Steady State and Transient Thermal Analysis of Switched Reluctance Machine

Transcription

1 Steady State and Transient Thermal Analysis of Switched Relctance Machine E. Annie Elisabeth Jebaseeli and S. Paramasivam Abstract This paper presents the two dimensional (-D) steady state and transient thermal analysis in Switched Relctance machine (SRM) to observe actal heat distribtion in the parts of the machine sing finite element method. Electromagnetic losses which form the heat sorce is calclated taking into consideration both skin effect and proximity effect. A -D steady state analysis is carried ot to observe the temperatre distribtion and maximm temperatre for wide range of speed and load conditions. From the analysis it is fond that the maximm temperatre is reached in the speed range of 1500 rpm. The load corresponding to maximm temperatre is taken as initial condition for the transient thermal analysis. From the transient analysis, heat distribtion at varios load steps and the time to reach the steady state are observed. Simlation reslts for a 6/4 SRM are presented nder steady state and transient conditions. As a reslt, thermal analysis plays a great significance for the long term stability of the machine. Index Terms Core loss, copper loss, finite element analysis, switched relctance machine, thermal analysis. I. INTRODUCTION ith the increasing pressre on the design of energy saving electrical machines, a new trend has come to carry ot thermal analysis along with the traditional Electromagnetic field analysis. The Electric crrents and friction in an electric machine generate heat. Hence temperatre of different parts of the machine rise which cold case deterioration of inslation in windings [1], thermal stress, efficiency redction and this may lead to motor failre. Also nder high loads, temperatre rise inflences the machine electrical and magnetic parameters []. It is therefore necessary to maintain the temperatre of the machine components within permissible limits for safety operation [3]. So the temperatre rise analysis of Switched relctance machine is implemented in this paper. For accrate calclations, the effect of electromagnetic losses and the heat transfer mechanisms are discssed. Heat transfer coefficients are calclated based on two conditions sch as iron-otside air and iron- inside air convection. This paper in its Section II deals with electromagnetic losses estimation and the thermal analysis of Switched relctance machine. The simlation reslts nder steady state and transient conditions are presented in section III for a 6/4 SRM whose specifications are given in Table I. Section IV incldes the conclsive remarks. Manscript received September 13, 01; revised October 4, 01. E. Annie Elisabeth Jebaseeli is from Sathyabama University, Chennai, India ( annjeba@yahoo.co.in). II. THERMAL ANALYSIS OF SITCHED RELUCTANCE MACHINE Sbmit yor manscript electronically for Modern thermal analysis can be classified into three methods [4] namely 1) Experimental method ) Lmped parameter thermal model method 3) Nmerical analysis method Experimental method is sitable for already designed and fabricated machine to decide the precise cooling strategy based on its thermal behavior. Bt accracy is less in the case of complex geometrical machine strctres and the non-linear characteristics of the materials. In Lmped thermal model method, thermal problem is solved sing thermal networks analogos to electrical circits. It involves many assmptions and a simplified form of empirical formla. The reslt shows only the overall distribtion of the temperatre of the motor bt does not show the point of internal temperatre [5]. To design energy-saving Electrical machines, nmerical analysis is one of the most promising technologies. Most commercially available nmerical analysis compter programs se finite element method. No assmptions are made regarding flx path or related empirical factors. A field soltion can be obtained even with time-variable fields and with materials that are non-homogeneos, anisotropic or non linear. A. Heat Sorce The two main components of electromagnetic losses in Switched relctance Machine are core losses in the laminations and copper losses in the windings. These losses are the heat sorce in a thermal analysis [6]. For any motor the copper losses can be calclated from the I R prodcts, where R is the effective resistance of one phase winding. De to Skin and proximity effects, the vale of R is greater than the DC resistance. hen an electromagnetic wave interacts with a condctive material, mobile charges within the material oscillates with the freqency similar to the impinging fields. This constittes an alternating electric crrent, the magnitde of which is greatest at the condctor srface. The decline in crrent density with depth is known as the skin effect and the skin depth is a measre of the distance over which the crrent falls to 1/e of its original vale. The vale of eddy crrents in a separated condctor depends on the proximity of the condctor to the steel core. In addition, the magnetic field created by any single condctor inflences other condctors which are called proximity effect. Considering the above, the expression for the calclation of copper losses in the switched relctance 794

