DTC strategy for a DSP-based Five-Level Flying-Capacitor Drive with improved flux estimation

Transcription

1 Mohammad ARASTEH 1, Abdolreza RAHMATI 1, Shahrokh FARHANGI, Adib ABRISHAMIFAR 1 Iran Univerity of Science and Technology (1), Univerity of Tehran () DTC trategy for a DSP-baed Five-Level Flying-Capacitor Drive with improved flux etimation Abtract. Thi paper give a detailed analyi of direct torque control (DTC) trategy in a five-level drive and propoe a 4-ector witching table. Alo, flux etimation ha been improved by a dicrete-time low-pa filter (LPF) with variable cut-off frequency. Algorithm to compenate the amplitude and phae error i introduced and algorithm to determine digital filter coefficient at different peed i preented. Simulation and practical reult on a prototype uing an induction motor 400V, 3kVA are given. To implement the DTC trategy, proceor TMS30F81 i ued. Strezczenie. Przedtawiono analizę trategii DTC w napędzie pięciopoziomowym i zaproponowano 4-ektorową tabelę przełączeń. Strumień był ulepzony dzięki zatoowaniu cyfrowego filtru dolnoprzeputowego o różnej czętotliwości odcięcia. Wprowadzono algorytm kompenacji błędu amplitudy i fazy dla różnych prędkości. Przeprowadzono ymulację i badania prototypu dla ilnika indukcyjnego 400 V, 3 kva. Wykorzytano proceor TMS30F81. (Strategia DTC w pięciopoziomowym napędzie wpomaganym przez proceor ygnałowy) Keyword: direct torque control, witching table, flying capacitor multilevel inverter, flux etimation. Słowa kluczowe: bezpośrednia kontrola momentu DTC, napęd. Introduction Nowaday, high power medium voltage drive are widely ued in petrochemical, tranportation, cement and teel indutrie. Reearch in the field of improving performance and increaing power of thee medium voltage drive i increaed and in the lat decade it ha been one of the mot active area of power electronic. Development of thee drive began in lat decade uing the GTO and today IGCT and high voltage IGBT with the improved witching feature, implicity of control and low loe are prominent choice [1]. Although numerou tructure are provided for medium voltage drive, three tructure of diode-clamped, H-bridge and flying capacitor find more application and are commercially available []-[5]. Among the above tructure, the flying capacitor inverter a hown in Fig. 1 ha been noteworthy becaue it doe not require a tranformer a H-bridge inverter and it doe not caue ditortion a diode-clamped. It i more attractive at high witching frequencie where lead to low capacitor value. Among the method of induction motor peed control, direct torque control (DTC) trategy with a high performance level in the low-voltage drive, alo ha been implemented in multilevel drive [6]-[9]. One crucial point i that DTC drive performance depend on the peed and accuracy of flux etimation. The tator flux i generally etimated uing the voltage model [10]-[13]. In thi model, the tator flux i achieved by the integration of back-emf and only the meaurable electrical parameter (voltage and current) in addition to the tator reitance are required. On the other hand, meauring voltage and current i alway aociated with dc offet. A mall dc offet, no matter how mall it i, can drive the pure integrator into aturation and degrade the drive performance, epecially at low peed. To olve thi problem there are two common method: uing the current model and uing the LPF intead of pure integrator in the voltage model. The current model avoid the drawback of pure integration. However, it require accurate value for the rotor parameter and the motor peed. Rotor parameter are not directly meaurable and depend on the operating condition (temperature and magnetic aturation level). Alo, the peed meaurement need an encoder which will reduce the drive reliability. On the other hand, the voltage model offer ditinct advantage compared with the current model. The main advantage of the voltage model i that it doe not need the rotor parameter. Alo, only one parameter (the tator reitance) need to be known. The tator reitance can be meaured quite accurately and it variation can be etimated in real time uing tator-mounted temperature enor. So in thi paper, an LPF-baed voltage model i ued. The paper contribution i a follow. Firt, it give a detailed analyi of DTC for a five level drive and how to deign the related witching table. Then, a dicrete-time LPF with variable cut-off frequency uitable for flux etimation i introduced and a routine to determine the filter coefficient i given. Direct Torque Control for Multilevel Drive Thi ection i devoted to the analyi of DTC for a five level drive. A. Principle In a three-phae ymmetrical induction motor, electromagnetic torque can be expreed by: 3 Lm (1) Te p r Sin L Lr where and r, are the tator and rotor flux amplitude repectively and δ ψ, the angle between the two flux vector, i called the torque angle. L m, L and L r are the magnetizing, tator and rotor inductance, repectively and σ i the total leakage factor of the motor defined a: () 1 L m L Lr In DTC, the flux amplitude i maintained in about nominal value and the torque angle i ued to control the torque according to (1). Obviouly, the maximum torque i achieved for δ ψ = π/. On the other hand, the torque angle i adjutable uing the tator voltage vector. Stator voltage equation i given by: d (3) u ri dt Alo, (3) can be rewritten a: d dt u r i (4) 13 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/011

