Applied Thermal Engineering

Applied Thermal Engineering 30 (2010) 1133 1139 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng Effect of sun radiation on the thermal behavior of distribution transformer Ebrahim Hajidavalloo *, Mohamad Mohamadianfard Mechanical Engineering Department, Shahid Chamran University, Ahvaz, Iran article info abstract Article history: Received 16 September 2009 Accepted 22 January 2010 Available online 1 February 2010 Keywords: Solar radiation Transformer Sun shield Lifetime Load ratio Performance and life of oil-immersed distribution transformers are strongly dependent on the oil temperature. Transformers, working in regions with high temperature and high solar radiation, usually suffer from excessive heat in summers which results in their early failures. In this paper, the effect of sun radiation on the transformer was investigated by using experimental and analytical methods. Transformer oil temperature was measured in two different modes, with and without sun shield. Effects of different parameters such as direct and indirect solar radiation on the thermal behavior of the transformer were mathematically modeled and the results were compared with experimental findings. Agreements between the experimental and numerical results show that the model can reasonably predict thermal behavior of the transformer. It was found that a sun shield has an important effect on the oil temperature reduction in summer which could be as high as 7 C depending on the load ratio. The amount of temperature reduction by sun shield reduces as the load ratio of transformer increases. By installing a sun shield and reducing oil temperature, transformer life could be increased up to 24% in average. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction * Corresponding author. Tel.: +9 373532; fax: +9 611 3336642. E-mail address: hajidae_1999@yahoo.com (E. Hajidavalloo). Oil temperature has important effects on the long time performance of oil-immersed distribution transformer. The oil temperature depends on various parameters including load rate, insulation type of the winding, cooling fluid, cooling method and ambient conditions. In countries with very high temperature and strong solar radiation in summers, oil temperature may increase over its maximum permissible limit. This increase can considerably reduce insulation life of the transformer. The increasing number of transformer failure reported in hot summer days confirms this argument. Based on the Mont Singer formula, for each C increase in working temperature, insulation life reduces to half [1]. t ¼ t 0 2 ðt T 0Þ=DT ð1þ In this equation, DT =,t 0 is transformer life and T 0 is temperature at normal condition which for class A insulator are 10 years and 105 C, respectively. To solve the overheating problem, transformer manufacturers recommend that permissible load ratio of transformers should be reduced where they are used in the hot regions. This approach is not the best solution since it lowers the transformer capacity and therefore more transformers should be used to compensate the capacity reduction. Another approach introduced in this article is installing the sun shield above the transformer in order to prevent it from direct solar heating. If installing a sun shield around a transformer considerably reduces the amount of solar heat, it would reduce the oil temperature and therefore, the transformer can work at its nominal capacity. To support this simple idea, it is required to understand the role of solar radiation and ambient temperature on the thermal behavior of distribution transformers under various conditions by proper experimental or analytical methods. Although the effects of solar radiation in many industrial applications have been investigated, there is limited research to address the effect of sun radiation on the transformer heating. Schlabbach [2] studied the effect of solar shield on the performance of power transformers by using an analytical method based on the energy balance equation and concluded that shielding the transformer against solar radiation is a suitable method to increase the permissible load ratio, especially in countries with high ambient temperature and solar radiation. His analysis shows that the solar radiation contributes to the transformer heating in a range of 5 25% depending on the rating of the transformer. Pradhan and Ramu [3] attempted to assess hot spot temperature of a large transformer with a reasonable degree of accuracy. They developed a theoretical model based on the boundary value problem of heat conduction equation in transformer winding using finite integral transformer techniques. They concluded that their model could precisely predict hot spot temperature. El Wakil et al. [4] used a numerical method to study heat transfer and fluid flow inside an element of a 3-phase 40 MVA power transformer and came up with some suggestions which can enhance the cooling rate of transformer. Godec and Sarunac [5] studied a 40 MVA transformer and proposed that by installing a pump between the tank and the radiator body, the output efficiency can be improved. 1359-4311/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.01.02

