A Compaison Between Electical Cicuit and Finite Element Modeling Methods fo Pefomance Analysis of a Thee-Phase nduction Moto unde oltage Unbalance A. Ebadi*, M. Mizaie* and S. A. Gholamian* Abstact: nduction moto is the most popula load in the industy, it is vey impotant to study about the effects of voltage quality on induction moto pefomance. One of the most impotant voltage quality poblems in powe system is voltage unbalance. This pape evaluates and compaes two methods including finite element method (FEM) and equivalent electical cicuit simulation fo investigation of the effects of voltage unbalance conditions on the pefomance of a thee- phase induction moto. Fo this pupose, a theephase squiel cage induction moto is simulated using Finite Element Method and equivalent electical cicuit paametes of the FEM model is estimated by genetic algoithm. Then, some unbalanced voltages ae applied on the FEM model of the Moto and the esulted powe and losses ae compaed with calculated values using equivalent electical cicuit simulation in same voltage conditions. Keywods: Thee-Phase nduction Moto, Finite Element Method, Genetic Algoithm, UF, Unbalanced oltage. 1 ntoduction1 Powe system unbalance, due to uneven distibution of single-phase loads in thee-phase powe systems, asymmetical tansfome winding impedances, open-y, open-δ tansfome banks, incomplete tansposition of tansmission lines, blown fuses on thee-phase capacito banks and so on, has been botheing many powe companies [1]. Theefoe, pefomance analysis of equipments in powe systems unde voltage unbalance condition is impotant. Because of vaious techno-economic benefits, nduction Motos (Ms) ae widely employed in industial, commecial and esidential applications fo enegy convesion puposes. Based on U.S. Depatment of enegy, industial motos consume 70% of electicity, and induction motos ae almost 80% of the loads in a typical industy []. Although an induction moto is designed and built to wok in balanced condition most of them ae connected diectly to the electic powe distibution system and they ae exposed to unbalanced voltages and consequently, the pefomance evaluation of thee-phase induction moto unde voltage unbalance conditions is vital. anian Jounal of Electical & Electonic Engineeing, 01. Pape fist eceived 9 Aug. 011 and in evised fom 17 Ma. 01. * The Authos ae with the Depatment of Electical and Compute Engineeing of Babol Univesity of Technology, P. O. Box 484, Babol, an. E-mails: a.ebadi@stu.nit.ac.i, mizaie@nit.ac.i, gholamian@nit.ac.i Accoding to above desciption, many authos attempt to evaluate unbalanced voltage opeation of motos thoughout last centuy. n a classic pape published in 1954, equations fo calculating the positive- and the negative-sequence paametes of the induction machine wee pesented by Williams that may be used in the equivalent electical cicuit to analyze machine pefomance unde voltage unbalance conditions [3]. Effects of unbalanced voltages on the efficiency [4], deating in the machine [5], incease of losses, and the undesiable effects on the insulation life [6], and life eduction due to tempeatue ise [7, 8] ae some othe contibutions in this aea. Note that, up to now, most of the authos have used expeimental test and/o Fotescue symmetical component developed by Williams fo pefomance analysis of induction motos unde unbalanced voltage. Also Finite Element Method as a poweful tool has been used to simulate electical machines in ecent yeas. n fact, high accuate electical machine pefomance simulation by this method is possible just in pesence of advanced computes. This pape evaluates and compaes two mentioned simulation methods including Finite Element Method and the equivalent electical cicuit (classic method) fo the pefomance analysis of thee-phase induction moto. Achieving this aim, a. kw, 380 thee-phase squiel cage induction moto has been simulated using Maxwell 1.1 softwae based on FEM [9], and paametes of the equivalent electical cicuit of the 188 anian Jounal of Electical & Electonic Engineeing, ol. 8, No., June 01
