Torque Density Improvement in a Six-Phase Induction Motor With Third Harmonic Current Injection

Transcription

1 Toque Density Impovement in a Six-Phase Induction Moto With Thid Hamonic Cuent Injection Renato O. C. Lya Thomas A. Lipo Univesity of Wisconsin - Madison Dept. of Electic and Compute Engineeing 1415 Engineeing D. Madison, WI Abstact-The use of six-phase induction moto fo industial dives pesents seveal advantages ove the conventional theephase dive such as impoved eliability, magnetic flux hamonic eduction, toque pulsations minimization and eduction on the powe atings fo the static convete. Fo these easons, sixphase induction motos ae beginning to be a widely acceptable altenative in high powe applications. A typical constuction of such dives includes an induction machine with a dual theephase connection, whee two thee-phase goups ae spatially shifted thity electical degees, a six-leg invete and a contol cicuit. By contolling the machine s phase cuents, hamonic elimination and toque ipple eduction techniques could be implemented. This pape descibes a technique of injecting thid hamonic zeo sequence cuent components in the phase cuents, which geatly impoves the machine toque density. Analytical, finite element and expeimental esults ae pesented to show the system opeation and to demonstate the impovement on the toque density. Keywods - Industial dives, Induction machine analysis and design, Six-phase dives. I. INTRODUCTION Thee-phase induction machines ae today a standad fo industial electical dives. Cost, eliability, obustness and maintenance fee opeation ae among the easons these machines ae eplacing dc dive systems. The development of powe electonics and signal pocessing systems has eliminated one of the geatest disadvantages of such ac systems, that is the issue of contol. With moden techniques of field oiented vecto contol, the task of vaiable speed contol of induction machines is no longe a disadvantage. The need to incease system pefomance, paticulaly when facing limits on the powe atings of powe supplies and semiconductos, motivates the use of phase numbe othe than thee, and encouages new PWM techniques, new machine design citeia and the use of hamonic cuent and flux components. In a multi-phase system, hee assumed to be a system that compises moe than the conventional thee phases, the machine output powe can be divided into two o moe solidstate invetes that could each be kept within pescibed powe limits. Also, having additional phases to contol means additional degees of feedom available fo futhe impovements in the dive system. With split-phase induction machines, and appopiate dive system, the sixth hamonic toque pulsation, typical in a sixstep thee-phase dive, can be eliminated [1,2]. Also, ai gap flux ceated by fifth and seventh hamonic cuents in a highpowe six-step convete-fed system is damatically educed with the penalty of inceased convete hamonic cuents [3]. PWM techniques ae employed to ovecome this poblem by eliminating the hamonic cuents in the modulation pocess when the powe atings ae not pohibitive. Dual-stato machines ae simila to split-phase machines with the diffeence that the stato goups ae not necessaily equal. A dual-stato machine with diffeent numbes of poles in each thee-phase goup has been poposed in [4] to obtain contollability at low speeds. Two independent stato windings ae used in [5] fo an induction geneato system. One set of windings is esponsible fo the electomechanical powe convesion while the second one is used fo excitation puposes. A PWM convete is connected to the excitation windings and the load is connected diectly to the powe windings. A paticula case of split-phase o dual-stato machine, the six-phase machine can be built by splitting a thee-phase winding into two goups. Usually these thee-phase goups ae displaced by thity electical degees fom each othe. This aangement composes an asymmetical six-phase machine since the angula distance between phases is not all the same [6]. The analysis of an induction machine fo multiple phases and abitay displacement between them is pesented in [2] whee the six-phase induction machine is used as an example and an equivalent cicuit has been deived. The dq0 model fo a six-phase machine was developed in [7]. Reliability is one of the advantages in using six-phase systems. In the case of failue of one of the phases, eithe in the machine o in the powe convete, the system can still opeate at a lowe powe ating since each thee-phase goup can be made independent fom each othe. In the case of losing one phase, the six-phase machine can continue to be opeated as a five-phase machine as descibed in [8]. The inheent thid hamonic component in the machine s winding functions [9,10] suggests the use of thid hamonic cuents to impove its pefomance. Toque impovement can be obtained by using multi-phase windings with injection of thid hamonic cuents. Such a nine-phase induction machine X/01/$10.00 (C) 2001 IEEE 1779