1134 E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 Nomenclature A area (m 2 ) c specific heat (W m 1 K 1 ) D fin space (m) G sc solarconstant (W m 2 ) h heat transfer coefficient (W m 2 K 1 ) H fin height (m) I n nominal current (A) k load ratio ( ) k thermal conductivity (W m 1 K 1 ) k T hourly clearness index L fin length (m) n day number ( ) Nu H Nusselt number ( ) Pr Prandtl number ( ) q solar radiation (W) Q heat loss (W) r s ratio of shadow area to fin area (ohm) Ra H Rayleigh number ( ) R b ratio of radiation on tilt to horizontal surface ( ) T temperature (K) t time (s) V volume (m 3 ) x distance (m) Greek symbols a solar altitude (rad) a thermal diffusivity (m 2 s 1 ) a surface absorption ( ) b tilt angle (rad) b expansion coefficient (K 1 ) e emissivity ( ) c s Azimuth angle (rad) q mass density (kg m 3 ) q reflection coefficient ( ) m kinematics viscosity (m 2 s 1 ) h z Zenith angle (rad) r Stefon Boltzman coefficient (W m 2 K 4 ) Subscripts a air dir direct ind indirect h horizontal gr ground si internal surface so outer surface sk sky w wall Despite a few studies which have addressed the effect of solar radiation on the power transformer, there is no significant research to address the effect of solar radiation on the thermal behavior of distribution transformer. In this paper, experimental and analytical methods were used to estimate the effect of solar radiation on the performance of a distribution transformer at high ambient temperatures. Knowing the share of solar energy in transformer heating will help to decide if a sun shield should be used around the transformer or not. 2. Experimental set-up Experimental tests were performed in Ahvaz, a city located in South of Iran. Ahvaz climate is characterized by high temperatures up to 52 C and high solar radiation of 1 kw/m 2 in the summer months. In order to consider the effect of real ambient condition, an existing transformer connected to the power network with 15% load ratio was used in the experimental tests. It has nominal power of about 500 kv A and was manufactured by Iran Transfo Company. Since the transformer was connected to the network, it was not possible to vary the load ratio due to practical reasons. Figs. 1 and 2 show different views of the transformer used in this study. It has 10 and 24 fins in its width and length, respectively. The sun shield was made from plain wood. Three windings, as shown in Fig. 2, are located inside the transformer and are made of copper. A digital thermometer (Testo 175-T 3) with two K-type thermocouples was used to measure the temperatures. One of the probes was installed inside the thermo-well which was located on the roof of the transformer to measure the oil temperature and the other probe was installed in the oil tank. Data were recorded every 5 min and stored in the memory of the thermometer during the test period. solar radiation for 26 days (from 2th May to 22th June). At the second mode, a sun shield was installed around the transformer and measurements were performed for 27 days (from 1st to 2th July), so there was no direct sun radiation on the transformer in this mode. For comparison of the data at two modes, we used only the days which had similar weather temperature and clearness indices. Fig. 3 and Table 1 show weather conditions of two typical days which were used for comparison of transformer data at the two modes. As can be seen, there is no major difference in weather conditions. Fig. 4 compares the transformer oil temperature at these two days. As shown, the oil temperature under shadow mode is considerably lower than the normal mode. The maximum temperature difference is around 7 C. Fig. 5 compares the transformer oil temperature at two other days which had the same weather condition and clearness index. As shown in this figure, the oil temperature under the shadow mode is considerably lower than the normal mode and maximum difference is around 6.5 C. These figures show that the maximum 3. Experimental findings Experimental tests were conducted at two different modes on the transformer. At the first mode, the transformer worked under Fig. 1. Schematic view of transformer with solar shield.

