUNDARY CONDITIONS Boundary Temperature values ( o C) Top side 72.6 Left side 72.6 Bottom side 72.6 Right side 72.6 Dimensions are defined as shown in Fig. 4 for clarity. Fig. 4 defines, and as such the line describes the top paper layer location, gives the bottom paper layer location, while shows where the conductor nodes Fig. 5. Results with uniform temperature boundary conditions. B. Case II: linearly increasing temperature In the real case scenario, it is unlikely that surrounding cooling oil temperature is uniformly distributed. Since there is heat flux from the winding disc heat source to the oil flowing along the ducts, the oil temperature will increase gradually. Therefore an increasing series of temperature values for bottom and top boundaries is now applied so as to take this effect into consideration. With respect to the vertical oil ducts, the temperature is considered staying uniform; being a reasonable approximation given that the disc height is comparably small. Oliver (1980) [3] assumed the oil temperature variation along the horizontal cooling ducts to be linear. The boundary temperature values applied in this case are shown in Table II.

102 5 TABLE II LINEARLY INCREASING BOUNDARY CONDITIONS Boundary Temperature values ( o C) Top side 67.0 to 78.2 Left side 67 Bottom side 67.0 to 78.2 Right side 78.2 With the linear boundary conditions, the calculation reproduced different results, as shown in Fig. 6. There is an obvious peak value, rather than the plateau shape in Fig. 5. It is interesting to note that the peak value is located close to the downstream end of the winding disc (the 19th conductor), instead of the end conductor itself. This is reasonable since the end conductor has a much lower temperature due to its lack of a neighbor and consequent extra free surface area to dissipate. TABLE III COMPARISON OF STATISTICAL RESULTS BETWEEN OLIVER S METHOD AND TEDISC Conductors temperature Oliver s Equation TEDISC Average ( o C) Maximum ( o C) The hottest conductor number 22nd (at the downstream end) 19th From Table III it can be seen that the difference between average and maximum temperatures from both methods is less than 1%, which implies the assumption made by Oliver s equation is sufficient to predict the magnitude of the hot-spot although it is unable to predict hot-spot s precise downstream location. Fig. 6. Results with linearly increasing boundary conditions. C. Discussion In Fig. 6 the solid curve is a prediction of conductor temperatures using an expression derived in Oliver (1980) [3], given below as (7); to obtain average and maximum values of the conductors temperatures in a winding disc. The necessary parameters include wall temperatures of bottom and top horizontal cooling ducts. V. SUMMARY AND FUTURE WORK It is anticipated that CFD modelling will be able to provide an improved prediction of the temperature distribution in transformer cooling oil circulation and it is the long term aim to undertake a comprehensive CFD analysis of this study case. However for this aim to be realized, it is important to provide an accurate representation of the winding discs surface temperatures to be used as CFD boundary conditions. As such, the work was set out to define a mathematical model and lead to the development and validation of TEDISC code. In this way, TEDISC is able to provide a detailed heat flux distribution at the paper layer surfaces. Based on the temperature values obtained for the insulating paper layers, heat flux distribution as shown in Fig. 7 can be obtained, which would replace the basic assumption which regards the winding disc as a uniformly distributed heat source. (7) Fig. 6 displays a comparison of results from (7) with results predicted by TEDISC code. Away from either end of the disc, in the mid-section, the gradient of both results are clearly seen to be in good agreement. However, it is important to note that Oliver s method assumes the hot-spot to be located at the downstream end of the winding disc whereas TEDISC s result shows that the hot-spot is close to, but not exactly at the downstream end. Table III provides a quantitative summary of these results. Fig. 7. Heat flux distribution at the top surface with both the uniform and the linearly increasing boundary conditions, as shown in Table I and Table II.

103 6 The ongoing work on winding discs will incorporate coupling between thermal calculations for both winding discs and surrounding cooling oil. The current boundary conditions used for TEDISC are obtained from previous cooling oil models, in which the heat flux from discs to oil is regarded to be uniformly distributed as well as the temperature development along the cooling ducts is assumed to be linear. However, Fig. 7 clearly displays a non-uniform distribution of heat flux at the surface of winding discs; it is therefore considered to be valuable to update the heat flux assumption used in former cooling oil models in order to recalculate oil temperatures. Using an iterative numerical process, a converging result matching both of the winding discs and the cooling oil models simultaneously can be expected. Zhongdong Wang was born in Hebei Province, China in She received her BEng. and MEng. degrees in high voltage engineering from Tsinghua University of Beijing in 1991 and 1993, respectively, and her PhD degree in electrical engineering and electronics from UMIST in Dr. Wang is a Senior Lecturer at the Electrical Energy and Power Systems Group of the School of Electrical and Electronic Engineering at University of Manchester. Her research interests include transformer condition monitoring and assessment techniques, transformer modeling, ageing mechanism, transformer asset management and alternative oils. She is a member of IEEE since 2000 and a member of IET since VI. ACKNOWLEDGMENTS Financial support is gracefully received from the Engineering and Physical Sciences Research Council (EPSRC), National Grid and Dorothy Hodgkin Postgraduate Award (DHPA). The authors appreciate the technical support given by Paul Jarman from National Grid, John Lapworth from Doble PowerTest and Edward Simonson from Southampton Dielectric Consultants Ltd. Mr. Wei Wu would also like to thank EPSRC-National Grid Dorothy Hodgkin Postgraduate Award for providing the PhD scholarship at The University of Manchester. VII. REFERENCES [1] P. H. G. Allen and A. H. Finn, "Transformer winding thermal design by computer," IEE Conf. Publ., vol. 51, pp , [2] E. J. Kranenborg, C. O. Olsson, B. R. Samuelsson, L.-A. Lundin, and R. M. Missing, "Numerical study on mixed convection and thermal streaking in power transformer windings," 5th European Thermal- Sciences Conference, The Netherlands, [3] A. J. Oliver, "Estimation of transformer winding temperatures and coolant flows using a general network method," IEE PROC., vol. 127, no. 6, pp , Wei Wu was born in Shaanxi Province, China in He received his BEng. and MEng. degrees in Electrical Engineering from Tsinghua University, Beijing in 2004 and 2006, respectively. Wei is a PhD student at the Electrical Energy and Power Systems Group of the School of Electrical and Electronic Engineering at University of Manchester. His research interests lie in transformer thermal modelling and simulation. Alistair Revell was born in Buckinghamshire, England in He graduated from UMIST in 2002 with a degree in Aerospace Engineering with French. He received his PhD in Turbulence Modelling and Computational Fluid Dynamics at The University of Manchester in 2006, including placements at ENSMA, EDF and IMFT in France and Stanford in the USA. Recent research topics relate to applications in Aerospace and Nuclear engineering and in particular, the development, validation and dissemination of the open-source CFD software Code_Saturne.

104 94

105 Chapter 4 CFD calibration for network modelling 4.1 Paper 3 CFD calibration for network modelling of transformer cooling oil flows Part I heat transfer in oil ducts W. Wu, Z.D. Wang, A. Revell, H. Iacovides and P. Jarman 2011 IET Electric Power Applications Accepted 95

106 ISSN CFD Calibration for Network Modelling of Transformer Cooling Oil Flows Part I Heat Transfer in Oil Ducts W. Wu 1, Z.D. Wang 1, A. Revell 2, H. Iacovides 2 and P. Jarman 3 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK. 2 School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK. 3 Asset Strategy, National Grid, Warwick, CV34 6DA, UK. zhongdong.wang@manchester.ac.uk Abstract In the context of thermal performance and thermal lifetime, it is of great importance to predict the magnitude and location of the hot-spot temperature inside a transformer. Various calculation approaches have been developed in the attempt to gain an accurate prediction of hot-spot, including so-called network models such as TEFLOW. In terms of the methodology used in network modelling, the complex pattern of oil ducts and passes inside a winding is reduced to a matrix of simple hydraulic channel approximations, where empirical analytical expressions are employed to hydraulically and thermally describe oil flow and heat transfer. The heat transfer equations contain empirical parameters, often obtained and verified by a limited number of experimental cases of relatively simple flows. Applicability of these equations should therefore be carefully evaluated and if necessary corrected, when being used in the wide range of conditions of transformer oil flow; this is the primary objective of this paper. A detailed parametric study has been performed using the COMSOL multiphysics software package for Computational Fluid Dynamics (CFD), which offers a higher order of accuracy relative to network modelling. The resulting data sets are processed, based on which a new set of parametric heat transfer equations are proposed specifically for transformer cooling oil flow. Comparison is finally made between the newly proposed equations and the currently used off-theshelf expressions. 1 NOMENCLATURE a, b = Constant parameters for Nusselt number expressions A s = Area of fluid duct (duct height H duct length L) c, d = Constant parameters for friction coefficient expressions C p = Specific heat capacity of fluid D = Equivalent hydraulic diameter of fluid duct f = Average dimensionless friction coefficient of fluid duct f c.p. = Average dimensionless friction coefficient of fluid duct with constant property fluid H = Height of fluid duct h c = Convective heat transfer coefficient of fluid duct k = Thermal conductivity of transformer oil L = Length of fluid duct m, n = Constant parameters for the viscosity terms in IET Electr. Power Appl., The Institution of Engineering and Technology

107 Nu and f expressions part, the effect of a non-uniform oil flow rate [2]. In this Nu = Nusselt number scenario the magnitude and the location of the hot-spot inside Nu c.p. = Nusselt number of constant property fluid the windings is important since it identifies the location of the Pr = Prandtl number worst insulation ageing. q = Heat flux from winding to fluid duct Numerical modelling has been used to predict the hot-spot R 2 = The square of the correlation between the response values and the predicted response values for over 40 years [3]. These numerical approaches can generally be categorised as either network models [2, 4-5] or methods which incorporate a degree of Computational Fluid Re = Reynolds number Dynamics (CFD) [1, 6-7]. Generally CFD simulations can be t b = Bulk temperature of fluid duct expected to provide more detailed results but with a large t w = Wall temperature of fluid duct increase in the required computational effort. In comparison to u = Local flow velocity at the differential element A CFD, network models are regarded as a quick and simple numerical approximation which is often convenient for U = Average flow velocity of fluid duct industry to use, as a large range of design parameters can be α, β, γ = Extra constant parameters for friction coefficient expressions trialled for a relatively low computational effort. However, network models incorporate significant assumptions about the μ b = Dynamic viscosity of fluid at bulk temperature flow and subsequently empirical equations to describe μ w = Dynamic viscosity of fluid at wall temperature physical properties of the fluid, and the principle objective of ρ = Density of fluid this series of paper is therefore to assess the accuracy of these A = Area of a differential element empirical equations and underlying assumptions within a well ΔP = Pressure drop between the inlet and outlet of fluid duct defined range of transformer cooling oil flow parameters, with a view to providing more consistent expressions. Subscripts b Value at bulk temperature 3 APPROXIMATIONS IN NETWORK MODELLING c.p. Value at constant property fluid In brief, network modelling is the process of reducing a w Value at wall temperature complex pattern of multiple passages down to a matrix of Acroynms/Shorthand simple hydraulic duct approximations, interconnected by junction points or nodes. A node is defined as a cross-point CFD Computational Fluid Dynamics linking a horizontal duct with a vertical duct [8]. As an JPL Junction pressure loss example, Figure 1 shows the process by which the domain LV Low voltage dimensions for a 2D network model are approximated from a 2 INTRODUCTION Power transformers are key, and one of the most expensive, components of electric system networks. Transformer lifetime and insulation ageing are strongly dependent upon the temperature distribution and fluctuation. An improved understanding of the thermal ageing of insulation can assist the policy making of transformer asset management [1]. In power transformers, windings are commonly cooled by oil flowing up, from the bottom to the top, through an extensive network of crossover ducts and passages. As the oil flows upwards, it gains in temperature by absorbing heat transferred to it from the windings, yet the maximum temperature, called hot-spot, is generally not found on the top-most winding disc as one might expect. This is due to, in 3D disc-type transformer winding; retaining geometric elements such as discs, ducts, nodes and passes. As the winding is axial symmetric and the circumferential width of a oil duct is significantly longer than the duct s radial length, 2D channel flow models between infinite parallel plates are suitable approximations and will be applied for all the oil ducts following the experiences in [2, 6, 9]. This 2D geometry also neglects the spacers and assumes that there is no circumferentially directed oil flow. The oil flow through horizontal ducts, between rows of heat generating winding discs, acts to transfer the heat away. Horizontal ducts join up with a single vertical duct which carries the oil upwards and through a gap to next pass. Bulk averaged parameters are assumed to represent the variation of physical quantities across each duct and at each node, and a set of lumped IET Electr. Power Appl., The Institution of Engineering and Technology

108 parameter expressions are applied, thereby constructing both thermal and hydraulic networks across the transformer. discs ducts Winding raduis nodes a pass oil Figure 1 Geometric derivation of a 2D network model for a disc-type transformer winding. To derive a practical and tractable set of equations to describe the network model, the following physical assumptions are further made in addition to the geometric assumptions previously outlined: a. Oil flow inside ducts is assumed to be entirely laminar due to the low Reynolds number (Re = 25 ~ 100 [9]). b. Oil ducts are approximated by a pair of infinite parallel flat plates. c. Oil temperature is assumed to increase linearly as it flows along the duct and gains heat from adjacent discs, i.e. the heat source [2]. d. Oil flow is completely mixed at nodes in terms of both hydraulic and thermal aspects; i.e. the flow velocity and temperature distribution becomes uniform upon departure from the junctions. The real scenario could deviate from these conditions, so the suitability of these assumptions must be verified. Assumption (b) was shown by [8] as deemed reasonable with a predictive error of less than 5%, whereas [10] found that although assumption (c) precludes an accurate prediction of the hot spot location, the prediction error in hot-spot temperature is less than 1%. The set of network model equations based on the assumptions outlined above can be found in [2]. These equations require an iterative approach to solve, because the hydraulic and thermal variations are coupled via the temperature dependent properties of oil, such as oil viscosity and density. Crucially, it should be noted that the following empirical expressions are incorporated into the network model equations: i. Convective heat transfer: expressions for both Nusselt ii. number, Nu, and temperature corrected friction coefficient, f. Junction pressure loss (JPL): expressions used to estimate mixing losses occurring at junctions. In [2] and [5], forms and parameters for Nu, f and JPL expressions have been identified from heat transfer literature but, to the authors best knowledge, their suitability for transformer oil flow has never been fully explored. Therefore, the current work will focus on evaluating existing expressions for Nu and f, and proposed modifications will be given. Additional work to evaluate expressions for the JPL shall be addressed in an accompanying paper. 4 ANALYSIS ON OIL FLOW IN COOLING DUCTS The majority of heat transfer occurs along the horizontal oil ducts between adjacent discs rather than vertical ducts, as vertical ducts are much shorter and have only a single contact surface with the heat source. In view of this [2] made the assumption that the heat transfer to oil in vertical ducts may be neglected altogether; the present paper follows the same assumption and thus in the following paragraphs, cooling ducts refer to the horizontal ducts only. Table 1 gives typical cooling duct dimensions, duct inlet temperature and velocity ranges, covering a wide spread design parameters for transformers from 22 kv to 500 kv, 20 MVA to 500 MVA. It is granted that duct dimensions vary with rated voltages and power ratings of transformers and the inlet temperature and velocity depend on the operating cooling mode and loading condition, as well as the position of the duct in a winding, however the expert experiences on the vast amount of existing designs show that they are expected to lie within the parameter ranges listed in the table. Table 1 Typical parameters of power transformer cooling Parameter name Duct height, H (m) Duct length, L (m) ducts. Variation range IET Electr. Power Appl., The Institution of Engineering and Technology

109 Inlet temperature ( o C) Inlet velocity, U (m/s) Nusselt number, Nu, is the ratio of convective heat transfer coefficient to conductive heat transfer coefficient and is used to evaluate the efficiency of convective heat transfer in fluid flow. One may compute Nusselt number as follows: hc D Nu (1) k where h c is convective heat transfer coefficient, D is equivalent hydraulic diameter and k is the thermal conductivity of fluid. A common value of the thermal conductivity of transformer oil, k, is 0.13W/(m K) [2]. For infinite parallel plate models, the hydraulic diameter is generally taken to be twice the duct height, i.e. D = 2H. Thus if the Nusselt number is known, the convective heat transfer coefficient can be obtained directly. A number of expressions have been developed to approximate Nu for engineering applications, and the proper form of the expression depends upon which of the three laminar flow regimes is in operation [11], LF1: Fully developed (both hydraulically and thermally), LF2: Thermally developing (hydraulically fully developed), LF3: Simultaneously developing (hydraulically and thermally developing). In order to identify a regime, the entrance length must be known, which is defined as the distance downstream of a duct entrance that the fluid travels before centreline values of friction coefficient (hydraulic system) or Nusselt number (thermal) attain values within 1% away from the fully established centreline value. In each case, hydraulic and/or thermal flow is considered to be fully developed only for duct lengths beyond this entrance length. 4.1 Hydraulic entrance length For hydraulically fully developed flow between infinite parallel plates, the friction coefficient can be shown to scale as f c.p. = 24/Re. As a flow develops the friction coefficient will progress towards this fully developed value. The subscript c.p. refers to values derived for a constant property fluid, in which the fluid properties are independent of fluid temperature. Based on the data provided by [12], Figure 2 illustrates the development of local friction coefficient f loc for laminar flow between parallel plates. The local friction coefficient is defined at a distance x, from the inlet of the duct, and f is the average value of the local friction coefficient f loc along the duct. Figure 2 Local friction coefficient f loc development for the laminar flow between parallel plates. According to the correlation between f loc and x shown in Figure 2, the flow becomes fully developed at around x = 0.015Re D. Using typical values for transformer cooling ducts, i.e. Re = 100 [9] and D = 0.01m [2], the hydraulic entrance length is estimated to be 0.015m, which accounts for 15% of the typical cooling duct length, 0.1m. This implies that the oil flow will generally be at a fully developed state through around 85% of the duct length. 4.2 Thermal entrance length The thermal entrance length can be estimated as the product of the hydraulic entrance length and the Prandtl number, Pr (typically ~ 200 for oil [2]), and using the same values as above, the thermal entrance length is therefore of the order of 3m, which is much longer than the typical cooling duct length, 0.1m [2]. Consequently, the typical oil flow in transformer cooling ducts belongs to the second flow category, LF2. Since the flow is thermally developing, it implies that the Nusselt number is continuously developing along the flow direction and does not reach a stable value. 4.3 Average Nusselt number along duct IET Electr. Power Appl., The Institution of Engineering and Technology

110 In the context of lumped parameter modelling, the local Nusselt number is generally represented as a single value, averaged over the entire duct length. In [5], empirical equation (2) was used to estimate the average Nusselt number for the oil flow in cooling ducts, where constants a and b are empirical parameters. These constants are taken to be a = 1.86 and b = -1/3 [5], which are derived for flow through circular pipes [13-15]. The implication of (2) is that Nu depends on the dimensionless group {L/D, Re, Pr}. b L / D Nu c. p. a (2) Re Pr Similarly, [2] adopted the same value for b but proposed a ~30% higher value of a = 2.44 for duct models of flow between infinite parallel plates; obtained by fitting data provided by [12]. It should be noted that neither of the Nu expressions described above accounts for the variation of the fluid properties with temperature. There is, however, a significant functional dependence of viscosity upon temperature which may be included in a network modelling framework, and this is discussed in the following section. 4.4 The variation of oil viscosity with temperature Neglecting thermal effects, [8] proposed a frictional pressure drop equation for a cooling duct and demonstrated that the velocity profile across the duct height takes the form of a parabolic curve, as shown by curve (a) in Figure 3. Yet, in practice, the oil viscosity is known to decrease significantly with temperature [2, 12], and the associated velocity variation that results from the change in oil viscosity, from the wall surfaces towards the centre of the duct, is shown as curve (b) in Figure 3. As the flow temperature increases further, the observed distortion will increase. Flow direction Figure 3 Velocity in a heated duct (a) constant viscosity; (b) temperature dependent viscosity. For engineering applications, [12] proposed a simple correction to account for the temperature dependency of viscosity upon both bulk Nusselt number and friction coefficient, shown as (3) and (4). [2] proposed constant values b a of n = and m = Since the viscosity ratio μ w /μ b < 1, a negative value for n implies that the heat transfer efficiency is augmented by the velocity distortion while, conversely, a positive m factor weakens the friction force due to viscosity, in line with intuition. Nu Nu IET Electr. Power Appl., The Institution of Engineering and Technology 2011 f c. p. f c. p. w b w b Equations (5) and (6) summarise the thermal and hydraulic expressions for oil flow in 2D cooling ducts. However, both expressions are empirical and [2] specifically emphasised that m = 0.58 was obtained for flow through a circular pipe; a clear indication that these values may not be directly applicable to a transformer cooling duct which is better represented by an infinite parallel plate model, so further verification is required. 5 CFD MODELLING L / D Nu 2.44 Re Pr f f c. p. 5.1 Nusselt number m 1/ 3 w b n w b As the Nu equation is assumed to take the general form as (3) (4) (5) (6) b n L / D w Nu a (7) Re Pr b our subsequent work is then to verify the suitability of this form for Nu in cooling ducts and to identify the constants a, b and n. CFD as a numerical approach with much higher discretisation, is used to calculate a large number of flows in 2D cooling duct models, and heat transfer data can be extracted. Nusselt number would then be computed from its definition equation as Nu hd k t q t w where heat flux q, thermal conductivity k and hydraulic diameter D are all known a priori, and the bulk and wall temperatures, t b and t w can also be extracted. The bulk temperature t b, expressed by (9), is the energy-average temperature over the fluid flow domain, and the wall b D k (8) 5

