Better DC Bus Utilization and Torque Ripple Reduction by using SVPWM for VSI fed Induction Motor Drive

Transcription

1 Better DC Bu Utiliation and Torque Ripple Reduction by uing SPWM for SI fed Induction Motor Drive K.Gopala Krihna, T. Kranthi Kumar, and P. enugopal Rao Abtract The maximum value of the peak-phae voltage that can be obtained from a -Ph inverter with Sinuoidal Pule Wih Modulation (SPWM technique i equal to.5 It can be improved to.577 by Space ector Pule Wih Modulation (SPWM. So that a better DC bu utiliation compared to SPWM (by about 5.4%. With the Conventional Direct Torque Control cheme employing a oltage Source Inverter (SI, it i poible to control directly the tator flux linkage and the electromagnetic torque by the optimum election of inverter witching vector. The election of inverter witching vector i made to retrict the flux and torque error within the repective flux and torque hyterei band. However, DTC drive utiliing hyterei comparator uffer from high torque ripple and variable witching frequency. The mot common olution to thi problem i to ue the Space ector Modulation. Thi achieve lower witching loe, better DC bu utiliation, lower torque ripple, contant witching frequency. In thi paper the modeling and imulation of induction motor drive employing SM-DTC wa carried out uing MATLAB/SIMULINK imulation package and reult are compared with Conventional DTC. Index Term DTC, SI, SM. I. INTRODUCTION The name Direct Torque Control i derived from the fact that, on the bai of error between the reference and the etimated value of torque and flux, it i poible to directly control the inverter tate in order to reduce the torque and flux error with in precribed limit. In [4], [7]-[9], different method have been preented which allow contant witching frequency operation. In general, they require control cheme which are more complex with repect to the baic DTC cheme. With reference to current and torque ripple it ha been verified that a large influence i exerted by the amplitude of flux and torque hyterei band, and the voltage vector election criteria [], []. It can be noted alo that a given voltage vector ha a different effect on the drive behavior at high and low peed. Taking thee conideration into account, a good compromie ha been obtained uing different witching table at high and low peed []. In general, the determination of the witching table i carried out on the bai of phyical conideration concerning the effect determined by radial and tangential variation of the tator flux vector on torque and flux value. Although Manucript received February, ; revied March,. K. G. Krihna i with the EEE Department at Adam Engineering College (Accredited by NBA, Paloncha. T. K. Kumar i with the EEE Department at Avanthi Intitute of Engineering and Technology, Hyderabad. P.. Rao i with the Department at SR Engineering College (Autonomou, Warangal, Andhra Pradeh. imple, thi approach lead to unexpected torque variation in ome particular operating condition. The undertanding of thee phenomena require a rigorou analytical approach taking the electromagnetic behavior of the machine into account [], [6]. A ubtantial reduction of current and torque ripple could be obtained uing, at each cycle period, a preview technique in the calculation of the tator flux vector variation required to exactly compenate the flux and torque error [4], [8]. In order to apply thi principle, the control ytem hould be able to generate, at each ampling period, any voltage vector (e.g., uing the Space ector Modulation technique. The cloed-loop tator flux predictive control, open-loop torque control uing pace-vector Modulation (SM implementation i hown in [5]. The SM i a Performant open-loop vector modulation trategy []. Thi paper introduce a new direct torque and flux control baed on SM (DTC-SM for IM drive. It implement cloed-loop control for both flux and torque in a imilar manner a DTC, but the voltage i produced by an SM unit. Thi way, the DTC tranient performance and robutne are preerved and the teady-tate torque ripple i reduced. Additionally, the witching frequency i contant and totally