Study and Harmonic Analysis of SVPWM Techniques for VSI-Fed Double-Star Induction Motor Drive

Transcription

1 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- Study and Haronic Analysis of SPWM Techniques for SI-Fed Double-Star Induction Motor Drive Khoudir Marouani, Farid Khoucha, Lotfi Baghli, Djafar Hadiouche, Abdelaziz Kheloui. UER-Electrotechnique - EMP, BP7 Bordj El-Bahri, Algiers, Algeria. G.R.E.E.N. - Université H. Poincaré, B.P. 9 - F-55 andoeuvre-lès-nancy, Cedex, France. GE Industrial Systes, GE Fanuc, Luxebourg E-ail: arouani_khoudir@yahoo.fr Abstract In this paper, a coparison between continuous and discontinuous space vector PWM control of six-phase SI fed a double-star induction otor drive (DSIM) is presented. The induction achine has two sets of three-phase stator windings spatially shifted by electrical degrees. Each set of three-phase stator windings is fed by a three-phase inverter. The haronic characteristics of the SI feeding DSIM are investigated and presented graphically as function of the odulation index with the introduction of a leakage coupling coefficient between the two sets. Ipleentation on a DSP Controller Board is achieved and experiental results on a 5 kw DSIM prototype achine are carried out. dc K a K a K a K b K b K b K c K c K c Keywords Double star induction otor, six-phase voltage source inverter, space vector PWM, DSP. I. INTRODUCTION High power drives eploying ultiphase achines are required in a lot of applications, such as traction, electric/hybrid vehicles and ship propulsion. In the past decade, ulti-level inverter fed electric achine drive systes have eerged as a proising approach in achieving high power ratings with voltage liited devices. The typical structure of such systes is a three-level inverter feeding a three-phase electric achine syste []. The parallel circuit dual to the ulti-level syste is, essentially, the base of the concept of the ulti-phase inverter. In ulti-phase achine drive systes, ore than three-phase windings are ipleented in the sae stator of the electric achine, and one coon exaple of such structure is the Double-Star Induction Motor (DSIM). This otor has two sets of threephase windings spatially phase shifted by electrical degrees and each set of three-phase stator windings is fed by a three-phase voltage source inverter(si), as shown in Fig.. Copared with the standard three phase syste, the ultiphase one brings significant advantages, the ain ones are: - A higher torque density for the sae achine volue with reduced torque pulsations: windings with higher phase nubers produce fields with a lower haronic content and reaining space haronic fields contribute positively to the torque []. - A greater fault tolerance and a higher reliability: because the loss of one phase in ulti-phase drive syste does not prevent the achine fro starting and running, K a K b K c Figure. Six-phase SI fed DSIM whereas the loss of one phase in a three-phase syste results in a single-phase drive which can not start and that will produce a assive pulsating torque if running. - The possibility to divide the controlled power on ore inverter legs []. Hence, it will reduce the current stress of each switch and the need for parallel and/or series connection of seiconductor switches ay be reduced or reoved entirely in power conditioning equipent. Due to the iproveent of fast switching seiconductor power devices, SI with pulse wih odulated (PWM) control arouses a great interest. Control ethods that generate the necessary PWM patterns have been discussed extensively in the literature. Two basic concepts ay be distinguished: for sall and ediu power drives, the current controlled PWM has proved to be advantageous. For high power drives eploying inverters with low switching frequency, PWM voltage control is ore advantageous []. Nevertheless, in a DSIM, the two stator windings are utually coupled and sall unbalances in the supplied voltages generate circulating currents [5]. Furtherore, because of the low ipedance to haronic currents there is a high level of circulating currents when a nonsinusoidal voltage source supply is used [,7], adding losses and deanding larger seiconductor device ratings. Consequently, to iniize these haronic currents various PWM techniques have been developed.