111 temperature t w is the average temperature along the length of the duct walls [16]. In (9), ρ, C p, u and t denote the density, specific heat, fluid velocity and temperature respectively at the differential element A of the entire duct area A s. t b A s A C uta s p C ua 5.2 Friction coefficient From these CFD calculations, the pressure drop between the two ends of the duct is extracted, and the friction p (9) within 1% error bounds. For laminar flow modelling, CFD has been proved by practical cases to be highly reliable. Inlet (velocity, temperature) Wall (heat flux) Flow direction Wall (heat flux) Outlet (pressure = 0) (a) Boundary conditions set for CFD simulations. coefficient f is computed from (10); thus the quantity f/f c.p. may then be obtained to verify (6). 5.3 CFD simulations P D f (10) 2 U 2L COMSOL Multiphysics software package was used for the CFD simulations reported here. As an example, duct geometry of height 0.005m and length 0.1m from the 22 kv low voltage (LV) winding of a 250 MVA transformer was constructed. The winding current is 6561 A and the loss power generated by per unit length of conductor is 55 W [2]. For this duct example the ratio of the length against its circumferential width is only 3% and therefore 2D channel flow model between infinite parallel plates is suitably applicable for the geometry. Boundary conditions were defined as shown in Figure 4 (a). Constant values of fluid velocity and temperature were defined at the inlet of the duct, while the pressure at the outlet was set to 0, i.e. the reference value. A no-slip condition was applied at the walls (i.e. u = 0) where a heat flux of 6111W/m 2, due to the losses, was also prescribed. A grid independence study was undertaken for mid range values and a computational grid of cells was deemed sufficiently fine to ensure calculation accuracy to an acceptable degree. Figure 4 (b) illustrates the oil velocity development along the duct centreline from an individual CFD calculation (typical geometry, inlet temperature of 40 o C and inlet velocity of 0.08m/s); the distance from the inlet to the peak velocity location is the hydraulic entrance length, and the subsequent decrease is due to the temperature dependent oil viscosity. As shown in the figure, the COMSOL result was verified by CFD results calculated using the open source CFD software, Code_Saturne [17], which indicated an agreement (b) Development of fluid velocity along duct centreline. Figure 4 CFD simulation boundary conditions and velocity results using typical parameter values. A sensitivity study for key parameters of duct height, length, inlet temperature and velocity, across an informed range around typical baseline values [2] as listed in Table 1, was performed. A number of steps were chosen within the parameter ranges to form combinations of the parameter values. For each combination, a data sample was extracted from the fully converged 2D CFD calculation. The resulting dataset of 2520 samples was then used to approximate the parameters in (7) and (4). 6 DERIVATION OF CORRELATION 6.1 Study on Nusselt number The 2520 CFD samples are used to plot the relationship between Nusselt number and (L/D)/(Re Pr), as depicted in Figure 5 (a). The four different parameters, duct height, length, inlet temperature and velocity, govern curve trends IET Electr. Power Appl., The Institution of Engineering and Technology

112 along different directions as indicated in the figure. For example, with inlet oil velocity higher than 0.01m/s and duct height above 0.004m, most samples gather on the left hand side where (L/D)/(Re Pr) is below At the highest oil velocity, 0.16m/s, and the greatest duct height, 0.01m, Nu reaches to the maximum. Highest inlet velocity & biggest duct height Duct height Duct length Inlet velocity Longest duct length Inlet temperature (a) CFD simulated Nu samples. (b) Comparison between the samples, fitted equation (11) and originally proposed equation (5). Figure 5 Curve fitting results on Nusselt number of flow between infinite parallel plates. A range of different equation forms were tested upon the Nu correlation and the fitness scores are compared in Table 2. A form which does not include a term of the viscosity ratio μ w /μ b can yield a high correlation fitness score, R 2 = ; 12 5 although this implies that the impact of viscosity variation upon Nu is not dramatic, the dispersity of the samples observed from the figure indicates possibilities to have better fittings. Table 2 reveals that the introduction of a viscosity ratio term can improve the correlation fit, while the inclusion of a constant acts to restrain the error range. The best fit is then (11), with an error below 1%. L / D Nu 1.29 Re Pr 0.38 w b (11) On average (11) gives Nu values that are 15% lower than (5), which is listed at the last row of the table as a comparison baseline; a detailed comparison between (11) and (5) in Figure 5 (b) illustrates that (11) yields Nu values which match the samples better than (5). Lower Nu will predict higher winding temperatures. 6.2 Study on friction coefficient As for expression (4), the term (μ w /μ b ) m was incorporated into the formulation approximating friction coefficient f, in order to account for the temperature dependency of fluid viscosity. From the same set of CFD results described above, data samples of f/f c.p. and their corresponding values of μ w /μ b were obtained for each of the parametric conditions proposed in Table 1, so that a similar curve fitting analysis could be performed; in order to identify a suitable value for the exponent m. The CFD predictions of f/f c.p. versus μ w /μ b are illustrated in Figure 6. These samples are observed to cluster in a discontinuous pattern and indeed distinct groups are formed. When the duct becomes shorter and/or wider, the friction coefficient values will deviate more from the constant property fluid scenario. The original expression given by (6) is also plotted in Figure 6, though clearly a simple form of this nature is unable to adequately fit the sample distribution. Consequently, additional dimensionless groups must be introduced to account for this discontinuity of the samples. As in common practice, the dimensionless groups Re, Pr and L/D are added to incorporate the hydraulic, thermal and dimensional factors into the expression respectively, and thus a form is proposed as f f c. p. c Re Pr L D m w b d IET Electr. Power Appl., The Institution of Engineering and Technology

113 Table 2 Comparison between different Nu expressions. (Relative error: the relative difference from expression value to sample value.) Relative error (%) Expressions R 2 Mean error Error range L / D Nu 2.45 Re Pr L / D Nu 1.60 Re Pr L / D Nu 2.03 Re Pr 0.34 w b L / D Nu 1.29 Re Pr 0.38 w b L / D Nu 2.44 Re Pr 1/ 3 w b f f c. p Re 0.37 Pr 0.15 L D 0.55 w b (12) Duct length Duct height Table 3 Ranges of the dimensionless groups. Inlet temperature Inlet velocity Dimensionless groups Mean value Min value Max value Re Pr L/D Table 4 compares the performances of the expressions, (12) Figure 6 Curve fitting results on f/f c.p. of flow between infinite and (6). The average error of (12) is around 3%, which is ~10 parallel plates. times lower than that of (6). In Figure 6, the comparison with the samples reveals that (6) consistently underestimates the Curve fitting was conducted onto this form and (12) returned an acceptable correlation (R 2 impact of the viscosity variation on the friction coefficient f. = ). Since the On average, the new equation (12) predicts higher f values form is newly proposed, extracted dimensionless group ranges than (6) by 48%. Higher f values imply that it is more difficult are listed in Table 3 to give the underlying governing for oil to flow along the ducts. hydraulic-thermal and dimensional regime. IET Electr. Power Appl., The Institution of Engineering and Technology

114 Table 4 Comparison between the two f/f c.p. expressions. Relative error (%) Expressions R 2 Mean error Error range f f c. p Re 0.37 Pr 0.15 L D w b f f c. p. w b Moreover, Figure 6 shows that there is a region where μ w /μ b < 0.3 and (12) has errors in this region higher than the overall average error of 3%. An example falling into this region is when cool oil slowly flows along long ducts (inlet temperature 20 o C, velocity 20 mm/s and duct length > 100 mm). Still, the average error of (12) in this region would be above 15%; far better than 30% yielded by (6). It implies that one should be careful when using (12) to design long oil ducts for natural cooling transformers. 7 EVALUATION OF EMPIRICAL EQUATIONS IN NETWORK MODEL The LV winding example from [2] was used to evaluate the influence of the proposed modifications of the Nu equation in network modelling. In this test case there are 100 horizontal ducts in the winding, divided into 5 passes by block washers. The heat source input was assumed to be entirely constituted from constant DC loss (Ohmic loss), i.e. not affected by local temperature of the conductors. Furthermore, minor pressure losses occurring at junction nodes were neglected in order to focus upon the influence of the models from parameters Nu and f. Calculations of this case were performed with the TEFLOW, a network model implementation developed in the UK in the late 1980 s, and the influence of different Nu and f equations upon the resulting oil flow and temperature distributions is assessed, as shown in Figure 7. Results from the original models are regarded as a baseline. While the new Nusselt number equation does not alter the oil flow rate distribution among horizontal ducts, the magnitude of winding temperatures is predicted to take values which are approximately 3 degrees higher than those of the original model. This follows logically as a smaller value of Nu will result in a lower heat transfer efficiency. Otherwise, the qualitative variation of the winding temperature distribution is seen to remain largely unaffected. (a) Comparison between oil mass flow distributions from using different expressions. IET Electr. Power Appl., The Institution of Engineering and Technology

115 higher pressure drop requires a bigger pump to guarantee the same oil flow. For natural oil mode, a higher winding pressure drop means that it is more difficult for the cooling oil flow upwards through the winding structure. (b) Comparison between maximum disc temperature distribution from using different expressions. Figure 7 Comparison between resulting distributions from using different expressions. Figure 7 (a) indicates that a more uniform oil flow distribution is predicted by the newly derived equation for f; this is because the new equation calculates more friction on faster oil flows than slow ones, and thus the flows in the vicinity of block washers are constrained and the flow distribution then becomes slightly evener. However, the effect is not dramatic; Figure 7 (b) reveals that the reduction of the hot-spot temperature resulting from the newly derived equation for f is around 0.1 o C compared to the original one. The low impact of friction coefficient in this particular case is because μ w /μ b values lie within the range 0.5 ~ 0.6, and the average f is 18% higher than the original model, still relatively small as compared to the mean difference of 48% in the full sensitivity study range. In another word, the frictional pressure loss at cooling ducts of this case is 18% higher. On the other hand, if we consider the relative pressure drop over the entire winding, which can be computed by integrating a complete oil duct routine from the inlet to the outlet minus the static pressure due to oil gravity, the new Nu equation does not affect, but the new f equation (12) predicts a relative pressure drop 6% higher than the original equation (6), resulting into a value of 722 Pa for this particular design. For forced oil cooling mode, an accurate prediction on the winding pressure drop is of importance for determining a pump to supply the required inlet oil flow, and logically, a 8 CONCLUSIONS Accurate transformer thermal modelling is of significance for investigating convective heat transfer phenomena in winding cooling ducts and predicting hot-spot temperature and its location. The Nusselt number and friction coefficient expressions employed in network models are often empirical and their validities need to be verified. By employing a detailed parameter study using a large set of 2D CFD calculations, functional dependence of the result data was analysed and curve fitting then applied to obtain new equations for both Nusselt number and friction coefficient. These equations are presented and compared with the corresponding equations from [2]. Using the LV winding from [2] as an example, the evaluation reveals that, compared to the original model, the newly proposed equations predict an increase in winding temperature as a consequence of lower Nusselt number values along horizontal oil ducts. In particular, the new f equation, (12), predicts a slightly more uniform oil flow rate distribution across the ducts, and also calculates a higher pressure drop over the entire winding. Experiments using non-intrusive flow measurement facilities such as Particle Image Velocimetry (PIV) are planned to be carried out for validating the oil duct CFD models. With the help of PIV measurement, flow velocity distributions across the oil channels can be obtained with details and accuracy, and it would then be possible to assess the CFD results in a more profound way. An accompanying paper will address an improved modelling of the pressure loss at the junction nodes (JPL), and evaluate their impacts on network modelling. ACKNOWLEDGMENT Financial support is gracefully received from the Engineering and Physical Sciences Research Council (EPSRC) Dorothy Hodgkin Postgraduate Award (DHPA) and National Grid. Due appreciation should be given to our MSc project student Mr Joseph Awodola who carried out the initial investigation of the idea in this paper under the supervision of the authors. REFERENCES IET Electr. Power Appl., The Institution of Engineering and Technology

116 [1] Tanguy, A., Patelli, J. P., Devaux, F., Taisne, J. P., and Ngnegueu, T.: Thermal performance of power transformers: thermal calculation tools focused on new operating requirements. Session 2004, CIGRE, rue d'artois, Paris, 2004 [2] Oliver, A. J.: Estimation of transformer winding temperatures and coolant flows using a general network method. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp [3] Allen, P. H. G., and Finn, A. H.: Transformer winding thermal design by computer. IEE Conf. Publ., 1969, vol. 51, pp [4] Simonson, E.A., and Lapworth, J.A.: Thermal capability assessment for transformers. Second Int. Conf. on the Reliability of Transmission and Distribution Equipment, 1995, pp [5] Del Vecchio, R.M., Poulin, B., Feghali, P. T., Shah, D. M., and Ahuja, R.: Transformer Design Principles: With Applications to Core-Form Power Transformers (Gordon and Breach Science Publishers, 2001) [6] Takami, K. M., Gholnejad, H., and Mahmoudi, J.: Thermal and hot spot evaluations on oil immersed power Transformers by FEMLAB and MATLAB software's. Proc. Int. Conf. on Thermal, Mechanical and Multi-Physics Simulation Experiments in Microelectronics and Micro-Systems, EuroSime 2007, 2007, pp. 1-6 [7] Kranenborg, E. J., Olsson, C. O., Samuelsson, B. R., Lundin, L-A., and Missing, R. M.: Numerical study on mixed convection and thermal streaking in power transformer windings. 5th European Thermal-Sciences Conference, The Netherlands, 2008 [8] Wu, W., Wang, Z.D., and Revell, A.: Natural convection cooling ducts in transformer network modelling. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 [9] Zhang, J., and Li, X.: Coolant flow distribution and pressure loss in ONAN transformer windings. Part I: Theory and model development. IEEE Transactions on Power Delivery, 2004, vol. 19, pp [10] Wu, W., Revell, A., and Wang, Z.D.: Heat Transfer in Transformer Winding Conductors and Surrounding Insulating Paper, Proceedings of The International Conference on Electrical Engineering 2009, Shenyang, China, 2009 [11] Rosenhow, W.M., Cho, Y.I., and Hartnett, J.P.: Handbook of heat transfer (New York: MCGraw-Hill, 1998, 3rd edn.) [12] Rosenhow, W.M., and Hartnett, J.P.: Handbook of heat transfer (New York: MCGraw-Hill, 1973) [13] Knudsen, J.G., and Katz, D.L.: Fluid dynamics and heat transfer (New York: McGraw-Hill, 1958) [14] Muneer, T., Jorge, K., and Thomas, G.: Heat transfer : a problem solving approach (London: Taylor & Francis, 2003) [15] Kreith, F., and Bohn, M. S.: Principles of heat transfer (New York: Harper & Row, 1986, 4th edn.) [16] Incropera, F.P., and Dewitt, D.P.: Fundamentals of heat and mass transfer (New York: John Wiley & Sons, 2002, 5th edn.) [17] Archambeau, F., Mehitoua, N., and Sakiz, M.: Code_Saturne: a finite volume code for the computation of turbulent incompressible flows industrial applications. International Journal on Finite Volumes, 2004 IET Electr. Power Appl., The Institution of Engineering and Technology

117 4.2 Paper 4 CFD Calibration for Network Modelling of Transformer Cooling Flows Part II Pressure Loss at Junction Nodes W. Wu, Z.D. Wang, A. Revell and P. Jarman 2011 IET Electric Power Applications Accepted 97

118 ISSN CFD Calibration for Network Modelling of Transformer Cooling Flows Part II Pressure Loss at Junction Nodes W. Wu 1, Z.D. Wang 1, A. Revell 2 and P. Jarman 3 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK. 2 School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK. 3 Asset Strategy, National Grid, Warwick, CV34 6DA, UK. zhongdong.wang@manchester.ac.uk Abstract Two important factors affecting the characteristics of hot-spot inside an oil cooled transformer winding are the total amount of oil being supplied into the winding and its flow distribution across the discs arrangement. The latter is unavoidably related to the hydraulic network of winding ducts where oil flow is combining or dividing at duct junctions. The expressions describing junction pressure loss (JPL) often contain a significant number of empirical parameters obtained by limited experimental tests. Applicability of these parameters should therefore be carefully verified for the use in network modelling; this is the objective of this paper. Computational Fluid Dynamics (CFD) simulations have been performed upon a large set of 2D junction models, based on which new values of the empirical parameters were then obtained specifically for winding oil ducts. A validation test showed that the newly proposed parameter values give better performance than the currently used off-the-shelf values. 1 NOMENCLATURE D = Equivalent hydraulic diameter of fluid duct f = Average dimensionless friction coefficient of fluid duct H = Height of fluid duct K = Junction pressure loss coefficient L = Length of fluid duct Nu = Nusselt number Q = Volume flow rate of fluid duct R 2 = The square of the correlation between the response values and the predicted response values Re = Reynolds number U = Average flow velocity of fluid duct ν = Kinematic viscosity of fluid ρ = Density of fluid ΔP = Pressure drop between the inlet and the outlet of the duct ΔP w = Pressure drop between the inlet and the outlet of the winding Subscripts 1 Value at the duct of the straight-through direction 2 Value at the duct of the branch direction m Value at the common duct 1 m Value for combining junction, from duct 1 to m 2 m Value for combining junction, from duct 2 to IET Electr. Power Appl., The Institution of Engineering and Technology

119 m m 1 Value for dividing junction, from duct m to 1 m 2 Value for dividing junction, from duct m to 2 Acroynms/Shorthand 2D 2 dimensional 3D 3 dimensional BOT Bottom oil temperature CFD Computational fluid dynamics HSF Hot-spot factor HST Hot-spot temperature JPL Junction pressure loss LV Low voltage MWT Mean winding temperature TOT Top oil temperature 2 INTRODUCTION prescribed in Figure 1 (b) and (c) respectively. Literally, in a combining scenario the straight-through direction flow, flow 1, is combined with the branch direction flow, flow 2, and a common flow forms after the junction. On the other hand, a dividing junction is defined when a common flow divides at the junction into two separated flows, i.e. flow 1 and 2 along the straight-through direction and the branch direction respectively. In both types the fluid mixing which takes place at the junction results in a pressure loss, namely junction pressure loss. According to [4], the pressure loss at a junction in a transformer winding becomes of equal or even greater magnitude than the frictional pressure loss occurring at an oil duct, especially for the short vertical ducts. As junction pressure loss plays an important role in governing the oil flow distribution, the expressions for describing JPL in network models must be carefully identified. Temperatures represent the most limiting factors for power transformers loading operations, and the maximum temperature of winding conductors, so-called hot-spot, has to be under certain limits for it affects insulation ageing and transformer lifetime. In the attempt to accurately predict the hot-spot inside a transformer, a range of numerical modelling approaches have been developed, which can generally be categorised as either network models [1-4], or methods which incorporate a degree of Computational Fluid Dynamics (CFD) [5-7]. In comparison to CFD methods which require unreasonably long computation time from the thermal design viewpoint, network models can provide quick and convenient numerical approximations which are often easier for industries to use as design tools. However, the suitability of the assumptions and the empirical expressions applied in network modelling has to be ascertained [8-10] to guarantee the calculation accuracy. Part I of this series of paper attempted to evaluate the expressions for Nusselt number (Nu) and temperature affected friction coefficient (f), and to propose calibrated equations by CFD simulations [10]. In this accompanying paper, the currently employed empirical junction pressure loss (JPL) equations will also be evaluated through CFD simulations, with a view to proposing more consistent expressions for constructing accurate and reliable network models. Figure 1 (a) pictorially shows the junction nodes in network model geometry. According to the flow behaviour at the junctions, the junction nodes are commonly classified into two types: combining and dividing nodes; denotation for both is Junction nodes oil (a) Junction nodes in a network model. IET Electr. Power Appl., The Institution of Engineering and Technology 2011 m 1 2 (b) A combining node. 2 1 m (c) A dividing node. Figure 1 Junction nodes in a network model and denotations for the flows (combining and dividing scenarios). 3 ANALYSIS ON PRESSURE LOSSES IN NETWORK MODELS When viscous fluid flows through a straight duct, a viscous force acts at the duct wall to resist the fluid moving, which incurs a frictional pressure loss along the duct. This frictional 2

