JOURL OF ELEROI SIEE D EHOLOGY OF HI, VOL. 6, O., JUE 8 9 SVPWM echniques and pplications in HS PMSM Machines ontrol heng-guang Wang, Jian-un Jin, You-Guang Guo, and Jian-Guo hu bstract his paper introduces the principle of space vector pulse width modulation (SVPWM), and discusses a method for implementing the SVPWM based on ML/SIMULI, as well as modeling of servo system with permanent magnet synchronous motor (PMSM). Simulation results show that the model is effective, and the method provides a frame of reference for software and hardware designs which can be applied in high temperature superconducting (HS) flywheel energy storage system (FESS) and linear motor (LM). Index Flywheel energy storage system (FESS), linear motor (LM), modeling and simulation, permanent magnet synchronous motor (PMSM), space vector pulse width modulation (SVPWM).. Introduction Digital control techniques of motors, such as the space vector pulse width modulation (SVPWM), have been developed with wide range industrial applications. he SVPWM was brought forward in the 98 s, specifically for the frequency varying and speed regulation of motors. It controls the motor based on the switching of space voltage vectors, by which an approximate circular rotary magnetic field is obtained. In other words, the inverter is controlled to output an appropriate voltage waveform. his forms the basis of the magnetic flux linkage tracking pulse width modulation []-[6]. he basis of SVPWM is different from that of sine pulse width modulation (SPWM). SPWM aims to achieve symmetrical -phase sine voltage waveforms of adjustable voltage and frequency, while SVPWM takes the inverter and motor as a whole, using the eight fundamental voltage vectors to realize variable frequency of voltage and speed adjustment. If the voltage drop across stator resistance is ignored, when the stator windings are supplied with perfect Manu script received March 5, 8; revised pril 8. his work is supported by the hinese High echnology Development Plan Project under Grant o. 78..-G. Wang and J.-. Jin are with the enter of pplied Superconductivity, University of Electronic Science and echnology of hina, hengdu, 65, hina (e-mail: zhengguangw@6.com and jxjin@uestc.edu.cn). Y.-G. Guo and J.-G hu are with the Faculty of Engineering, University of echnology, Sydney, SW 7, ustralia (e-mail: youguang@ eng.uts.edu.au and joe@eng.uts.edu.au). sine waveform voltages, a rotating voltage space vector is formed with constant magnitude and hence the airgap flux density rotates with constant speed and circular track [8],[9].. HS PMSM Machines he flywheel energy storage system (FESS) has features of high energy density, high power density, high efficiency, long life and no pollution, etc. High temperature superconducting (HS) materials have brought great opportunity to this technology [7]. With the rapid development of high-intensity fibers, power electronic devices, rare-earth permanent magnet materials, microcomputer technology, and control theory, the practical applications of the HS FESS will be used in various areas, such as electrical power peaking modulation, UPS, electric automobile battery, control of satellite attitude, and electromagnetic cannon requesting short-time large-power supply [],[]. HS linear motor (LM) is another related HS application, which can be applied to maglev driving systems and also the electromagnetic cannons with high efficiency. Due to a number of merits of the HS permanent magnet synchronous motor (PMSM), it has become the best choice for the FESS which requires the electric machine featuring small volume, light weight, high efficiency, small moment of inertia, and high reliability. he PMSM is also suitable to develop a HS LM. HS FESS consists of high speed flywheel, bearing support system, electromotor/dynamo, power electronic converter, electronic control equipment, and extra equipment such as vacuum chamber, etc. It is a kind of integrated building block systems. FESS has three operation modes as follows: ) Flywheel charge mode: supply offers power supply to the flywheel controller, which controls the input of electrical energy that flywheel runs at the maximal rating rotary speed. ) Flywheel energy maintenance mode: FESS depends on the least current input which keeps flywheel at the maximal rotary speed. ) Flywheel discharge mode: when the supply is off, the flywheel offers power supply to the flywheel controller, which feeds UPS and user load. hen, the flywheel rotary speed decreases. he HS PMSM servo mathematical model is able to realize digitization control of the HS FESS and LM. he models are built as shown in Fig. and Fig..