2 peed. Since there are four hexagon in αβ-plane, the zero peed to nominal peed can be divided into four range a (6): very low, low, medium and high peed (m i the rotor angular peed and nom i nominal rotor angular peed): (6) 0 m nom / 4 nom / 4 m nom / nom / m 3 nom / 4 3 nom / 4 m nom Fig.1. One leg of a five-level flying capacitor inverter B. Switching table deign The tator voltage vector in a multilevel drive i given by the well-known relation: (7) j0 j / 3 j4 / 3 u uae ube uce Thi pace voltage vector can be indicated a number cba in which a, b and c, repectively, how the voltage level in the related phae. All the pace voltage vector for a five-level drive except the redundant vector are hown in Fig. 3. Compared to two-level inverter, multilevel inverter have a high number of voltage vector with different ize o that the flux vector can be accurately controlled. Thu multilevel drive have a fater and more precie control on the flux and torque. Fig.. Impact of tator voltage vector on torque In multilevel drive like two-level drive, the tator flux trajectory can be controlled by electing the appropriate tator voltage vector. Let the rotating reference ytem be aligned with the tator flux vector a hown in Fig., (hence r ) and can be controlled by d- and q-component of ū, repectively. In other word, the modulu of the tator flux i affected by u d and angle of the tator flux vector i affected by u q. For intance, applying ū 1 and ū vector hown in Fig., letting u q1 = u q, applying ū 1 and ū generate the ame torque. Although both vector increae the flux amplitude, ū lead to a fater variation in the modulu of the tator flux, ince u d > u d1. On the other hand, the torque angle depend on the angle of the rotor flux. The change of rotor flux poition angle related to the tator current and the rotor peed i given by [14]: d (5) r L m iq dt Tr r where r i the poition angle of r, i the rotor electrical peed, T r i the rotor time contant, and i q i the q-component of i with repect to the tator flux axi. ū develop i q with a delay related to the leakage time contant of the tator while the mechanical time contant of the drive inhibit fat change of. For intance, at the medium peed a medium-ize u q can increae the torque angle and conequently the amount of torque, while at high peed the ame u q caue the torque to be reduced. Therefore the vector election will be related to the rotor Fig. 3. Voltage pace vector in a five-level inverter Fig.4. 4-ector diviion for a multilevel inverter A hown in Fig. 3, voltage vector are incribed in four hexagon. Since in the outer hexagon there are 4 voltage vector, in thi paper αβ-plane i divided into 4 ector a hown in Fig.4. Flexibility and only one-level tranition during ector variation are the important advantage of a 4-ector witching table. In order to deign the witching PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/