2 dive was investigated in [11]. The complexity of the powe system, which includes seies and paallel tansfomes, inceases the system cost and must be evaluated fo each paticula application. The use of a voltage-contolled system does not guaantee the phase alignment between fundamental and thid hamonic cuents, especially at low speeds, and a poo low speed and dynamic behavio can be expected fo this system. This pape descibes a technique of injecting thid hamonic, zeo sequence cuent components in the phase cuents that impove the machine toque density. Analytical, finite element and expeimental esults ae pesented to show the system opeation and to demonstate the impovement on the toque density. II. TORQUE IMPROVEMENT WITH THIRD HARMONIC CURRENT INJECTION The asymmetic six-phase machine is deived fom a conventional thee-phase induction machine. Fo a two pole concentated winding thee-phase machine, the mmf acting acoss the ai gap associated with the stato cuents is: F = F a + F b + F c = N a (I)i a + N b (I)i b + N c (I)i c (1) whee N a, N b, and N c ae the machine s winding functions [12] and compose a set of 120 degees phase shifted squae waves with amplitude 2N s (each coil has 4N s tuns). Using Fouie analysis decomposition, and assuming balanced theephase cuents with amplitude I, it can be shown that the even and all tiple hamonics ae zeo and the mmf is given by: F = F 1 + F 5 + F 7 + (2) whee: F 1 = 34 2S ¹ s)i[sin(i-t)] (3) F 5 = S ¹ s)i[sin(5i-t)] (4) F 5 = S ¹ s)i[sin(7i-t)] (5) and the wave contains a 0% thid hamonic, 20% fifth hamonic and 14% seventh hamonic, plus smalle potions of highe hamonics. Setting the sine function agument equal to a constant, to establish a fixed point in the wavefom, and diffeentiating with espect to time, the otational speed can be calculated. The peak fundamental component otates in the diection of inceasing I with angula speed Z, the fifth hamonic otates in the diection of deceasing I at 1/5 the speed of the fundamental component and the seventh hamonic otates at the same diection of the fundamental with 1/7 of its speed. The fifth hamonic poduces a negative sequence component of flux that poduces negative o baking toque. The seventh poduces positive toque but it is only useful between 0 and 1/7 of the synchonous speed. If a neutal connection is povided, zeo sequence cuent components can flow in the machine. Consideing a zeo sequence cuent I 0 the mmf due to this cuent can be calculated to be: F 0 = 4 S ¹ (2N 1 s) 3 sin(3i)+1 9 sin(9i)+ ¹ I 0 (6) whee the tiple hamonic of the squae wave winding functions ae clealy epesented. This suggests the use of tiplens of the fundamental cuent fequency to poduce toque coesponding to the zeo sequence winding functions. Since most of the machine have a discete distibuted winding, the zeo sequence winding function is non-zeo and can be exploed to poduce exta toque. Injecting a thid hamonic cuent component I 0 =I 3 sin(3t) and neglecting highe hamonics, the mmf is: F 0 = 4 S ¹ (2N s) I 3 3 ( sin(3i)sin(3t) ) (7) This quantity epesents a standing o pulsating wave in the ai gap and not a otating wave. This component is undesiable since it poduces baking and pulsating toques. Distibuting the windings ove moe slots can educe the hamonic content of the mmf. Fo a distibution ove two slots, o two slots pe pole pe phase, the new fundamental mmf is: F 1 = S¹ N ª º si sin(i - T)+sin I - S 6 - T ¹ ¼ (8) This esult coesponds to a thee-phase machine with distibuted windings o to a six-phase concentated winding machine. Two thee-phase winding goups, spatially phase shifted by 30 degees, compose the six-phase machine. The amplitude of the fundamental component is then: F 1 = S¹ 2N si «ª ¼»º = k d1 34 2S¹ 2N si (9) and the