9 Rectifier Power supply Inverter i aib urrent detection Fig.. HS FESS principle diagram. Rectifier Inverter i c Drive circuit Superconductive magnetic bearing Feedback JOURL OF ELEROI SIEE D EHOLOGY OF HI, VOL. 6, O., JUE 8 Speed detection Vacuum PMSM stator PMSM rotor ryostat Rotor Y Stator off state with, the on-off states of three phases have eight combinations, correspondingly forming eight voltage space vectors, as shown in Fig. [],[]. refers to the operation times of two adjacent non-zero voltage space vectors in the same zone. oth V () and V 7 () are called the zero voltage space vector, and the other six vectors are called the effective vector with a magnitude of /. For example, when the output voltage vector V is within zone one, it is composed of V, V 6, V and V 7 and can be obtained by V out = V /+ 6 V 6 / () he eight on-off states of inverter are listed in able. able : Eight on-off states of the inverter Inverter State S SS S S S V / V / V / / / / / / / / / / / / / 5 / / / 6 / / / 7 V () V 6() Power supply Drive circuit Fig.. HS LM principle diagram.. Principle of SVPWM SVPWM aims to generate a voltage vector that is close to the reference circle through the various switching modes of inverter. Fig. is the typical diagram of a three-phase voltage source inverter model []. For the on-off state of the three-phase inverter circuit, every phase can be considered as a switch S. Here, S (t), S (t) and S (t) are used as the switching functions for the three phases, respectively. n / a Fig.. ypical diagram of a three-phase inverter. b he space vector of output voltage of inverter can be expressed as V(S, S, S ) = (S +αs +α S )/ () where is the D bus voltage of inverter and α=e j. If we express the on state of the upper-arm with and the c n V out V () V V V/ V () V 5() Fig.. Diagram of voltage space vector. 6 6/ (). SIMULI Simulation of SVPWM ased on the principle of SVPWM, the simulation models for generating SVPWM waveforms mainly include the sector judgment model, calculation model of operation, time of fundamental vectors, calculation model of switching time, and generation model of SVPWM waveforms.. Sector Judgment For applying the technology of SVPWM, firstly it is requested to determine the sector which the voltage vector is within. onsidering that the expression of vector in the α-β coordinate is suitable for controlling implementation, the following procedure is used for determining the sector. When V β >, = ; when V α V β >, =; when V α +V β <, =. hen, the sector containing the voltage
WG et al.: SVPWM echniques and pplications in HS PMSM Machines ontrol 9 vector can be decided according to = ++, listed in able. Fig. 5 shows the corresponding model. able : he sector containing the voltage vector versus eta lpha Sector Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ 5 6 Fig. 5. Model of sector judgment.. alculation of Operation imes of Fundamental Vectors able lists the operation times of fundamental vectors against, where and m refer to the operation times of two adjacent non-zero voltage space vectors in the same zone. Fig. 6 shows the calculation model, where =( V α +V β )/( ), Y=( V α +V β )/( ), = [V β /( )]. he sum of and m must be smaller than or equal to (PWM modulation period). he over saturation state must be judged: if + m >, take = [/( + m )], m = m [/( + m )]. Fig. 7 illustrates the SIMULI-based model. able : Operation time of fundamental vector lph eta Gain 5 6 Y Y m Y Y Gain Gain Gain onstant Switch Switch Switch Fig. 6. Model for counting, Y and. Subtract dd onstant Subtract Subtract Gain Gain Divide Divide Divide dd Gain Y Gain Y Fig. 7. alculation model of operation times of fundamental vectors.. Generation of SVPWM Waveform he relation between and switch operation times is shown in able and realized in Fig. 8 and Fig. 9, where a =( m )/, b = a + /, and c = b + m /, cm, cm and cm are the operation times of the three phases respectively. able : Relation between, cm, a, b, and c m Fig. 8. Model of switch operation time.. alculation Model of Switch Operation ime y comparing the computed cm, cm and cm with the equilateral triangle diagram, a symmetrical space vector PWM waveform can be generated and its model is shown in Fig. [5]-[7]. he waveforms of PWM, PWM and PWM6 are obtained by reversing those of PWM, PWM and PWM5, respectively. he PMSM is controlled by switching on or off the power electronic parts. Fig. illustrates the overall model of SVPWM. F cn f(u) f(u) F cn F cn f(u) 5 6 cm b a a c c b cm a c b b a c cm c b c a b a m onstant / / onstant Product Product Product a b c m
9 JOURL OF ELEROI SIEE D EHOLOGY OF HI, VOL. 6, O., JUE 8 cm are in mechanic degrees, but in the actual coordinate transform the electrical angle is adopted, the measured angle and speed are multiplied by the number of pole-pairs of the motor. he simulation model of the control system is shown in Fig.. a b c Switch Switch Fig. 9. Relation between, cm, a, b, and c. Repeating sequence cm cm cm Relay Relay Relay Fig.. Generation model of SVPWM waveforms. cm cm Switch PWM PWM PWM5 5. PMSM Simulation Model he PMSM simulation model of closed loop system can be built by connecting the above-mentioned sub-models. ecause the measured rotor angle and speed 6. Simulation Results When the sampling period of PWM is. s, the D bus voltage is V, the carrier frequency of PWM waveform is khz, the dead zone time is μs, the SVPWM waveform in a sampling period is shown in Fig., s refers to sampling time, refers to the time of zero vector operation, k and k+ refer to the operation times of two adjacent non-zero voltage space vectors in the same zone, then the resultant torque increases to times. he phase is switched to the next in every 6 electrical degrees. he operation duration of each power electronic part is electrical degrees. he exciting duration of each winding is electrical degrees: including degrees for positive direction and degrees for negative direction. When the parameters of speed regulator are set as P =.5, i =.5; the q-axis current regulator is set as p =, i =; the d-axis current regulator is set as p =, i =, the simulated current, rotor speed, torque and rotor angle of the PMSM are shown in Fig.. It can be seen that the simulations agree with common operational characteristics, proving the validity of the presented model. he simulation reference speed is set as rad/s, the simulation step is. s, and the simulation time is. s. t t= s, the motor starts up with no-load; at t=. s, a load torque of m is applied. From the simulations, it can be seen that the startup speed of motor is fast and is able to follow the reference speed. With load torque, the fluctuation of rotary speed waveform is very small. he PMSM used in the simulation model is Y55-, whose major parameters are listed in able 5. beta beta Y beta Y m m b a a b c cm cm cm cm PWM PWM O O double double g onstant c cm cm PWM5 double O Fig.. Overall model of SVPWM.
WG et al.: SVPWM echniques and pplications in HS PMSM Machines ontrol 95 PI PI PI d q theta a b dq/abc a b c beta abc/ab onstant beta g SVPWM Step g Universal bridge Machines measurement demux is_abc PMSM m is_qd vs_qdm S wm Scope thetam Scope Scope e Scope Gain Fig.. Simulation model of control system of PMSM. = / =s / = s / / = / = ( k+)/ = s / / = / = / = s / / =(+ k+ )/ = / = s / / = s / = / / = s / / = s / / = / = ( k+ )/ 6 = s / / = / = / = s / / =+( k+ )/ = / = s / / = s / / = / = ( k+ )/ = s/ / = / = / = s / / = / = / = s / / =+ k+ 8 6 Fig.. SVPWM waveform in a single sampling period. able 5: Major parameter of a PMSM Item Parameter Power range W to55 W Moment of inertia.8 kgm Rated torque.5 m Voltage range 76 V to 8 V Rated current.5 Stator resistance.875 Ω Stator inductance 8.5 mh Rated speed 5 rpm Frequency varying range Hz to 5 Hz Fig. 5 shows the simulated waveforms of d-q axis stator currents. When t=. s, a torque