2 machine taking into accont the fndamental and n higher harmonic components of the phase crrent [7] is given by n I k dn. w 4nL 1 dn. R DC sk + pk k 1 δk 3 δk P c Ns (1) where dn. w sk δ k is the factor which acconts for the losses de to the skin effect, d. n w pk δ k is the factor which acconts for the losses de to the proximity effect, 1 T ik dt I k T 0 is the root mean sqare vale of the k-th harmonic crrent δk is the skin depth in copper of the k-th harmonic crrent. Core losses in switched relctance machine are relatively low bt in high speed applications they become the dominant component of the total losses. Prediction of core loss is difficlt becase the flx waveforms are non-sinsoidal and have different shapes with varios freqencies for different parts of the magnetic circit. Ths sing a modified Steinmetz eqation core loss can be calclated as α 1 β pfe fsincm feq B () fsin 1 c, α, β are the coefficients sed in the where T, m conventional Steinmetz eqation.based on the above expressions losses are calclated from [8] and listed in Table I. TABLE I: RESULTS OBTAINED FROM THE SIMULATION FOR THE CORE AND COPPER LOSSES Rotational speed (rpm) Average crrent (amps) Copper loss (watts) Core (watts) loss B. Geometrical Model A two dimensional (-D) model is shown in Figre. 1. hose specifications are given in Table II. The model consists of (a) stator of machine (b)stator windings(c) rotor (d)air and (e) shaft. TABLE II: SPECIFICATIONS OF 6/4 SRM Nmber of stator phases 6 Nmber of rotor phases 4 Stator oter diameter(m) Rotor oter diameter(m) 0.06 Shaft length(m) Air gap length(m) Corresponding to the physical dimensions given in Table III and from the core and copper losses of the machine, qantity of heat generation Q is calclated for different parts like stator core and coils and are presented in Table IV. A finite element heat rn [9] is simlated with the vale of Q 3 (watts/ m ) which is the main heat sorce. TABLE III: PHYSICAL DIMENSIONS OF 6/4 SRM Area of the coil segment 134 E-006 sq.m Total coil area Shaft Length Volme of coil Area of the stator Volme of the stator 1608 E-006 sq.m 85.E-003 m E-009 c.m 4640 E-006 sq.m E-009 c.m TABLE IV: QUANTITY OF HEAT GENERATION Speed in rpm Heat generation in coil (watts/m 3 ) Heat generation in core (watts/m 3 ) 500.7E E E E E E E-013.E E-013.4E-013 Fig. 1. Geometrical model of 6/4 SRM Fig.. -D Finite element model of SRM 795

3 In finite Element Analysis, to increase the accracy, a fine sbdivision of the strctre is carried ot with finite elements of smaller dimension. In practice several types of elements are sed depending pon the geometrical shape of the region nder consideration. In two dimensional problems, the elements sed are triangles, rectangles and qadrilaterals. In this method, loss analysis is carried ot by finite element analysis and the reslts can be applied to the temperatre analysis. Using these reslts as the heat sorce, the temperatre rise is estimated. A -D Finite element model of SRM is shown in Fig.. In this model, plane55 element is sed for analysis. The model is meshed with two dimensional qadrilateral element and fine discretization is done at the expected high gradient area of the machine. In the above model, the element has for nodes with a single degree of freedom and temperatre at each node. The element is applicable to a -D steady state or transient thermal analysis. The element can also compensate for mass transport heat flow from a constant velocity field. If the model containing the temperatre element is also to be analysed strctrally, the element shold be replaced by an eqivalent strctral element, which can be sed for copled field analysis also. Thermal parameters listed in Table V are reqired for the prediction of the temperatres in the electrical machine [10]. Material TABLE V: THERMAL PARAMETERS Thermal Condctivity (w/m K) Density (Kg/m3) Copper Steel Air III. SIMULATION RESULTS