120 pressure loss depends on the Reynolds number of the flow, Re = UL/ν, however for sufficiently low Re, it implies a laminar flow and can be expressed by Darcy-Weisbach Equation as 2 4 fl U P (1) D 2 where f = 24/Re is often called friction coefficient. Besides frictional pressure losses occurring at horizontal ducts, there are additional pressure losses in transformer windings due to the change of oil flow directions when these flows combine or divide at junctions, which are referred as junction pressure loss in this paper. At a junction, energy is lost due to the mixing or re-circulating or both flow regimes; junction pressure loss is actually a reflection of this energy loss. As an example, when a slower flow is combined into a faster one, the resulting flow velocity shall reduce and a pressure loss has occurred. In contrast, when a faster flow is combined into a slower one, the resulting flow velocity shall increase which means it has gained energy and mathematically, a negative pressure loss has occurred [11]. Figure 2 gives symbolic representations of the frictional and junction pressure losses around junctions, which correspond to Figure 1 (b) and (c) respectively. P 1, P 2 and P m are referred to the frictional pressure losses expressed by (1). P 1 m, P 2 m, P m 1 and P m 2 are junction pressure losses occurring at the flow turning paths 1 to m, 2 to m, m to 1 and m to 2 respectively, and they are added accordingly onto the two branch paths before or after the junction. It is a common practice [12] to represent the JPL with the product of a coefficient and the velocity head (ρu 2 /2) as in (2). Thus K 1 m, K 2 m, K m 1 and K m 2 in (2) are named as JPL coefficients for different junction pressure loss types. m P m 2 P 2 m P 1 m P 2 P 1 2 P 2 1 P 1 P m 2 P m 1 P m m (b) Dividing junctions. Figure 2 Frictional and junction pressure losses in the vicinity of junction nodes (combining and dividing scenarios). P P P P 1m 2m m1 m2 K K K K 1m 2m m1 m2 U 2 U 2 U 2 U 2 The JPL coefficients K can be derived analytically by considering the conservation of momentum as introduced in [12]. After obtaining the analytical expressions, [12] used experimental results to obtain correlations between the four JPL coefficients K and Reynolds number (Re 1 and Re 2 ) as well as the velocity dispatch ratio at the junction (U 1 /U m ). In the experiments, SAE No. 10 cylinder oil flowing through 3/4 inch standard black iron pipes and galvanised screwed tees was used to observe junction pressure loss, and the pipes were sufficiently long, 590 diameters, to be consistent with the assumption that the flow can re-gain hydraulically fullydeveloped status after the junction disturbance. Based on the experimental data samples published in [12], equation (3) was then derived in [1] for quantifying the JPL coefficients (2) 1 (a) Combining junctions. IET Electr. Power Appl., The Institution of Engineering and Technology

121 K K K K 1m 2m m1 m2 U U 7300 Re 2 U U 7000 Re 2 1 m 1 m U 11.2 U U 11.2 U 1 m 1 m Re 1 (3) Re 1 Equation (3) basically relies on the assumptions which are made by analysing the experimental results presented in [12], which include For combining scenarios, K 1 m is related to the velocity ratio U 1 /U m [1, 12]. Oppositely, K 2 m is largely unaffected by the flow combination, because at a low Reynolds number below 1000, the branch flow is directed by the straight-through direction flow and gradually and smoothly turns around the bend with a minimum of interruption, and as such the loss is stabilised [12]. So is for dividing scenarios, i.e. K m 1 is velocity ratio dependent and K m 2 is only related to Re 2 [12]. These assumptions and the expression formats of (3) are followed in this paper. Other literature which discussed the issue of junction pressure loss are [4] and [13]. It was reckoned in [4] that K 1 m should be independent of U 1 /U m and therefore (4) should be used instead. The work of [13] included an expression for coefficient K m 2, (5), in which the volume flow ratio Q 2 /Q m is used instead and K m 2 is irrelevant to Reynolds number. Unfortunately, [13] did not give corresponding expressions for the other three coefficients, K 1 m, K 2 m and K m 1, and the only equation of (5) cannot be tested independently in network models K 1m (4) Re Q 2 2 K m (5) Qm Qm 4 CFD MODELLING 1 Q 2 Rather than extracting the empirical JPL coefficients from a set of experimental data as in [12], this paper uses sets of numerical CFD simulations to obtain the dataset of pressure losses across a range of different parameters, corresponding to variation in geometry and flow conditions of transformer windings. Before proceeding to use the numerical datasets to optimise the JPL coefficients, CFD simulations were first undertaken on the case exactly as described in [12] to validate the CFD modelling methodology, and since the experiments used circular pipe junctions, 3D rather than 2D simulations are necessary for the validation. 4.1 Validations of CFD methodology A numerical mesh was created corresponding to the geometry described in [12]. The modelling process can be clarified into the following steps: a. Construct a 3D geometry model of circular pipes, illustrated by Figure 3. b. Mesh the geometry with a sufficiently fine grid; the proper order of fineness was obtained by sensitivity studies so as to guarantee the accuracy of simulation results. c. Configure the boundary conditions and the CFD solver. As an example, Figure 3 shows the boundary configuration for a combining junction. Fully developed velocity profiles with average values U 1 and U 2 were prescribed at the inlets respectively, and a pressure reference value, 0, was assigned to the outlet boundary; the rest are all configured as wall boundaries. d. Run CFD solver to obtain the converged solution of the problem. e. Extract the pressure drop results between the inlets and the outlet. In Figure 3, the pressure drops from duct end 1 to m and 2 to m are extracted from the CFD results. JPL are then calculated by subtracting the frictional losses along the ducts from these obtained pressure drops. COMSOL multiphysics software was used to perform CFD calculations. By modelling the combining junction of Figure 3, fixing the ratio U 2 /U 1 = 1/3, and varying U 2 from 0.04 m/s to 0.19 m/s (the corresponding Re 2 = 35 ~ 170, i.e. the flow remains laminar) [12], a set of simulations was undertaken. The correlation of K 2 m against Re 2 was extracted and shown in Figure 4, together with the experimental results presented in [12] and the K 2 m expression in (3) for comparison. On IET Electr. Power Appl., The Institution of Engineering and Technology

122 average, the relative difference between the CFD simulation samples to the results calculated from (3) is 4%. Equation (6) is deduced from these CFD samples by curve fitting, and the difference between the constants in (6) and (3) is only 1%, which confirms that CFD methodology is as good as experimental approach. H 2 L m Wall Outlet (pressure = 0) Inlet (U 1 ) Wall Flow direction L 1 L 2 H 1 Inlet (U 2 ) Figure 3 Denotations and boundary conditions for a combining junction model K 2m (6) Re CFD simulations Literature [1, 4] used the experimental test results published in [12] for deriving the JPL coefficient expressions which are currently used in network modelling, yet the tests were based on circular pipeline models. In contrast, oil ducts in disc-type windings are axial symmetric, which are formed by the space between stacked parallel discs (horizontal ducts) or between the discs and inner or outer pressboard cylinders (vertical ducts); because the circumferential width of the oil ducts is significantly longer than their radial length, 2D duct flow models between infinite parallel plates are sufficient approximations. Following the experiences in [1, 4, 6], 2D models are applied in this paper. Notwithstanding the model outlined by Figure 3, the ducts 1, 2 and m were modelled specifically as 2D channels instead of 3D circular pipelines; the boundary definitions stay the same as described in Section 4.1. In the 2D model, the duct heights H 1 = 0.015m and H 2 = 0.005m, which are the heights of the vertical and the horizontal ducts of the low voltage (LV) winding example in [1]. Although H 1 : H 2 = 3:1, the JPL expressions derived from the model can also be applied for other dimensions, as long as the ratio H 1 : H 2 1 [11]. For a combining junction, the duct lengths L 1 = m, L 2 = 0.05m [1] and L m = 0.12m; L m must be adequately long because the merged flow should re-gain fully developed state before reaching the zero pressure outlet. As for a dividing model, L m = m, instead L 1 should be long enough to allow the flow to fully develop after the junction separation. This geometry was meshed afterwards with a density of ~16 cells per mm 2 ; as this mesh order could guarantee the required calculation accuracy. Table 1 lists the variation ranges of velocity U 2 and velocity ratio U 1 : U m ; the ranges are basically from Part I of this series of papers [10]. The principle work of this paper is a parametric study using a large set of CFD simulations across the parameter ranges. For each combination in Table 1, a fully converged 2D CFD calculation was performed and the data sample was produced. Consequently, two resulting datasets, each comprising 63 samples, were summarised to approximate the JPL coefficients for both combining and dividing junctions respectively. Figure 4 Correlations of K 2 m versus Re 2 on a circular pipeline model. Table 1 Typical parameters for junction nodes of transformer oil ducts. IET Electr. Power Appl., The Institution of Engineering and Technology

123 Parameter name Variation range Variation steps U 1 : U m steps U 2 (m/s) steps 4.3 Derivation of correlation The obtained dataset for both combining and dividing scenarios are shown in Figure 5. Curve fitting was undertaken upon these CFD samples, and the correlations of the JPL coefficients, K, were then studied. By following the forms of (3), four expressions have been derived as listed in (7). (c) K m 1 versus Re 1 at dividing scenario. (a) K 1 m versus Re 1 at combining scenario. (d) K m 2 versus Re 2 at dividing scenario. Figure 5 Correlations between JPL coefficients K and Reynolds number at both combining and dividing scenarios. K K K K 1m 2m m1 m2 U U 72 Re 2 U U 276 Re 2 1 m 1 m U U U U 1 m 1 m Re 1 (7) Re 1 (b) K 2 m versus Re 2 at combining scenario. IET Electr. Power Appl., The Institution of Engineering and Technology

124 Equation (7) has lower constant coefficient values than (3) by almost one order of magnitude; this means for oil ducts the junction pressure losses yielded by (3) which is based on circular pipes would unrealistically govern the oil flow distribution than frictional pressure losses. In view of this, next section will focus on evaluating the representation of junction pressure loss to show that (7) better represents the reality than (3). In (3), the expressions for K 1 m and K m 1 are identical and K 2 m and K m 2 use similar constants, which means that the junction pressure losses at a combining junction and a dividing one are almost equivalent. It implies that the JPLs at both of the inner and outer vertical oil ducts of a winding are symmetrical. However, equation (7) reveals that it is relatively easier for oil flows to combine than to split. Asymmetrical oil flow distribution might be predicted from this asymmetrical equation. Moreover, in (7) K 1 m and K m 1 are from curve fitting which include the impact of the velocity ratio, U 1 /U m ; both fittings yielded high correlation scores, R 2 > K 2 m and K m 2 expressions however represent the average orders of the JPL across the laminar zone [12]. As a matter of fact, sample variations from the average curves are observed in Figure 5 (b) and (d); the upper bound of the variation range is at the velocity ratio U 2 : U m = 0.2 and the lower bound U 2 : U m = 0.8. It is actually possible to obtain velocity ratio dependent JPL equations for both K 2 m and K m 2 with better fitting scores. However, those fitted equations would practically prevent network models from converging and yielding any calculation results; this could be the reason why [1, 4] used the velocity independent formats for K 2 m and K m 2. Tests were therefore undertaken to evaluate the impact of the variation bands upon network modelling results. By using the typical LV winding example in [1], the upper bound at U 2 : U m = 0.2 and the lower bound at U 2 : U m = 0.8 were curve fitted and applied for K 2 m and K m 2 coefficients, and it was found that the upper bound value slightly decreases the average winding and hot-spot temperatures, whereas the lower bound increases them. However the resulting difference was so minor that only less than 1% for the average winding temperature and less than 2% for the hot-spot temperature were found. This test indicates the high reliability to use (7) for calculating K 2 m and K m 2 to be used in network models. 5 EVALUATION OF EMPIRICAL EQUATION IN NETWORK MODEL The disc-type winding model of one-pass and its experimental and CFD simulation results from [14] were used to validate (7). There are 8 discs in the winding pass example; the pass starts from the block washer equipped just below the bottom disc and thus there are 8 horizontal ducts in total. The dimensions are briefly described in Table 2. In order to be consistent with [14], this paper neglects the heat source input at discs in order to focus on the hydraulic aspect. The model was calculated with the network model implementation, TEFLOW, and different sets of JPL coefficient expressions, (3), (4) and (7), were tested. Table 2 Dimensions of the winding pass example in [14]. Parameter Height of vertical oil ducts (mm) Height of horizontal oil ducts (mm) Height of discs (mm) Radial length of discs (mm) Value IET Electr. Power Appl., The Institution of Engineering and Technology Figure 6 shows the relationship between the pressure drop over the pass and the rate of oil flow supplied at the inlet. This is often defined as the hydraulic characteristic curve of a winding design. First of all, the model without including junction pressure losses predicts lower pressures than the experiment results, which implies the necessity to incorporate JPL expressions; the results yielded by the existing two JPL models, both (3) and (3) & (4), show similarly unrealistically higher pressures, and finally (7) produced a much better match with the experimental results as well as the CFD predictions. It is of significance to derive an accurate hydraulic characteristic curve for the winding structure at the thermal design stage, since this curve will then affect the choice of oil cooling pump. Figure 7 shows the different oil flow rates distributed across the eight horizontal oil ducts in the pass, corresponding to the four JPL models and the CFD simulation results presented in [14]. Figure 7 (a) illustrates almost symmetrical flow distribution profiles that are irrelevant to the inlet oil flow velocity ranging from 2 to 25 L/min, which are corresponding to around 50 to 625 mm/s. It shows that the two original JPL models do not affect the flow distributions. On 7

125 Relative pressure drop over the pass, Pa the other hand, the newly proposed JPL model, equation (7), predicts non-uniform flow distributions which are sensitive to different inlet oil flow velocities and this is similar to the results calculated by CFD simulations [14] shown as the dash curves in Figure 7 (b) Oil flow, L/min No JPL Experimental result [14] CFD result [14] Eqn. (7) Eqn. (3) [1] Eqn. (3) & (4) [4] Figure 6 Pressure drop over the entire pass. (a) Relative flow rate without JPL included and with JPL equations [1, 4] applied. (b) Relative flow rate by CFD simulations in [14] and with equation (7). Figure 7 Oil flow rate distribution across the horizontal ducts. In Figure 7 (a), the profiles predicted by (3) are symmetrical because the K 1 m and K m 1 expressions in this JPL model are exactly the same, and thus the JPLs added onto the inner and outer vertical ducts are then the same. Although as previously addressed, equation (3) causes higher pressure loss upon the pass than the measured one, this junction pressure loss equation does not affect the flow distribution profile and are even overlapped with the calculation results without the consideration of JPL. The application of (4) for K 1 m does bring asymmetry but only to a tiny extent. In brief, equation (3) and (4) do not show any trend sensitivity of flow distribution for low to high inlet oil flow rates. In Figure 7 (b), at higher oil flow rates, e.g. 25 L/min, more oil will tend to flow through the upper half of the pass, whereas at low flow rates, more oil tends to go through the lower half. This is logical since fast oil flow will easily reach the upper half, being blocked by the washer and then turning its direction to the upmost horizontal duct. In contrast, the CFD results in Figure 7 (b) are severely less uniform. CFD predicts that much more oil flow is distributed to the top ducts, irrespective of the flow rate. At the high flow rate of 25 L/min, inversely directed flow even occurs at the 2 bottom ducts as it is seen that the oil velocity is negative. This could be an implication of internal recirculation phenomena happening at extremely high oil velocities, and such recirculation phenomena have also been observed by other CFD study cases. IET Electr. Power Appl., The Institution of Engineering and Technology

126 Obviously there are deviations exiting when comparing flow distributions from network and CFD modelling in detail, nevertheless the improved JPL equations (7) could capture the apparent trend sensitivity of flow distribution for low to high inlet oil flow rates, while the old equations (3) and (4) showed nothing related to this. From this aspect an incremental forward progress has been made. Moreover, neither of the exact patterns predicted by (7) or CFD simulations has been validated by experiments due to the difficulties in measuring flow distributions [14], therefore non-intrusive flow measurement facilities such as Particle Image Velocimetry (PIV) are planned to be carried out in order to verify either model s closeness to the reality. It is hoped that with the help of PIV measurement, flow velocity distributions across the oil channel regions can be obtained with details and accuracy, it would then be possible to assess the results in Figure 7 although the acceptable agreement on the global pressure drops in Figure 6 has shown the progress achieved in this paper. 6 CONCLUSIONS An accurate model to assess the pressure losses at oil duct junctions is of great importance for determining the hydraulic characteristics of windings and predicting flow distributions across horizontal ducts. Following the work of Part I, which has proposed modifications on Nusselt number and friction coefficient expressions [10], this paper studied the JPL expressions in network models. By performing CFD simulations on a large set of 2D oil duct junction models instead of conducting experimental tests, a detailed parametric study was undertaken for identifying JPL coefficient correlations. With the help of curve fitting on the CFD results, new constant values for JPL coefficient expressions were finally obtained and then compared with the currently used ones from [1, 4]. The expressions have been evaluated with the network model implementation TEFLOW on a winding pass example from [14]. The results indicate that the presence of JPL will rise the hydraulic pressure needed to supply an oil flow rate into the pass; however the off-the-shelf JPL models, i.e. equation (3-4) from [1, 4], yield unrealistically high pressure losses due to the fact that they are derived from circular pipeline junctions rather than transformer winding duct junctions. On the other hand, the prediction given by the newly obtained equation (7) could provide a better match to the experimental results. Unlike JPL models (3-4) which predict symmetrical oil flow distribution patterns across the pass that are identical irrespective of inlet oil flow rates, equation (7) reveals that more oil will tend to flow through the upper half of a pass if at a high inlet oil flow rate. Because of the exaggerated junction pressure loss the network model with (3) or (3-4) will prescribe an oil pump bigger than that really required, and the extra oil flow supplied can reduce the winding temperature. However, the overestimated Nusselt number in [1] would underestimate the winding temperature. In consequence, both effects from JPL and Nu are adverse and probably cancel each other to some extent, so the network model presented in [1] might give reasonable results. A possible limitation of (7) might come from the fact that short vertical oil ducts are designed for windings. Vertical duct lengths are so short that the upward oil flow just departing from a junction will shortly arrive at the next junction, which implies that it may be difficult for the vertical oil flow to re-achieve fully developed state in the real scenario. Future CFD study on the interaction between neighbouring junctions should therefore be conducted. ACKNOWLEDGMENT Financial support is gracefully received from the Engineering and Physical Sciences Research Council (EPSRC) Dorothy Hodgkin Postgraduate Award (DHPA) and National Grid. The authors appreciate the technical support given by Professor Hector Iacovides from School of Mechanical, Aerospace and Civil Engineering, University of Manchester. Due appreciation should also be given to our MSc project student Mr Qi Li who carried out the initial investigation of the idea in this paper under the supervision of the authors. REFERENCES [1] Oliver, A. J.: Estimation of transformer winding temperatures and coolant flows using a general network method. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp [2] Simonson, E.A., and Lapworth, J.A.: Thermal capability assessment for transformers. Second Int. Conf. on the Reliability of Transmission and Distribution Equipment, 1995, pp [3] Del Vecchio, R.M., Poulin, B., Feghali, P. T., Shah, D. M., and Ahuja, R.: Transformer Design Principles: With Applications to Core-Form Power Transformers (Gordon and Breach Science Publishers, 2001) IET Electr. Power Appl., The Institution of Engineering and Technology

