Loss Minimization in an Induction Motor Driven by a Voltage-Source-Inverter

Aian J. Energy Environ., Vol. 3 Iue 1-, (00), pp. 53-78 Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter S. Sujitjorn and K-L. Areerak School of Electrical Engineering, Suranaree Univerity of Technology Nakhon atchaima, Thailand 30000. arawut@cc.ut.ac.th (eceived: 15 January 00 Accepted : 15 Augut 00) Abtract: Energy aving via lo minimization in an induction motor ha been known for year. The concept i ometime introduced eparately from the drive mechanim. Conventionally, mot of the method utilize approximated machine model; ome aume known parameter that are difficult to meaure or etimate. Thi article decribe power lo minimization in mall induction motor driven by voltage-ource inverter. It i hown that numerical computing i the effective approach to obtain optimum excitation voltage and frequency ubject to load torque variation uch that loe are minimized. The method employ the motor parametric model with accurately known parameter, i.e. reitance and inductance of the tator and the rotor, repectively. The article decribe an eay-toconduct experiment to capture the motor peed-torque characteritic Copyright 003 by the Joint Graduate School of Energy and Environment 53

S. Sujitjorn and K-L. Areerak that in turn are ued for parameter identification via genetic algorithm. The propoed method of lo minimization i ueful under variable load torque condition. It uefulne and limitation are dicued with experimental reult hown. Keyword : power lo minimization, induction motor, genetic algorithm, energy aving Introduction Small three-phae induction motor have been widely ued in indutrie for everal decade. Their drive technology utilize variou type of inverter. The drive mot commonly found employ voltageource inverter (VSI) to achieve the contant v/f, the fixed-v/variablef, and the variable-v/variable-f cheme, repectively. Such drive can produce controlled characteritic that are ueful for indutrial application. Additionally, the inverter i conidered a an efficient mean to ave energy in the electrical drive. However, more energy aving are till poible with power lo minimization incorporated into the drive control cheme. Lo minimization of electric drive may follow two main route: (1) lo minimization for ome predefined peed profile, and () lo minimization at every teady-tate peed and torque required. The former i dominant in railway and traction application. The latter, that i the main interet of thi paper, i ueful for a variety of 54 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter indutrie. Under the aumption of contant motor parameter, and equal tator and rotor frequencie, the exciting frequency to minimize loe in ac machine can be found. The method i effective in a narrow region of operation where the lip i around 1. Furthermore, the motor parameter change with frequencie leading to ome error in derived expreion for lo minimization thereof. Significant energy aving could be achieved providing motor parameter are accurately known. Thi method i very limited becaue the required parameter are difficult to meaure or etimate. At light load, ignificant energy aving are poible via field-oriented control. The inertion of an external impedance to improve the power factor of the rotor circuit i effective for wound-rotor induction motor at the expene of the I lo. In addition, thi approach caue harmonic into the ytem, and care mut be taken to guarantee atifactory tranient repone. Modification of the contant v/f inverter commercially available to attain the minimum lo operating point i poible via perturbing rotor frequency. The cheme require no knowledge of motor parameter and i uitable for nonlinear load uch a fan and pump. Minimizing lo in induction motor via optimum input voltage and frequency when aturation, kin effect, and ource harmonic are taken into account i alo poible. However, thee factor are very difficult to meaure or predict in practice. The major work in thi area utilize flux control to minimize loe. Artificial intelligence technique have been applied to identify optimum flux a well a to control flux and magnetizing current for Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 55