ANALYSIS A. Steady State Thermal Analysis In steady state analysis, condctive heat transfer with varios bondary conditions is obtained from the Forier law as 1 T 1 T T kr + k k q r r r r θ θ Ζ Ζ 1) Heat transfer by convection Liqid and gas particles near heated body become lighter and rise, giving way to cooler particles which in trn get heated and rise. Ths de to changes in flid density, natral convection takes place. This takes place on the external hosing of the machine. In modern machines heat is removed by forced convection. The sal method is by blasting air on heating srfaces. In convection the rate at which heat is removed is governed by Newton s Law (3) P ht ( 1 T ) A (4) where (T 1 T ) is the temperatre difference between the srface being cooled and the cooling medim. The vale of convection heat transfer coefficient h depends on viscosity, thermal condctivity, specific heat and other properties of the coolant. ith the help of empirical expressions, an estimation of the coefficients is possible. The set of dimensionless nmbers sed in the calclation of convection heat transfer coefficients are [11], [1]. Reynolds nmber where Re ρν L ρ 3 -flid density(kg m ) 1 1 -flid dynamic viscosity ( kgs m ) 1 ν - flid velocity ( ms ) L- characteristic length of the srface(m) Grashof nmber βgθρ L Gr 3 where β -coefficient of cbical expansion of flid ( 0 C -1 ) g - gravitational force of attraction ( ms ) θ - temperatre difference between srface and flid ( 0 C) Prandtl nmber P r c where c specific heat capacity of flid ( JKg C ) thermal condctivity of flid ( m C ) Nsselt nmber N hl Nsselt nmber is often sed for the calclation of the 1 convection heat transfer coefficient h ( m C ) h L For natral convection the general form of convection correlation is N N a( GrPr) b (5) (6) (7) (8) (9) (10) For forced convection the general form of convection correlation is N where a, b and c are constants. b a( R ) (Pr) e c (11) 796

4 Gr. Pr Ra is the Rayleigh nmber. In a forced convection system the vale of Re jdges if there is laminar or trblent flow. It is identified by Gr. Pr prodct in natral convection system. 5 For laminar flow (Re<5 x10 ) and (0.6 <Pr< 50) 5 10 ) For trblent flow (Re >5 x If the flid velocity is larger then trblence is indced. In this case, heat transfer is increased de to efficient mixing of hot and cold air. The ambient temperatre was set as 30 0 C and a steady state analysis was carried ot. From figre 3, it is clear that at 1000 RPM maximm temperatre of 50.0ºC. occrs in the internal coil which is de to higher copper loss. At steady state, the temperatre rise de to copper loss depends on the crrent passing throgh the coil and the convective coefficients. As load increases, say at 000 RPM, core loss has higher vale than the copper loss. Hence maximm temperatre in the internal coil gets redced to 43.70ºC de to lesser amont of heat generation. Table VI is the smmary of steady state thermal analysis performed on the machine. In the steady state analysis, the temperatre increases and reaches the maximm temperatre of 50.5ºC. at 1500 RPM.This region is considered as initial condition and Transient thermal analysis was carried ot. 1 T 1 T T T kr k k + q ρc + + rr r r θ θ Ζ Ζ t (1) where q is the heat sorce which is sbstitted by the losses. Frame, stator yoke and rotor core of Switched relctance machine can be considered as hollow cylinders. Stator teeth and rotor teeth are considered as partial hollow cylinders with stator and rotor to be laminated. Also, the bondary conditions are condctive heat transfer from the body and the axial shaft at two ends. Natral Convection is considered on stator external srface. Internal srfaces are sbjected to have forced convection de to the rotation of the rotor. The bondary conditions are at t 0, the machine has atmospheric temperatre t >0, the temperatre increases de to heat generation in the machine. Fig. 4. Temperatre distribtion after 10 seconds Fig. 3. Steady state temperatre distribtion at 1000 rpm TABLE VI: RESULTS OF STEADY STATE THERMAL ANALYSIS FOR VARIOUS SPEED Speed (RPM) Maximm Temperatre(ºC) B. Transient Thermal Analysis In Transient thermal analysis, temperatre varies with respect to time [13]. In a hollow cylinder containing heat sorce, Condctive heat transfer with varios bondary conditions is obtained from the Forier law[14] in cylindrical coordinate as Fig. 5. Transient temperatre-time crve In the Transient thermal analysis, the time taken by the machine to reach steady state temperatre can be fond ot. The reslts of simlation showing temperatre variation from 0 to 1000 seconds is shown in the Table VII. It is observed that after 10 seconds the temperatre has increased only in the coil wond on the stator and then gradally increases in the stator pole. Figres 4 and 5 represent the reslts of transient thermal analysis. It shows that steady temperatre is reached after 10 seconds. Hence heat distribtion within the components of the machine with respect to time can be analysed accrately with transient thermal analysis. 797