127 [4] Zhang, J., and Li, X.: Coolant flow distribution and pressure loss in ONAN transformer windings. Part I: Theory and model development. IEEE Transactions on Power Delivery, 2004, vol. 19, pp [5] Tanguy, A., Patelli, J. P., Devaux, F., Taisne, J. P., and Ngnegueu, T.: Thermal performance of power transformers: thermal calculation tools focused on new operating requirements. Session 2004, CIGRE, rue d'artois, Paris, 2004 [6] Takami, K. M., Gholnejad, H., and Mahmoudi, J.: Thermal and hot spot evaluations on oil immersed power Transformers by FEMLAB and MATLAB software's. Proc. Int. Conf. on Thermal, Mechanical and Multi-Physics Simulation Experiments in Microelectronics and Micro-Systems, EuroSime 2007, 2007, pp. 1-6 [7] Kranenborg, E. J., Olsson, C. O., Samuelsson, B. R., Lundin, L-A., and Missing, R. M.: Numerical study on mixed convection and thermal streaking in power transformer windings. 5th European Thermal-Sciences Conference, The Netherlands, 2008 [8] Wu, W., Wang, Z.D., and Revell, A.: Natural convection cooling ducts in transformer network modelling. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 [9] Wu, W., Revell, A., and Wang, Z.D.: Heat Transfer in Transformer Winding Conductors and Surrounding Insulating Paper, Proceedings of The International Conference on Electrical Engineering 2009, Shenyang, China, 2009 [10] Wu, W., Wang, Z.D., Revell, A., Iacovides, H., and Jarman, P.: CFD calibration for network modelling of transformer cooling oil flows Part I Heat transfer in oil ducts, IET Electric Power Applications, 2011, to be published [11] Blevins, R. D.: Applied Fluid Dynamics Handbook (New York: Van Nostrand, 1984) [12] Jamison, D. K., and Villemonte, J. R.: Junction losses in laminar and transitional flows. J. Am. Soc. Civ. Eng. 1971, 97, (HY7), pp [13] Yamaguchi, M., Kumasaka, T., Inui, Y., and Ono, S.: The flow rate in a self-cooled transformer. IEEE Transactions on Power Apparatus and Systems, 1981, vol. PAS-100, pp [14] Weinläder, A., and Tenbohlen, S.: Thermal-hydraulic investigation of transformer windings by CFD- Modelling and measurements. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 IET Electr. Power Appl., The Institution of Engineering and Technology

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129 Chapter 5 Comparison between network model and CFD predictions 5.1 Paper 5 Prediction of the Oil Flow Distribution in Oil-immersed Transformer Windings by Network Modelling and CFD A. Weinläder, W. Wu, S. Tenbohlen and Z.D. Wang 2011 IET Electric Power Applications Provisionally accepted 99

130 ISSN Prediction of the Oil Flow Distribution in Oil-immersed Transformer Windings by Network Modelling and CFD Andreas Weinläder 1, Wei Wu 2, Stefan Tenbohlen 1 and Zhongdong Wang 2 1 Institute for Power Transmission and High Voltage Technology, University of Stuttgart, Stuttgart, Germany ( andreas.weinlaeder@ieh.uni-stuttgart.de) and ( stefan.tenbohlen@ieh.uni-stuttgart.de). 2 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK ( wei.wu-2@postgrad.manchester.ac.uk) and ( zhongdong.wang@manchester.ac.uk). Abstract In the context of thermal performance and thermal design, it is of significance to predict the magnitude and the location of the hot-spot temperature inside a power transformer. In the attempt to accurately predict this hot-spot in an oilimmersed transformer, various numerical modelling approaches have been developed for calculating the cooling oil flow distribution, which are generally categorised as either network models or the methods which incorporate forms of Computational Fluid Dynamics (CFD). In network modelling, the complex pattern of oil ducts and passes in a winding is approximated with a matrix of simple hydraulic channels, where analytical expressions are then applied to describe oil flow and heat transfer phenomena. On the other hand, CFD models often adopt discretisations of much higher fineness, which can be expected to offer a higher order of accuracy but also comes with a large increase in the required computational resources. In order to compare both modelling approaches, the network model implementation TEFLOW and a commercial CFD package, ANSYS-CFX, were applied on a typical zigzag oil channel arrangement of a disc type winding to predict oil flow distribution and disc temperatures; experiments on hydraulic models have also been performed to validate the models. The principle work of this paper is then comparing the results and concluding recommendations to industrial practices. 1 NOMENCLATURE D = Equivalent hydraulic diameter of fluid duct d p = Thickness of insulating paper f = Average dimensionless friction coefficient of fluid duct k = Thermal conductivity of transformer oil L = Length of fluid duct Nu = Nusselt number Pr = Prandtl number q = Heat flux from winding to fluid duct Re = Reynolds number t b = Bulk temperature of fluid duct t c = Temperature of winding conductor t w = Wall temperature of fluid duct T = Absolute temperature U = Average flow velocity of fluid duct ΔP = Pressure drop between the inlet and outlet of the duct μ = Dynamic viscosity of fluid ρ = Density of fluid Subscripts IET Electr. Power Appl., The Institution of Engineering and Technology

131 cond Value of heat conduction conv Value of heat convection b Value at bulk temperature c Value at winding conductor w Value at wall temperature 1 Value at the duct of the straight-through direction of a junction 2 Value at the duct of the branch direction of a junction m Value at the common duct of a junction 1 m Value for combining junction, from duct 1 to m 2 m Value for combining junction, from duct 2 to m m 1 Value for dividing junction, from duct m to 1 m 2 Value for dividing junction, from duct m to 2 Acroynms/Shorthand CFD Computational Fluid Dynamics HTC Heat transfer coefficient JPL Junction pressure loss LV Low voltage NM Network modelling 2 INTRODUCTION Power transformers are key and expensive components in electric system networks. To avoid failure and ensure continual power supply, the thermal management of a power transformer is critical in controlling its ageing due to high hotspot temperatures that degrade insulation materials, finally causing electrical failure. Thereby, accurate thermal assessment is of significance for both design procedure in manufacturers and asset management policy making in utilities [1]. In particular, large power transformers are generally cooled by natural or forced oil flow, and as such for these oil-immersed transformers, improved understanding of the oil flow distribution across the oil ducts inside transformer windings is meaningful to avoid localised oil starvation and hot-spot temperatures. Commonly, the cooling oil flows up from the bottom to the top of a winding; however the hot-spot is not always found on the top-most winding disc, due to, in part, the effect of a non-uniform oil flow distribution [2]. Numerical modelling has been used to predict the oil flow and hot-spot for over 40 years [3]. During the period, two categories of numerical approaches were developed, which are network modelling such as TEFLOW (developed in the UK in the late 1980 s) [2, 4-7], and methods which incorporate Computational Fluid Dynamics (CFD) [1, 8-11]. Generally, with the help of much higher fineness of the discretisation, CFD simulations can be expected to provide more detailed results but meanwhile, with a large increase in the required computational resources. In comparison to CFD, network modelling however provides a fast solution which is often more convenient for industry to use. In addition, a large range of parameters can be tested with this tool for relatively low computational effort, when only critical temperatures such as hot-spot are required and a high level of local flow/temperature information is not really necessary. The objective of this paper is using a same winding pass design as an example to compare the two different numerical approaches with the experimental results; a pass is defined as the section of a winding between two adjacent oil block washers. The differences between the results from them would provide recommendations for those who are choosing thermal analysis tools for oil-immersed transformers. 3 DIMENSIONS OF THE INVESTIGATED GEOMETRY, MATERIAL PROPERTIES AND EXCITATION CONDITIONS The pass example is from a disc-type winding and the studied section is between two neighbouring spacers, as shown in Figure 1 (a), followed by the other 3 sub-pictures depicting the front, side and top views of the model structure respectively. There are 8 discs in the pass; they are cooled with oil which flows in from the bottom inlet, through horizontal channels between the rows of heat generating discs, and joins up with a single vertical channel at the opposite side that carries the oil upwards and through a gap to next pass. The next pass starts from the oil block washer equipped just below the 9th disc; all washers are assumed as fully tight. A winding can then be periodically composed by a series of this type of passes, resulting in a zig-zag like oil flow, and due to the periodicity, only a single pass is investigated in this paper. In an ideal cooling design, firstly sufficient oil should be supplied into the pass by buoyancy or oil pumps, and secondly the oil can be distributed uniformly across the horizontal ducts for avoiding any localised oil starvation. IET Electr. Power Appl., The Institution of Engineering and Technology

132 Side view Front view Disc Spacers In order to perform numerical modelling on the pass example, the geometric parameters, the physical properties of the material and the investigated parameter ranges are summarised into Table 1-3 respectively. The dimensions were used to construct the geometry of the numerical models, and the inlet oil flow rate and temperature, listed in Table 3, were applied as boundary conditions. Table 1 Geometric parameters of the winding pass example. Washer Horizontal duct Disc (a) The studied section in winding. Washer Top view Lexan glasses (b) Front view. Stick One pass Parameter name Width of vertical channels (mm) Width of horizontal channels (mm) Height of discs (mm) Clear distance between the spacers (circumferentially uncoiled) (mm) Radial length of the discs (mm) Bevel corner radius the disc (mm) Thickness of insulating paper (mm) Value Spacer (c) Side view. Table 2 Physical properties of oil and solid materials. Parameter name Value a. Oil properties of Shell Diala DX at absolute temperature T K Dynamic viscosity (mpa s) exp[605.8 / (T 178.3)] Lexan glass Spacers Lexan glass Density (kg/m3) Heat conductivity (W/(K m)) (T ) (T ) Sticks (d) Top view. Figure 1 Structure of the disc-type winding pass used for study. Heat capacity (J/(K kg)) ,375 (T ) b. Oil properties of Shell Diala DX at absolute temperature 60 C Dynamic viscosity (mpa s) Density (kg/m3) Heat conductivity (W/(K m)) IET Electr. Power Appl., The Institution of Engineering and Technology

133 Heat capacity (J/(K kg)) The scheme of equipments for acquiring the pressure drop is outlined in Figure 2. c. Properties of the solid materials Thermal conductivity of conductors (W/(K m)) 410 Computer Thermal conductivity of insulating paper (W/(K m)) 0.15 Pressure Sensor (1) Pressure Sensor (6) Thermal conductivity of spacers (W/(K m)) 0.15 Shortt Circuit Valve Shortt Circuit Valve Table 3 Investigation parameter ranges. Point A Point B Reference Point Parameter name Flow rate at the pass inlet (L/min) Value 2, 5, 10, 15, 20 Winding Model Figure 2 Scheme of equipments for pressure acquisition. Oil temperature at the pass inlet ( C ) (only for the hydraulic-thermal models) Loss power per disc (W) (only for the hydraulic-thermal models) 4 EXPERIMENTAL MEASUREMENTS 60 15, 30 Hydraulic measurements were especially done to validate the simulations. The procedure of the hydraulic measurements was taking a physical model of the winding pass example, illustrated in Figure 1, and inputting the specified oil flow rate from the pass inlet. The supplied flow rate causes a pressuredrop along the flow path, and this pressure-drop can be measured at some locations that are reachable without disturbing the flow considerably. Only the pressure-drop was measured because it is often difficult to measure the in-duct pressure profiles accurately; on the other hand numerical simulation can yield detailed results in the entire domain with much less practical effort [8]. The model that was applied in this experiment represents a section of a real transformer winding. Since a typical disc-type winding repeats periodically in both axial and circumferential directions, it is sufficient to investigate only such a section which also saves effort compared to the operation at a complete winding. Such a section is usually small and it is possible to keep its dimensions according to a real transformer; therefore there was no need to apply laws of similarity to the measured data afterwards. Since for the first step only hydraulic data were of interest, the discs were made of transformer board according to the outer form of real discs. From the picture, it can be seen that each pressure transducer is switched between two channels. The measured data are constantly recorded by a computer until a steady state is reached. Once finished, a new flow rate can be imposed and studied. To have realistic properties of the fluid according to them of transformer oil at a typical operating temperature, a special hydrocarbon was used instead of regular transformer oil. This hydrocarbon is similar to kerosene but has a higher flame point, an eligible viscosity and density at room temperature, listed in Table 4. Due to this in the measurements there is no heating required and the oil temperature remains constant. Table 4 Properties of the hydrocarbon used for hydraulic Parameter name Dynamic viscosity (mpa s) Density (kg/m 3 ) measurements at ambient temperature. 5 NETWORK MODELLING Value In brief, network modelling first reduces the complex pattern of the oil flow inside a transformer winding down to a matrix of simple hydraulic channel approximations, interconnected by junction points or nodes [12]. Figure 3 shows the geometry approximated from the experimental setup in Figure 1 for 2D network model; lumped elements IET Electr. Power Appl., The Institution of Engineering and Technology

134 such as discs, ducts and nodes are indicated. Bulk averaged parameters are assumed to represent the variation of physical quantities at each duct and node, based on which a set of lumped parameter equations are applied to construct both socalled thermal and hydraulic networks across the entire winding. ducts nodes e. Convective heat transfer equation, (3), along horizontal ducts to express the heat convection from the duct walls to the flow bulk. Nu k q conv ( t w tb ) (3) D Moreover, empirical equations are incorporated for estimating the Nusselt number, Nu, friction coefficient, f, at oil ducts and junction pressure losses (JPL). These equations were previously from general fluid dynamics and heat transfer handbooks, but have recently been calibrated by large sets of CFD simulations for a wide range of transformer designs, with overall minimised deviation from CFD predictions [15-16]. The calibrated equations (4-6) were applied in this paper. oil disc Figure 3 Geometry for 2D network modelling of the experimental setup. Additionally, the following physical assumptions are made in network modelling: oil is modelled as laminar flow between a pair of infinite parallel flat plates [12-13]; oil temperature is assumed to rise linearly along horizontal channels due to the uniform heat flux at disc surfaces [14]; oil mixing at nodes is complete hydraulically and thermally. A group of mathematic expressions, i.e. (a-e) as follows, are then employed to constitute the hydraulic and thermal networks respectively. Due to the temperature dependence of the physical properties of oil, such as viscosity and density, the hydraulic and thermal networks are coupled and as such an iterative approach is required for a solution. a. Mass conservation at nodes; b. Pressure drop equation, namely Darcy-Weisbach Equation, (1), applied onto ducts [12]; 2 4 fl U P (1) D 2 c. Thermal energy conservation at nodes; d. Conductive heat transfer equation, (2), to express the heat conduction across insulating paper; k q cond ( tc tw) (2) d p K K K K L / D Nu 1.29 Re Pr 24 f 0.17Re Re 1m 2m m1 m w b 0.16 w b which bounds the horizontal ducts in the circumferential 5 IET Electr. Power Appl., The Institution of Engineering and Technology 2011 Pr 0.15 U U 72 Re U U 276 Re 1 m 1 m L D 0.55 U U U U 1 m 1 m CFD MODELLING AND VISUAL LOCALISED RESULTS Re1 (4) (5) (6) Re1 The CFD computation was done with commercial CFD software ANSYS-CFX, which is a finite-volume based CFDsolver, while the mesh generation with ICEM-CFD. Because modelling in 2D saves an enormous amount of computational effort, but CFX does not have the explicit capability to treat 2D problems, (due to the underlying finite-volume algorithm), the approach was modelling the geometry in an ordinary 2D way and then extruding only one cell into the circumferential direction for constructing 3D elements. For the simulation, this model was assumed as infinitely extruded along this direction. It implies that the small wall effect of the spacers,

135 direction, was neglected. This is justified because of the large ratio between channel width and channel height [12]. On the other hand, the radial boundaries, where in reality pressboard cylinders are bounding the winding, were applied as isothermal wall boundaries since the heat flux through those surfaces is commonly regarded as negligible. Finally for the hydraulic-thermal modelling, constant loss density was impressed into the conductor volumes. At the inlet oil flow with homogenous velocity and temperature was impressed respectively, while the outlet was closed by a zero static-pressure condition, as shown in Figure 4. As a matter of fact, there are 3 passes involved in this model and only the middle pass was intended to deliver the results, because the upper and lower passes were facilitated to deliver proper boundary conditions for the middle pass. When modelling the material, Newtonian fluid model was applied, where viscosity only depends on temperature in an exponential manner. The density, the specific heat capacity and the heat conductivity are all assumed to be temperature dependent in a linear manner. Since the Reynolds number was reliably low, no turbulence model was employed in the simulation. The discretisation was done with around 900,000 elements, shown in Figure 4. For the shape functions the 2nd order upwind scheme was used and the single-precision solver was tested to be sufficient for this problem. The convergence criterion was set as a RMS-residual of 10-5, and a global balance of each conservation quantity of 10-3 has been required and reached. Figure 4 Principal model and details with mesh. IET Electr. Power Appl., The Institution of Engineering and Technology

136 In Figure 5 the streamlines resulting from hydraulic-only models were plotted for both flow rates of 2 and 20 l/min. It gets obvious that separation eddies are blocking a portion of the entrance for horizontal channels, especially at the lower region, because the oil washer equipped at the top prevents oil flowing up, effectively forcing them turn to the horizontal channels, and thus the eddies at these channels are largely suppressed. The entrance separation eddies actually account for the junction pressure losses described by equation (6) in network modelling. By the comparison between Figure 5 (a) and (b), the eddies are strengthened with high inlet flow rates, and because of this the flow distribution becomes more unequal; for example, in (b) of 20 l/min, the 3 upmost channels obtains almost the whole amount of flow rate which has been supplied into the pass. Due to this reason the 5 lower channels get small proportion of oil and they would get relatively higher oil temperature if constant heating power were imposed. (a) 2 l/min. (b) 20 l/min. Figure 5 Streamlines for two oil flow rates. IET Electr. Power Appl., The Institution of Engineering and Technology

137 (a) 2 l/min and 15 W per disc. (b) 20 l/min and 30 W per disc. Figure 6 Contours of fluid temperature. With a hydro-thermal model, Figure 6 displays the temperature distribution within the fluid domain for the case with loss power of 15 W per disc and flow rate of 2 l/min and the case with 30 W per disc and 20 l/min. For the case with 2 l/min, the oil flowing through the middle region is less and local temperature at these ducts therefore becomes higher; in Figure 6 (a) the highest temperature is observed to occur at the thermal boundaries of the middle ducts and the cooling for the bottom and top ducts is better. In particular, due to high Prandtl number (typically ~200 for oil [2]), it can be seen that a strong cold streak from the former pass is entering the bottom duct and moves from there lasts until the outer vertical duct; however, the cold streak does not reduce the thermal boundary temperature because it flows almost along the centreline rather than contacting a channel wall. On the other hand, at the outer side vertical duct, there are hot-streaks formed and lasting till the pass outlet and they could affect the cooling efficiency at the entrance of next pass [9]. For the case with 20 l/min, most extra supplied oil flows through the upper half of the pass and the duct wall temperatures at the lower half remain higher. In Figure 6 (b) the worst temperature is observed at the lower right corner; at the dead corner oil is almost stagnated. Secondly, due to the high flow rate at some horizontal ducts, there are second eddy circulations generated at the entrance regimes; fortunately it was not found that these second eddies would reduce the flow rate at the ducts. Furthermore, at the outer vertical duct there are also hot-streaks discovered, but these hot-streaks have lower temperatures than those in the sub-figure (a), (due to high flow velocities), and therefore, their influence upon the next pass is smaller than that in the case of 2 l/min. To emphasize the effect from the flow rate on the convective heat transfer, the heat transfer coefficient (HTC) distribution around the bottom disc of the studied pass was plotted in Figure 7 for both the case of 2 l/min and 15 W per disc and the case of 20 l/min and 30 W per disc. These HTC values were evaluated from the heat flux and the wall temperature difference, on the oil side of the insulating paper, from a reference temperature; the heat flux and wall temperature could be extracted from the CFD results, and the inlet temperature of the pass, 60 C, was taken as the reference temperature. As network modelling assumed, the heat flux is uniform and the wall temperature difference rises linearly from the upstream to the downstream of a channel, so the HTC profile follows a linear reduction. With the help of CFD, the assumption can be examined in a more detailed way. Figure 7 shows the local HTC values for the cases with 2l/min and 15W per disc and 20l/min and 30W per disc. Figure 7 (a) shows the values along the bottom side of the disc, which actually bounds on the last horizontal duct of the previous pass. Since the portion of flow in this horizontal duct is the highest of all passes, the HTC values are also high. The kink distribution patterns at the upstream end, i.e. the lefthand end, are due to the entry eddy circulations, then the HTC value gradually reduce, typically following hyperbolic trends, and are finally involved into the downstream flow combination. The difference between the two cases can be explained by the difference in the oil flow rates; high flow rate brings high HTC values. Figure 7 (b) displays the HTC values at the upside of the disc. Beginning with the entry eddy caused kink patterns at the upstream end, i.e. the right-hand end, the HTC values decrease hyperbolically along the duct; this is known from literatures for heated infinite parallel channels. At the downstream combination profiles are then observed. The HTC values after 40 mm from the entry is almost overlapped because the flow velocities within the duct are in a quite similar range; for the high flow rate case, this first duct is actually blocked by the separation eddy at its entry. 7 RESULTS COMPARISON As the first step, the pressure drop along the complete pass has been compared. The pressure drop over a winding describes the hydraulic impedance the supplied oil flow should resist to flow upwards through the winding; at a design stage, structures and dimensions of windings are supposed to be carefully optimised to minimise this pressure drop. It is especially significant for forced oil cooling mode, because capable oil pumps have to be chosen and equipped to guarantee oil flow. IET Electr. Power Appl., The Institution of Engineering and Technology