constant k d1 = , as expected, is the usual distibution facto fo two slots pe pole pe phase. The fundamental component is theefoe educed by 4.1% when compaed to the no phase shift, full pitch case. Doing simila analysis fo the fifth and seventh hamonics, it can be shown that with the distibution ove two slots, the fifth hamonic component is educed fom 20% to 5% and the seventh hamonic goes fom 14% to 3.7%. Fo this case, if a thid hamonic zeo sequence component is injected, it would again poduce a standing wave and is of no pactical value again. If, howeve, two sets of thee-phase cuents phase ae shifted in time by 30 degees to compise the cuents in the six-phase machine, the fundamental component of the mmf can be found to be the same as in the concentated winding 1780

3 machine (3) but now both fifth and seventh hamonics ae educed to zeo. With injection of thid hamonic zeo sequence cuent components as: I 0,abc =I 3 cos(3t) and I 0,xyz =I 3 sin(3t), (10) whee abc and xyz coespond to the two thee-phase winding goups, the zeo sequence mmf is now: F 0 = 4 N s ¹ 3 I 3{ sin[3(i T)] } (11) S This esult coesponds to a otating field with angula speed equal to the fundamental angula speed. Hence, the zeo sequence component can be now used to poduce a second positively otating flux component synchonized with the fundamental component. A. Flux distibution with thid hamonic cuent injection The possibility of injecting thid hamonic cuent components into the machine without poducing pulsating toques enables the ability to eshape the machine s flux distibution in a simila manne to the technique applied in PWM modulatos. In PWM modulatos, a thid hamonic voltage efeence is added to the fundamental component to incease the modulation index beyond the unity modulation index without distotion poduced by dopping pulses. Fo the equivalent appoach applied to the modulating machine flux, it is desied to incease the fundamental component of flux without satuating the machine. The appopiate taget efeence flux wavefom, containing the thid hamonic contibution is defined as: B g (I)=B 1 sin(i) + B 3 sin(3i) (12) Using an optimization pocess, the elation between fundamental and thid hamonic components can be detemined fo the best ion utilization and the ai gap flux is defined as a function of the maximum allowed flux distibution B max as: B g (I) = 2 3 B max ª sin(i) + 1 sin(3i) ¼ º (13) 6 Fom (13), it is clea that fo keeping the same peak value fo the flux density in the ai gap, with injection of the thid hamonic component the peak of the fundamental flux component is highe. B. Toque impovement with thid hamonic cuent injection The benefit of using the thid hamonic component can now be investigated. Using an appoximate equivalent cicuit fo the induction machine, as shown in Fig. 1, whee the oto leakage inductance is neglected, and assuming peak values fo the vaiables, the oto cuent is: I = E s ' (14) and the toque is defined by: T = 3 P E 2 s (15) 22 Z e ' The peak voltage E is popotional to the peak ai gap flux density [12] by: E = Z e 2 S B max A ¹ pole N s (16) whee A pole is the aea of one magnetic pole and N s is the numbe of seies connected tuns. The facto 2/S expess the aveage value of B in tems of its peak value. In the case of the asymmetic six-phase machine, the maximum allowable fundamental flux density can be inceased by 2/ 3. Since all othe paametes in (15) emain the same fo this machine, the incease in toque obtained by aising the fundamental component of flux density, while keeping the same peak tooth and ai gap flux density is: T 6phase-fund = T baseline 2 ¹ 2 =1.33 (17) 3 whee T baseline coesponds to the toque poduction in a theephase induction machine used as baseline fo the evaluation. Thee is an additional 33% in the toque poduction fo the six-phase machine with thid hamonic injection due to the incease in the fundamental flux. In addition to that, the contibution of the thid hamonic component must be consideed. The toque poduced by the thid hamonic cuents in the six-phase machine is: T = 3 P E 2 3h s 3h (18) 2 3Z e ' 3h and the thid hamonic voltage can be computed as: E 3h = 3Z e 2 S B max ¹ A pole 3 ¹ 3 N s 3 ¹ = Z e 2 S B max A ¹ pole N s (19) Figue 1 Appoximated equivalent cicuit of a thee-phase induction moto whee the oto leakage inductance is neglected. 1781