E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 1135 Fig. 2. Top view of transformer (units are in millimeter). Fig. 4. Experimental temperature of transformer oil at roof with and without sun radiation. Fig. 3. Air temperature variation at June 1st and July 6th 200 in Ahvaz. Fig. 5. Experimental temperature of transformer oil at roof with and without sun radiation. temperature difference between the two modes occurs at around 2:00 3:00 PM. For other similar days, the oil temperatures at both modes were compared and it was found that the oil temperature under the shadow mode is considerably lower than the normal mode. Maximum oil temperature difference measured in the similar days is shown in Fig. 6. This figure also shows the maximum oil temperature difference of transformer at both modes in offload condition at the top two rows. As it is clear, the temperature difference was increased when the transformer is in offload condition. Offload measurements were carried out on a similar transformer located on the ground. 4. Mathematical modeling of the components Having found the experimental results, the next step was to develop a reasonable model to predict transformer behavior under different conditions and to compare the results with the experimental ones for validation. If the validation process is carried out successfully, the model can be used to predict the transformer behavior at other ambient conditions. 4.1. Transformer electrical heating The transformer losses consist of two parts, iron losses Q Fe and copper losses Q Cu. Iron losses depend on the voltage and are considered to be constant as they are independent of the transformer loading. Copper losses Q Cu are not constant (Eq. (2)) and depend on the square of the current load. Q Cu is usually measured in factory and given to the consumer at load ratio of 70%. Q Cu ¼ R t ðk I n Þ 2 In this equation, k is load ratio, I n is the nominal current in the winding and R t is total resistance of windings. If the variation of winding resistance with temperature is neglected, the total transformer loss is [1]: Q loss ¼ Q Fe þ Q Cu 4.2. Solar radiation model The hourly solar radiation data were generated by using the mean monthly clearness index [6,7]. The direct and indirect radia- ð2þ ð3þ Table 1 Comparison of weather conditions of June 1st and July 6th 200 in Ahvaz. Date Max. temp. ( C) Min. temp. ( C) Avg. temp. ( C) Horizontal view (m) Transformer mode 1 June 200 46.0 2.0 37.7 Min. 300 m With shield Usually 6000 m 6 July 200 37. 2.0 45.0 Min. 3000 m Without shield Usually infinity

1136 E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 H s H ¼ 1 d sin b þ cos b cos b þ sin b cos c s = tan a L s L ¼ 1 jsin c s j l tan a d sin b þ cos b cos b þ sin b cos c s = tan a ðþ ð9þ In above equations d = D/H c, l = L/H c, and H c = H sin b. The ratio of shadow area to fin area is: r s ¼ H sl s HL ð10þ The amount of direct radiation on a fin q diri is: Fig. 6. Maximum temperature difference of experimental data due to installation of sun shield. tions were considered to be absorbed by transformer external surfaces. The total solar input is: q solar ¼ q dir R b þ 0:5 q ind ð1 þ cos bþþq gr ðq dir þ q ind Þ 0:5ð1 cos bþ where the direct solar radiation q dir, the indirect solar radiation q ind, and hourly solar radiation on horizontal surface q h were calculated from the following equations [7]: q dir ¼ q h q ind q >< 1:0 0:249k T for k T < 0:35 ind ¼ 1:55 1:4k T for 0:35 < k T < 0:75 q h >: 0:177 for k T > 0:75 360n q h ¼ G sc k T 1 þ 0:033 cos cos h z 365 The value of k T, hourly clearness index, is used from Ref. [6]. Since there are many fins on the external body of the transformer, it is required to consider the effect of each fin shade on the adjacent fin in order to calculate the exact exposed area of direct and indirect radiation as shown in Fig. 7. The ratio of shadow height (H s ) to the fin height (H), and the ratio of shadow length (L s ) to the fin length (L) are as follow []: ð4þ ð5þ ð6þ ð7þ q diri ¼ q dir ð1 r s Þ 4.3. Thermal modeling and governing equations ð11þ Since in this study the effect of solar radiation on the average oil temperature inside the transformer was of primary importance, a lump capacity model for oil was used to predict the effect of different parameters on its thermal behavior. The energy equation for oil in the transformer can be written as: X 6 i¼1 h i A i ðt i T oil Þþ _ Q loss þ X6 i¼1 e w rt 4 si ¼ qcv @T oil @t ð12þ The wall thickness is 1.5 mm and to predict the transformer wall temperature, one-dimensional heat conduction equation was used because the thickness to the width ratio is very small. Four nodes were considered in each side of the transformer wall as shown in Fig.. The heat conduction equation is as follows: @ 2 T @x ¼ 1 @T 2 a @t The energy equation for internal surfaces of transformer is: h s ðt oil T si Þ k @T si @x e wrt 4 dx @T si si ¼ qc 2 @t ð13þ ð14þ The first term stands for wall convection with oil, the second for conduction and the third for wall radiation loss to the oil. The energy equation for external surfaces is: h a ðt a T so Þ k @T so @x þ h skðt sk T so Þþh grs ðt gr T so Þ þðq solar Þa so ¼ qc dx 2 @T so @t ð15þ The first term stands for wall convection with air, the second for conduction, the third and fourth for radiation heat transformer with sky and ground, respectively, and the fifth term stands for absorption of the sun radiation. Fig. 7. View of the shadow on the transformer fins. Fig.. Schematic view of nodes in the transformer wall.