138 - 2l/min and 15W per disc - 20l/min and 30W per disc - 2l/min and 15W per disc - 20l/min and 30W per disc (a) Bottom side. (b) Top side. Figure 7 Heat transfer coefficient around first disc. Since only pressure drop of unheated cases was available from measurements, hydro-only calculations with the material data, Table 4, were performed for comparison. The obtained results are shown in Figure 8 (a); the calculation results closely match the measurement values with the maximum deviation less than 15 Pa, which equates to 1.8 mm hydraulic head. In Figure 8 (b), the pressure drop for the case of 30 W per disc losses is shown and the deviation between the network model and the CFD results is still small, less than 30 Pa. The difference of the pressure drop between the cases with 15 W and 30 W per disc losses was below 2%, so that the results for 15 W are relinquished to display here. By the comparison the network modelling was proved to give well fit pressure drop correlations. In the following Figure 9 the flow distribution among the horizontal channels is shown; the percentage refers to the whole oil flow, which enters the inlet of the pass and distributes among the individual horizontal channels. As it can be seen in Figure 9 (a) and (c), the flow distribution calculated by the network model is quasi-parabolic and nearly symmetrical to the axial middle of the pass, though slightly more oil tends to flow through the upper half of the pass for the cases with higher flow rates. In contrary to this, the flow distribution calculated by CFD is distinctly and visibly asymmetrical even for low flow rates. It gets increasingly imbalanced for higher flow rates; for example, in the case of 10 l/min most of the flow passes through the top two ducts. This is what was indicated by the streamline plots in Figure 5, in which it got visible that separation eddies are blocking the lower ducts of the pass in the case with such a high flow rate. The difference in the flow distribution between the cases with losses of 15 W per disc and 30 W per disc is obviously small, which implies that buoyancy forces are not very dominant, especially for high flow rates. In particular the network model did not show any difference between 15 W and 30 W and tiny difference is only shown within the CFD cases of 2 l/min, visible in Figure 9 (b) and (d). At such a low flow rate, the buoyancy forces are able to drive the oil flow from the hotter outlet vertical channel to the colder inlet vertical channel, and this tends to reverse the flow in the upper horizontal ducts into the opposite direction and the flow in the lower horizontal ducts into its original direction. Finally the flow distribution with higher losses becomes more symmetrical. IET Electr. Power Appl., The Institution of Engineering and Technology

139 Oil mass flow rate percentage Oil mass flow rate percentage Oil mass flow rate percentage Oil mass flow rate percentage Relative pressure drop, Pa Relative pressure drop, Pa Pressure drop from NM Pressure drop from CFD Pressure drop from measurements Pressure drop from NM Pressure drop from CFD Oil flow, l/min (a) Case without losses Oil flow, l/min (b) Case with 30 W per disc. Figure 8 Pressure drop over the pass. 50% 50% 40% 30% 2 l/min 5 l/min 10 l/min 15 l/min 20 l/min 40% 30% 2 l/min 5 l/min 10 l/min 15 l/min 20 l/min 20% 20% 10% 10% 0% Duct number (from bottom to top) (a) From network model for 15 W per disc. 0% Duct number (from bottom to top) (b) From CFD for 15 W per disc. 50% 50% 40% 30% 2 l/min 5 l/min 10 l/min 15 l/min 20 l/min 40% 30% 2 l/min 5 l/min 10 l/min 15 l/min 20 l/min 20% 20% 10% 10% 0% Duct number (from bottom to top) 0% Duct number (from bottom to top) (c) From network model for 30 W per disc. (d) From CFD for 30 W per disc. Figure 9 Flow distributions on the horizontal oil ducts. IET Electr. Power Appl., The Institution of Engineering and Technology

140 Average conductor temperature in C Average conductor temperature in C Average conductor temperature in C Average conductor temperature in C In Figure 10 the maximum temperature of the individual discs is displayed. In network modelling assumptions this maximum temperature locates at the downstream end of each disc; however in CFD results the whole volume of each conductor bears almost the same temperature due to the high thermal conductivity of copper, and this temperature is taken as the maximum temperature. The temperature profiles in Figure 10 correspond to the flow distributions in Figure 9. As observed the temperatures calculated by the network model are scaled by the factor of loss density. For the CFD results the situation is similar, but the only exception is in the case of 20 l/min, where a slight temperature peak is recognisable at the second disc from the bottom, probably due to the channel entry eddy circulations. Another difference between the two modelling approaches is that, for the low flow rates, particularly 2 l/min, the network model predicted higher temperatures than the CFD for both losses. This is because the network model predicted less uniform flow profiles than the CFD at the low flow rates. For high flow rates, especially 20 l/min, the network model temperature prediction is relatively lower than the CFD, since CFD showed that the bottom oil ducts are blocked by entry eddy circulations and thereby localised temperature peaks are formed l/min 5 l/min 70 2 l/min 5 l/min l/min 15 l/min l/min 15 l/min l/min l/min Disc number (from bottom to top) (a) From network model for 15 W per disc Disc number (from bottom to top) (b) From CFD for 15 W per disc l/min 79 5 l/min l/min l/min l/min Disc number (from bottom to top) l/min 5 l/min l/min l/min l/min Disc number (from bottom to top) (c) From network model for 30 W per disc. (d) From CFD for 30 W per disc. Figure 10 Temperature distributions on the winding conductors. 8 CONCLUSIONS As transformer thermal modelling tools, network models and CFD both require the same input parameters such as model geometry, oil properties and boundary conditions IET Electr. Power Appl., The Institution of Engineering and Technology

141 including loading and bottom oil flow rate and temperature. Fundamentally, network models employ the mathematic Austausch Dienst (DAAD) for facilitating this collaborated paper. equations for the average quantities, such as oil velocity and temperature etc, on each lumped element, i.e. oil duct or junction node, and some of the equations are empirical. On the REFERENCES [1] Tanguy, A., Patelli, J. P., Devaux, F., Taisne, J. P., and other hand CFD uses much higher spatial discretisation and Ngnegueu, T.: Thermal performance of power gets rid of empirical equations especially when the flow is laminar. In this paper, both modelling approaches were compared based on the same winding pass model in order to assess the influence of the different discretisation of both approaches upon the modelling results. From the comparison conducted, it was concluded that the deviation between the pressure drop calculated by CFD and the measured values is quite low and that, once adapted, the network modelling method delivered reliable results for the pressure drop as well. It is a proof to show that network transformers: thermal calculation tools focused on new operating requirements. Session 2004, CIGRE, rue d'artois, Paris, 2004 [2] Oliver, A. J.: Estimation of transformer winding temperatures and coolant flows using a general network method. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp [3] Allen, P. H. G., and Finn, A. H.: Transformer winding thermal design by computer. IEE Conf. Publ., 1969, vol. 51, pp modelling would be able to provide a quick solution for [4] Simonson, E.A., and Lapworth, J.A.: Thermal predicting winding pressure drops and thereby assist to choose capable oil pumps for forced oil cooling at thermal design stage. It is to remark that only the model and material parameters were inputted into the CFD and network model programs and no any calibration or adaption from the capability assessment for transformers. Second Int. Conf. on the Reliability of Transmission and Distribution Equipment, 1995, pp [5] Del Vecchio, R.M., Poulin, B., Feghali, P. T., Shah, D. M., and Ahuja, R.: Transformer Design Principles: With measurement results was applied. Applications to Core-Form Power Transformers Secondly, with high total oil flow rates such as 20 l/min, the flow distribution across the horizontal ducts delivered by the network modelling bore deviation from the one by CFD. The main difference was particularly due to the entry eddy circulations at the bottom ducts; the phenomena were observed from the CFD results. Moreover, the resulted disc temperatures from network model are lower than those from CFD for high oil flow rates; however the comparative relation acts oppositely for low flow rates. (Gordon and Breach Science Publishers, 2001) [6] Zhang, J., and Li, X.: Coolant flow distribution and pressure loss in ONAN transformer windings. Part I: Theory and model development. IEEE Transactions on Power Delivery, 2004, vol. 19, pp [7] Radakovic, Z., and Sorgic, M.: Basics of detailed thermal-hydraulic model for thermal design of oil power transformers. IEEE Transactions on Power Delivery, 2010, vol. 25, pp [8] Takami, K. M., Gholnejad, H., and Mahmoudi, J.: ACKNOWLEDGMENT Stefan Tenbohlen and Andreas Weinläder would like to thank the Deutsche Forschungsgemeinschaft (DFG) for Thermal and hot spot evaluations on oil immersed power Transformers by FEMLAB and MATLAB software's. Proc. Int. Conf. on Thermal, Mechanical and sponsoring this research project. Zhongdong Wang and Wei Multi-Physics Simulation Experiments in Wu would like to thank the Engineering and Physical Sciences Research Council (EPSRC) National Grid Dorothy Hodgkin Postgraduate Award (DHPA) and National Grid for their financial sponsorship. Due appreciation should be given to the colleagues of CIGRE WG A2.38 for inspiritive discussions. Financial support is also gracefully received from the Academic Research Collaboration (ARC) Programme between the British Council and Deutscher Akademischer Microelectronics and Micro-Systems, EuroSime 2007, 2007, pp. 1-6 [9] Kranenborg, E. J., Olsson, C. O., Samuelsson, B. R., Lundin, L-A., and Missing, R. M.: Numerical study on mixed convection and thermal streaking in power transformer windings. 5th European Thermal-Sciences Conference, The Netherlands, 2008 [10] Weinläder, A., and Tenbohlen, S.: Thermal-hydraulic investigation of transformer windings by CFD-modelling 12 IET Electr. Power Appl., The Institution of Engineering and Technology 2011

142 and measurements. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 [11] Torriano, F., Chaaban, M., and Picher, P.: Numerical study of parameters affecting the temperature distribution in a disc-type transformer winding. Applied Thermal Engineering, 2010, vol. 30, pp [12] Wu, W., Wang, Z.D., and Revell, A.: Natural convection cooling ducts in transformer network modelling. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 [13] Zhang, J., and Li, X.: Coolant flow distribution and pressure loss in ONAN transformer windings. Part I: Theory and model development. IEEE Transactions on Power Delivery, 2004, vol. 19, pp [14] Wu, W., Revell, A., and Wang, Z.D.: Heat Transfer in Transformer Winding Conductors and Surrounding Insulating Paper, Proceedings of The International Conference on Electrical Engineering 2009, Shenyang, China, 2009 [15] Wu, W., Wang, Z.D., Revell, A., Iacovides, H., and Jarman, P.: CFD Calibration for Network Modelling of Transformer Cooling Oil Flows Part I Heat Transfer in Oil Ducts, IET Electric Power Applications, 2011, to be published [16] Wu, W., Wang, Z.D., Revell, A., and Jarman, P.: CFD Calibration for Network Modelling of Transformer Cooling Oil Flows Part II Pressure Loss at Junction Nodes, IET Electric Power Applications, 2011, to be published IET Electr. Power Appl., The Institution of Engineering and Technology

143 Chapter 6 Optimisation of transformer thermal design 6.1 Paper 6 Optimisation of Transformer Directed Oil Cooling Design Using Network Modelling W. Wu, Z.D. Wang and P. Jarman 2011 IET Generation, Transmission and Distribution Submitted 101

144 ISSN Optimisation of Transformer Directed Oil Cooling Design Using Network Modelling W. Wu 1, Z.D. Wang 1 and P. Jarman 2 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK. 2 Asset Strategy, National Grid, Warwick, CV34 6DA, UK. zhongdong.wang@manchester.ac.uk Abstract The requirement on thermal design of a transformer is to guarantee that the transformer is able to pass factory heat run test and to restrain hot-spot temperature. The network model implementation has been developed to gain accurate prediction of the hot-spot inside oil-immersed transformers. In this paper, based on a CFD calibrated network model, the impacts of oil duct dimensions and block washer number on oil flow and temperature distributions are investigated for design optimisation using a directed oil (OD) cooled low voltage (LV) winding as an example. During the parametric study oil pump performance curves are incorporated to determine the inlet oil flow rate. Narrower horizontal ducts, wider vertical ducts and less disc numbers per pass are recommended for optimising oil flow distribution and reducing average winding and hot-spot temperatures. 1 NOMENCLATURE H = Hydraulic head of winding, in meters Q = Oil flow rate supplied to a winding, in liters per minute Acroynms/Shorthand CFD HCC HST JPL LV MWT OD OF PPC WP 2 INTRODUCTION Computational fluid dynamics Hydraulic characteristic curve Hot-spot temperature Junction pressure loss Low voltage Mean winding temperature Directed oil cooling mode Forced oil cooling mode Pump performance curve Working point Power transformers are key, and one of the most expensive components of electric system networks. Their performance and reliability inevitably influence the reliability of electricity transmission and distribution systems, especially when a significant fraction of the UK transformer fleet has been in operation for more than their designed lifetime [1-2]; for instance, by 2010 almost 50% of the in-service transformer population were 50 years old. Ageing is strongly associated to the degradation of insulating paper which is a function of temperature, and as such hot-spot temperature becomes significant since the insulation at hot-spot undergoes the worst thermal ageing. The overall demand for energy in the UK is expected to increase by 1% per annum over the period of 2007 to 2023, which is an rise from 351 to 373TWh [3]. The increasing demand as well as the financial constraints placed on electric network companies by the Office of Gas and Electricity IET Gener. Transm. Distrib., The Institution of Engineering and Technology

145 Markets (OFGEM) force the companies to be more strategic with the maintenance and replacement of their transformer assets. The electric network companies are interested in purchasing the transformers with lower hot-spot temperatures, especially when overloading transformers beyond the rated capacities is considered [4]. Transformer manufacturers are consequently under the pressure from their customers to design transformers with lower hot-spot temperatures. Numerical thermal modelling such as network modelling is applied as a tool to assess the oil flow distribution and hotspot temperature of power transformers and to assist the design of oil cooling systems [5-6]. The recent advance on network modelling techniques includes using highly discretised CFD simulations to calibrate and to improve the calculation accuracy [7-8]. One of the merits of network models is that they can be used to carry out a large amount of sensitivity studies on design parameters due to its low requirement on computational effort. To the authors best knowledge, the only recent work which evaluated the impact of structural dimensions of transformer windings is [9]. It was found that the oil duct dimensions as well as the disc number per pass strongly affect both oil flow distributions and pressure losses across the winding. [9] focused on the hydraulic model and thus did not consider winding power losses or oil viscosity and density variation upon temperatures. However the optimisation in terms of restraining hot-spot temperature can only be performed in conjunction with temperature calculations. Moreover, it did not consider the oil flow rate altered by design parameter modifications, i.e. a constant flow rate was used alone within the whole parametric investigation. This deviates from the reality; taking forced oil cooling (OF/OD) modes as an example, the hydraulic impedance of the entire winding changes while oil duct dimensions are altered, and as such the oil flow rate would vary according to the oil pump capabilities. In this paper, by applying the CFD calibrated network model and incorporating the pump specifications, winding design parameters are optimised to achieve the best winding temperature and oil flow distribution. 3 DIRECTED OIL COOLING DESIGN PRINCIPLE The goal of thermal design is to pass the heat run test, in which average winding temperature rise of 65 o C and top oil temperature rise of 60 o C are the criteria [10]. In order to guarantee the temperature rises, a sufficient oil flow rate is required [5]. For a directed oil cooling transformer, a capable pump should be equipped for driving this oil flow. Pumps are generally specified in terms of the hydraulic head, or head for short, in meters versus the flow rate in litres per second. Head reflects the total hydraulic resistance that a pump must overcome in the flow system. In oil-cooled transformers the hydraulic resistance comes from not only the frictional pressure losses along the oil channels inside cores and windings, pipe fittings and external radiator fins, but also the local pressure losses due to pipe bends and junction connections. As the oil circulation is a closed system, the static head which represents the gravity effect does not need to be resisted by the oil pump. Pump manufacturers release performance curves for all their models of pump. Pump performance curve (PPC) describes the head a pump can generate at different flow rates, as shown in Figure 1. Although the curve starts from zero flow rate, the head at zero flow does not represent a static head but the reference maximum pressure, and a pump should not be allowed to run at zero flow due to the issue of overheating. Head, m 0 Pump performance curve System hydraulic characteristic curve Guarenteed flow rate Working point Flow, L/s Figure 1 Intersection of pump performance curve and system hydraulic characteristic curve is pump working point. On the other hand, at the design stage, the pump pressure head required for the complete oil circulation at different oil flow rates are calculated and a system hydraulic characteristic curve (HCC) can be derived, as shown in Figure 1. The intersection of the system characteristic curve and the pump performance curve is the pump working point. A proper pump model should meet with the system characteristic curve at a working point whose flow rate does not deviate from the designed value much, in order to meet the temperature criteria. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

146 Head, m Some pumps have a performance curve which starts with a plateau pattern but after a knee point, the head rapidly reduces along with a small increment of flow rate. For this type of pump, the working point should be designed at the vicinity of the knee point to utilise the maximum stable pump head, otherwise any small disturbance of flow rate would greatly affect the head. 4 HYDRAULIC HEAD OF WINDINGS Although the thermal design for an entire transformer is not as simplistic as for a single winding, the principle is the same and the paper takes the low voltage (LV) winding example from [5] to perform the parametric analysis for identifying optimised design parameters. This 3-phase delta connection disc type winding, from a 250 MVA transformer, was operating at 22 kv and winding current of 6561 A. There are 95 discs cooled with 100 horizontal oil ducts arranged into 5 equal size passes by 4 oil washers. The widths of the horizontal, the inner and outer vertical ducts are 5 mm, 15 mm and 15 mm respectively. These duct dimensions and the washer number are to be further optimised in this study. While cooling oil with different flow rates are forced into the winding, the oil flow should require different pump heads to resist the pressure losses inside the winding, including the frictional losses occurring along oil ducts and the local losses caused by duct bends and junctions, i.e. junction pressure loss (JPL). The head varies with the inlet oil flow rate and the correlation between them is referred as the hydraulic characteristic curve of the winding. With a winding structure designed, its characteristic curve can be calculated by network modelling, in which junction pressure loss equations play important roles [8]. For instance, Figure 2 presents the three characteristic curves of the LV winding example [5] when JPL are calculated by three different sets of mathematic expressions. If JPL are neglected when calculating the hydraulic characteristic curve, the low curve values would result in a smaller oil pump than the one really required. Consequently the expected oil flow rate cannot be guaranteed and the winding will suffer from higher temperatures than designed values. Furthermore the JPL existence also makes the disc temperature distribution across the whole winding less uniform which often causes severer hot-spot temperature. Modelling excluding JPL is thereby unreliable. Inversely, if people use the unrealistically high characteristic curve predicted from the equations in [5], the chosen pump will be unnecessarily more powerful than required. It may seem good since this pump will supply more oil flow than desired. However, a dramatically high oil flow rate will affect the oil flow distribution across horizontal ducts and result in hot-spot shifting downwards to the pass bottom [11]. For optic-fibre measurement, sensors which have been installed at a previously predicted hot-spot location will incorrectly underestimate the hot-spot temperature. Besides, a bigger pump costs more and consumes unnecessarily more power. In contrast, the characteristic curve deduced from the CFD calibrated equations provide a better match with experimental results and will be used in this paper [8] Oil flow rate, L/s No JPL Eqn. in [5] CFD calibrated eqn. [7-8] Figure 2 Hydraulic characteristic curves of the LV winding example [5]. In order to guarantee the temperature criteria, a sufficient oil flow rate, 21.3 L/s, is aimed at for the LV winding example [5]. Note that this designed flow rate is only for a single winding; the necessary oil flow rate for the entire transformer will however be several times greater. A pump is chosen to deliver cooling oil into this single winding and its performance curve is illustrated in Figure 3, in which the winding characteristic curve is also overlapped to identify the feasible working point. The intersection of both curves yields the working point (24.5 L/s, 2 m); the corresponding flow rate is 24.5 L/s, 15% higher than the design value, 21.3 L/s. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