controllable. II. PRINCIPLE OF SM-DTC Space ector Modulation i one of the PWM technique in which, when the drive i excited by -ø balanced current produce a voltage pace vector which trace a circle with uniform velocity by ampling that rotating reference voltage pace vector with high ampling frequency different witching can be poible. It i imilar to Sine-Triangle PWM in which inuoidal frequency i proportional to rotating pace vector and triangle wave frequency i proportional to ampling frequency. Fig.. Block diagram of SM-DTC. In the block diagram directly AC upply i not connect to Induction Motor becaue for majority of application, a wide range of frequency variation i deirable. That why -øac i connected diode rectifier which convert AC to DC, diode rectifier becaue it improve power factor. Rectified DC output i fed to inverter to convert it to AC. They are broadly

2 claified depending upon ource feeding them: oltage or Current ource. In both thee ource, the magnitude hould be adjutable. The output frequency become independent of input upply frequency, by mean of link. The link filter conit of a capacitor to keep the input voltage to the inverter a tiff DC. Thi i power converion tage. The torque and flux of induction motor are etimated and they are compared with reference torque and flux, that error i modulated in SM and fed to the inverter o that repective inverter tate i witched. In cae of DC eparately excited machine by contruction armature and field are orthogonal and it i eaily poible to control torque and flux producing component independently. Similar to that for induction machine it i required to reolve tator current into flux producing and torque producing component for independent control. In detail -ømachine dynamic model i complex becaue the -ø rotor winding move with repect to -ø tator winding. So by converting -ømachine into equivalent -ø machine complexity reduce. Conider a ymmetrical three-phae induction machine with tationary a-b-c axe at π/-angle apart, a hown in Fig. Our goal i to tranform the three-phae tationary reference frame (a~b~c variable into two-phae tationary reference frame (d ~q variable and then tranform thee to ynchronouly rotating reference frame (d e ~q e, and vice-vera. Aume that the d q. Axe are oriented at Ө angle, a hown in Fig. The voltage d and q can be reolved into a~b~c component and can be repreented in the matrix form a a q b q d c q d And inverely q a b c d b c In term of tator reitance and flux linkage d q Riq q d d Rid d d Rriqr qr r dr d Rridr dr r qr And the torque can be written a P Te diq qid Firtly model of a three-phae voltage ource inverter i preented on the bai of pace vector repreentation i hown in Fig. Sto S6 are the ix power witche that hape the output, when top witch i ON taken a and when bottom witch i ON taken a. That mean for each limb two tate are poible, a there are limb total tate are poible hown in Fig. 4 a Fig.. Stationary frame a~b~c to d ~q axe tranformation a b c = co co( co( in in( in( The correponding invere relation i q co co( co( d = in in( in( o where o i added a the ero equence component, which may or may not be preent. We have conidered voltage a the variable. The current and flux linkage can be tranformed by imilar equation. It i convenient to et Ө=, o that the q axi i aligned with the a-axi. Ignoring the ero equence component, the tranformation relation can be implified a q d o a b c Fig.. Power circuit of a three-phae SI. A a reult, ix non-ero (active vector and two ero vector are poible. Six non-ero vector ( - 6 Shape the axe of a hexagonal a depicted in Fig 5. and feed electric power to the ytem. The angle between any adjacent two non-ero vector i 6 degree. Meanwhile, two ero vector ( and 7 are at the origin and apply ero voltage to the load. The eight vector are called the baic pace vector and are denoted by (, (, (, (, 4(, 5(, 6(, 7(. The ame tranformation can be applied to the deired output voltage to get the deired reference voltage vector ref in the d-q plane. The objective of SPWM technique i to approximate the reference voltage vector ref uing the eight witching pattern. One imple method of approximation i to generate the average output of the inverter in a mall period, T to be the