simulated model is estimated using genetic algoithm. Also powe and losses of the machine ae calculated unde voltage unbalance using FEM and equivalent electical cicuit and then the esults ae compaed. Simulation using Time-Stepping FEM n this section, a thee-phase squiel cage induction moto is simulated using finite element and its pefomance unde balanced and ated voltage is analyzed..1 Analysis Model Fig. 1 and Table. 1 show the meshed quate coss section of the analyzed moto and its bief specifications, espectively.. Time-Stepping D FEM n this wok, time-stepping FEM is used fo the Table 1 Technical data of the M tem alue tem alue Rated oltage () Rated Output Powe (W) 380 Connection Y 00 Stato oute diamete (cm) Roto oute diamete (cm) Coe length (cm) Fequency (Hz) 50 9 Rated cuent (A) 5.3 9 Powe facto 0.8 Ai gap (cm) 0.03 Rated speed All laminations M530-1410 (pm) type 50A Pole numbe 4 tuns No. in stato coil 44 15 analysis of the magnetic field. Fo the time-stepping FEM, time step should be fixed and the input voltage should be defined at each time step. The govening equation fo two-dimensional (-D) FE analysis is given by [10, 11]: 1 A 1 A da J 0 (1) x x y y dt n above equation, µ is the pemeability, A is the component of magnetic vecto potential, σ is the conductivity of the mateials, and J 0 is the exciting cuent density of the stato winding. The voltage equation pe each phase is: d d a a R L () dt dt a a a e whee a, a, R a, Ф a and L e ae the input voltage, the cuent, the esistance, the flux linkage of each phase and the end-coil inductance, espectively. Note that, L e is calculated using RMxpt toolbox in Maxwell 1.1..3 Calculation of the Coppe Loss The stato winding and the conducto ba losses ae calculated using FEM. The conducto ba loss (W R ) can be Calculated as follows [10, 11]: W R E. s. L R (3) A B (4) B A E (5) t t in which, B, E, σ and Δs.L ae magnetic flux density, Electic field intensity, the oto ba conductivity and an element volume in the conducto bas, espectively..4 Calculation of the Coe Loss Accoding to taditional ac machine theoy, ion loss in watts pe kilogam can be calculated in each element using Eq. (6) and theefoe total ion loss would be obtained fom the summation of ion losses in the all elements. P P P K fb K f B (6) c h e h m e m n the above equation, P h and P c ae espectively, hysteesis loss component and eddy cuent component, both in watts pe kilogam. B m and f ae the peak value of the flux density and the fequency, espectively. K h, K e and α ae constants povided by the manufactue. Fig. 1 Meshed model of the M..5 Dynamic Mechanical Equation of the Machine The dynamic mechanical equation of machine is [1]: Ebadi et al: A Compaison Between Electical Cicuit and Finite Element Modeling Methods 189
d T T J B LOAD m (7) dt n ode to ealize the vaiations of the load unde voltage unbalance conditions, a linea load toque with the following equation has been consideed as the load: T FL T LOAD (8) ated n Eq. (8), T FL is full load toque, ω ated, ω ae speed and ated speed of the machine, espectively..6 Simulation Setting Tansient solve with step time equal to 10-4 s has been used in simulations and quate coss section of moto is meshed with 9688 of tiangles. Simulation of each cycle (0.0 s) consumed 36.3 seconds of time in a compute with 3 GHz coe Duo CPU and Giga Byte of DDR Ram. t must be noted, Coe magnetic behavio has been consideed to nonlinea magnetic cuve fo M 530-50A lamination. 3 Results unde Rated oltage Condition The distibution of the magnetic flux density (in steady state) and the stato cuents unde ated condition esulted by FEM simulation ae shown in the Figs. and 3, espectively. The calculated input and output powes, losses, powe facto, ms value of the cuent and oto speed ae tabulated in Table.. Note that, all mentioned values ae fo steady state condition. By compaison the calculated values of the output powe, the cuent, the powe facto and the oto speed and the consideing ated values of the machine ( that ae shown in Table. 