S. Sujitjorn and K-L. Areerak lo minimization. The d-q lo model ha been propoed for lo minimization in variou type of dc and ac motor. It i the central idea of the preent work that the factor rendering lo minimization mut be eaily controlled. Since the work i propoed for the VSI induction motor drive, to control the excitation voltage and frequency i therefore the main tak. egarding the lo minimization objective, the motor parameter, i.e. reitance and inductance of the tator and the rotor, of the teady-tate model mut be accurately known. We propoe that thee parameter be identified from the actual peed-torque characteritic obtained from imple experiment. We apply the genetic algorithm (GA) to identify the parameter that appear to be nonlinear function of the excitation voltage. The term repreenting the core loe can be obtained from the no-load and the blocked-rotor tet. With our propoed lo expreion, it i poible to calculate the optimum excitation voltage and frequency that minimize loe at all time correponding to the load torque variation and peed demand. In term of implementation of the lo minimization controller, one may conider either real-time and on-line calculation or a viewable table approach to earch for the optimum excitation. The choice depend on the performance of the hardware ued. Thi paper i organized into four ection, including the introduction. In the material and method ection, we have included 56 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter an explanation on the motor equivalent circuit, identification of it parameter, a review of the genetic algorithm (GA), lo expreion and an approach to lo minimization. The experimental reult, advantage, and limitation of the propoed method are alo dicued can be found under the ection on reult and dicuion. The lat ection provide our concluion. Material and Method Motor equivalent circuit and parameter Mot portion of motor loe arie during teady-tate operation. Thu, an equivalent circuit of the motor play an important role in lo minimization. For a mall three-phae induction motor, the electrical model hown in Figure 1 i widely accepted. The hunt branch appear at the input terminal becaue it impedance i large compared to the tator impedance. eferring to Figure 1, i lip, while i and L i are motor parameter. Thee parameter are aumed contant conventionally and obtained from the no-load and the blocked-rotor tet. ealitically, only the core lo term repreented by c and L m may aume contant value. c =3.3114 kω, and L m =0.5098 H are obtained from the conventional tet for our lip-ring induction motor of 4 pole, 1500 rpm ynchronou peed, 1.5 hp, 380 V rm, 50 Hz rating. The other parameter vary according to excitation voltage and frequency, temperature, aturation characteritic, harmonic and kin effect. From the practical viewpoint, it i more Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 57

S. Sujitjorn and K-L. Areerak convenient to conider the parameter a the function of excitation voltage while the other effect are lumped within. Our aumption i acceptable becaue the motor parameter are baed on the true peed-torque characteritic. The reulting nonlinear function repreenting the parameter lead to a fine treatment of lo minimization. tator rotor L r Lr - V in, ω in c V m - Lm I r (1 - ) r Figure 1. Equivalent circuit of an induction motor. To obtain accurate parameter require obervation of the true motor characteritic and offline identification. Figure depict the equipment et-up for monitoring the motor peed-torque curve. Thi work utilize GA for identification and it i reviewed herewith. The propoed method lead to impler modelling and identification, a well a the eay addition of an energy aving controller for the motor. Ocillocope Tacho 3φ 380 V rm (line) 3φ IM 50 Hz Tranformer T m T L Variable load torque torque tranducer Figure. Experimental et up for obervation of motor peed-torque characteritic. 58 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Genetic algorithm (GA) GA i one of the efficient earch method baed on the principle of natural election. It ha been uccefully ued a a tool for optimization problem in broad field uch a engineering, economic, etc. GA can provide approximate olution for multivariable optimization problem. It ha alo been applied uccefully to identify the parameter of induction motor. To apply GA appropriately, the problem mut firtly be converted to a criterion function called fitne function. Thi function repreent the performance of the ytem. The higher the fitne value, the better the performance. GA conit of three main procedure, namely; election, genetic operation and replacement, repectively. Generally, at the firt tep, GA tart a random election of population from the population et. Then the fitne evaluation i invoked. The retained population mut pa the minimum requirement of the fitne evaluation while the ret i dicarded. Thee retained member are then parented to produce offpring. All the parent and offpring have to go through the proce of fitne evaluation again and only the trong one are retained. Thee trong member are then ued a replacement to the tartup population. Following thi, parenting reoccur and the proce i repeated until the fittet member or optimum olution i found. More detailed information regarding GA may be found in the literature. A brief ummary of the contruction of GA i a follow: Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 59