3 table, the impact of different voltage vector on torque i invetigated. Here, witching table deign in high peed i preented. For intance, aume that the tator flux vector i located in ector 1 along the a-axi. In thi cae, all vector in α>0, β 0 increae the flux amplitude and all vector in the region α>0, β<0 caue the flux amplitude to decreae. Among thee vector, the group vector 0-x, 1-x and -x, repectively, reult in a mall, medium and large variation in the tator flux angle. Therefore, thee group can decreae, keep contant or increae the electromagnetic torque, repectively. Among a group of vector, a vector with a low d-component i preferred becaue a large d-component caue the rapid flux variation and increae the torque ripple. Although the torque ripple can be decreaed by increaing the witching frequency, it i not deirable due to the lo. Vector with a low d-component are hown in Fig. 5. Therefore, the propoed witching equence will be a Table 1 in which the mall-, mediumand large vector are elected to reduce, keep contant or increae torque, repectively. TI and FI indexe are related to the torque and flux error. A value of 1 or -1, repectively, mean that the deired quantity exceed and 0 mean that it i within the range. Similarly, the table for other peed can be provided. The tator flux can be etimated by the voltage model or the tator voltage equation. The pure integration 1/ in (4) with an infinite dc gain may lead to the output aturation owing to DC offet. To deal with the problem, the integrator i ubtituted with an LPF which ha a limited DC gain. Frequency repone of a pure integrator and the two LPF with cut-off frequencie rad/ec and 0rad/ec are hown in Fig. 7. At frequencie much higher than c, the LPF characteritic are imilar to the pure integrator characteritic and integration run well. However, at low frequencie there are the amplitude and phae error. Hence, it hould be noted that although with increaing c the dc offet can be more attenuated, but the amplitude and phae error will increae. The pure integrator characteritic at the tator frequency are given by 1/ e and π/, repectively. The LPF tranfer function and it characteritic at the tator frequency are given by: (9) (8) H( ) 1/( ) (10) H( e ) e 1 c e c H( ) tan 1 e c Comparing two characteritic, it i clear that, the LPF lead to the amplitude and phae error which increae with c. Thu, the real tator flux amplitude i larger than the etimated value by the following factor: (11) 1 ( c / e ) Fig.5. Selected vector baed on low d-component in ector 1 Flux etimation uing the voltage model Block diagram of direct torque control trategy i hown in Fig. 6. A mentioned before, DTC performance depend on the peed and accuracy of the torque and flux etimator. So, the poibility of flux aturation i high. On the other hand due to the phae error, then Sin _ et Sin _ real, that lead to the torque etimation error and increae the torque ripple. The etimated and real torque hown in Fig. 8, are given by (1). Table 1. 4-ector witching Table in high peed TI FI Fig.6. DTC tructure in a flying capacitor inverter 134 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/011

4 1 ( c / e ) 1 1/ k (15) k c (16) 1 1 tan ( k ) tan (1/ k ) Therefore, the real flux vector _ real can be obtained by: (17) _ real _ et k c ( Co jsin ) In [10], the integration algorithm, in dicrete time, i propoed a (18) with α <1. Alo, it i uggeted to reduce α with increaing the tator frequency: Fig.7. Integrator and LPF Frequency Repone (18) y[ k ] y[ k 1] x[ k ] T where, x and y denote the back-emf and the tator flux, repectively. However, the routine to calculate α and how to reduce it with increaing the tator frequency wa not provided. The dicrete time integration algorithm can be derived uing the trapezoidal form of z: z 1 (19) T z 1 Subtituting (19) in (8) give: (0) d [ k ] q [ k ] 1 d [ k 1] 1 q [ k 1] ed [ k ] T eq [ k ] T where e d and e q denote the back-emf value in dq-coordinate and coefficient of α 1 and α are given by: Fig.8. Flux vector and the torque angle (real and etimated) (1) 1 (1 ct ) 1/(1 ct ) (1) T T e _ et e _ real 3 Lm p L L 3 r r Lm p L L 1 Sin r Sin Hence, the torque error i now obtained a: r _ et _ real The tator frequency e can be obtained by: ( vq iqr ) d ( v () e d i r ) d Finally, the flow diagram of flux etimation i hown in Fig.9. q (13) Te Te _ real Te _ et ( Sin _ real 1 Sin _ et ) Te ( Sin _ real Sin _ et ) The torque error can degrade the drive performance epecially in a high performance drive in which torque need to be controlled. Indeed, due to the etimation error, the controller mitakenly aume that the requeted torque i generated. Torque etimation error at light load i more important becaue the requeted torque i about the torque error. To reduce the torque error while efficiently attenuate dc-offet preent in the back EMF, low-pa filter with a variable cut off frequency i ued in which c i proportional to e : (14) e c k However, amplitude and phae error till exit and an efficient integration algorithm hould compenate for them. To compenate for thee error, the etimator output amplitude hould be multiplied by gain (15) and it phae hifted by (16): Fig.9. Flowchart for flux etimation PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/