1), it can be seen the simulated model is accuate enough to use. t must be noted that the stay loss is ignoed in all calculations at this wok. 4 Paamete Estimation using Genetic Algoithm n this section the needed fitness function fo paamete estimation of the simulated moto is obtained and it has been minimized using genetic algoithm. Fig. 3 The steady state distibution of the magnetic flux density unde ated voltage condition. Table The calculated steady state esults by FEM unde ated voltage condition. Stato cuent (A) 5.156 Powe facto 0.796 nput powe (W) Stato coppe loss (W) 700.45 319.9 Coe loss (W) Roto coppe loss (W) Speed (pm) Output powe (W) 33.41 137.3 1406.6 189 4.1 Fitness Function Detemination Fig. 4 shows the induction moto equivalent cicuit. Thee ae five unknown paametes in this cicuit, namely: stato leakage eactance X s, coe loss esistance R c, magnetizing eactance X m, oto leakage eactance X and oto esistance R. Note that, the stato esistance o R s is assumed to be detemined accoding to Eq. (). The used objective function in this wok is the aveage eo of the input cuent s, the input active powe P in, the input eactive powe Q in, the coe loss P Coe and the oto coppe loss P CU, i.e.: f 100 1 sfem sec sfem (9) f P P 100 P infem inec infem (10) f Q Q 100 Q 3 infem inec infem (11) Fig. Stato winding cuents unde ated voltage condition. Fig. 4 nduction moto equivalent cicuit. 190 anian Jounal of Electical & Electonic Engineeing, ol. 8, No., June 01
f P P 100 P 4 CoeFEM CoeEC CoeFEM (1) f P P 100 P 5 CU FEM CU EC CU FEM (13) Note that, indexes of FEM and EC shows the calculation method of mentioned values, i.e., the Finite Element Method and the Electical Cicuit. t must be noted that the values esulted fom Finite Element Method can be found in Table. Based on above desciption, the fitness function to minimize is: (a) Eo 5 f (14) i 1 i 4. Genetic Algoithm The genetic algoithm is a method fo solving both constained and unconstained optimization poblems that is based on natual selection, the pocess that dives biological evolution. The genetic algoithm epeatedly modifies a population of individual solutions. At each step, the genetic algoithm selects individuals at andom fom the cuent population to be paents and uses them to poduce the childen fo the next geneation. Ove successive geneations, the population "evolves" towad an optimal solution. 4.3 Fitness Minimization using Genetic Algoithm The fitness function is minimized using GA tool in MATLAB envionment. To un the GA tool, a population of 1000 individuals was selected. Cossove facto is set to 0.8 and selection method is oulette wheel. The othe genetic opeatos have been selected accoding to default setting in GA tool. Note that, constains of the paametes ae as follows: X 3., s 000R 5000, c 70X 75, m (15) 5X 7,.5R 3. The estimated paametes of the machine ae shown in Table. 3. These paametes can be employed in positive- and negative-sequence electical cicuit of the studied induction moto. 5 A Compaison of Two Methods Afte a eview on symmetical component theoy at this section, two mentioned simulation methods including Finite Element Method and the equivalent electical cicuit fo the pefomance analysis of theephase induction moto unde voltage unbalance ae compaed. Table 3 The estimated paametes by genetic algoithm. X s (Ω) R c (Ω) X m (Ω) X (Ω) R (Ω).41 345.14 70.869 5.035 3.008 Fig 5 Equivalent electical cicuits (a) positive-sequence (b) negative-sequence. 5.1 Symmetical Component Theoy Analysis of a thee-phase induction moto opeating unde unbalanced voltage using symmetical component theoy equies positive- and negative-sequence equivalent cicuit, as it is shown in Fig. 5. Each cicuit pefoms both positive- and negativesequence cicuits. The load esistance defined by positive- and negative-sequence slips is the only diffeence between the cicuits. Positive- and negativesequence slips ae s 1 = s and s =- s, espectively. Slip s is: n n s s (16) n whee n s is synchonous speed and n is oto speed. Let sa, sb, and sc ae the phase voltages of the stato. The coesponding zeo-, positive-, and negativesequence voltages ( s0, s1, and s3 ) ae given by s0 1 1 1 sa 1 s1 1 a a sb 3 (17) s 1 a a sc j /3 whee a e is the Fotescue opeato. Note that, EC definition fo voltage unbalance o voltage unbalance facto (UF) can be calculated as follows: UF s 100 (18) S 1 Consideing mentioned equivalent cicuits, phase stato and oto cuents must be used to calculate the stato and the oto losses. The phase cuents ae detemined by pefoming the tansfomation back. Tansfoming the stato and oto cuents using the Fotescue matix can be seen in Eqs (19) and (0), espectively. (b) Ebadi et al: A Compaison Between Electical Cicuit and Finite Element Modeling Methods 191