S. Sujitjorn and K-L. Areerak 1) Define chromoome: For an optimization problem, the parameter to be earched have to be defined a parameter tring. Thee tring can be coded a binary or real and are called chromoome. ) Define the fitne function: The fitne function i the performance index of GA ued to reolve for acceptable olution. The deign of the fitne function can be baed on the problem requirement, e.g. error, convergent rate, etc. 3) Generate initial population: The initial population of N et are generated randomly with the ize of N choen arbitrarily. 4) Generate next generation or top: To generate the next generation, GA ue the operation of reproduction, croover and mutation. A top criterion mut be defined uch a a number of repetitive loop, acceptable error, etc. Identification To obtain the parameter of the equivalent circuit require true motor characteritic. Some experiment were conducted on the tet bed depicted in Figure to capture the motor peed-torque characteritic. Line-to-line voltage of variou rm value are fed to the motor and the peed-torque characteritic recorded. Some of the tet reult are illutrated in Figure 3 where the voltage value are lineto-line. The jagged curve hown in Figure 3 repreent the oberved motor characteritic. The mooth curve are obtained from calculation baed on the equivalent circuit model. In GA term, the 60 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter motor parameter, r, L, and L r are defined a chromoome. In order to have an efficient GA earch, ome initial aumed olution and earch boundarie fed into the earching routine are particularly ueful. The reult obtained from the conventional tet of the motor are uitable for initial aumed olution with earch boundarie given. The conventional tet yield = 6.4333 Ω, r = 4.1178 Ω, and L = L r = 0.089 H. Figure 3. Motor characteritic. The earch boundarie are : 7-15 Ω, r : 4.5-7.5 Ω, L and L r = 0.039-0.0446 H, repectively. eolution of the earch for each parameter i 30 bit. Thee parameter are concatenated to form a ingle chromoome of 10-bit reolution. After random election of Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 61

S. Sujitjorn and K-L. Areerak the initial population, they are converted to real value and ubjected to the fitne tet. The fitne function i given by where Fitne function 1 = ε (1) N e(i) i= 1 ε = N () The error term e(i) i defined by. T a i the actual torque obtained from meaurement. i the etimated torque expreed by Tˆ [Tˆ (i) - Ta (i)] Tˆ V = ω ( ˆ ˆ r / ˆ r / ) ( Xˆ Xˆ r ) (3) where,, and any ymbol with repreenting Xˆ = πf L Xˆ r = πf Lr etimated value. At each trial of the earch, the torque i etimated according to the equation (3), and the error calculated. The cloer the value of the etimated torque to the actual torque, the higher the fitne value. The earch top at 3,000 count. The error convergence i monitored through the earching proce. One example howing the convergence of error to zero during the earch i depicted in Figure 4. 6 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Mean quared error kth Generation Figure 4. Convergence of etimation error during the earch by GA. Thi cae i for the 160 Vrm line input Voltage. Figure 5 illutrate the etimated motor parameter compoed of tator and rotor reitance and inductance, repectively. Figure 5(a) depict the tator and rotor reitance, while the inductance are depicted in Figure 5(b). Table 1 give the detail of correponding numerical data. The data exhibit nonlinear relationhip to the exciting line voltage, that are, in thi work, repreented by the cubic pline approximation. Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 63

S. Sujitjorn and K-L. Areerak (a) reitance(ω) --- tator reitance o --- o rotor reitance line-to-line voltage(vrm) (b) inductance(h) --- tator inductance o --- o rotor inductance line-to-line voltage(vrm) Figure 5. Identified motor parameter (a) reitance, (b) inductance. 64 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Table 1. Numerical data reulting from GA identification for variou voltage. line-to-line (Ω) r (Ω) L (H) L r (H) voltage(vrm) 60 14.8863 4.7375 0.048 0.0441 100 14.818 5.4533 0.048 0.0359 140 11.4050 6.107 0.0396 0.0317 180 10.110 6.4891 0.0356 0.0357 0 11.0193 6.119 0.038 0.098 80 8.6603 6.638 0.040 0.065 Lo expreion and approach to minimization In electrical machinery, tator, rotor, and core loe dominate the overall power loe. Stray, friction and windage loe exit, however they are mall enough to be conidered negligible. When drive i brought into play, converter loe exit and can be lumped into tator lo. In thi cae, the total power loe of the motor can be expreed a P lo, total = tator copper lorotor copper locore loe. Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 65