4 The slip fo the thid hamonic is: 3Z e - 3P 2 ¹ Z m s 3h = = 3Z e Z e - P 2 ¹ Z m Z e (20) and the oto esistance can be detemined [13] to be: 3(12) N s 2 3 ¹ ' 3h = S be (21) whee N s /3 is the numbe of seies connected tuns of one of the thee pais of poles of the thid hamonic, S is the numbe of oto slots and be is the esistance of a oto ba taking into account the effect of the end ing. The facto of 3 is used since the thee pole pais of the thid hamonic ae connected in seies. Inseting these expessions in the toque equation fo the thid hamonic (18): T 6phase-3h = 3 P 2 ¹ ª 1 º S B max A ¹ pole Z ¼ 2 e - P 2 Z m ¹ (22) 12 S be Using a simila deivation, an equivalent expession can be found fo the baseline machine toque: T baseline = 3 2 P 2¹ ª 2 º S B max A ¹ pole Z ¼ 2 e - P 2 Z m ¹ (23) 12 S be Taking the atio the contibution of the thid hamonic can be found: T 6phase-3h = «ª 1 ¼» º = 2 = (24) T baseline fundamental component kept constant. In this case the slot aea available fo coppe could be inceased pemitting a 14% incease in cuent and a 14% incease in toque fo the same tooth and coe flux density. III. MACHINE DESIGN Fo veification, an asymmetic six-phase induction moto was designed using a conventional thee-phase moto as baseline. The new winding distibution accommodates in the same fame size as the baseline thee-phase moto and both machines have simila peak ai gap fluxes. Fom a single laye thee-phase stato, a double laye sixphase distibution is implemented by dividing the thee phases into two goups that ae spatially shifted 30 electical degees. Fig. 2 shows the winding functions fo phases a and x. It can be seen the spatial phase shift between the two windings and the pesence of the thid hamonic component in the distibution necessay to inteact to the injected thid hamonic cuents. Fo the baseline machine, fom the nameplate and geometical data, the ai gap flux is calculated. The stato phase voltage of the machine is calculated as [13]: V sf = Z e k 1 N s ) p (26) whee, ) p = 2 D is l s P B g1 (27) whee D is the stato inne diamete, l s the stato length, P the numbe of poles and B g1 the peak fundamental ai gap flux. The numbe of seies connected tuns pe phase is defined as: (tuns/coil)(coil side/slot)(numbe of slots) N s = (numbe of phases)(cicuits) Thus, fo a single laye, thee-phase machine, one has: N s = (n s/2)(1)s 1 3C (28) (29) Also, the contibution of the thid hamonic is 7.4% of the value poduced by the baseline machine. The total toque impovement is then, T 6phase-fund + T 6phase-3h - T baseline T baseline 100% = 40.7% (25) It must be noted howeve that the peak value stato coe flux has not been maintained constant so that the amount of impovement that can actually be ealized depends upon the satuation level pemitted in the stato coe. Altenatively, athe than maintain the peak ai gap flux constant afte addition of the thid hamonic, the peak flux density could be educed by 1.732/2 o and the Figue 2 Phases a and x winding functions. 1782

5 Fo a 230V connection with n s = 98 conductos pe slot, C= 4 cicuits and S 1 = 36 stato slots, the numbe of seies connected tuns pe phase N s = 147. Using the machine s physical dimensions, the peak fundamental ai gap flux density is calculated to be B g1 = 0.53T when 60Hz opeation and unit winding facto ae consideed. Fo a six-phase machine with a double laye winding, N s = (n s/4)(2)s 1 6C (30) With same physical dimensions and same peak fundamental ai gap flux density, the flux pe pole ) p is the same fo the six-phase machine when only the fundamental component is consideed. Fom (26) it is seen that the numbe of seial connected tuns pe phase must be the same fo the six-phase machine and so, fo keeping the same N s, eithe n s has to be doubled o C has to be educed to its half. Fo this machine configuation, the eduction of C guaantees the accommodation of the conductos in the slots. Finally the electic loading has to be checked fo the new winding configuation. The electic loading fo the machine is detemined by: eaches its pevious value. This makes the fundamental flux to incease without sending the peak value beyond its limits. Fig. 6 shows the distibution fo I pk =0.58A and I 3pk =0.4A whee a flattened flux distibution is obtained. V. SYSTEM DESCRIPTION An expeimental setup was built to test the poposed technique. Fig. 7 shows the setup configuation. A common DC link is