147 Head, m Flow, L/s PPC Winding HCC WP Designed WP Figure 3 Intersection of pump performance curve (PPC) and winding hydraulic characteristic curve (HCC) is working point (WP). 5 PARAMETRIC ANALYSIS AND DISCUSSION As discussed in Section 4 the working point is at Q = 21.3L/s, H = 2m for that particular design. Fixing the pump model, when the winding design is further modified, the winding hydraulic characteristic curve will possibly be shifted downwards or upwards, the working point then moves along the pump performance curve and the oil flow rate may also change accordingly. In most scenarios, it is not necessary to replace the pump model anew if the altered oil flow rate can still guarantee the temperature rise criteria. In this paper, design changes are made by varying major dimension parameters, including oil duct widths and the number of block washers equipped. Their impact is discussed in consistence with the pre-condition not to change the pump. 5.1 Effect of Oil Duct Widths In the sensitivity study, the oil duct widths were varied around their designed values within ±20% ranges; for example, for the horizontal duct which is designed to be 5 mm wide, the widths of 4 mm, 5 mm and 6 mm were tested respectively, and similarly for inner and outer vertical ducts. There are 4 cases conducted; in the first 3 cases only one type of duct was changed and in the 4th case all the three types were modified simultaneously. The modified winding hydraulic characteristic curves of the 4 cases are shown in Figure 4 respectively, in which the pump performance curve (PPC) is overlapped to identify the new working points and oil flow rates. In Figure 4, it is observed that narrower ducts require higher hydraulic head to retain a same oil flow rate and thus the winding characteristic curve is shifted upwards. While the pump performance curve is fixed, the narrowed ducts move the working point to lower flow rates; the widened ducts result in higher flow rates. The results show that the degree of impact follows the order, outer side vertical duct inner side vertical duct > horizontal duct. The flow rate variations are summarised in Table 1; the magnitude of the variations is limited and thus verifies the pre-assumption that it is unnecessary to change the pump. The corresponding results of mean winding temperature (MWT) and hot-spot temperature (HST) are obtained into Table 1 and the oil flow distributions in the top pass are illustrated in Figure 5 for comparison; only the top pass is presented because hot-spot locates in this pass. In Table 1, the combinations are grouped in correspondence to the 4 cases and the investigated duct width in each case is highlighted for clarity. Conclusions drawn from Table 1 include: the narrowed horizontal duct reduces the average winding and hot-spot temperatures; the narrowed vertical duct increases the temperatures; with all ducts narrowed altogether, their effects cancel each other but the temperatures still reduce slightly, because the degree of impact follows the order, horizontal duct > outer side vertical duct inner side vertical duct. The impacts of oil duct widths upon winding temperatures relies on the fact that both narrowed horizontal ducts and widened vertical ducts improve the uniformity of flow distribution, as observed in Figure 5. The distribution becomes more uniform because either narrowed horizontal ducts or widened vertical ducts or both can force more proportion of oil to flow upwards from the inlet to the centre of the pass and compensate the oil flow starvation there. Inversely, with narrowed vertical ducts or widened horizontal ducts more oil will turn direction upon departure from the inlet and flow through the bottom horizontal ducts, and the pass centre then has less cooling oil. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

148 (a) Of different horizontal duct widths. (b) Of different inner side vertical duct widths. (c) Of different outer side vertical duct widths. (d) All types of duct widths are altered together. Figure 4 Impact of oil duct widths upon winding characteristic curves. Table 1 Impacts of oil duct widths upon oil flow and winding temperatures. Duct dimensions, mm Horizontal duct width (MWT = mean winding temperature, HST = hot-spot temperature) Inner vertical duct width Outer vertical duct width Calculation results Oil flow variation MWT, o C HST, o C % % IET Gener. Transm. Distrib., The Institution of Engineering and Technology

149 % % % % % % (a) Of different horizontal duct widths. (b) Of different inner side vertical duct widths. (c) Of different outer side vertical duct widths. (d) All types of duct widths are altered together. Figure 5 Impact of oil duct widths upon oil flow distributions in top pass. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

150 Moreover, hot-spot location is almost not affected by the variation of horizontal duct width; however narrowed vertical ducts would shift the hot-spot upwards (by inner side vertical duct) or downwards (by outer duct). This is because, for example, with a narrowed inner duct, more oil tends to flow through the bottom horizontal ducts to the wider outer duct that has relatively lower hydraulic impedance, rather than to flow upwards, and as such the upper half of the pass will be hotter. The reason for narrowed outer duct is similar. Finally, as shown in Figure 5 (d), adjusting all the duct widths synchronously does not modify the flow distribution largely, which implies that the width proportion between ducts determines the flow distribution pattern. 5.2 Effect of Block Washers With network modelling, the significance of block washer number was examined. The winding characteristic curves of the original block washer arrangement (19 discs per pass) and the doubled block washer number arrangement (interleaved 9 and 10 discs per pass) were both calculated and are exhibited for comparison in Figure 6 (a). Doubled washers increase the hydraulic impedance of the winding, which then results in an flow rate reduction of 7.76%. On the other hand, Figure 6 (b) shows the maximum disc temperature distribution across the topmost pass, 19 discs. The figure reveals that, although with the flow rate reduced, the disc temperatures are significantly restrained. In particular, the hot-spot temperature reduces by 7.4 K and shifts upwards to the 5th disc counted from the winding top; previously it was at the 8th disc. (b) Impact of block washer arrangements upon maximum disc temperature distributions in top pass. Figure 6 Impacts of doubled block washer arrangement. It seems that pass size of ~10 discs is more optimal for this LV winding design than the original size, 19 discs per pass, in terms of lower and more uniform temperature distribution with a slightly reduced oil flow rate. 5.3 Performance at Different Loads Apart from the design parameters, the impact of loading variations was also studied with network modelling. Loadings can be varied depending on the different demands of different areas and periods. It is thereby meaningful to examine the thermal performance of a transformer under different loadings even though it has passed factory heat run test under rated load. In a similar way, the impact of different load factors upon winding hydraulic characteristic curves was calculated and shown in Figure 7 (a). While the load factor rose from 0.5 per unit up to 1.5 per unit, the characteristic curve shifted slightly and the altered working point only caused flow rate variation within ±5%. Higher loadings resulted in higher flow rates; this follows logically as oil becomes less viscous at higher temperatures. (a) Impact of block washer arrangements upon winding characteristic curves. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

151 (MWT = mean winding temperature, HST = hot-spot temperature) Figure 7 Impacts of load variation. (a) Impact of load factors upon winding characteristic curves. Figure 7 (b) shows the oil flow distribution in the top pass, affected by load factors 0.5, 1.0 and 1.5 respectively. It can be observed that the impact of load upon the flow distribution is almost negligible except the distinctiveness at the bottom and the top of the pass. The distinctiveness is due to the single side heated bottom and top ducts in this particular design; the other side of the ducts is non-heating oil washer. In single side heated ducts oil is relatively cooler and more viscous and thus flow rate is lower. High loadings would deepen the effect as observed in Figure 7 (b). Figure 7 (c) indicates that with directed oil cooling mode, the correlations of average winding and hot-spot temperatures versus loading factors follow parabolic trends. This is logical because the DC loss, namely Joule loss, of conductors is proportional to load current square and the impact of the flow variation within ±5% upon temperatures remains limited. (b) Impact of load factors upon oil flow distributions in top pass. (c) Correlation of mean winding and hot-spot temperatures versus load factors. 6 CONCLUSIONS Numerical approaches especially network modelling are helpful for optimisation of the design parameters for new transformers, such as oil duct dimensions and block washer arrangement etc. A recent CFD calibrated network modelling implementation was thereby applied to conduct a parametric study for analysing the impacts of design parameters upon oil flow rate, flow distribution and average winding and hot-spot temperatures. The study focused on directed oil cooling mode and in particular pump performance curves were incorporated to determine the inlet flow rate. The results obtained indicated that narrowed oil ducts shift the winding hydraulic characteristic curve upwards and oil flow rate then reduces to some extent. Although the flow rate is reduced, narrowed horizontal ducts optimise the uniformity of flow distribution and consequently lower down average winding and hot-spot temperatures. Narrowed vertical ducts result in less uniform flow distributions and higher average winding and hot-spot temperatures. Doubled number of oil block washers reduces the inlet flow rate slightly, due to the increment of winding hydraulic impedance, but significantly optimises the uniformity of flow distribution and thus effectively restrains the average winding and hot-spot temperatures. IET Gener. Transm. Distrib., The Institution of Engineering and Technology

152 In general, narrowing horizontal ducts, widening vertical ducts and reducing disc numbers per pass are recommended for optimisation of directed oil cooling transformers. ACKNOWLEDGMENT Financial support is gracefully received from the Engineering and Physical Sciences Research Council (EPSRC) Dorothy Hodgkin Postgraduate Award (DHPA) and National Grid. The authors appreciate the technical support given by John Lapworth from Doble PowerTest and Edward Simonson from Southampton Dielectric Consultants Ltd. Due appreciation should also be given to our MSc project student Mr Lee Smith who carried out the initial investigation of the idea in this paper under the supervision of the authors. REFERENCES [8] Wu, W., Wang, Z.D., and Jarman, P.: CFD calibration for network modelling of transformer cooling oil flows Part II Pressure loss at junction nodes, IET Electric Power Applications, 2011, to be published [9] Zhang, J., and Li, X.: Coolant flow distribution and pressure loss in ONAN transformer windings. Part II: Optimization of Design Parameters. IEEE Transactions on Power Delivery, 2004, vol. 19, pp [10] IEC standard : Power transformers part 2: Temperature rise, 1997 [11] Weinläder, A., and Tenbohlen, S.: Thermal-hydraulic investigation of transformer windings by CFD- Modelling and measurements. Proceedings of the 16th International Symposium on High Voltage Engineering, South Africa, 2009 [1] Bossi, A., Dind, J.E., Frisson, J.M., Khoudiakov, U., Light, H.F., Narke, D.V., Tournier, Y., and Verdon, J.: An international survey on failures in large power transformer in service, Electra, 1983, no. 88, pp [2] White, A.: Replacement versus refurbishment end of life options for power transformers, IEE colloquium on transformer life management, London, UK, 1998, pp. 10/1-10/3 [3] UK Department for Business, Innovation and Skills (2007) 2008 Energy Market Outlook - Electricity Demand Forecast Narrative. [Online] Available from: [Accessed: 27th September 2010] [4] Taghikhani, M.A., and Gholami, A.: Heat transfer in power transformer windings with oil-forced cooling, IET Electr. Power Appl., 2009, vol. 3, No. 1, pp [5] Oliver, A. J.: Estimation of transformer winding temperatures and coolant flows using a general network method. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp [6] Simonson, E.A., and Lapworth, J.A.: Thermal capability assessment for transformers. Second Int. Conf. on the Reliability of Transmission and Distribution Equipment, 1995, pp [7] Wu, W., Wang, Z.D., Revell, A., Iacovides, H., and Jarman, P.: CFD calibration for network modelling of transformer cooling oil flows Part I Heat transfer in oil ducts, IET Electric Power Applications, 2011, to be published IET Gener. Transm. Distrib., The Institution of Engineering and Technology

153 Chapter 7 Conclusions Accurate transformer thermal modelling is of great importance for predicting the hotspot temperature and its location. Because the thermal models proposed in IEC and IEEE loading guides [9,49] is over-simplified and strongly relies on the empirical hot-spot factor, thermal network modelling has been relied upon whenever a fundamental understanding of oil flow and temperature distributions in a transformer structure is required. Network modelling is developed and has gained spread usage also because it is well balanced between its calculation speed and approximation details and requires relatively low computational effort. With network modelling sensitivity studies can be more easily performed upon a large range of thermal design parameters and loads. In comparison to network modelling, CFD are general numerical methods with much higher spatial discretisation, and can be expected to exhibit more details about the flow and temperature patterns inside oil ducts or junction node regions, although this requires a tremendous increase of computational effort. The principle of this PhD work concentrated on developing a more accurate and reliable network model. Firstly a mathematic analysis was conducted to prove that the 2D channel flow between infinite parallel plates is a sufficient approximation to model the flow in winding oil ducts; the relative error due to the radial expansion of the oil ducts is less than 5% for typical transformer designs. Secondly based on thermal conduction principles, a mathematic model, TEDISC, was developed to predict the conductor temperature distribution of winding discs. From the study using TEDISC, it was identified that the network model s assumption, i.e. the conductor temperature linearly increases towards the oil flow downstream end of discs, could predict the hot-spot temperature with relative error below 1%. The major research of this PhD is then focusing on conducting large sets of highly discretised 2D CFD simulations to calibrate the empirical equations employed in network modelling. The empirical equations for Nusselt number (Nu), friction coefficient and junction pressure losses (JPL) were fully calibrated for transformer 103

154 oil and oil duct dimensions. The newly calibrated Nu equation predicted a winding temperature increase as the consequence of on average 15% lower Nu values along horizontal oil ducts. The new friction coefficient equation predicted a slightly more uniform oil flow rate distribution across the ducts, and also calculates a higher pressure drop over the entire winding. The calculation results based on the new JPL equation constants were compared with the results with the current off-the-shelf constants from [19,28] and also the experimental results from [40]. The new constants showed significantly better match to the experimental results and revealed that more oil will tend to flow through the upper half of a pass if at a high inlet oil flow rate. The oil flow distribution was calculated on the same winding pass model by both the calibrated network modelling and CFD. The calculation results were also compared with the experimental results, and it was concluded that the deviation between the oil pressure drop over the pass calculated by the network model and the CFD and the measured values is acceptably low. It verified that network modelling could deliver quick and reliable calculation results of the oil pressure drop over windings and thereby assist to choose capable oil pumps at the thermal design stage. However the oil flow distribution predicted by the network model deviates from the one by CFD, especially at high flow rates. Sensitivity studies on various thermal design parameters and loads were conducted by using the CFD calibrated network model in conjunction with a pump model. The studies were using a directed oil cooling low voltage winding case [19]. The conclusions basically include: 1) Narrowed oil ducts increase winding hydraulic impedance and as such reduce the inlet oil flow rate, but their effect on temperatures depends: narrowed horizontal ducts optimise the uniformity of the oil flow distribution and reduce the average winding and hot-spot temperatures; narrowed vertical ducts increase the average winding and hot-spot temperatures. 2) Arranging doubled number of oil block washers would significantly decrease the disc temperatures with the inlet oil flow rate slightly reduced, 7.8%, due to the increment of winding hydraulic impedance. 104

155 3) The impact of different loadings, 50%~150% of rated load, upon the inlet flow rate is limited, relative change below 5%. The correlations between the average winding and hot-spot temperatures versus load factors follow parabolic trends. The future work can be classified into several points: 1. For deriving the junction pressure loss (JPL) equations, a possible limitation might come from the fact that short vertical oil ducts exist in windings. Vertical duct lengths are so short that the upward oil flow upon departure from a junction will shortly arrive at the next junction, which implies that it may be difficult for the vertical oil flow to re-achieve fully developed status after the junction interruption. Further studies on the interaction between adjacent junctions along the vertical duct will be a necessity. 2. The flow distribution predicted by the network modelling deviates from the one by CFD. This is particularly obvious for the cases with high flow rates probably due to the entry eddy circulation phenomena that were observed in CFD. Neither of the predictions on flow distribution has been validated by experiments; experimental validation is therefore a necessity for future work. 3. Sensitivity study on natural oil cooling transformers requires external radiator models. Suitable external radiator models need to be researched for the thermal design optimization of natural oil cooling transformers. 105

156 106

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164 114

165 Appendix I Reference [19] Estimation of transformer winding temperatures and coolant flows using a general network method A.J. Oliver 1980 IEE PROC, Vol. 127, Pt. C, No

166 Estimation of transformer winding temperatures and coolant flows using a general network method A.J. Oliver, M.A., Ph.D. Indexing term: Transformers Abstract: The windings of large modern transformers are generally cooled by pumping oil through a network of ducts in the winding. The resulting value of the hottest conductor temperature and the position it occurs in the winding are important parameters in the design and operation of a transformer. There is a standard method for estimating the value of this hot spot but there is very little information on the position at which it occurs. Also, devices have been developed which when inserted in a winding will measure the local temperature. These instruments could be used to measure the hot-spot temperature of a winding in a transformer on load. However, it would obviously be advantageous if the position of the hot spot could be estimated so that the device could be installed in the optimum position. The work reported here attempts two things: first, to improve on the standard method for estimating the winding temperature distribution and hot-spot temperature and secondly to estimate the position of the hot spot. The computer program developed to do this can be used to estimate the flows, fluid temperatures and boundary temperatures for any network of flow paths. However, only its application to a transformer is considered here. The method used to obtain the required predictions is described, and estimates are presented of the winding temperature distribution for a particular design of transformer operating with a steady load. List of symbols Q ijibi,cij,di coefficients defined in the Appendix A = duct cross-sectional area A c = conductor cross-sectional area. A s = duct surface area ^c b = radial thickness of conductor and insulation, R Re S t d tl v = width of vertical ducts in transformer see Fig. 3b to f friction factor (fanning) g = gravitational acceleration h = vertical height hf = convective heat transfer coefficient / = current K, K', K" = pressure-loss coefficients k = thermal conductivity of fluid c,w k c = thermal conductivity of conductor kp = thermal conductivity of paper L = duct length for the disc type transformer winding problem this is equivalent to the radial width of the winding, see Fig. 3b M = total number of nodes in the network m = number of parallel paths joining two nodes m = mass flowrate at a source of mass flow (m > 0 denotes an input of mass, m < 0 denotes an output) Nu = Nusselt number P = pressure (in the transformer predictions it denotes total pressure) Pr = Prandtl number see Fig. 3b perimeter) b c d c = radial thickness of conductor, see Fig. 3b = axial conductor depth, see Fig. 3b Cp dp = specific heat of fluid = insulation thickness D d s = duct = thickness of spacer in transformer depth of cooling duct, see Fig. 3b equivalent diameter (4/4 4- wetted Paper 997C, first received 31st October 1979 and in revised form 30th July 1980 Dr. Oliver is with the Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Subscripts H power input at a source of heat (Q > 0 denotes an input of heat, Q < 0 denotes an output) wall heat flux heat generated in unit time by unit length of conductor electrical resistance for unit length of conductor Reynolds number based on equivalent diameter change in pressure caused by a pressure source temperature bulk temperature of fluid conductor temperature temperature of any fluid injected at a node reference temperature for electrical resistance at which R= R o average wall temperature fluid velocity distance along a duct in the direction of flow thermal admittance between the conductor and the oil for unit length of conductor thermal admittance of insulation for unit length of conductor distance along the conductor temperature coefficient of electrical resistance connection matrix for the flow network, its value is: + 1 if nodes / and / are connected and / >/ 1 if nodes / and / are connected and / </ 0 if nodes / and / are not connected dynamic viscosity of fluid at its bulk temperature dynamic viscosity of fluid at the wall temperature kinematic viscosity of fluid at its bulk temperature a dependent variable Refers to disc H /80/ $01-50/0 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