sa 1 1 1 s 0 1 a a sb s 1 (19) 1 a a sc s a 1 1 1 0 1 a a b 1 (0) 1 a a c n Eqs. (19) and (0), thee ae non zeo-sequence cuents ( s0 = 0 =0) because of the moto connection in delta o ungounded wye. Based on the above desciption, the stato and oto coppe losses of the moto ae: CU s s sa sb sc P R (1) CU a b c P R () The coe loss can be calculated with: 3 P Coe e1 e (3) Rc Finally, input active powe of the moto (P in ) and its impue output powe (P out ) ae: the input powe inceases by aising UF. nceasing of the stato and the oto coppe losses with UF inceasing can be seen in Fig. 7. Accoding to Fig. 8, vaiation of the coe loss in voltage unbalance condition with the same positivesequence voltage is negligible. Regula eduction of efficiency by inceasing UF can be seen in Fig. 9. Based on these Figues, the esults deived fom two methods ae too close, but fo the oto coppe losses, (%) 10.5 10 101.5 101 100.5 100 99.5 99 nput powe-fem nput powe-ec Output powe-fem Output powe-ec 0 1 3 4 5 6 UF(%) Fig. 6 nput/output powes unde unbalanced voltages. * * P 3Re in s 1 s 1 s s (4) 1 s 1 P P P 3 R out 1 1 s1 3 1 s s R (5) 15 10 115 (%) 110 105 Stato coppe loss-fem Roto coppe loss-fem Stato coppe loss-ec Roto coppe loss-ec 5. Pefomance Analysis of the M unde oltage Unbalance Conditions Fo the puposes of this pape EC definition of voltage unbalance has been selected to be used. But this is clea that thee ae many unbalanced voltages with the same UF [13]. Theefoe, hee the aveage teminal voltage of the machine and thei positivesequence component ae consideed to be equal to the ated voltage and the UF vaies fom 1% to 6% [14]. By applying these voltages, pefomance of the machine is analyzed using FEM simulation and equivalent electical cicuit method, and then esults of two methods ae compaed in this section. alues of calculated input/output powes, coppe losses and coe loss using two methods unde mentioned voltages ae shown as chats in Figs. 6, 7 and 8, espectively. Note that, esults of powe and losses fo unbalanced conditions have been nomalized with the coesponding values fo the balanced condition (FEM esults). Accoding to Fig. 6, two methods pedict the output powe unde mentioned unbalance conditions expeiences negligible eduction by inceasing UF and 100 95 0 1 3 4 5 6 UF(%) Fig. 7 Coppe losses unde unbalanced voltages. 10 Coe loss-fem Coe loss-ec 101 100 (%) 99 98 97 96 95 Fig 8 Coe loss unde unbalanced voltages. 19 anian Jounal of Electical & Electonic Engineeing, ol. 8, No., June 01
(%) 81.5 81 80.5 80 79.5 79 78.5 Efficiency-FEM Efficiency-EC 0 1 3 4 5 6 Fig. 9 Efficiency unde unbalanced voltages. the diffeence is elatively moe than othes which is due to eo duing the paamete estimation pocess egading to esults in balanced conditions (UF=0%). 6 Conclusion n this wok, Equivalent Electical Cicuit and Finite Element Method as two modeling methods of theephase induction moto simulation have been studied and compaed based on its pefomance analysis unde voltage unbalance. Also in ode to have a justly compaison, the used electical cicuit paametes have been estimated by Genetic Algoithm using balanced voltage condition FEM esults. Thus, this estimation ensues that simila esults can be achieved by both methods unde balanced voltage. Studying of calculated powe, losses and efficiency of machine unde diffeent unbalanced voltage conditions using Electical Cicuit and FEM show the fact that appoximately same and closed esults can be achieved by two methods. Sue, FEM esults include moe details, but it is a complicated and time consuming method compaed to Electical Cicuit simulation. Totally, Equivalent Electical Cicuit Simulation is moe appopiate to analyze opeating pefomance of thee-phase induction machine unde unbalanced voltages because of its moe simplicity, lowe simulation time and elatively suitable accuacy. Acknowledgment The authos would like to thank M. Rahmani and M. Setaeh (R&D management office of Motogen Copoation, Tabiz, an) fo poviding data of the studied thee-phase induction moto. Refeences [1] Jouanne A. von, and Banejee B., Assessment of oltage Unbalance, EEE Tansactions on Powe Delivey, ol. 16, No. 4, pp. 78-790, Oct. 001. [] Souto O., Oliveia J., and Neto L., nduction