of m is applied from no-load. It can be observed that the q-axis current is directly proportional to the torque, while the d-axis current is nearly zero. It can be concluded that the three-phase stator currents have well been decoupled. With a reference speed of rad/s, the simulated line-to-line voltage (-) and phase voltage waveforms are shown in Fig. 6 and Fig. 7, respectively. he section transform of the voltage vector is shown in Fig. 8. It can be seen that the voltage vector rotates anticlockwise in proper order, i.e. Ⅲ(), Ⅰ(), Ⅴ(),Ⅳ(), Ⅵ (), Ⅱ(). Fig. 8 accords with Fig. and able. is_abc wm e θ 5 5.5..5..5..5. Fig.. Simulated current, rotor speed, torque and rotor angle. I () ngular velocity/rad (s) ngle (deg) orque (m)
I () 96 is_qd.5..5..5..5. ime offset: Fig. 5. Simulated waveforms of d-q axis stator currents. v (V) v (V)...6.8. ime offset: Fig. 6. Simulated waveform of line voltage......5 ime offset: Fig. 7. Simulated waveform of phase voltage. Sector () 7 6 5.5..5..5..5. ime offset: Fig. 8. Sector transform of voltage vector. From the rotor speed response curve, it is observed that after starting-up, the motor accelerates to a stable value quickly. Similarly, the electromagnetic torque and the three phase currents maintains at the steady values with small fluctuation shortly. JOURL OF ELEROI SIEE D EHOLOGY OF HI, VOL. 6, O., JUE 8 isq isd 7. onclusion omparing with the SPWM, the main SVPWM advantage is that it has a 5% higher utilization ratio of voltage. SVPWM is achieved by implementing the zero voltage space vectors in the phase modulation wave of SPWM. SPWM is easier to be realized in hardware circuit, while SVPWM is more suitable for digital control system. ased on the rotor field orientation control of PMSM, this paper presents the ML/SIMULI-based simulation model by adopting the classical double closed loops of speed and current and vector control method. he simulation results reveal that the waveforms are in accord with theoretical analysis, the system can operate stably with fairly good steady-state and dynamic characteristics, providing sound bases for developing both software and hardware to realize HS FESS and LM machines [8]-[]. References []. J. Li. djusting Speed System of Synchronous Machine, eijing: Science Publishing ompany, ch., 7, pp. -5. [] Y.. hin and J. Soulard, permanent magnet synchronous motor for traction applications of electric vehicles, in Proc. IEEE International Electric Machines and Drives onference, IEMD, Madison, Wisconsin US,, pp. 5-. [] D. G. u, H. Wang, and J.. Shi, PMSM servo system with speed and torque observer, nnual Power Electronics Specialists onference, vol., no., pp. -5,. [] S. Ogasawara, M. ishimura, H. kagi,. abae, and Y. akanishi, high performance servo system with permanent magnet synchronous motors, IEEE ransactions on Industrial Electronics, vol., no., pp. 87-9, 986. [5] Y. L. u, J. Q. u, W.. Wan, and R. Y. ang, Development of permanent magnet synchronous motor used in electric vehicle, in Proc. 5th International onference on Electrical Machines and Systems, Shenyang, hina,, pp. 88-887. [6] J. Q. u, Y. L. u, and R. Y. ang, Development of full digital control system for permanent magnet synchronous motor used in electric vehicle, in Proc. 5th International onference on Electrical Machines and Systems, Shenyang, hina,, pp. 55-556. [7] J.. Jin and L. H. heng, Development and applications of high temperature superconducting material, Journal of University of Electronic Science and echnology of hina, vol. 5, no., pp. 6-67, 6 (in hinese). [8].. Ooi, J.. Salmon, J. W. Dixon, and.. ulkarni, three phase controlled-current PWM converter with leading power factor, IEEE ransactions on Ind. pplication, vol., no., pp. 78-8, 987 [9] J. W. Dixon and.. Ooi, Indirect current control of a unity power factor sinusoidal current boost type three-phase rectifier, IEEE ransactions on Ind. Electron, vol. 5, no., pp. 58-55, ov. 988.