167 / Refers to node i j Refers to node /. Similarly for k and m J Refers to disc J loc Local value 0 Reference value corresponding to temperature t 0 i, j Refers to duct connecting nodes i and / p, q Refers to duct connecting nodes p and q i, j, I Refers to /th duct connecting nodes i and j when there is more than one duct between / and j Superscripts 00 Refers to nth iteration 1 Introduction The windings of large modern transformers are generally cooled by pumping oil through a network of ducts in the winding. Usually the oil enters at the bottom of thewinding and exhausts at the top. This results in an overall increase in temperatures up the winding. However, the hottest conductor temperature does not occur at the top of the winding. This usually considered to be due to the combined effect of maldistribution of oil flow and losses. Knowledge of the temperature and position of this hot spot is important for the design and operation of the transformer. For example, the rate of deterioration of the winding insulation increases as the conductor temperature increases. Therefore, it is necessary to know the hottest conductor temperature in order to ensure a reasonable life for the insulation. At present, design methods for a transformer give values for the rise of average winding temperature above the average bulk oil temperature. This value is then added to the oil temperature at the top of the winding to give the conductor temperature at the top. Then an arbitrary 10% of the average winding temperature rise is added to the top conductor temperature to get an estimate of the hot-spot temperature. This is the standard method for estimating this temperature. 1 The position of the hot spot is not known with any accuracy. Several devices have been developed to measure the local conductor temperature, for example, the 'Vapourtherm' device described by Hampton and Browning. 2 However, if any of these devices are to be used it would be advantageous to know the approximate position of the hot spot so that they can be positioned there. The purpose of the work reported here is to improve on the standard method for estimating the hot-spot temperature and to provide an estimate of the position of the hot spot. The mathematical model which has been developed to do this also provides estimates of the temperature, oil flow and oil pressure throughout the winding. The model has been developed into a computer program called TEFLOW. TEFLOW can be used to estimate the flows, fluid temperatures and boundary temperatures for any network of flow paths. However, only its application to a transformer is considered here. Fig. 1. Each element of the network represents a single path with the nodes usually being placed at the junctions. In the model, values of the pressure and bulk temperature are determined for each node. Values of fluid velocity and average wall temperature are determined for each path. If the temperature varies significantly along a path, then that path could be split into several elements in order to calculate this variation. The required values of pressure, bulk temperature, fluid velocity and wall temperature are obtained by solving the set of equations which can be obtained from the following: (a) conservation of mass applied to each node (b) conservation of thermal energy applied to each node (c) pressure-drop equation applied to each path (d) heat-transfer equation applied to each path. The actual equations and the method of solution are discussed in the next section. 2.2 Solution Procedure The following assumptions were made in deriving the equations: (i) conduction along the duct wall is negligible (ii) there is complete mixing at a junction so that the fluid entering each of the exits from a junction is at the same bulk temperature. The set of equations which are obtained from (a) to (d) in Section 2.1 are given below. Application of the conservation of mass to a node i, see Fig. 1, gives M 1 "-' i= where 2 a,- ; - represents all the paths which connect nodes j j to node /. 2 allows for more than one path between a node / and a node /. The case of / > 1 can be handled by the solution procedure, but to simplify the equations it will be assumed for the rest of this Section that two nodes / and / are directly connected by only one path (i.e. /= 1). In this case eqn. 1 reduces to (1) M I a i,jpij u U A U = ~ m i (2) The pressure drop equation for a path (/, /) joining nodes i (i.j ) (j.k.2) 2 The mathematical model 2.1 Approach used A collection of interconnecting flow paths or ducts can be represented on the network diagram of the type shown in 396 Fig. 1 node duct Simple network diagram IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

168 i and / can be expressed as Pi-Pi = - V II.Q «P,Q - Pu 8 (hf - where term I represents the losses which are related to the velocity head, for example friction; terms II and III are the losses which are proportional to the velocity head in another pipe, these could occur at junctions; term IV represents the gravitational head; term V allows for any pressure sources (pumps) or sinks. Conservation of thermal energy applied to each node gives '"' KJ IV (3) Eqns. 2 to 5 are the required equations. These represent the flow and heat transfer in the network considered. The equations have been written so that the correct flow directions in the network will be predicted even if these are not known a priori. Before these equations can be solved information must be supplied which enables the coefficients of the equations to be derived. This information consists of: the physical properties of the fluid; the geometry of the network; pressure loss coefficients; friction factors; Nusselt numbers or heat transfer coefficients; source/sinks of pressure, heat and mass. Clearly, the values of these coefficients are dependent on the particular problem being considered. Also the relevant boundary values for the problem need to be specified. This is discussed further in Section 3 for a particular case. These equations form a complete set for the network considered. Their solution provides values of pressure, Pi, and bulk temperature (f b ),- at each node and values of velocity, u t} -, and mean wall temperature (t w ) it j for each duct. In order to solve the equations, they are rearranged to give: (a) a set of simultaneous linear equations for pressure with variable coefficients depending on velocity (and temperature if the properties are temperature dependent) (b) a set of simultaneous linear equations for bulk temperature with variable coefficients (c) nonlinear equations for velocity and wall temperature. These equations are solved by an iterative technique. Further details of the solution procedure are given in the Appendix. The method described so far is of general applicability. The remainder of this paper describes its application to the prediction of temperatures and cooling oil flow rates for the winding of a large transformer. 3 Representation of the cooling in a large transformer The first term in curly brackets is + 1 if the flow is from node / to node / and is zero otherwise. The second term in curly brackets is + 1 if the flow is from node / to node / and is zero otherwise. The last two terms of eqn. 4 allow for the injection or extration of mass at node /. The equation for the transfer of heat from the wall to the fluid for the path (i, j) can be written as (4) 3.1 The cooling of a transformer winding The case considered is a disc type of winding which is cooled by the direct forced flow of oil. The basic design of a single phase of a transformer is shown in Fig. 2. It consists of an iron core around which is wound a low-voltage and a high-voltage winding. The mathematical model described in this section applies to either of these windings. The winding consists of an insulated conductor which is wound l.v. winding h.v. winding (5) where the term in square brackets is the mean bulk temperature of the fluid in the path (/, /). Fig. 2 Schematic diagram of windings for single phase of a transformer IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

169 spirally into discs. Each disc is separated from its neighbours so that there are gaps, referred to as ducts, between the adjacent conductor discs through which cooling oil can flow, see Fig. 3. Oil is pumped into the bottom of the transformer. From there it flows into the regions occupied by the windings and then the design is such that is should flow up the windings in the manner shown in Fig The blockwashers completely block the oil duct on one side of the winding. Thus, at that level all the oil flows past the winding on one side. The blockwashers, which are approximately equispaced up the winding, alternate from one side of the winding to the other. The group of cooling ducts between adjacent blockwashers is known as a pass. Thus the winding is made up of several similar passes in series. On reaching the top of the winding the oil passes into a header and then onto the coolers. 3.2 The network model The group of cooling ducts which constitute a pass can be represented by a network such as that shown in Fig. 4 for a pass with seven cooling ducts. The conductor discs and blockwashers are shown for clarity. The model of the complete winding is constructed by joining together several networks like that of Fig. 4 so that there is one for every pass in the winding. If necessary additional resistances can be added to the model to allow for entrance and exit effects on the oil flow at the top and bottom of the winding. - -oil retaining wall -conductor disc Eqns. 2 and 4 may then be applied to each node of the.network and eqns. 3 and 5 to each duct of the network. The resulting set of equations can then be solved using the solution procedure of Appendix 9.1 to give the flow and the wall temperature for each duct of the network together with the pressure and temperature for each node. The following subsections describe the quantities that need to be defined in eqns. 2 and 5 and they also suggest ways of obtaining these quantities. The method of obtaining conductor temperatures is also described. It is necessary to define the winding geometry, the cooling fluid properties, the heat generation, the boundary values and the following coefficients for the ducts: friction factors, pressure-loss coefficients and Nusselt numbers. The source term, S it j, in the pressure equation is zero for the network considered. For the application considered the oil flow into the bottom of the winding and its inlet temperature also need to be specified. 3.3 Coefficient values The Reynolds numbers for the flows in the cooling ducts of a winding will generally be considerably less than 2000, so the flow is assumed to be laminar. For the friction factors, the solution procedure assumes / \ = a Re c [ d where a, c and d are constants. The values used for a and c were those given by Rosenhow and Hartnett 4 for a parallel plate duct, i.e. a rectangular duct with a very high aspect ratio, namely a = 24 and c = 1. The value of d used, 0-58, was that given by Rosehnow for a liquid flowing in a tube no other more relevant information could be found. For Nusselt number, the assumed form is. blockwasher Nu = (6) pass For transformer oil, Pr ~ 200, thus thermal entrance effects Fig. 3A 3' Flow paths in winding - vertical section [conductor disc insulation b ; conductor t>, \ V 1 pass < block washer Fig. 3B 398 conductor disc Details of conductor disc vertical section Fig. 4 Network representation of pass with seven cooling ducts IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

170 could be important. Rosenhow and Hartnett 4 give analytical values for the local Nusselt number in the thermal entrance region of a parallel-plate duct with a constant heat flux at each wall and a constant property fluid. These can be represented by Nu loc = Nu loc = /3 x/d RePr > 0008 x/d RePr < 0008 (7) (8) The pressure-loss coefficients which require specification for this problem represent the pressure losses which are attributable to the junctions. Following Stephenson 6 the junction loss between the main combined flow and a branch of a junction is incorporated into the loss coefficient for the branch. The only information found on the pressure losses at junctions with laminar flow is the measurements of Jamison and Villemonte 7 for tee-joints with pipes of equal size and short radiused corners. Using the notation shown on Fig. 5, their measurements can be approximated by (Junctionloss),. = [lo g \pu? (Junction loss) x 10 3 Re, x combining (Junction loss) ^! = ^- dividing (Junction loss) 7 0 x Re-, I 2 x 2 P U 2 However, the value Nu required by the solution procedure is an average value over the length L of the duct, therefore Nu = \ 0Nu loc dx Also, it is necessary to take account of the effect of viscosity variations with temperature. According to Knudsen and Katz s this can be approximately represented by a factor (idw/ubt 0 ' 14 ThiS' combined with eqns. 7 to 9 gives the following expression for Nu: Nu = / o. LID\ //O KRePrl \P (9) L/D RePr < LID RePr It is assumed that these formulae apply to the cooling-duct junctions in a transformer. 3.4 Boundary values For any flow network problem, a pressure must be specified at one node at least. Furthermore for a node i with a mass source it is necessary to either (i) specify w,- and (t b )j or (ii) specify P t and (f b ),- and for a node / with a mass sink then either (iii) specify m } or (iv) specify Pj For the transformer network conditions (ii) and (iii) were used. The heat source at a node which is represented by Q was zero for all nodes. The only other boundary value to be specified was the wall heat flux for each duct q t j. This can be derived from the heat generated within the conductor. 3.5 Representation of heat generation Comparison of eqns. 6 and 10 gives r, = 2-44 I -1/3 0 = y = 1/3, 5 = -014 LID RePr < 0026 As mentioned in Section 2.2, the solution procedure ignores heat conduction in any boundary. This means that heat conduction along the conductor is assumed to be negligible. Justification of this assumption is given in Appendix = 8-2, 0 = 7 = 0, 6 = LID RePr > IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Fig. 5 Notation used for junction losses 399 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

171 The heat removed by the cooling oil consists primarily of the ohmic losses of the winding conductor plus losses which are caused by the induced eddy currents in the winding. Most transformer windings are designed so that the eddy losses are comparatively small. In the case investigated in this paper, they have been ignored for simplicity. Thus, the losses for a disc /, see Fig. 4, can be expressed as (QC)J = (11) where q c is the heat generated in unit length of the conductor. However, the quantity required by the network model is the heat flux through unit surface area of the duct. For duct (i, /), this is denoted by q t j. Using the notation of Fig. 4, (q c )j can also be expressed as (QC)J = Yew [(t c )j-(t w ) it j] + Y CiW [{t c )j-{t w ) ktl ) (12) where the thermal admittance, Y is defined for unit c w length of conductor. In this case, the heat flow out of the vertical ends of each disc is ignored as it is generally small in comparison. However it can be allowed for if necessary in eqn. 12 and in the following analysis. The heat flow into the duct (/, /) comes from the discs J and H. Together, unit lengths of conductor in discs </ and H contribute 2x6 to surface area of the duct (/, /). Therefore for unit surface area Qij = ^ {Y c,u,[(t c )j-(.t w ) u ] +Y c>w [(t c ) H -(t w ) u ]} (13) By equating eqns. 11 and 12 the following eqns. for {t c )j can be obtained The conductor temperature t c can be obtained from the converged temperature predictions by using eqn Estimation of temperature variation through a disc Using a network as illustrated in Fig. 4 results in temperature predictions which are values averaged over a given disc. As the oil flows through a given cooling duct, its temperature will rise as it picks up heat and the convective heat-transfer coefficient may change due to thermal-entrance effects. Assuming the heat-transfer coefficient varies conventionally and decreases with downstream distance, then the conductor and insulation temperatures towards the downstream end of the disc will be higher than those towards the upstream end. In order to estimate the maximum conductor temperature for each disc, the following method was used. The oil temperature at the downstream end of the disc where the temperatures will be, approximately, maximum is given by ML = (t b ) i + 2[(t b ) m -(t b ) i ] where (t b ) m is the average value obtained from TEFLOW. Thus the maximum oil/insulation interface temperature can be obtained from 2[(t b ) m -(t b ) i )} (Mu loc ) L /D where (Nu loc ) L is defined by eqn. 7 or eqn. 8 with* = L, the properties being evaluated at the known average temperature. Then the estimated maximum conductor temperature for a disc J, can be obtained from eqn. 14 with t w replaced by (t w ) L. (t w ) kj ] + I 2 R 0 (1 -at 0 ) T; T^T (14) Similarly an eqn. for (t c ) H can be obtained from equations which are equivalent to eqns. 11 and 12 but for conductor disc H. Substitution of eqn. 14 and the corresponding equation for (t c ) H into eqn. 13 gives the required equation for wall heat flux: Y Ic ' w 2 2b(aI 2 R 0-2Y CtW ) -l {[(t w )u-(t w ) 8th ] 2b\I 2 R 0 2Y C>1 05) The thermal admittance between the conductor and the insulation/oil interface for unit length, Y c w, was taken as -*c,w 3.7 An illustrative example In order to illustrate the method, the following example was chosen. The l.v. winding of a 250 MVA transformer operating at 22 kv has been considered. This gives a winding current of 6561 A for a 3-phase delta connection. This current is assumed to be carried by all the 22 turns in one disc of the winding connected in parallel. The winding geometry used was that given by Lampe, Persson and Carlsson 8 for a winding model to which they refer. The geometrical details are given in Table 1, using the notation explained in Fig. 3. A winding with five passes and 20 ducts per pass was considered.. Property values for transformer oil based on those specified in the British Standard for transformer oil 9 are given in Table 2. These values were taken as constant except for the density and viscosity. The density was calculated from the expansion coefficient and the viscosity of the oil was calculated using the following formula suggested by Spiers 10 for oils: lo gl0 (uxl0 6 ) = The coefficient A was taken as 2-34 and B as This gives values which for t > 10 C are within 5% of the viscosity values specified in the British Standard. 400 IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

172 Table 1: Geometrical detailst Oil duct length (L) Oil duct depth id s ) Vertical oil duct width (d v ) Width of conductor + insulation (b) Thickness of paper insulation [d p ) Width of conductor {b c ) Depth of conductor (d c ) Density (at 20 C) Expansion coefficient Specific heat Thermal conductivity 4. Results 100 mm 5 mm 15 mm 4-5 mm 0-6 mm 3-3 mm 10 mm Table 2: Properties of transformer oil X 10 3 kg/m /K J/(kgK) 0-13W/(mK) Predictions of the oil-flow distribution in the first two passes are shown in Fig. 6. The results for the remaining three passes are the same to within 1%. Predictions of mean and maximum conductor disc temperatures are shown in Fig. 7. Also shown are the predictions of oil temperature at the inlet and outlet of each pass. The variation in heat flux up the transformer winding owing to the thermal effects represented in eqn. 15 is not insignificant for the conditions investigated. These effects are due to the change in electrical resistance with temperature and the dependence of heat distribution from a disc on the conductor to oil temperature difference on each side of the disc. The variation was of the order of 10% through a pass owing to a combination of these effects. However, the variation up the winding for a given duct in each pass was only 4%; this explains why there is no noticeable deviation from a linear profile for the oil temperature predictions in Fig. 7. The peaks in conductor temperatures towards the centre of each pass are a direct consequence of the low flows existing there Predictions were also obtained for constant oil properties to illustrate the importance of allowing for property variations. This resulted in the velocities of Fig. 6 being changed by a maximum of 5% and the conductor temperatures of Fig. 7 were increased. The maximum increases in temperature occurred towards the centre of each pass where the mean values were increased by approximately 3 C and the maximum values by 5 C. Also shown in Fig. 7 are estimates of the conductor hot-spot temperature calculated by the standard method described in Section. The average conductor temperature and the oil temperatures required for these calculations were obtained from the predictions ) 70 i [so ' 50 *. x x ** *** " "* ** 30 pass number Fig. 7 Conductor temperatures in each disc mean value for each disc X maximum value for each disc o mean winding temperature Q hot-spot temperature (standard method) A oil temperature D C» c on "o o 0 07 * = 004 o Fig number 1 pass number 2 pass Distribution of flow between cooling ducts cooling ducts numbered from bottom of pass t See Figs. 3 and 5 IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

173 5 Discussion Clearly the computer program TEFLOW that has been developed can be used to predict the conductor temperatures and the oil flow and pressure in a directed flow, forced oil cooled transformer. Qualitative experimental confirmation of the predicted oil flow distribution (Fig. 6) is provided by the measurements of Allen, Szpiro and Campero. 11 They have measured oil flows in a Perspex model of a pass of a disc type winding. Their experimental results confirm the shape of the profile in Fig. 6 with minimum flows being measured in the ducts towards the centre of the pass and maximum flows in the ducts at the top and bottom of the pass. The predictions indicate that the hot spot for the representation used occurs in the middle-conductor disc of the top pass of the winding. It is thus possible to get an indication of where to position a device which seeks to measure the hot-spot temperature, such as the Vapourtherm instrument mentioned in Section 1. The program could also be used to study the effects of modifications to existing cooling-circuit designs or to investigate new designs. It is worth noting from the predictions that the peak conductor temperature in each of the top few passes does not differ by more than a few degrees from the winding hot-spot temperature. The conventional hot-spot computation, which gives no information on position, agrees with the maximum value of the predicted mean conductor temperature averaged over a disc, but it underestimates the absolute maximum conductor temperature, this is for a situation where the conductor temperature rise across a disc is significant. Also the conventional hot-spot computation may not do as well as the described procedure when there are nonuniformities in a winding which may produce high local temperatures without significantly affecting the mean winding temperature. Clearly, all the predictions presented are dependent on the relationships used for the loss coefficients, friction factors and heat-transfer coefficients of the network. The coefficients used for the winding example can only be regarded as estimates. In order to get accurate predictions for a transformer it will be necessary to either check these coefficients experimentally or to use alternative validated values if they are available. However the technique, even with the unvalidated coefficient values reported, provides far more useful information than the standard method for predicting the winding hot-spot temperature. 6 Conclusions A numerical procedure has been developed that predicts the flow and pressure of a fluid flowing in a network of interconnecting ducts. If heat is transferred to or from the fluid then the fluid and duct-wall temperatures can also be predicted. The variation of viscosity and density with temperature is allowable. The procedure, which has been incorporated into a computer program, has been applied to the oil flow in a typical directed flow, forced-oil-cooled transformer. Predictions of oil flow and temperature and conductor temperature have been obtianed. This enables the winding hot-spot temperature and its position to be determined. For the particular representation of a transformer considered, the results indicate that the hot spot occurs in the top pass of the winding on the middle-conductor disc. 402 The computer program could also be used to investigate new designs and the effect of modifications of existing cooling-circuit designs. 7 Acknowledgements This work was carried out at the Central Electricity Research Laboratories and it is published by permission of the Central Electricity Generating Board. 8 References 1 ALLEN, P.H.G.: 'Transformer rating by hottest spot temperature', Electr. Times, March 1971, pp HAMPTON, B.F., and BROWNING, D.N.: 'Rating of power transformers', CEGB Tech. Disclosure Bull, 1967, 79 3 CEGB Modern Power Station Practice, Vol. 4 (Pergamon Press, 1971) 4 ROSENHOW, W.M., and HARTNETT, J.P.: 'Handbook of heat transfer' (MCGraw-Hill, 1973) 5 KNUDSEN, J.G., and KATZ, D.L.: 'Fluid Dynamics and Heat Transfer' (McGraw-Hill, 1958) 6 STEPHENSON, P.L.: 'MORIA: a program to calculate the flowand pressure drop in a pipe network'. Central Electricity Research Laboratories Report. RD/L/P7/76, JAMISON, D.K., and VILLEMONTE, J.R.: 'Junction losses in laminar and transitional flows, /. Am. Soc. Civ. Eng. 1971, 97, (HY7),pp LAMPE, W., PERSSON, B.G., and CARLSSON, T.: 'Hot spot and top-oil temperatures proposal for a modified heat specification for oil immersed power transformers'. Proceedings of the International conference on large high tension electric systems, 1972, Paper British Standard: Insulating oil for transformers and switchgear, 1972, No SPIERS, H.M.: 'Technical data on fuel.' British National Committee, World Power Conference, ALLEN, P.H.G., SZPIRO, O., and CAMPERO, E.: 'The power transformer winding as a thermal problem'. Proceedings of the CNR symposium on power and measurement transformers, positano, September 1979, pp WOOD, D.J., and CHARLES, C.O.A.: 'Hydraulic network analysis using linear theory', Proc. Am. Soc. Gv. Eng., 1972,98, (HY7),p Appendix 9.1 Details of the solution procedure As described in Section 2,2, the first step was to derive a set of simultaneous linear equations for pressure. The method used was derived from that used by Stephenson 6 and Wood and Charles. 12 From eqn. 3: [-.,.,,.,,4,, Table 3: Further property and coefficient values Thermal conductivity of insulation (k p ) Temperature coefficient of electrical resistance (a) Thermal conductivity of conductor (k c ) Heat generated per unit length of conductor at f 0 = 75 C (/ 2 R o ) Convective heat-transfer coefficient (/»/ ) from predictions Approximate half-length of winding in a disc (/) Typical temperatures for a disc, f, obtained from predictions f 2 fa 0-2W(mK) 43 X10""/K 3-8 X 10 2 W/(mk) 55W/m 325W/(m 2 K) 35m 82 C 95 C 39 C IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