2 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- This paper present a perforance evaluation and haronic analysis of continuous and discontinuous space vector PWM control of six-phase SI fed a double-star induction otor drive (DSIM). For purpose of coparison the rs values of the phase current haronics are presented graphically as function of the odulation index. Also, experiental results carried out on a 5 kw DSIM prototype achine are given. II. SPACE ECTOR PWM CONTROL OF DOUBLE-STAR INDUCTION MOTOR With the introduction of ulti-phase electrical achines, various odulation techniques have been developed for pulse wih odulation (PWM). Aong these, the space vector pulse wih odulation (SPWM) provides a nuber of alternative choices of switching vectors whose tie average over one switching period equals a sapled reference voltage vector [8,9]. A. Six Phase SI Model The drive syste is a six-phase SI fed DSIM, as shown in Fig.. A cobinatorial analysis of the inverter switch state shows switching odes. So, different voltage vectors can be applied to the achine. By using the (x) transforation atrix [ ], we can decopose the into (d-q), (x-y) and (o -o ) voltages. The (o -o ) ones are all equal to zero because the neutrals of the two windings sets are isolated. So the ai of the PWM is to control during each sapling period four variables siultaneously, by generating axiu (d-q) and iniu (x-y) voltages aplitude. The choice of particular switching odes has to be ade in order to satisfy these two conditions. Hence, by choosing the switching odes which perit to select the (dq) voltage vectors having axiu aplitude, we obtain two coplex planes (d-q) and (x-y) divided into sectors and each sector is π radian, as shown in Fig.. Each voltage vector is represented by a decial nuber corresponding to the binary nuber (Kc -Kb -Ka -Kc - Kb - Ka ). This binary nuber gives the state of the upper switches. Only the voltage vectors with axiu aplitude are presented in Fig.. [ ] = () B. Proposed SPWM Techniques Principle This SPWM strategy operates in two coplex planes (d-q) and (x-y). Since there are four variables to control, four active voltage vectors,, and and zero voltage vector need to be chosen during each sapling period, according to the reference voltage vector aplitude and the sector location. Therefore, the reference vector ν sdq is used to locate four adjacent switching state vectors (for exaple: 5,, 9 and in the first sector) and to copute the space vector switching instants (T 5, T, T 9 and T respectively), during the sapling period. For the reaining tie T =-(T 5 +T +T 9 +T ), zero state vectors, 7, 5 or are applied. So SPWM locally averages, over sapling period, adjacent and zero state vectors to be equal to the reference vector []. So that the following equation has a unique and positive solution [,5]: T T T T 5 9 = T = T s sd 5 sq5 sx5 sy5 sd sq sx sy sd 9 sq9 sx9 sy9 ( T5 + T + T9 + T) sd sq sx sy Zero vectors :, 7, 5, Zero vectors :, 7, 5, v v v v sd sq sx sy sdq sxy = Figure. The inverter voltage vectors on (d-q) and (x-y) planes. ()

3 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- a. Switching Sequences : In order to iniize (x-y) haronic currents and aintain the lowest switching frequency, there are different choices to allocate zero voltage vectors, 7, 5 or. The ethod proposed in this paper is to choose switching sequences in such a way that on the (x-y) plane, two consecutive non-zero vectors are practically opposite in phase. By this way, each change of applied vectors will lead to a succession of increase and decrease in (x-y) currents around zero. The difference between reaining possible switching sequences is due to the selection and placeent of zero vectors during the sapling period, as shown in Fig.. The switching sequences proposed in this paper lead to continuous and discontinuous odulation techniques and, consequently, to different haronic distortion characteristics. A odulation technique is continuous when on/off switching occurs within every sapling period, for all inverter legs and all sectors. A odulation technique is discontinuous when one (or ore) inverter leg stops switching, i.e. the corresponding phase voltage is claped to the positive or negative dc bus for at least one sector [,]. b. Continuous Modulation For exaple, when voltage reference vector ν sdq is located in sector-i, a continuous odulation technique (C φ SPWM) is obtained with the following sequences: c. Discontinuous Modulation sequence A For the sae sector-i, a discontinuous odulation technique (D φ SPWM_A) can be obtained with the following sequence: d. Discontinuous Modulation sequence B In the D φ SPWM_B, the zero-voltage vectors are applied at the beginning and at the end of the switching sequence as follows: e. Discontinuous Modulation sequence B In the D φ SPWM_B, the zero-voltage vectors are applied in the iddle of the switching sequence as follows: III. EXPERIMENTAL RESULTS To confir the feasibility of the proposed SPWM techniques on the whole voltage range under /f and vector control, a