E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 1137 4.4. Convection heat transformer coefficients To solve the governing equations, it was required to calculate the convection coefficients for internal and external surfaces of the transformer. For internal surfaces, only natural convection exists. Since there are two different geometries, two different correlations of natural convection should be used; one for main body surfaces with oil and second for fin surfaces with oil. For the main body surfaces with oil, a correlation for rectangular cavity which has one cold and one warm wall were used because the same pattern of oil flow circulation exits inside the transformer between main body as a cold surface and the winding body as a hot surface. The correlation is [9]: 0:2 0:09 Pr Nu H ¼ 0:22 0:2 þ Pr Ra L H H for 2 < H L < 10; Pr < 10 5 ; Ra H < 10 13 ð16þ Fig. 9. Comparison of experimental and numerical temperature of transformer oil working under sun radiation in 3rd of June 200. For convection between fin surfaces and oil, a correlation for natural convection inside vertical channel, with fully developed flow, was used because the distance between fin surfaces is very small (1 cm) and the thermal entrance length is very short compared to the fin height. The correlation is [10]: Nu H ¼ gbd3 ðt s T 1 Þ 24am ð17þ External surfaces have both forced and natural convection with air. Forced convection was assumed for the west, the roof and the floor surfaces, since the dominant wind direction is from the west with wind velocity of 6 km/h. For other external surfaces natural convection was used. Eq. (17) can still be used for natural convection between external surfaces of adjacent fins with air. For external surface of the main body with air, vertical natural convection coefficient was used as follows [9]: 92 >< 0:37Ra 1=6 >= H Nu H ¼ 0:25 þ h i =27 ð1þ >: 1:0 þð0:492=prþ 9=16 >; Fig. 10. Comparison of experimental and numerical temperature of transformer oil under shadow mode in 4th of July 200. Having all coefficients calculated, numerical method based on the implicit finite difference technique was used to solve the governing equations and to find temperatures at different points of the transformer. 5. Comparison of numerical with experimental results Fig. 9 shows the result of oil temperature prediction by numerical model and compares it with the experimental data for a day that the transformer worked under the sun radiation. Fig. 10 shows the same results but for the day when the transformer worked under the sun shield, without direct sun radiation. It can be seen that the numerical and experimental results are in good agreement and the difference between them is negligible. Fig. 11 shows the percentage of maximum error between the numerical results and the experimental results for different days which were used in calculation. This value was calculated by using the maximum difference between numerical and actual results divided by actual result. Fig. 12 shows the average error between numerical and actual results. The average error was calculated by finding the difference between numerical and actual results divided by actual result for all 24 h a day and taking average of them. The highest local error is 9.6% and the highest average error is 3.7%. Since the errors between the numerical results and experimental results are acceptable, it can be concluded that the model can reasonably predict the thermal behavior of the transformer under different conditions. Fig. 11. Maximum percentage of local error between experimental and numerical results. Fig. 12. Maximum percentage of average error between experimental and numerical results.