used fo two thee-phase invetes connected to each winding goup of the six-phase machine. The neutal is connected to the mid point of the DC link capacitos. An additional invete leg is povided fo futue investigation on the neutal cuent diect contol. A DSP cad that incopoates two independent thee-phase PWM modulatos with complementay outputs contols the system. The softwae was developed in C language and the contol panels wee developed using HTML scipting and ActiveX commands. This enables the system contol and monitoing ove any intenal o extenal netwok. K s ms = S 1 n s (I s /C) 2SD is (31) with all geometical vaiables in (30) constant, the eduction in the numbe of cicuit by half causes the stato cuent to educe by half. This is easonable since now thee ae two thee-phase windings instead of one in the baseline machine. To measue the flux distibution in the ai gap, a full pole pitch seach coil [14] was inseted in the machine stato, and with the aid of an opeational amplifie based integato the flux can be detemined. IV. FINITE ELEMENT ANALYSIS Finite element analysis is conducted in the six-phase machine to calculate the ai gap flux distibution and to demonstate the incease in the fundamental flux component. Fig. 3 shows the finite element mesh utilized fo the epesentation of one quate of the machine. Bounday condition symmety is used to obtain the esults fo the entie machine. The flux density distibution coesponding to half magnetic pole fo the no thid hamonic injection and peak phase cuent I pk = 0.5A is shown in Fig. 4. This cuent is not enough to dive the machine into satuation and the distibution esembles a sinewave. The oto and stato slot openings flux hamonics ae also clea on this plot. Injecting thid hamonic cuents causes the peak flux density to decease as it can be seen on Fig. 5 whee the peak cuent is kept the same and a thid hamonic cuent I 3pk =0.4A is added. Since the peak flux deceases, the fundamental cuent can be inceased until the peak flux Figue 3 Finite Element Mesh with 6063 nodes and 3006 sufaces. Figue 4 Ai gap flux density distibution without thid hamonic cuent injection. Peak phase cuent I pk = 0.5A. 1783

6 Figue 5 Ai gap flux density distibution with thid hamonic cuent injection. Peak phase cuent I pk = 0.5A. Peak thid hamonic phase cuent I 3pk = 0.4A. To obtain the necessay alignment between fundamental and thid hamonic cuents, a cuent egulated supply must be used. With a voltage supply the alignment is not guaanteed since the machine s impedance changes with opeational conditions. Also, it was obseved that with a voltage supply (no cuent egulation) even shaing of the output powe between the two invetes is not possible when pactical aspects such as diffeences in the winding functions ae consideed. A cuent egulated PWM invete was then implemented as shown in Fig. 8. Hee the coss-coupling decoupling is omitted but fo a high pefomance opeation, it must be included. A modified abc-xyz/dq0 tansfomation is used to map the altenate cuents into dc quantities in the dq0 domain. This tansfomation follows the standad abc/dq0 decomposition but it is modified to include the thid hamonic fequency and also maps thid hamonic signals into dc quantities. This appoach facilitates the design of the contol system. Figue 6 Ai gap flux density distibution with thid hamonic cuent injection. Peak phase cuent I pk = 0.58A. Peak thid hamonic phase cuent I 3pk = 0.4A. Figue 7 Six-phase machine dive system. Figue 8 Cuent contol block diagam. VI. EXPERIMENTAL RESULTS The six-phase machine was tested expeimentally to veify the opeation with thid hamonic cuent injection. The flux distibution is obtained using seach coils installed in the machine and the toque is measued diectly in the shaft by means of a toque tansduce. When supplied by a voltage souce invete, asymmeties in the machine design cause uneven distibution of powe between the two thee-phase invetes. This featue can be seen in Fig. 9 whee the machine is tested at ated voltage and no thid hamonic injection. Phases a and x cuents ae shown togethe with the ai gap flux distibution. Since phase a cuent is pactically zeo, all powe is supplied though phase x. This opeational condition is not desied and has to be avoided by using diect cuent contol. The eshaping of the ai gap flux distibution is demonstated by pefoming a locked oto test in