set of experiental results are carried out []. The experiental test bench is coposed of a six-phase SI feeding a 5kW DSIM prototype and the whole control algorith is tested on a dspace DS controller board. This board has a aster PowerPC running at 5 MHz and a slave TMS F DSP. On PowerPC, we ipleented the vector control and /f control. The original F firware does not allow the change of PWM copare registers and action registers any ties a period. Ka Kb Kc Ka Kb Kc T T 5 T T5 T 9 T T T s Ka Kb Kc Ka Kb Kc T T 9 T 5 (a): C φ SPWM T s T T T T 5.T s T T 5 T T9 T T T 9 T T 5 T. (c): D φ SPWM_B Ka Kb Kc Ka Kb Kc Ka Kb Kc Ka Kb Kc T T 5 T T 9 T T T T s T T 9 T T 5 (b): D φ SPWM_A T5 T T 9 T T T T T 9 T T 5 T s (d): D φ SPWM_B Figure. An exaple of the corresponding PWM outputs state for the switching sequences, when the reference voltage vector is located at sector-i Fro top to botto: Ka - Kb -Kc -Ka -Kb and Kc. Moreover, the siple and full PWM are not synchronized []. So, we reprograed the flashed firware to allow four changes, within a PWM period. Hence, it is possible to ipleent the continuous and discontinuous PWM.The reloading of copare register (CMPRx, SCMPRx) and action registers (ACTR, SACTR) is done on General Purpose Tier (GPT) underflow or period atch. We have to give the F slave DSP the right values before these ticks. Fortunately, the corresponding registers are shadowed. We can then, load the at each GPT period atch. This second tier has to run ties faster than GPT. It has a count period of 5 µs (half of the triangle pattern) if T s = µs. We use the "start with GPT" feature to get GPT synchronized with GPT. The only thing to carefully watch is that CMPRx coputed values ust not overflow or underflow the tier count liits. It eans that there are liitations corresponding to the voltage range that we can not trespass. This can be solved by choosing a correct placeent of zero voltage vectors. These PWM techniques are successfully tested The following conclusions can be drawn fro these experiental results: In the case of the C φ SPWM strategy usually ore than two transitions (for low to high or fro high to low) occur on the corresponding PWM outputs, which increase the switching frequency of the inverter legs. On the contrary, in the case of the discontinuous PWM strategies: D φ SPWM_A, D φ SPWM_B-(B) at least two PWM outputs reain unchanged during the entire sapling period, which allows a switching frequency iniisation. All these techniques are tested at the sae average switching frequency f sw = 5kHz, and the sapling frequency of each technique is: f = f for C φ SPWM. - s sw. T T. s

4 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- - s ( ) f sw - s f sw f = for D φ SPWM-A. f = for D φ SPWM_B-(B). However, for the DSP ipleentation of these strategies, soe adaptations are ade to ensure successful experients. In Fig., the phase current and (d-q) stator current coponents with constant /f control are presented. The average switching frequency is set to 5 khz and the otor is running at 75 rp with load connected. As expected, the phase current presents a pure sinusoidal shape as well as the (d-q) stator current coponents for all these PWM techniques, which confir that these SPWM techniques allow the control of the (d-q) and (x-y) current coponents siultaneously. I. HARMONIC CURRENT ANALYSIS The voltage and current wavefor quality of the PWM- SI drives is deterined by the switching frequency haronics. Since they deterine the switching frequency copper losses and the torque ripple of a otor load and the line current total haronic distortion (THD) of a lineconnected SI, the switching frequency haronic characteristics of a PWM-SI drive are iportant in deterining the perforance. While the copper losses are easured over a fundaental cycle and therefore require a per fundaental cycle (acroscopic) rs ripple current value calculation, the peak and local stresses are properly investigated on a per-carrier cycle (icroscopic) base. Therefore, first a icroscopic and then a acroscopic investigation is required []. Because, the achine odel include (d-q) and (x-y) coponents, so the haronic current analysis ust be ade for the (d-q) and (x-y) currents.. Noralized haronic currents and fluxes calculation The stator voltage equations in the stator coordinate syste are expressed as follows: dφ s vsdq = Rsisdq + () disxy vsxy = Rsisxy + Llsxy Where the stator and the rotor flux equations are given by: φs = Lsis + Mir () φr = Lrir + Mis The stator flux equation can be rewritten: M φ s = σlsis + φr () Lr Substituting () in (), the stator voltage equation can be expressed as follows: disdq M dφr vsdq = Rsisdq +σ Ls + (5) Lr If the relation only between the haronic voltages and currents is considered, it will be assued that the reference voltage vector v s is constant over the sapling period T s because the switching frequency f s is uch higher than the ias (A) ias (A) ias (A) (a). i as phase current (b). isd current coponent Figure. Experiental results with otor operating under constant /f control with load connected for f= 5Hz, at 75rp and for the sae average switching frequency f sw. Fro left to right: (a): i as phase current, and (b): i sd current coponent. Fro top to botto: C φ SPWM, D φ SPWM-A D φ SPWM-B. fundaental frequency f e and that the stator and the rotor tie constants are uch larger than the switching periods, with the resistance drops neglected [5]. Under these assuptions, the voltages and currents can be separated on the haronic coponents, which change over T s while the fundaental coponents reain constant over the sae period. Fro eq.