5 TABLE VII: RESULTS OF TRANSIENT THERMAL ANALYSIS Time (seconds) Maximm Temperatre (ºC) IV. CONCLUSION In electrical machines, the inslation life time varies inversely with the working temperatre. Hence to improve the machine performance and its reliability, a thermal analysis is carried ot by -D finite element analysis nder steady state and transient conditions. It is observed that a maximm temperatre of 50 ºC is obtained after 10 seconds. So, the machine has a temperatre rise within the permissible limits. Based on this, the weight of the materials sed and the nmber of prototypes bilt can be minimised. REFERENCES [1] S. Inamra, T. Sakai, and K. Sawa, A Temperatre Rise Analysis of Switched Relctance Motor De to the Core and Copper Loss by FEM, IEEE Trans. Magn, vol. 39, no. 3, pp , May 003 [] Balamrgan and P. Smathi, Analysis of Temperatre Rise in Switched Relctance Motor De to the Core and Copper Loss by Copled Field Finite Element analysis, International conference on Power System Technology, pp , November 004. [3] D. S. B. Fonseca, C. M. P. Cabrita, and M. R. A. Calado, Thermal Modelling and characterization of Electrical achines and calclation of crrent ratings, Forth IET conference on power electronics, Machines and Drives, pp , April 006 [4] K. Vijayakmar, R. Karthikeyan, S. Paramasivam, R. Armgam, and K. N. Srinivas, Switched Relctance Motor Modeling, Design, Simlation,and Analysis: A Comprehensive Review, IEEE Trans. Magn, vol. 44, no. 1, pp , December 008. [5] H. Sn, J. Gao, Y. Dong, and Yi Zheng, Analysis of Temperatre Field in Switched Relctance Motor Based on Finite- element, 11th international conference on Electrical Machines and systems, pp , Oct [6] J. Faiz, B. Ganji, C. E. Carstensen, K. A. Kasper, and R.. D. Doncker, Temperatre Rise Analysis of Switched Relctance Motors De to Electromagnetic Losses, IEEE Trans. Magn, vol. 45, no. 7, Jly 009. [7] A. Matveev, Development of Methods, Algorithms and Software for optimal design of Switched relctance drives, Doctoral Thesis, Eindhoven Technische Universiteit, Eindhoven, 006. [8] P. O. Rasmssen, Switched Relctance Design and Simlation-Thesis version. [9] K. N. Srinivas and R. Armgam, Thermal Characterization Throgh Finite Element Analysis of the Switched Relctance Motor, IEEE Region 10 International conference on Electrical and Electronics technology, pp , vol., 001. [10]., J. B. Dnlop, S. J. Collocott, and B. A. Kalan, Design optimization of a Switched Relctance Motor by Electromagnetic and Thermal Finite-Element Analysis, IEEE Trans. Magn, vol. 39, no. 5, pp , September 003. [11] D. A. Staton and A. Cavagnino Convection Heat transfer and Flow Calclations Sitable for Electrical Machines Thermal Models, IEEE trans. Indstrial Electronics, vol. 55, no. 10, 008. [1] D. A. Staton and A. Cavagnino, Convection Heat transfer and Flow Calclations Sitable for Analytical Modelling of Electrical Machines, IEEE Annal conference on Indstrial Electronics, pp , Nov 006. [13] K. N. Srinivas and R. Armgam, Analysis and Characterization of Switched Relctance Motor: Part II- Flow, Thermal, and Vibration Analyses, IEEE Trans. Magn, vol. 41, no. 4, April 005. [14] H. Rohani, J. Faiz, and C. Lcas, Lmped thermal model for Switched Relctance Motor applied to mechanical design optimization, J. Mathematical and compter modelling, pp , 007. Machines. E. Annie Elisabeth Jebaseeli received her B.E degree in Electrical and Electronics Engineering from Madrai Kamaraj University, Tamilnad, India in 1993 and M.E degree from Sathyabama University, Tamilnad, India in 004. In 1998 she joined in the department of Electrical and Electronics Engineering and working as a Assistant professor in Sathyabama University, India. Her Research interest is modeling of Electrical S. Paramasivam received his BE from GCT, Coimbatore, in 1995 and ME from PSG College of Technology, Coimbatore in 1999 and his Ph.D in Electrical Engineering from Anna University, Chennai, India. He is the Assistant General Manager, ESAB Engineering Services Pvt. Ltd., Chennai, India. His research interest inclde power Electronics, special machines analysis, drives and control. 798