the machine still with a voltage souce invete. Fig. 10 shows phases a and x cuents and the flux density distibution fo a peak value of B pk =0.17T and no thid hamonic injection. The cuents ae 30 degees phase shifted fom each othe as necessay fo the poposed machine opeation. It can be seen some cuent shaing poblems, but not as evident as in the no-load case. Without the thid hamonic cuents, the sixphase machine opeates similaly to the thee-phase baseline machine. Adding thid hamonic cuents causes the peak flux density to decease as seen in Fig. 11. This coesponds to a sub-utilization of the machine ion when compaed to the pevious case. To aise the peak flux, the fundamental cuent can be inceased until the pevious level is eached. This esult is shown in Fig. 12 whee the peak flux coection is applied and the peak levels with the no thid hamonic case. Seveal tests like those descibed peviously have been conducted and fo each case the toque poduction was measued. Fig. 13 shows the esults of the toque 1784

7 measuement as a function of the peak ai gap flux density fo two cases, no thid hamonic injection and thid hamonic injection with peak flux coection. It is clea an impovement in the toque poduction exists due to the incease in the fundamental cuent keeping the flux level within its limits. Results shown in Fig. 13 demonstate the toque impovement that is caused by two factos. Fist, the lage contibution in added toque esults fom the incease on the fundamental ai gap flux. Second, additional toque esults due to the otating field ceated by the zeo sequence thid hamonic cuents. Fig. 14 shows this second facto. Hee, the fundamental peak ai gap flux is kept constant and thid hamonic cuents ae injected. The peak ai gap flux deceases and is not coected. Fom this figue, one can obseve the slight incease in the toque poduction with thid hamonic injection. Figue 9 Six-phase machine flux density and cuent fo no load opeation at V ll = 230V. Tace1: Flux density distibution [0.32T/div]; Tace 2: Phase a cuent [4.2A/div]; Tace 4: Phase x cuent [4.2A/div]. Figue 12 Six-phase machine flux density and cuent fo locked-oto opeation at B pk = 0.17T. With Thid hamonic cuent injection and peak flux coection. Tace1: Flux density distibution [0.064T/div]; Tace 2: Phase a cuent [4.2A/div]; Tace 4: Phase x cuent [4.2A/div]. Figue 10 Six-phase machine flux density and cuent fo locked-oto opeation at B pk = 0.17T. Tace1: Flux density distibution [0.064T/div]; Tace 2: Phase a cuent [4.2A/div]; Tace 4: Phase x cuent [4.2A/div]. Figue 13 Six-phase machine toque poduction at locked-oto opeation fo no thid hamonic and thid hamonic injection. Figue 11 Six-phase machine flux density and cuent fo locked-oto opeation at B pk = 0.17T. With Thid hamonic cuent injection and no peak flux coection. Tace1: Flux density distibution [0.064T/div]; Tace 2: Phase a cuent [4.2A/div]; Tace 4: Phase x cuent [4.2A/div]. Figue 14 Six-phase machine toque poduction at locked-oto opeation fo no thid hamonic injection and thid hamonic injection without compensation fo peak ai gap flux density. 1785

8 VII. CONCLUSION Multi-phase systems ae boadly used in industy to achieve highe powe levels based in limited ange powe convetes. Additional toque poduction can be obtained in these systems if thid hamonic cuents ae injected so to eshape the flux distibution in the machine and theefoe obtain highe fundamental flux densities without extapolating the flux limits and focing the machine unde satuation. This pape poposes the use of a six-phase induction machine to gain these benefits. By constucting the machine with two thee-phase goups phase shifted by thity degees, it is possible to ceate an additional otating field in synchonism with the fundamental by using thid hamonic zeo sequence cuents. In so doing, the ai gap flux pesents a thid hamonic component that educes the peak flux density. Additional toque is then obtained by inceasing the fundamental flux component in such a manne to eestablish the ai gap flux to its oiginal peak value and by the exta thid hamonic otating field. Though analytical analysis, assuming satuation of the stato teeth as the constaint on flux density, it has been shown that an incease of up to 40% in the toque poduction can be expected with this technique when compaed to a standad thee-phase machine, fo same peak flux