5 Simulation reult Direct torque control trategy hown in Fig. 7 i imulated and implemented uing a prototype 400-volt, 3kW induction motor. Direct torque control and motor parameter are preented in the Appendix. To invetigate the performance of different flux etimation algorithm, the following cenario i employed. The peed reference i et at 0.3pu and at t = 0.15, a load torque of 0.75pu i applied. Alo, a 0.003pu offet i added to the meaured voltage for phae a. Firt, the etimator with the pure integrator i imulated and the flux vector component are hown in Fig. 10. Although the etimated flux matche the real flux very well for a definite time, finally the flux aturate. Alo, the torque etimation error hown in Fig. 11 i o large that the controller can t adjut the motor peed. The tator current and motor peed waveform hown in Fig. 1 preent a poor performance. aturation. Alo, the flux etimation error lead to the torque etimation error a hown in Fig. 17 and ytem can t preciely adjut the motor peed a can be een in Fig. 18. Fig.13. Real and etimated flux uing LPF (0.01 rad/ec) Fig.14. Real and etimated torque uing LPF (0.01 rad/ec) Fig.10. Real and etimated flux uing an pure integrator Fig.15. The waveform uing LPF (0.01 rad/ec) Fig.11. Real and etimated torque uing a pure integrator Fig.1. The waveform uing a pure integrator Simulation reult uing a low-pa filter with a cut-off frequency 0.01rad/ec are hown in Fig. 13 to 15. Although the limited dc gain prevent the flux from aturation, but the phae and amplitude error in the flux etimation, epecially in the tranient tate, caue the torque and peed to ocillate, a hown in Fig. 14 and 15. To avoid flux aturation, the filter cut-off frequency can be increaed. Simulation reult uing a filter with cut-off frequency rad/ec i hown in Fig. 16. Although the dc offet i more attenuated but the high phae error lead to an advere repone in the tranient tate and the flux Fig.16. Real and etimated flux uing an LPF ( rad/ec) An LPF with a variable cut off frequency i a prominent olution. The maller k, the larger c and hence the dc offet will be more attenuated. A hown in Fig. 19, for k= the etimated flux matche the real flux very well. Uing the gain and the phae compenator, the etimated torque matche the real torque very well a hown in Fig. 0. The motor peed ha accurately followed the peed command a can be een in Fig. 1. Selecting a larger k lead to reduction of the phae and amplitude error o that the tranient repone will be 136 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/011

6 improved. Comparing Fig. with Fig. 19, the etimated flux uing k=5 at the tranient tate matche the real flux very well. Alo, comparing Fig. 3 with Fig. 0, it i clear that, the torque error and hence, the peed ocillation are reduced. Baed on thee reult, k i elected between and 5 depending on dc-offet value in the meaured voltage. Fig.1. The waveform uing variable cut-off frequency LPF with k= Fig.17. Real and etimated torque uing LPF( rad/ec) Fig.. Real and etimated flux uing a variable cut-off frequency LPF with k=5 Fig.18. The waveform uing LPF ( rad/ec) Fig.3. The waveform torque uing a variable cut-off frequency LPF with k=5 Fig.19. Real and etimated flux uing variable cut-off frequency LPF with k= Fig.4. The tator current and rotor peed uing a variable cut-off frequency LPF with k=5 Fig. 0. Real and etimated torque uing variable cut-off frequency LPF with k= Practical Reult Five-level flying capacitor drive i hown in Fig. 5. Different part of the ytem have been named including IGBT and related Driver, flying capacitor, voltage tranducer and DSP controller. The main proceor board ezdspf81 with 150MIPS capability i uitable for implementing DTC. The proceor i equipped with a 16- channel ADC which i ued to meaure nine floating-capacitor voltage, two phae-current, three- phae voltage and the DC link voltage. Six I/O port with 56-pin provide command to 4 IGBT eaily. To meaure the capacitor voltage, the iolated DC-voltage tranducer are PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/