S. Sujitjorn and K-L. Areerak 66 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 Equation (4) decribe the power loe mathematically where Decription of thee parameter are in the nomenclature. The reitance and inductance of the tator and the rotor, repectively, in the above relation can be ubtituted by numeric value reulting from cubic pline interpolation. Furthermore, the torque of an induction motor can be expreed by From the equation (4) and (10), one can realize that (4) / V V I I P c T m r T m T m c m r r total lo, = = (9) N N N lip and (8), (7) L f j L f j (6) L f j (5) L f j m m m 1 1 T m c m c m r r 1 = = π π = π = π = (10) 1 V P T r T m ag ω = ω = (11) T P c r m m r total lo, ω =

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Equation (11) i a ueful model for implementing lo minimization in an induction motor. It how that the total power loe depend on load torque, ynchronou peed, motor peed, exciting voltage and frequency. The analyi i imple, yet the lo model can cope with the machine nonlinear characteritic via the accurately identified parameter. Figure 6. Surface plot of the total power loe in an induction motor driven by a VSI a a function of peed, exciting voltage, frequencie, and contant load torque at 0.45 p.u. With uitable ubtitution of the impedance in the equation (11), one can compute the power loe accurately. A an example of the reult, Figure 6 illutrate the urface plot of the loe. Sliding urface can be noticed a the peed varie. The illutration how clearly that ome particular frequencie yield minimum power lo Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 67

S. Sujitjorn and K-L. Areerak line. Thee frequencie can be computed accordingly. Thi computing approach i more attractive than conventional differentiation to find the minimum point becaue the conventional method reult in a very high order polynomial. In practice, reduced order via ome approximation i unavoidable. Thi could eventually introduce a coniderable amount of error to practical reult. eult and Dicuion eferring to Figure 6, the urface plot of the total power loe reveal the poibility of minimum lo attainment. Thi figure i of the cae 0.45 p.u. load torque. Similarity in the hape of thee urface can be aumed for different load. The rpm value indicated in the figure repreent the teady-tate peed demanded. The urface lide upward in accordance with the increae in peed. The amount of total power loe alo varie due to change in line-to-line voltage (rm) excitation. Still, minimum lo line can be found for each cae at a pecific exciting frequency. eferring to the equation (11), the load torque T i known from meaurement or etimation, the motor reitance and inductance are obtained from identification and the ynchronou peed i alo known. In term of implementation, real-time computing baed on thi equation to obtain optimal exciting voltage and frequency i poible. The optimal excitation will reult in minimum power lo according to individual peed command. Offline calculation with a viewable table 68 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter approach i alo an alternative. The real-time computing approach require a high performance proceor for implementation. The viewable table approach need only a low-cot proceing unit with omewhat more complicated programming. The olution of optimal excitation can be ued to intruct ome witching device to drive the motor. Furthermore, the propoed method of lo minimization can be viewed a the adaptive algorithm of an energy aving controller for the ac drive. Simulation ha become a tool to ae the uefulne and limitation of the propoed method. Simulation run were conducted for varied load (0-50 % full-load) and peed (600-1800 rpm). Figure 7 illutrate the imulation reult that provide a comparion of three drive cheme in term of total power loe. Thee cheme are v/f contant, fixed voltage with varied frequency and the propoed method, repectively. The rating of the motor under tet are 380 Vrm, 1.5 hp, 50 Hz, 4 pole, and 1500 rpm ynchronou peed. eferring to Figure 7, the voltage parameter hown therein are lineto-line. Figure 7(a) and (b) how that the propoed method i the mot efficient approach to minimize loe in induction motor with light load, e.g. 0.15 and 0.3 p.u., repectively. When the load torque i up to about half the manufacturer rating, the propoed method i till efficient a can be een from Figure 7(c) in which the torque i 0.6 p.u. With high load torque (above half rated), the propoed method i not attractive becaue the amount of energy aved i not ignificant and exceive voltage mut be applied to the motor. The tre caued by Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 69