WG et al.: SVPWM echniques and pplications in HS PMSM Machines ontrol 97 [] R. F. Post,.. Fowler, and S. F. Post, high-efficiency electromechanical battery, Proceedings of the IEEE, vol. 8, no., pp. 6-7, Mar. 99. [] J. R. Hull, Flywheels on a roll, IEEE Spectrum, vol., no. 7, pp. -5, 997. []. Vladimir and. Vikram, new mathematical model and control of a three-phase D voltage source converter, IEEE ransactions on Power Electronics, vol., no., pp. 6-, 997. [] R. Wu, S.. Dewan, and G. R. Slemon, PWM to D converter with fixed switching frequency, IEEE rans. on Industry pplications, vol. 6, no. 5, pp. 88-885, 99. [] R. Wu, S.. Dewan, and G. R. Slemon, nalysis of an -to-d voltage source converter using PWM with phase and amplitude control, IEEE ransactions on Industry pplications, vol. 7, no., pp. 56-6, 99. [5] M. adjoudj and M. E. H. enbouzid, robust hybrid current control for permanent magnet synchronous motor drive, IEEE ransactions on Energy onversion, vol. 9, no., pp. 9-5, Mar.. [6].. Gupta and. M. hambadkone, Space Vector PWM Scheme for Multilevel Inverters ased on wo-level Space Vector PWM, IEEE ransactions on Industrial Electronics, vol. 5, no 5, pp. 6-69, Oct. 6. [7]. D. Fernando, D. W. Michael, and L. D. Robert, Dynamic analysis of current regulators for motors using complex vectors, IEEE ransactions on Industry pplication, vol. 5, no. 6, pp. -, 999. [8] J.. Jin, Y. G. Guo, and J. G. hu, Principle and analysis of a linear motor driving system for HS levitation applications, Physica, vol. 6-6, pp. 5-6, Sep. 7. [9] Y. G. Guo, J.. Jin, J. G. hu, and H. Y. Lu, Design and analysis of a prototype linear motor driving system for HS maglev transportation, IEEE ransactions on pplied Superconductivity, vol. 7, no., pp. 87-9, 7. [] J.. Jin, Y. G. Guo, J.. hen, L. H. heng, and J. G. hu, HS levitation and transportation with linear motor control, in Proc. of the 6th hinese ontrol onference, hangjiajie, hina, 7. pp. -. [] J.. Jin,. G. Wang, J. Wen, Y. G. Guo, and J. G. hu, High temperature superconducting energy storage techniques, Journal of the Japan Society of pplied Electromagnetics and Mechanics, vol. 5, Supplement, pp. S8-, Sep. 7. direction is in control technology. Jian-un Jin was born in eijing, in 96. He received.s. degree from eijing University of Science and echnology in 985, M.S. degree from University of ew South Wales, ustralia in 99, and Ph.D. degree from University of Wollongong, ustralia in 997. He was a research fellow and ustralian R project chief investigator and senior research fellow with ustralian University of Wollongong from 997 to. He is currently a professor and the Director of the enter of pplied Superconductivity and Electrical Engineering, UES. His research interests include applied high temperature superconductivity, measurement, control and energy efficiency technology. You-Guang Guo was born in Hubei Province, hina, in 965. He received the.s. degree from Huazhong University of Science and echnology (HUS), hina, in 985, the M.S. degree from hejiang University, hina, in 988, and the Ph.D. degree from University of echnology, Sydney (US), ustralia, in, all in electrical engineering. From 988 to 998, he lectured in the Department of Electrical Engineering, HUS. From March 998 to July, He was a visiting research fellow with the enter for Electrical Machines and Power Electronics, Faculty of Engineering, US. He is currently an R (ustralia Research ouncil) postdoctoral research fellow with US. His research interests include measurement and modeling of magnetic properties of magnetic materials, numerical analysis of electromagnetic field, motor design and optimization, power electronic drives and control of electrical appliance. He has published over refereed technical papers including 75 journal articles in these fields. Jian-Guo hu was born in Shanghai, hina, in 958. He received his.s. degree in 98 from Jiangsu Institute of echnology, hina, M.S. degree in 987 from Shanghai University of echnology, hina, and Ph.D. degree in 995 from US, ustralia. He is the professor with Electrical Engineering and the Director of the enter for Electrical Machines and Power Electronics at US, ustralia. His research interests include electromagnetics, magnetic properties of materials, electrical machines and drives, power electronics, and renewable energy systems. heng-guang Wang was born in Jilin Province, hina, in 98. In, he received the.s. degree from the University of Electronic Science and echnology of hina (UES). He is currently pursuing the M.S. degree with UES. His research