174 L ' u i,j* ' i,j' Substituting in eqn 3 and applying it to each node / = 1 (16) j M X OijPj = b t i = 1 -> M (17) where M a u = I a u Pu A u fl ij a U = ~ a b t = -rhi j -1 a u p u A u a u - Q u 2 PfQ fl Eqn. 17 represents the required simultaneous linear equations for pressure. For a node / = / where the pressure is specified as /*, = Pj, then the coefficients are aj,j = 1; ajj = 0.../ * J M \;lj AM,- bj = Pj Eqn. 4 applied to each node can be expressed as M where (18) Eqn. 18with/= 1 -> M represents the required simultaneous linear equations for bulk temeprature. For a node where the bulk temperature is specified the treatment is the same as that for the pressure equation. The wall-temperature equation can be obtained by rearranging eqn. 5 to give M ll i UjCn \U U \ AM; = -\ct u \\ The set of equations represented by eqns. 16 to 19 were solved by an iterative procedure. For the «th iteration the steps in the solution were IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

175 Step 1: the linear simultaneous equations M i = \ were solved for P < i - n) using Gaussian elimination with partial pivoting. The superscript {n 1) indicates that the values of the dependent variables occurring in the coefficient are to be obtained from the (n l)th iteration. 2: the linear simultaneous equations M were solved for (?b), (n). M i = I -*- M Step 3. the equation for wall temperature was expressed in the form (t V (n) \knu u ^' "ft (n-l) ^ i,j\ (n-1) and was solved for (t w )i/ n) for each path (/, /). t: the equation for velocity was expressed as where the value chosen depends on the particular problem. 9.2 Importance of heat conduction in the winding of a transformer Consider a given disc conductor in a winding. The oil flows across the disc surface in a direction normal to the conductor. A simple heat balance shows that the rise in oil temperature as it flows across the disc is small for the magnitude of heat fluxes that occur. For a simplified analysis, the situation can be represented by a fluid at a constant temperature flowing across a conductor of length /, where / is the length of the conductor in the disc. The conductor is surrounded by paper insulation and heat is generated in the conductor. A heat-balance equation for unit length of the conductor allowing for heat conduction in the conductor is (20) where the first term represents conduction, the second term represents the heat flow to the oil and the third term is the heat generation. The admittance Y c a represents the thermal admittance between the conductor and the oil for unit length of conductor. In deriving this quantity it is assumed that the heat flow through the insulation passes only through regions of width b c at the top and bottom of the conductor, see Fig. 3; in the conductor disc most of the remaining insulation faces onto adjacent conductors so the heat loss through this insulation is small. Thus 1-1/2) vj Pj) (n-l) Solving eqn. 20 for t c gives \/l i ~ hj) - a u S u (n-d (n-1) with This denotes an iteration equation with underrelaxation. The value of the relaxation coefficient is 0-4. These equations were solved for w, j y < " ) for each path (/, /). Step 5: go to step 1 and repeat steps 1 -> 5 for the («+ 1 )th iteration. The iterative loop represented by steps 1 -» 5 was repeated until the following convergence criterion was satisfied for each dependent variable: 404 where t c = A exp (mz) + B exp ( mz) + I 2 R o (l-oct o )+Y Cta t c Y c>a -oti 2 R o m -J Y ca-oci 2 R o (21) The constants A and B can be evaluated from the following IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

176 boundary conditions: atz = 0, t c = t x atz = /, t c = t 2 where z = 0 denotes a position on the conductor in the disc where the temperature is known to be t x and z = / represents a position where it is known to be t 2 This gives A = t x exp ( ml) I 2 R 0 (l-at 0 )+Y c>a t c ai 2 R 0 ca exp (ml) exp ( [1 exp ( ml)] (22) B = exp I 2 R 0 (l-at 0 )+ Y c. a t a t 2 Y c, a -ai 2 R 0 [exp (m/) 1 ] exp (ml) exp ( ml) (23) The importance of conduction is indicated by the value of the following ratio r = k c Y c A c d 2 t c dz 2 tc-ta) Substituting for t c using eqn. 21 gives r = ( Y c,a - oj 2 R o )[A exp (mz) + B exp (- mz)\ Y c a I A exp (mz) + B exp ( mz) + I2 R 0 (l-at 0 )+ Y Cta -oti 2 R o t, (24) Typical values of the quantities required in the evaluation of eqn. 24 are given in Table 3. With these values z = 1 metre -> F ^ 1 x 10" 3 z = (I-I) metre -+ T ^ 1 x 10" 3 where / is approximately half the length of conductor in a disc. For z = 1 -> (/ 1) metre, F is smaller. This proves that for the conditions investigated heat conduction is certainly not important at more than one metre from the ends of the conductor. Therefore the neglect of conduction is justified. A similar calculation has been made for the magnitude of the conduction from conductor to conductor through the paper. This also has been found to be negligible. IEEPROC, Vol. 127, Pt. C,No. 6, NOVEMBER Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

177 Appendix II Reference [40] Thermal-hydraulic investigation of transformer windings by CFD-modelling and measurements A. Weinläder and S. Tenbohlen 2009 The 16th International Symposium on High Voltage Engineering (ISH) 117

178 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg THERMAL-HYDRAULIC INVESTIGATION OF TRANSFORMER WINDINGS BY CFD-MODELLING AND MEASUREMENTS A. Weinläder 1*, S. Tenbohlen 1 1 Universität Stuttgart, Institute of Energy Transmission and High Voltage Technology, Pfaffenwaldring 47, Stuttgart, Germany * awein@ieh.uni-stuttgart.de Abstract: In modern development of transformers there is a strong requirement for adherence of the temperature limits of the used insulation materials on the one hand and - on the other hand - not to use more material and further resources than necessary. These aims can only be achieved by a precise calculation of the temperature distribution in the windings. The conventional way of calculating the temperature distribution is to calculate the bulk temperature of the oil in the winding channels by the known losses, the flow rate and the thermal capacity of the oil. The temperature in the solid insulation is further calculated by an assumed heat-transfer coefficient which is in reality known only very roughly. The topic of this article is a more precise alternative way of calculating the temperature distribution. The flow field is calculated by CFD (Computational Fluid Dynamics) models and thus a much more accurate value for the local heat-transfer coefficient between oil and solid insulation is achievable. The paper also describes how the CFD models were validated by measurements of the oil flow in winding models. 1. INTRODUCTION A reliable calculation of the temperature distribution within oil cooled windings is a basic precondition for a fail-safe and material saving design of power transformers. The importance of an accurate determination of the temperature distribution becomes obvious when a basic law of ageing of insulation material is taken into account. This law says that the ageing rate increases exponentially whit the temperature of the insulation material. Particularly for the case of paper insulation as mainly used in power transformers- this means a doubling of the ageing rate each 6-8 C. Within this paper only oil cooled power transformers are regarded. In such a transformer, oil flows upwards through the winding channels while it warms up. Then it flows downwards through the cooler back again into the vessel (ON/OF mode) or directly back into the windings (OD mode). The oil flow is thereby forced by a pump (OD/OF mode) or occurs autonomous from the thermal caused change in density (ON mode). To estimate the temperature distribution within the windings, first the volume flow of the oil (oil volume/time) through the regarded winding needs to be known. When this size is known then it is possible to estimate the averaged oil temperature at a particular point of the flow path in the winding by evaluating the balance between the known losses of the winding and the thermal energy removed by the oil. To calculate this oil volume flow, it is mainly essential to know the hydraulic resistance of the winding. When the averaged temperature of the oil is known, the next step is to calculate the temperature of the conductor. This is nearly identical to the maximum temperature of the submerging solid insulation. To calculate the difference between the now known averaged oil temperature and the conductor temperature, it is now necessary to know the heat transfer coefficient at the boundary surface between oil and solid insulation. This coefficient is a function of a number of local variables, especially of the velocity in the respective channel, the channel length and the temperature. This means that -beneath the hydraulic resistance- especially the velocity within the particular channels is of fundamental meaning to the calculation of temperatures in the solid insulation. 2. DESCRIPTION OF THE INVESTIGATED GEOMETRY Representatively for often used winding types, a so called zigzag arrangement of a disc-type winding was investigated (Fig.1). In such a case, winding discs are layered above each other, while so called spacers keep the axial distance between the discs and determine the height of the horizontal ducts for the oil. The sticks ensure the proper fixation of the spacers and keep the radial distance between the discs and the outer cover. The vertical ducts are formed by the space between discs and outer cover. The oil is leaded from the bottom into the vertical ducts and flows from there upwards, while it distributes into the particular horizontal ducts. To ensure a proper distribution of the oil to the horizontal ducts, which should be as equal as possible, the vertical duct is intermitted -alternating between the inner and the outer duct- after a specified number of discs by so called washers. This leads to an oil flow in a zigzag Pg. 1 Paper D-22

179 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg manner. Two washers with the discs in between form a so called pass (see also Fig.2). By putting a washer between each pair of discs, it would be possible to supply each disc with the same oil flow. On the other side, the thermal resistance between the conductors and the oil would be increased by these washers and the hydraulic resistance of the pass would also be increased enormously. Therefore the ideal number of discs between two washers is an optimization problem, which can be treated well with the approaches described below. winding. Since such a section is usually small, it was possible to keep its dimensions according to an example of a real transformer and therefore there was no need to apply laws of similarity to the measured data. Since for the first step only hydraulic data were of interest, the discs were made of transformer board according to the outer form of real discs. Washer Oil A A B B A - A Outer Vertical Channel Inner Vertical Channel Stick Horizontal Channel Disc Lexan Glass Oil Figure 2: Side view of the model One Pass B - B Disc Outer Vertical Channel Inner Vertical Channel Washer Stick Spacer Stick Horizontal Channel Spacer Figure 1: Investigated winding geometry. 3. HYDRAULIC MEASUREMENTS Figure 3: Front view of the model The hydraulic measurements were especially done to verify the results of the CFD-simulations since it is much easier to achieve results by simulation. A further advantage of the simulation is that there all data from everywhere in the flow field are available for postprocessing, whereas in measurements it is a large effort to get data only at a few points of interest. Lexan Glass Spacer The procedure of the hydraulic measurements is to take a model of a section of a transformer winding, into which a specified flow rate is impressed. This flow rate causes a pressure-drop along the flow path, which is measured at some points which are reachable without disturbing the flow significantly. Stick Figure 4: Top view of the model The model, which is used, represents a section of a real transformer winding according to Fig.2-4. Since a typical winding of a transformer repeats periodically in circumferential and axial direction, it is sufficient to investigate only such a section which also safes a lot of effort compared to the operation at a complete The pressures were measured at boundary points at the front side of the model as the difference between a reference port (Bin) at the beginning of the pass and the particular points of interest. These points are shown in Fig.5 which shows again the side view according to Fig.2. Pg. 2 Paper D-22

180 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg As sensors, inductive differential pressure transducers of the type DP103 from Validyne were used. The typical accuracy of the pressure measurements was around +-3%. Fout F6 Oil B6 means that the small wall effect of the spacers which bound the horizontal ducts in circumferential direction is neglected. This seems to be justified because of the large ratio between channel width and channel height. Moreover, modelling in 2D safes an enormous amount of computational effort and time. Since CFX does not have the explicit capability to treat problems in 2D, the approach for that is simply to model in 3D and to pull only one layer of 3D-elements into the circumferential direction. The boundaries in this direction get just a symmetry boundary condition instead of a wall boundary condition. F4 F3 F2 F1 Oil Figure 5: Scanning points for the pressure B4 B3 B2 B1 Bin As the material, a Newtonian fluid was chosen, where viscosity and density depend only on temperature. The flow field was declared as isothermal. Since the Reynolds-number was reliably low, no turbulence model was employed. The discretization was done with about 1.2 Mio. elements (Fig.7). For the inlet it was assumed that there is a fully developed channel flow with parabolic velocity profile, the outlet was closed by a zero staticpressure condition. The pressure is acquired according to the scheme of Fig.6 where it can be seen that each pressure transducer is switched between two channels. The data are permanently logged by the computer until steady state is reached. After that a new (known) flow rate is impressed. Computer Pressure Sensor (1) Pressure Sensor (6) Shortt Circuit Valve Shortt Circuit Valve Point A Point B Reference Point Winding Model Figure 6: Measurement arrangement 4. CFD SIMULATIONS 4.1. Description Numerical computer simulations were done with commercial CFD software. The computation was done with Ansys-CFX, which is a finite-volume based CFDsolver, while the mesh generation was done with ICEM-CFD. For the numerical simulation, the model was assumed as infinitely extended in circumferential direction. This Figure 7: Discretized section of the geometry 4.2. Validation of the simulations by measurements on winding models Since the distribution of the flow over the horizontal ducts of a path is one of the main quantities of interest, one would like to measure them in such a model. On the other hand it would take a large effort to measure these velocities directly with a high accuracy and reliability. Therefore it was chosen to measure the pressure distribution along the boundary of the vertical ducts, as described in the upper section. From these pressures only the pressure drop over the whole pass is of direct interest since it indicates the hydraulic resistance of the pass. The pressure values from the points in between serve just as a kind of fingerprint for verification i.e. when the pressure distribution at the boundary is equal to that of the CFD-simulation it Pg. 3 Paper D-22

181 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg seems to be justified to assume the CFD-model as verified. From that point on, only the CFD-model is needed to deliver all quantities of interest within the whole modelled domain. In Fig.8 the pressure drop over the whole pass is plotted in dependence of the impressed flowrate. Pressure difference Pa CFD with points shifted from each other Flowrate lmin Measured CFD with points shifted to each other Figure 8: Pressure drop over the whole pass (From Bin to Fout) Fig.8 shows quite small deviations between the measurements and the simulations. Although the model was erected quiet thoroughly, it was not avoidable that inaccuracies of +-1mm within larger dimensions could occur i.e. especially the positions of the pressure taps in vertical direction were unsure within that range. For this reason we extracted from the results of the CFDsimulation different curves for each of these points: One curve (red) where the measurement point is shifted 1mm downwards while the reference point (Bin in Fig.5) is shifted 1mm upwards, a further curve (blue) where the measurement point is shifted 1mm upwards while the reference point is shifted 1mm downwards. Between these two worst cases the measured curve will lie if the CFD-model is correct and the inaccuracy of the model for measurements is not larger as the mentioned +-1mm. It can be seen from Fig.8 that the results for the pressure drop over the whole pass are less sensitive for this shift. For the scanning points in between the situation looks different as Fig.9 shows. The measured values lie fully within the possible range but this rage is quite huge. This means that especially for high flowrates- it gets really difficult to deliver the proof that the lab model is equal to the numerical model due to the manufacturing inaccuracies of the winding model. It is to mention that the supposed unphysical progress of the lower curves in Fig.9 is to explain with a large separation eddy in the range of the respective scanning point. Pressure difference Pa CFD with points shifted from each other Measured Flowrate lmin Figure 9: Pressure drop from Bin to B6 CFD with points shifted to each other 4.3. Example of a pure hydraulic simulation In this simulation typical mineral transformer oil at a temperature of 77 C was assumed. The flowrates mentioned in the following are referring to the volume flow of only one section between two spacers with typical dimensions. As a main result, the distribution of the velocity in the horizontal ducts is displayed in Fig.10. The values M_i are the massflows through the particular horicontal ducts while M_mean is the value of M_i, averaged over all eight horizontal ducts. The lines between the points are just for better orientation. For this example case it is obvious, that the distribution of velocity is getting worse for increasing flowrate i.e. increasing Reynolds Number. Mainly the flow in the ducts at lower position is getting very small and can even return into backflow, how the distribution for 25l/min shows. In Fig.11 for the same example, the streamlines at a flowrate at 25l/min as typical in OD mode- are displayed. Especially at the upper ducts there are large separation eddies which are reducing their effective width. It is therefore obvious that simple decomposition of the pass into primitives as straight channels, branches and confluences, as it is proposed in [3] and [4], is only applicable for low Reynolds Numbers. For higher Reynolds Numbers, the boundary condition of a fully developed pipe flow at the interfaces of each primitive element of the pass, which is assumed for the most data available for primitive pipe elements in literature, is no more given. Therefore especially for such high Re-Numbers, as occurring in OD mode, the pass has to be regarded as a whole. This means no great effort in the case of using CFD-simulation. Pg. 4 Paper D-22

182 ISBN Proceedings of the 16 th International Symposium on High Voltage Engineering Copyright c 2009 SAIEE, Innes House, Johannesburg Flow Rate Distribution M_i/M_mean 5 4,5 4 3,5 3 2,5 2 1,5 1 0,5 0-0,5 2l/min 10l/min 25l/min Horizontal Ducts Numbered from Bottom of Pass Figure 10: Velocity distribution in the horizontal channels marked range is shown in Fig.13. The marked range was chosen for postprocessing since the upper and the lower vertical boundaries of the model were assumed as adiabatic like all outer boundaries. This was necessary since the little heat fluxes from the bounding upper and lower parts of the winding are unknown. The errors caused by these unwanted thermal boundary effects are minimal in the middle of the model. Washer Conductor Figure 12: Scheme of the thermal-hydraulic model Figure 11: Streamlines for a flowrate of 25l/min 4.4. Example of a coupled thermal-hydraulic simulation It is further possible to incorporate also the effects of heat conduction into the CFD simulation. This was done in the now presented case. The flow modelling and the discretization is similar to the former case. The now focused heat transfer requires also modelling of the thermal conductivity of the oil and the solid materials and the thermal capacity of the oil. Beneath that, the solid domains need to be discretized and the known loss distribution within the conductor volume has to be impressed. In the simulation the Navier- Stokes-Equations, which describe the flow, are solved simultaneously with the equations for heat transfer. In this example a loss density of 142 kw/m 3 (according to a current density of 2.6 A/mm 2 ) was impressed into the whole conductor volume. The assumed flowrate at the inlet was 1.7 l/min and the oil temperature at the inlet was 70 C. Fig.12 shows the scheme of the model while the resulting temperature distribution within the Figure 13: Temperature distribution The computation of this both-side coupled thermalhydraulic system leads to a strongly increased effort, especially because of much slower convergence due to the increased number of variables. Therefore it seems to be more promising to get the values of the heat transfer coefficient from the calculated velocities over empirical correlations and to verify this approach by a low number of simulations that include heat transfer. This is especially a practicable way for OD/OF-cases, where the buoyancy effects are often negligible compared to the pump driven oil flow and therefore the mutual coupling between thermal and hydraulic system can be simplified to a one-way coupling. Pg. 5 Paper D-22