distibution. Altenatively, if both tooth and coe flux density ae to be constained to fixed values at least a 14% + 7% = 21% incease is possible by enlaging the stato slot ae. To obtain the benefits, the machine's winding function has to include thid hamonic components. This is tue fo most of electical machined due to the discete constuction of the windings that ae distibuted in finite numbe of slots. The best impovement would be obtained using a concentated winding machine since fo this case the highe thid hamonic component in the winding function is obtained. Finite element analysis has been used to show the behavio of ai gap and coe flux with thid hamonic cuents. This analysis is paticulaly impotant to coectly map the behavio of machine's flux in aeas too complicated to have a diect measuement. A fundamental issue in this application is the necessity of contolling the phase elation between fundamental and thid hamonic flux components. If this elation is lost, a peaked flux density could be geneated instead of the poposed flattened one. Cuent contol is theefoe necessay fo this application and a contol system is poposed whee a modified abc/dq0, now called abc-xyz/dq0, synchonous fame tansfomation is developed to include the thid hamonic components. This tansfomation maps all the machine's cuents into a dq0 domain as dc quantities what facilitates the contol design and tuning. The poposed system was tested expeimentally to show the expected toque impovement. It is shown that fo voltage fed systems the cuent shaing between the two thee-phase goups is uneven and can cause poblems. The expeimental esults show that fo same ai gap peak flux density, the toque can be inceased with the thid hamonic cuent injection as a esult of the incease in the fundamental component of cuent and flux. These esults validate the theoetical analysis and motivate additional investigation on this system. ACKNOWLEDGMENT This eseach has been suppoted by the WEMPEC consotium at Univesity of Wisconsin Madison, UFMG/Bazil and by CAPES/Bazil. REFERENCES [1] A. R. Bakhshai, G. Joos, and H. Jin, Space vecto PWM contol of a split-phase induction machine using the vecto classification technique, Poceedings of Applied Powe Electonics Confeence and Exposition, 1998, vol. 2, pp , Feb [2] R. H. Nelson and P. C. Kause, Induction machine analysis fo abitay displacement between multiple windings, IEEE Tansactions on Powe Appaatus and Systems, vol. 93, pp , May [3] L. Xu and L. Ye, Analysis of a novel stato winding stuctue minimizing hamonic cuent and toque ipple fo dual six-step convete-fed high powe ac machines, IEEE Tansactions on Industy Applications, vol. 31, pp , Jan [4] A. R. Munoz and T. A. Lipo, Dual stato winding induction machine dive, IEEE Tansactions on Industy Applications, vol. 36, pp , Sept [5] O. Ojo and I. E. Davidson, PWM-VSI invete-assisted stand-alone dual stato winding induction geneato, IEEE Tansactions on Industy Applications, vol. 36, pp , Nov [6] G. Oiti, L. Julian, and T. A. Lipo, An invete/moto dive with common mode voltage elimination, Thity-Second IAS Annual Meeting, IAS 97, vol. 1, pp , Oct [7] T. A. Lipo, A d-q model fo six phase induction machines, Poceedings of the Intenational Confeence on Electical Machines, Athens, pp , Sept [8] J. Fu and T. A. Lipo, Distubance fee opeation of a multiphase cuent egulated moto dive with an opened phase, IEEE Tansactions on Industy Applications, vol. 30, pp , Sept [9] H. A. Toliyat, T. A. Lipo, and J. C. White, Analysis of a concentated winding induction machine fo adjustable speed dive applications. I. Moto analysis, IEEE Tansactions on Enegy Convesion, vol. 6, pp , Dec [10] H. A. Toliyat, T. A. Lipo, and J. C. White, Analysis of a concentated winding induction machine fo adjustable speed dive applications. II. Moto design and pefomance, IEEE Tansactions on Enegy Convesion, vol. 6, pp , Dec [11] S.-S. P. Liou, Theoetical and expeimental study of polyphase induction motos with added thid hamonic excitation, Maste s thesis, The Univesity of Texas at Austin, [12] N. L. Schmitz and D. W. Novotny, Intoductoy Electomechanics. New Yok: The Ronald Pess Company, [13] T. A. Lipo, Intoduction to AC Machine Design. Madison WI: Univesity of Wisconsin, [14] T. A. Lipo, Flux sensing and contol of static ac dives by use of flux coils, IEEE Tansactions on Magnetics, vol. MAG-13, Sept