(5), the haronic voltage equation of the stator can be expressed as follows: di v s sdq = σls () di v sxy sxy = Llsxy Where v s is the space vector of the haronic voltage equal to the difference between the actual voltage vector and the reference vector v s. Because the haronic current and haronic flux are only different in scale, and to eliinate the need of load paraeters in eq.(), the haronic flux trajectories can be investigated. Fro eq.(), it is easy to calculate the haronic stator flux per-carrier cycle s as follows: ( N + ) sdq = ( sdqk vsdq ) NT s isd (A) isd (A) isd (A)

5 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- ( N + ) sxy = ( sxyk ) (7) NT s sdq = σls. i sdq and sxy = L lsxy. i sxy Where: In eq.(7), k is the inverter output voltage vector of the kth state, and within the carrier cycle it changes according to the selected switching sequence. Since for high f s /f e values the v ter can be assued constant within a carrier cycle and the k ters are coplex nuber, the above integral can be closed for calculated and the flux trajectories are linear over each state. Therefore, in the SPWM ethod only syetric switching sequences are generated, the integral need only be calculated in the first half of the carrier, and the second half of the trajectory is exact syetrical to the first [,]. Moreover, The (x-y) current coponents are liited by the stator leakage inductance L lsxy, which depends on the coil pitch of the stator windings [5], and consequently the haronic characteristics of the SI feeding DSIM should be investigated with the introduction of the coefficient kσ xy = σls Llsxy, which is necessary to evaluate and copare the perforances of the PWM techniques. So, eploying (7) and noralizing to b = dc π, the per-carrier cycle rs value of the noralized haronic flux srs can be calculated with: ( N + ) srs(, θ ) = ( + sdq k. sxy ) σxy NT s kσ xy = σls Llsxy Where: The per fundaental cycle rs value sfrs (8) of the haronic flux deterines the wavefor quality and haronic losses. Averaging eq.(8) over a fundaental period results in the global haronic flux calculation as follows: θ sfrs ( ) = ( θ + θ θ θ sdqrs (, ) k. sxyrs(, )) d (9) σxy The above integral yields a polynoial function of the odulation index. As an exaple, the per fundaental cycle rs noralized haronic flux sfrs have been calculated for C φ SPWM, D φ SPWM-A D φ SPWM_B-(B) PWM techniques, when the reference voltage vector is located in the sector-. This results in the following dependent analytical forulas: a. Continuous Modulation C φ SPWM : ( ) = ( π sdqfrs π π ( 7 ) π ( 5 π 7 π ) 9 ) ( ) = (7 ) sxyfrs + ( ) 9π () b. Discontinuous Modulation D φ SPWM-A : ( ) = + ( 59 ) sdqfrs 7 8π ( 8 π + 7 π ) 8π ( ) = ( 9 57 ) () sxyfrs 8π c. Discontinuous Modulation D φ SPWM_B-(B) : 5 5 ( ) = + ( 9 5 ) sdqfrs 57π ( 59 + π 57 π ) ( 79 ) 5 5π 7π 5 ( ) = (75 ) () sxyfrs 57π The per fundaental cycle rs curves of the noralized haronic flux sfrs as function of odulation index for all the discussed PWM techniques, at the sae average switching frequency with different leakage coupling coefficient k σ xy, are shown in Fig.5. Fro these curves, it is clear that the rs value of the haronic current varies according to the selected switching sequence. In the low odulation index range, C φ SPWM and D φ SPWM- A have practically the best perforance. As the odulation index increases, the C φ SPWM perforance rapidly degrades while the D φ SPWM_A is superior in the ediu odulation index range. In high odulation index range, D φ SPWM_B-(B) exhibit the best perforance. The intersection point of D φ SPWM-A and D φ SPWM_B-(B) defines the optial transition point. Therefore, an optial PWM can be obtained with a transition between these SPWM strategies to allow rs haronic current iniization over the whole voltage range. Thus, C φ SPWM strategy can be applied in a low voltage range, while D φ SPWM-A can be selected in a ediu voltage range and D φ SPWM_B-(B) is advantageous in a high voltage range. We need to underline that discontinuous PWM techniques allow the selection of a higher sapling rate.. CONCLUSION In this paper, the haronic characteristics of the SI feeding a Double-Star Induction Motor (DSIM) are investigated and presented graphically as function of the odulation index with the introduction of a leakage coupling coefficient. The switching sequences presented lead to continuous and discontinuous odulation strategies, according to the position of zero voltage vectors during the sapling period.