3 ame a that of ref in the ame period. Fig. 4. Eight inverter voltage vector ( to 7. Therefore, pace vector PWM can be implemented by the following tep: Step : Determination of d. q, ref and angle (α Step : Determination of time duration T, T, T Step : Determination of the witching time of each witch (S to S6 Step : Determination of d, q, ref, and angle (α From Fig. 5 we can write Fig. 5. Baic witching vector and ector. Step : Determination of the witching time of each witch (S to S6 The witching time for each witch i tabulate in Table I. The waveform conidered in Fig. 6 i the witching pule of the upper witch and mirror image repreent the pule of lower witch in ector imilarly we can realie in other ector alo. d q an bn co6 cn co6 = an bn cn co co bn Step : Determination of time duration T, T, T From Fig. 5 The witching time duration can be calculated a follow: Switching time duration at Sector can be realied by and vector and one of two null vector or 7.In other word, tate i active for time T, i active for T, and one of null vector ( or 7 i active for T.Becaue the vector and are contant and or 7 i, We can equate the olt time of reference vector to the Space ector a, (here f=fundamental frequency cn Sector TABLE I: SWITCHING TIME TABLE AT EACH SECTOR Upper Switche (S,S,S 5 S =T +T +T / S =T +T / S 5=T / S =T +T / S =T +T +T / S 5=T / S =T / S 5=T +T / S =T +T +T / S =T / S =T +T / S 5=T +T +T / S =T / S =T +T / S 5=T +T +T / S =T / S 5=T +T / S =T +T +T / Lower Switche (S 4,S 6,S S 4=T / S 6=T +T / S =T +T +T / S 4=T +T / S 6=T / S =T +T +T / S 4=T +T +T / S 6=T / S =T +T / S 4=T +T +T / S =T / S 6=T +T / S 6=T +T +T / S =T / S 4=T +T / S 6=T +T +T / S 4=T / S =T +T / T ref (where, α 6 T T q tan t ft d T ref T. T. co T. in T T T T T ( T co in T in a in in a in where T f and a ref ( Fig. 6. SPWM witching pattern of upper witch ector. III. DC BUS UTILISATION BY SPWM The principal advantage of the SPWM over SPWM i that it enhance the DC bu utiliation by about 5%. It i intructive to evaluate the ample-averaged pole voltage of a phae, AO for intance, to undertand thi fact. In eqn., r denote the amplitude of the reference vector and α repreent the poition of the reference vector with repect to the beginning of the ector in which the tip of the reference vector i ituated. From Fig. 5 During t the following are equation (, (, (4 4

4 During (6, (7 / T T T T AO, avg T / T T T T BO, avg T / T T T T CO, avg T ( ( (4 t 9 the following are equation (5, / T T T T AO, avg T / T T T T BO, avg T / T T T T CO, avg T (5 (6 (7 (/ * ph, peak r ( Maximum magnitude of the reference voltage pace vector correpond to the radiu of the bigget circle that can be incribed in the hexagon a hown in Fig. 5 and i equal to, / where i the input DC voltage. Thu, the maximum value of the peak-phae voltage i given by ( ph, peak,max * *.577 * It i known that the maximum value of the peak-phae voltage that can be obtained from a -Ph inverter with Sinuoidal Pule Wih Modulation (SPWM technique i equal to.5 It i therefore evident that SPWM achieve a better DC bu utiliation compared to SPWM (by about 5.4%. Subtituting eqn. in eqn. one obtain: (8 /, * r T * AO avg in(6 in T in 6 Noting that implifying, t AO, avg, when t and r Sin t (9 Subtituting eqn. in eqn. 5 one obtain equation ( below: /, * r T * AO avg in(6 in ( T in 6 Noting that t, when t 9 and implifying, r AO, avg Sin( t ( The average pole voltage variation i plotted in Fig. 7 The waveform of the average pole voltage conit of a fundamental component and component of triplen order. Fig. 8. d-q tator flux with SM-DTC. Fig. 9. d-q tator flux with a conventional DTC. Fig.. Output torque with SM-DTC. Fig.. Output torque with conventional DTC. Fig. 7. Waveform of averaged pole voltage, phae voltage and line-line voltage The waveform of the averaged line-line voltage i inuoidal a the triplen voltage component of the pole voltage cancel out each other, being cophaal. The averaged phae voltage alo remain inuoidal with a peak value, which i / time that of the peak value of the line-line voltage. The peak value of the A-phae voltage, while the inverter i operated in the range of linear modulation i given by: Fig.. SM-DTC Simulink model. 5