motos themal behavio and life expectancy unde nonideal supply conditions, Ninth ntenational confeence on Hamonics and Quality of Powe, ol. 3, pp. 899-904, Oct. 000. [3] Williams J. E., Opeation of 3-Phase nduction Motos on Unbalanced oltages, AEE Tans., ol. 73, pt. -A, pp. 15 133, Jan. 1954. [4] Lee C. Y., Effects of Unbalanced oltage on the Opeation Pefomance of a Thee-phase nduction Moto, EEE Tansactions on Enegy Convesion, ol. 14, No., pp. 0-08, June 1999. [5] Anwai M. and Hiendo A., New Unbalance Facto fo Estimating Pefomance of a Thee- Phase nduction Moto With unde and Ovevoltage Unbalance, EEE Tansactions on Enegy Convesion, ol. 5, No. 3, pp. 619-65, Sept. 010. [6] Pillay P. and Manyage M., Loss of Life in nduction Machines Opeating With Unbalanced Supplies, EEE Tansactions on Enegy Convesion, ol. 1, No. 4, pp. 813 8, Dec. 006. [7] Gnaci nski P., Windings Tempeatue and Loss of Life of an nduction Machine Unde-oltage Unbalance Combined With Ove- o Undevoltages, EEE Tansactions on Enegy Convesion, ol. 3, No., pp. 363-371, June 008. [8] Gnacinski P., Effect of unbalanced voltage on windings tempeatue, opeational life and load caying capacity of induction machine, Enegy Convesion and Management, ol. 49, No. 4, pp. 761 770, Apil 008. [9] Ansoft, Maxwell Softwae, esion 1.1. [10] Ebadi A., Mizaie M. and Gholamian S. A., Employing Finite Element Method to Analyze Pefomance of Thee-Phase Squiel Cage nduction Moto unde oltage Hamonics, Reseach Jounal of Applied Sciences, Engineeing and Technology, ol. 3, No. 10, pp. 109-113, Oct. 011. [11] Lee J. J., Kim Y. K., Nam H., Ha K. H., Hong J. P. and Hwang D. H., Loss Distibution of Thee- Phase nduction Moto Fed by Pulsewidth- Modulated nvete, EEE Tansactions on Magnetics, ol. 40, No., pp. 76 765, Mach 004. [1] Kause P.C., Analysis of Electic Machiney, McGaw-Hill, 1986, New Yok. [13] Faiz J., Ebahimpou H. and Pillay P., nfluence of Unbalanced oltage on the Steady-State Pefomance of a Thee-Phase Squiel-Cage nduction Moto, EEE Tansactions on Enegy Convesion, ol. 19, No. 4, pp. 657 66, Dec. 004. [14] Ebadi A., Mizaie M. and Gholamian S. A., Toque Analysis of Thee-Phase nduction Moto Unde oltage Unbalance Using D Fem, ntenational Jounal of Engineeing Science and Technology, ol. 3, No., pp. 871-876, Feb. 011. Ebadi et al: A Compaison Between Electical Cicuit and Finite Element Modeling Methods 193
Ali Ebadi was bon in Sai, RAN, in 1984. He eceived his B.Sc. and M.Sc. degees both in Electical Engineeing fom Noshivani nstitute of Technology, Univesity of Mazandaan, Babol, an in 007 and Babol Noshivani Univesity of Technology, Babol, an in 011, espectively. His eseach inteests include Powe System Analysis, powe electonics and its applications in powe systems and simulation and modeling of electical machines. Mohammad Mizaie was bon in GhaemShah, an in 1975. He Obtained B.Sc. and M.Sc. Degees in Electical Engineeing fom Univesity of Shahid Chaman, Ahvaz, an and an Univesity of Science and Technology, Tehan, an in 1997 and 000 espectively and PhD Degee in Electical Engineeing fom an Univesity of Science and Technology in 007. He woked as an Assistant Pofesso in the electical and compute engineeing faculty of Babol Univesity of Technology since 007. His eseach inteests include life management of high voltage equipments, high voltage engineeing, intelligence netwoks fo intenal faults assessment in equipments and studying of insulation systems in tansfomes, cables, geneatos, beakes, insulatos, electical motos and also ovehead tansmission lines. Sayyed Asgha Gholamian was bon in Babolsa, an, in 1976. He eceived his B.Sc. degee in electical engineeing fom K.N.Toosi Univesity of Technology, Tehan, an in 1999 and M.Sc. degee in electic powe engineeing (electical machines) fom univesity of Mazandaan, Babol, an in 001. He also eceived the Ph.D degee in electical engineeing fom K.N.Toosi Univesity of Technology, Tehan, an in 008. He is cuently an assistant pofesso in the depatment of Electical and Compute Engineeing at the Babol Univesity of Technology, Babol, an. His eseach inteests include powe electonic and design, simulation, modeling and contol of electical machines (moto, geneato and tansfome). 194 anian Jounal of Electical & Electonic Engineeing, ol. 8, No., June 01