113 E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 6. Transformer thermal behavior prediction After validation of the model, it could be used to predict thermal behavior of the transformer at different conditions. As mentioned before, the load ratio of transformer under the test was 15% but the load ratio of many transformers used in the power distribution network may be much higher than the 15%. The model can be used to predict thermal behavior of the transformer under the higher load ratio. Fig. 13 shows the predicted oil temperature for different load ratio as 25%, 50%, 70% and 100%. As expected, increasing the load ratio increases the oil temperature considerably, and at full load ratio the oil temperature reaches 107 C. Although increasing the load ratio decreases the effect of sun radiation and consequently the temperature difference between the two modes reduce, there is still considerable difference between oil temperatures at the two modes as seen in Fig 14. It seems that there is no linear relation between load ratio increase and temperature difference reduction. As seen, at high load ratio considerable oil temperature difference is realized. Fig. 14. Temperature difference created by installation of a sun shield in different load ratio. 7. Prediction of transformer lifetime increase Transformer lifetime can be calculated by using Monte Singer equation (Eq. (1)). As it clear, the transformer lifetime mainly depends on its temperature. Since the effect of sun shield on the transformer temperature varies at different days of a year and at different hours of a day, it is required to calculate transformer life based on the variable temperature at different time intervals. For example, if a transformer works at temperature T 1 for a period of s 1 and at temperature T 2 for a period of s 2, then the average reduction time can be calculated as: t s 1 þ s 2 ¼ s 1 s 1 þ s 2 2 ðt1 T0Þ þ s 2 s 1 þ s 2 2 ðt2 T0Þ ð19þ To simplify the calculation, a representative day was used for each month, and hourly temperatures were obtained for that day, using mean monthly data of the city. The detail method for calculating lifetime under variable temperature can be found in Ref. [1]. Fig. 15 shows percentage of transformer lifetime increase due to using sun shield at different load ratio. For example, the lifetime of transformer without sun shield at full load ratio is around 4.15 years, which is increased to 5.10 years if sun shield is used. This is about 22% increase in lifetime. Taking average values of Fig 15, it can be said that as a rule of thumb, transformer lifetime increase by using the sun shield is approximately about 24%. The cost of installing the sun shield on the transformer is very low because it has very simple construction and does not need any expensive equipment. It is estimated that the cost of sun shield would be around 3% of the transformer cost. Therefore, it seems that using the sun shield around the transformer in region with high solar radiation has important effect on the lifetime increase. Fig. 13. Predicted temperature of transformer oil at different load ratios.

E. Hajidavalloo, M. Mohamadianfard / Applied Thermal Engineering 30 (2010) 1133 1139 1139 important effects on the oil temperatures. When load ratio increases the effect of sun radiation on the transformer decreases, however, the relation is not linear. Analysis of transformer life shows that installing a sun shield increases the lifetime about 24% in average. Since the cost of using a sun shield is relatively low, it is recommended to use a sun shield in regions of high solar radiation. Acknowledgement The authors would like to thank Ahvaz Electric Distribution Company for technical and financial support of this research. Fig. 15. Percentage increase in the lifetime of transformer as a result of sun shield installation.. Conclusions It is well known that excessive temperature is a primary factor in reducing transformer life and performance. A sun shield was proposed to prevent the transformer from extra heat absorption of the sun. Experimental tests were performed at two different modes to measure the effect of sun radiation. A mathematical model was developed to simulate the effect of different temperatures and solar radiations on the transformer behavior. The results of the numerical simulation agreed with the results of the experimental tests on the transformer at different conditions with and without the sun shield. The average percentage error of the results was about 3.6% which indicates that the modeling process is valid and can accurately predict thermal behavior of the transformer. The results show that installing a sun shield on the transformer has an important effect on reducing the oil temperature as high as 7 C. It was also found that load ratio of the transformer has References [1] R.K. Agarwal, Principles of Electrical Machine Design, third ed., S.K. Kataria & Sons, Delhi, 1997. [2] J. Schlabbach, Improvement of Permissible Loading of Transformer by Solar Shield, EUROCON 2003 Ljubljana, Slovenia, pp. 305 309. [3] M.K. Pradhan, T.S. Ramu, Prediction of hottest spot temperature (HST) in power and station transformers, IEEE Transformer Action on Power Delivery 1 (4) (2003). [4] N.El. Wakil, N.C. Chereches, J. Padet, Numerical study of heat transfer and fluid flow in a power transformer, International Journal of Thermal Sciences 45 (2006) 615 626. [5] Z. Godec, R. Sarunac, Steady-state temperature rise of ONAN/ONAF/OFAF transformer formers, IEEE Proceedings-C 139 (5) (1992) 44 454. [6] M. Bahadorinejad, S. Mirhoseini, Air clearness coefficient for Iran several cities, in: 3th Congress of Optimal Fuel Consumption in Building, Tehran, Iran, 2003, pp. 603 615. [7] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Process, John Wiley & Sons, New York, 190. [] K.A. Joudi, N.S. Dhaidan, Application of solar assisted heating and desiccant cooling system for a domestic building, Energy Conversion and Management 42 (2001) 995 1022. [9] A. Bejan, Convection Heat Transfer, second ed., John Wiley & Sons, New York, 1995. [10] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, third ed., Wiley, New York, 1990.