5 Simulation wa carried out on a -øinduction motor having Stator reitance:.7ω, Stator inductance:.56h, Rotor reitance:. Ω, Rotor inductance:.56h, Mutual inductance:.45h, Frictional coefficient:.85, Number of pole:. Switching frequency: 5KH. Fig. how Simulink model of SM-DTC. Fig. 8- how the reult of conventional DTC, SM-DTC. I. CONCLUSION From the Simulation reult it i clearly oberved that DTC drive utiliing hyterei comparator (Conventional-DTC uffer from high torque ripple and variable witching frequency. By uing contant witching frequency technique (SM-DTC torque ripple i ignificantly improved. Thu it i poible to conclude that SM-DTC can offer high performance characteritic than conventional-dtc. REFERENCES [] A. Mir, D. S. Zinger, and M. E. Elbuluk, Fuy implementation of direct elf control of induction motor, IEEE Tran. Ind. Applicat, vol.. [] A. Tani, D. Caadei, and G. Serra, Analytical invetigation of Torque and flux ripple in DTC cheme for induction motor, in Proc. IECON 97, New Orlean, LA. [] A. Tani, D. Caadei, G. Grandi, and G. Serra, Effect of flux and torque hyterei band amplitude in direct torque control of induction machine, in Proc. IECON 94, Bologna, Italy, pp. 5 9, 994. [4] A. Tani, D. Caadei, and G. Serra, Stator flux vector control for high performance induction motor drive uing pace vector modulation, Electromotion, vol., no.. [5] A. Tani, D. Caadei, and G. Sera, Stator flux vector control For high performance induction motor drive uing pace vector modulation, in Proc. OPTIM 96. [6] B. de Fornel, E.. Weterholt, I. El Haan, and X. Roboam, Torque dynamic behavior of induction machine DTC in 4 Quadrant operation, in Proc. ISIE 97, Guimarae, Portugal. [7] C. Lochot, P. Mauion, and X. Roboam, A new direct torque control trategy for an induction motor with contant witching frequency operation, in Proc. EPE 95, Spain. [8] Contant frequency operation of a DTC induction motor drive for electric vehicle, in Proc. ICEM 96, vol. III, igo, Spain, Sept. [9] F. Profumo, L. M. Tolbert, M. Patorelli, and T. G. Habetler, Direct torque control of induction machine uing pace vector modulation, IEEE Tran. Ind. Applicat., vol. 8, Sept./Oct. 9. [] J. K. Pederen and P. Thoegeren, Stator flux oriented aynchronou vector modulation for AC-drive, in Proc. IEEE PESC 9. [] Switching trategie in direct torque control of induction machine, in Proc. ICEM 94, Pari, France, Sept. [] K. G. Krihna and P.. Rao, Space ector Pule Wih Modulation for Two Level Inverter feeding Induction Motor in Proc. NCEEE,. [] K. G. Krihna and P.. Rao, Torque ripple reduction by uing Space ector Pule Wih Modulation for SI fed Induction Motor drive in Proc. NPEC,. K. Gopala Krihna working a Aitant Profeor in EEE Department at Adam Engineering College Accredited by NBA, Paloncha. He completed hi Pot Graduation in Power Electronic from SR Engineering College (Autonomou, Warangal, Andhra Pradeh. And he completed Graduation in EEE from Adam Engineering College (Accredited by NBA, Paloncha. Hi paper publihed in International Journal, National and International Conference Proceeding. And he i life member of Indian Society for Technical Education. T. Kranthi Kumar working a Aitant Profeor in EEE Department at Avanthi Intitute of Engineering and Technology, Hyderabad. He completed Graduation in EEE from Adam Engineering College (Accredited by NBA, Paloncha. Hi paper publihed in International Journal, National and International Conference Proceeding. And he i life member of Indian Society for Technical Education. P. enugopal Rao working a Profeor and Head of the Department at SR Engineering College (Autonomou, Warangal, Andhra Pradeh. Many of hi paper publihed in International Journal, National and International Conference Proceeding. And he i life member of Indian Society for Technical Education. Hi Reearch area include Wavelet and their application to Power Sytem, Power and Indutrial Drive etc. 6