S. Sujitjorn and K-L. Areerak the exceive voltage can damage the motor inulation. Nonethele, the propoed method i till efficient in a low peed range a can be oberved from the reult hown in Figure 7(d). 00 T=0.15 p.u. 00 T=0.3 p.u. 180 180 Total power loe(w) 160 140 10 fixed voltage 100 varied frequency V = 05 Vrm 80 V = 53 Vrm 60 v/f contant 40 loe minimization 0 600 800 1000 100 1400 1600 1800 Speed(rpm) (a) Total power loe(w) 160 140 10 fixed voltage varied frequency V=13 Vrm 100 V=30 Vrm v/f contant 80 loe minimization 60 600 800 1000 100 1400 1600 1800 Speed(rpm) (b) 400 T= 0.6 p.u. 800 T = 1.0 p.u. 350 700 v/f contant Total power loe(w) 300 50 V=177 Vrm 00 150 fixed voltage varied frequency loe minimization v/f contant V=390 Vrm V=455 Vrm 100 600 800 1000 100 1400 1600 1800 Speed(rpm) loe minimization 100 600 800 1000 100 1400 1600 1800 Speed(rpm) (c) (d) Figure 7. Calculation reult compare the total power loe that occurred in the variou drive cheme namely lo minimization, contant v/f, and fixed-v-varied-f. (a) load torque = 0.15 p.u., (b) load torque = 0.3 p.u., (c) load torque = 0.6 p.u., and (d) load torque = 1.0 p.u. Total power loe(w) 600 500 400 300 00 V = 7 Vrm V = 35 Vrm fixed voltage varied frequency V = 600 Vrm 70 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Figure 8 how the diagram repreenting our hardware implementation. The IGBT module are main witching device. The propoed method ha been implemented a control oftware together with uitable data table. The PC execute the control algorithm coded in C. It read the peed and load torque from enor through a 1-bit A/D converter. The numerical reult obtained from the control algorithm are witching command in turn ent to two microcontroller through eight logical output. Thee microcontroller perform real-time witching function to drive the chopper and the inverter, repectively. ectifier Module IGBT Chopper Module L 380 V rm (line) 50 Hz CB V u V v V w D1 D3 D 5 D4 D6 D C 1 1650 µ F 800 V D m 1. H C 150 µf 800 V PC 8 bit 8 bit 1 bit A/D D/A interface card ω TL µc1 µc witching command 6 bit witching command IGBT Inverter Module S 4 S 5 u v S 1 S S 6 S 3 ω TL w LOAD IM Figure 8. Hardware implementation. Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 71