6 Proceedings of the 5th Mediterranean Conference on Control & Autoation, July 7-9, 7, Athens - Greece T- sdqfrs [] : CφSPWM [] : DφSPWM [] : DφSPWM B [] : DφSPWM B sxyfrs [] : CφSPWM [] : DφSPWM [] : DφSPWM B [] : DφSPWM B sfrs [] : CφSPWM [] : DφSPWM [] : DφSPWM B [] : DφSPWM B k xy = σ sfrs (a) (b) (c) sfrs [] : CφSPWM [] : DφSPWM [] : DφSPWM B [] : DφSPWM B k xy = 5 σ [] : CφSPWM [] : DφSPWM [] : DφSPWM B [] : DφSPWM B k xy = σ (d) (e) Figure 5. Per fundaental cycle noralized rs haronic flux as function of odulation index, for all the discussed PWM techniques (a): (d-q) rs haronic flux. (b): (x-y) rs haronic flux (c), (d), (e): The rs haronic flux with different leakage coupling coefficients ( k σ xy = ; 5; ), at the sae average switching frequency f sw. It is shown that the haronic current rs value vary according to the selected switching sequence. Also, fro this point of view, continuous C φ SPWM and discontinuous D φ SPWM_A strategies have an advantage over the others in a low and ediu voltage range, while the discontinuous D φ SPWM_B-(B) strategies have an advantage over the others in a high voltage range. In addition, we should reeber that with D φ SPWM_A the carrier frequency can be increased by factor / for % reduction of switching losses, or ties increased for 5% reduction of switching losses in the case of D φ SPWM_B-(B). Thus, the cobination of these strategies provides the best haronic current perforance over the whole voltage range. REFERENCES [] Y. Zhao and T. A. Lipo, Space ector PWM Control of Dual Three- Phase Induction Machine Using ector Space Decoposition, IEEE Trans. Ind. Appl., ol., No.5, pp. -9, Sept./Oct [] C. G. Hodge, S. Williason and A. C. Sith, Direct Drive Marine Propulsion Motors, ICEM Conference, Brugge,. [] D. Hadiouche, Contribution to the study of dual stator induction achines: odelling, supplying and structure, Ph. D. dissertation (in French), GREEN, Faculty of Sciences and Techniques, University Henri Poincaré-Nancy I, France, Déc.. [] H. Willi,.D. Broeck, H.C. Skudelny and G.. Stanke, Analysis and Realisation of a Pulsewih Modulator Based on oltage Space ectors, IEEE Tans. Ind. Appl. ol No, pp. -5, Jan/Feb 988. [5] D. Hadiouche, L. Baghli and A. Rezzoug, Space ector PWM Techniques for Dual Three-Phase AC Machines: Analysis, Perforance Evaluation and DSP Ipleentation, Conf. Rec. IEEE- IAS, ol., pp [] Alfredo R. Muñoz, Thoas A. Lipo, Dual stator winding induction achine drive, IEEE Trans. Ind. Applicat., vol., NO. 5, pp. 9-79, Sept./Oct.. [7] K. Gopakuar,. T. Ranganathan, and S. R. Bhat, Split-phase induction otor operation fro PWM voltage source inverter IEEE Trans. Ind. Applicat., vol. 9, pp. 97-9, Sept./Oct. 99. [8] A. R. Bakhshai, H.R. Saligheh Rad and G. Joos, Space ector Modulation based on classification ethod in three-phase ulti-level voltage source inverters, pp. 597, IEEE. [9] M. Saeedifard, A. R. Bakhshai, G. Joos and P. Jain, odified low switching frequency space vector odulators for high power ultiodule converters, pp , IEEE. []. Blasko, Analysis of a hybrid PWM based on odified spacevector and triangle coparison ethods, IEEE Trans. Ind. Appl., ol., No., pp. 75-7, May/June 997. [] J. W. Kolar, H. Ertl, F. C. Zach, Influence of the Modulation Method on the Conduction and Switching Losses of a PWM Converter Syste, IEEE Trans. Ind. Appl., ol. 7, No., pp. -75, Nov./Dec. 99. [] Ahet M. Hava, Russel J. Kerkan, and Thoas A. Lipo, Siple analytical and graphical ethods for carrier-based PWM-SI drives IEEE Trans. Power Electron., vol., NO., pp. 9, Jan [] K. Marouani, L. Baghli, D. Hadiouche, A. Kheloui and A. Rezzoug, Discontinuous SPWM Techniques for Double Star Induction Motor Drive Control, IECON Conference, Nov., Paris. [] Texas Instruents, TMSF/C DSP Controllers Reference Guide, Peripheral and Specific Devices, Literature Nuber SPRUC, 999. [5] S. Ogasawara, H. Akagi, and A. Nabae, A novel PWM schee of voltage source inverters based on space vector theory EPE-Proc., pp. 97-, Aachen, 989.