7 ued. A compreor hown in Fig. 6 i ued a a mechanical load. The motor peed i et equal to 85% pu. Firt motor i tarted uing a light-load and the etimated flux and torque are hown in Fig. 7 and 8. Reduction of the torque etimation error after compenation i evident in Fig. 8. Then, motor uing the compreor a load i tarted and the commanded torque, the etimated torque before and after compenation, the rotor peed and the tator current a per-unit are hown in Fig. 8. In thi cae reduction of the torque etimation error after compenation i obviou too. Fig.9. Torque command, actual torque, tator current, peed and tator flux with compreor load Fig.5. Five-level flying capacitor DTC drive Fig.6. Compreor ued a mechanical load Fig.7. Etimated tator flux after and before compenation with a light load Fig.8. Torque command and it difference with etimated torque with a light load Concluion Thi paper ha analyzed in detail a 4-ector DTC trategy for a five-level flying capacitor drive and preented a proper witching table. Alo, the routine to determine coefficient for the dicrete time LPF i preented. The tator flux wa exactly etimated by the dicrete time variable-frequency LPF. Simulation and practical reult on a prototype hown that uing accurate flux etimation, the etimated torque matche the real torque well, epecially at light load. Appendix Induction motor pecification: V=400V, Power=3 kw, p=(4 pole), R=1.873Ω, Rr=1.86Ω, Ll=Llr=7.54mH, Lm=10mH, J=0.01kg-m. Direct torque control parameter: Torque hyterei bandwidth =0.N.m, Flux hyterei bandwidth = 0.01Wb, Initial and nominal machine flux=0.8wb Maximum witching frequency=5000hz, DTFC ampling=50us REFERENCES [1] Joé Rodríguez, Steffen Bernet, BinWu, Jorge O. Pontt and Samir Kouro, Multilevel Voltage-Source-Converter Topologie for Indutrial Medium-Voltage Drive, IEEE Tran. Indut. Electron., vol. 54, no. 6, Dec. 007 [] S. Kouro, M. Malinowki, K. Gopakumar, J. Pou, L. G. Franquelo, B. Wu, J. Rodriguez, M. A. Pérez, and Joe I. Leon, Member, Recent Advance and Indutrial Application of Multilevel Converter, IEEE Tran. Indut. Electron., vol. 57, no. 8, Aug. 010 [3] H. Abu-Rub, J. Holtz, J. Rodriguez, and G. Baoming, Medium-Voltage Multilevel Converter State of the Art, Challenge, and Requirement in Indutrial Application, IEEE Tran. Indut. Electron., vol.57, no. 8, Aug. 010 [4] S. S. Fazel, Steffen Bernet, D. Krug, and K. Jalili, Deign and Comparion of 4-kV Neutral-Point-Clamped, Flying-Capacitor, and Serie-Connected H-Bridge Multilevel Converter, IEEE Tran. Ind. Applicat, vol. 43, Jul./Aug. 007,pp [5] D. Krug, S. Bernet, S. S. Fazel, K. Jalili, and M. Malinowki, Comparion of.3-kv Medium-Voltage Multilevel Converter for Indutrial Medium-Voltage Drive, IEEE Tran. Indut. Electron., vol. 54, no. 6, Dec. 007 [6] J. Rodríguez, J.Pontt, S. Kouro, and P. Correa, Direct Torque Control With Impoed Switching Frequency in an 11-Level Cacaded Inverter, IEEE Tran. Indut. Electron., vol. 51, Aug. 004 pp [7] A. Sapin, P. K. Steimer, and J.-J. Simond, Modeling, Simulation, and Tet of a Three-Level Voltage-Source Inverter 138 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 87 NR 6/011

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