S. Sujitjorn and K-L. Areerak Table and 3 give detail of the experimental reult in which the value of the input power (P in ) and the power factor (p.f.) were meaured at the input terminal of the motor by uing FLUKE TM 41B. Table. Experimental reult of the ytem without the energy aving controller. Load Speed P in (W) p.f. line-to-line f(hz) (%) (rpm) voltage (Vrm) 0 1500 145 0.5 380 50 10 1497 00 0.3 374.1 50 0 1487 80 0.44 365.1 50 30 1475 380 0.55 357.50 50 40 146 490 0.66 348.49 50 50 1450 600 0.7 339.14 50 Table 3. Experimental reult of the ytem with the controller. Load Speed P in (W) p.f. line-to-line f(hz) (%) (rpm) voltage (Vrm) 0 1500 56 0.87 81.41 55.5 10 1500 15 0.80 16.81 5. 0 1500 45 0.8 08.19 5.1 30 1500 370 0.83 4.14 51.7 40 1500 480 0.8 74.01 51.1 50 1500 590 0.81 305.19 50.5 7 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter Table 4. Experimental reult of the ytem with the controller for a contant peed (1800 rpm) drive. Load Speed P in (W) p.f. line-to-line f(hz) (%) (rpm) voltage (Vrm) 0 1800 66 0.83 103.9 65.3 10 1800 155 0.8 173.97 63.1 0 1800 90 0.80 40.41 6.4 30 1800 430 0.83 69.16 6.7 40 1800 590 0.83 306.9 6.6 50 1800 70 0.83 333.59 6.6 eferring to Table, for the cae of the motor driven a rated without the controller, the motor peed and the terminal voltage drop naturally when the load increae. The input power increae according to the load increae. The motor power factor i very low at light load. Even at about half the rated load, the power factor are till coniderably low. For the cae of the implemented ytem repreented by the diagram in Figure 8, to maintain a contant peed at variou load i poible with the propoed controller. However, the experimental reult hown in Table 3 reflect the actual input power fed to the motor under the ame condition of peed and load a for the cae of the motor running without the controller. Thi i for comparion purpoe of the input power and the power factor. The two right-hand column of Table 3 how the optimum excitation lineto-line voltage and frequency correponding to the load. It i Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 73

S. Sujitjorn and K-L. Areerak noticeable that the propoed method i very effective for 0-30% load in term of input power aving. The amount of energy aving range from 3-60% approximately. Above 40% load, the amount of energy aving i not ignificant. In term of power factor at the motor terminal, the propoed method ignificantly yield a power factor around 0.8 or better, for the whole load range. Additionally, the data in Table 4 give the general idea of driving the motor at a contant peed, i.e. 1800 rpm, with the propoed controller. The power factor at the motor terminal i maintained around 0.8. For all cae, the power factor at the utility interface i around 0.9. The imulation and experimental reult agree and confirm the effectivene of our propoed lo minimization method. Concluion Thi article preent a new approach to power lo minimization in mall induction motor driven by voltage-ource-inverter. The propoed method employ motor equivalent circuit, i.e. motor parametric model. The model parameter can be accurately identified from true motor characteritic. Experiment conducted are imple and require intrument commonly found in electrical machine laboratorie. The lo model incorporate the variation of exciting voltage, frequency, and load torque a major factor. Some minor factor, e.g. temperature and harmonic effect, are viewed a being lumped into the lo model. Under thi conideration, the 74 Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78

Lo Minimization in an Induction Motor Driven by a Voltage-Source-Inverter repreentation of motor parameter ubtantially include the motor nonlinear characteritic. Hence, the lo model and the propoed lo minimization method are very accurate and can cope with machine nonlinearity to a certain extent. The computing reult how that the propoed method i efficient when the load torque range from 0 to half the rating. Above half rated load, the method i attractive for low peed range. Implementation of the method a an adaptive algorithm for energy aving in ac drive i not complicated. The implementation approach can be either real-time computing. eference [1] Mohan N. (1983) "Improvement in energy efficiency of induction motor by mean of voltage control", IEEE Tran. Power Apparatu and Sytem, 99 (4), 1466-1471. [] Kuko A. and Galler D. (1983) "Control mean for minimization of loe in ac and dc motor drive", IEEE Tran. Indutry Application, 19 (4), 561-570. [3] Kirchen D. S., Novotny D. W. and Suwanwioot W. (1984) "Minimizing induction motor loe by excitation control in variable frequency drive", IEEE Tran. Indutry Application, 0 (5), 144-150. [4] Kirchen D. S., Novotny D. W. and Lipo T. A. (1987) "Optimal efficiency control of an induction motor drive", IEEE Tran. Energy Converion, (1), 70-76. Aian J. Energy Environ., Vol. 3, Iue 1-, (00), pp. 53-78 75

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