Harmonic analysis of armature current for high speed permanent magnet synchronous motor

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1 Electri c Machines and Control Vol. 20 No. 5 May SVPWM DSP DOI /j. emc TM 355 A X Harmonic analysis of armature current for high speed permanent magnet synchronous motor YU Ji-kun LI Li-yi DU Peng-cheng ZHANG Jiang-peng School of Electrical Engineering and Automation Harbin Institute of Technology Harbin China Abstract There are two methods in harmonic analysis of the high speed permanent magnet synchronous motor and they are analytical method and simulation method. The analytical method is suitable for continuous systems and the simulation method for discrete system. As the relevance of these two methods has been rarely studied one correlation analysis method was proposed which is based on the space vector pulse width modulation SVPWM technology. From Fourier series of the continuous function and the discrete function the deviation distribution law between these two methods in the harmonic calculation was analyzed. The analysis results show that the main influence factors of discrete harmonic calculation of armature are sampling frequency and load condition. The armature current harmonics oscillate damping attenuation with increase in sampling frequency and converge to the analytical results of the continuous system. The oscillation amplitude is reduced and the convergence speed is improved by load. The permanent magnet synchronous motor system experiment platform based on DSP is constructed and it is confirmed that the correlation analysis method is effective. Keywords high speed permanent magnet synchronous motor space vector pulse width modulation SVP- WM armature current harmonic analysis discrete fourier transform DFT

2 N PWM Fig. 1 Three phase bridge PWM inverter circuit PWM U 1 ~ U PWM SVPWM Fig. 2 Hexagonal voltage space vector U s = U s e jθ s U s = 2 3 U C 1 θ s = ( s - 1) π 3 s s = U s θ s 1 SVPWM 6 PWM 1 C O R L e 2 3

3 30 20 T c T 0 T A Table 2 Time of phase A with high level and its duty ratio θ s θ s + 1 T 4D - 2 / 槡 3 M 0 π /3 T 1 + T 2 + T 0 /2 cos θ - π /6 π /3 2π /3 T 2 + T 0 /2 槡 3 cosθ 2π /3 π T 0 /2 cos θ + π /6 π 4π /3 T 0 /2 cos θ - π /6 4π /3 5π /3 T 6 + T 0 /2 槡 3 cosθ 5π /3 2π T 5 + T 6 + T 0 /2 cos θ + π /6 Fig. 3 3 The linear combination of space voltage vector 2 UT c = U s T s + U s +1 T s +1 2 T s = 槡 3 2 MT csin θ s +1 - θ 3 T s +1 = 槡 3 2 MT csin θ - θ s θ s θ s + 1 U s 2T s / 槡 3 MT c U s + 1 2T s + 1 / 槡 3 MT c 0 π /3 100 sin π /3 - θ 110 sinθ π /3 2π /3 110 sin 2π /3 - θ 010 sin θ - π /3 2π /3 π 010 sin π - θ 011 sin θ - 2π /3 π 4π /3 011 sin 4π /3 - θ 001 sin θ - π 4π /3 5π /3 001 sin 5π /3 - θ 101 sin θ - 4π /3 5π /3 2π 101 sin 2π - θ 100 sin θ - 5π /3 ω 1 f t a n T 0 = 1 b n 2 T c - T s - T s +1 4 a n = 2 T 1 T 1 f t cosnω 1 tdt 0 1 b n = 2 5 T 1 T 1 f t sinnω 1 tdt 0 M T 1 T 1 = 2π /% 1 U U C 1 Table 1 Nonzero adjacent vector of the target vector and its operation time PWM 4 k PWM t 2k t 2k - 1 PWM 6 A 1 A T D 2 4 k PWM Fig. 4 On-off time sequence of PWM pulse in 2 the k th switching period

4 5 31 ( ) t 2k -1 = k D k T c 2 t 2k = k D k ( 2 ) T c 6 PWM a nu b nu = U C nπ 2Nc k = 1 = - U C nπ 2Nc k = 1-1 k sinnω 1 t k - 1 k cosnω 1 t k 7 a nu b nu N c n 3 a nu b nu 7 a ni b ni = Ra n u-e - ω 1 Lb n u-e R 2 + nω 1 L 2 = ω 1La n u-e + Rb n u-e R 2 + nω 1 L a ni b ni Fig. 5 a n u - e b n u - e with carrier ratio N c = N c = 15 Table 4 Analytical value of the typical current harmonics with carrier ratio N c = N c ±2 2N c ± 1 3N c ± Matlab /SIMULINK 3 Table 3 Parameters of the motor and control system in simulation and experiment 2 T sam = 1 μs f sam = 1 MHz 6 /V 540 /mω 66 /Hz 533 /mh /N m 11 /mwb 52 /khz 8 15 N c = 15 Analytical results of the current harmonics DFT 9 DFT x X

5 32 20 N N sam N sam = T 1 /T sam 6 N sam = N sam PWM Fig. 6 Simulation results of the current waveform with PWM voltage excitation X k x l = N x l e -j2π l -1 k -1 /N l = 1 = 1 X N N k e j2π l -1 k -1 /N k = 1 9 9DFT N/2 +1 x l = ReX - kcos 2π k - 1 l - 1 /N + k = 1 ImX - ksin 2π k - 1 l - 1 /N 10 N ReX - k ImX - k DFT ReX - k = ReX k N /2 ImX - k = - ImX 11 k N /2 k = 1 N /2 + 1 ReX - k ReX - k = ReX k N 12 Fig. 7 7 Simulation results of the low order harmonics current amplitude

5 33 4 9 1 IGBT TMS320F2808 2 SVPWM Tektronix TPS2014 Yokogawa DLM2054 Magtrol 2WB115 Fig. 9 9 Photograph of experimental System 8 1 μs 40 ns 1.

6 IGBT TMS320F SVPWM Tektronix TPS2014 Yokogawa DLM2054 Magtrol 2WB115 Fig. 9 9 Photograph of experimental System 8 1 μs 40 ns ms Fig. 8 Simulation results of the high order harmonics current amplitude DFT DFT 1 MHz 25 MHz DFT MHz MHz DFT

7 Fig. 10 f sam = 1 MHz Experimental results of no load with sampling frequency f sam = 1 MHz 12 Fig. 12 f sam = 25 MHz Experimental results of no load with sampling frequency f sam = 25 MHz 11 Fig. 11 f sam = 1 MHz Experimental results of full load with sampling frequency f sam = 1 MHz 13 Fig. 13 f sam = 25 MHz Experimental results of full load with sampling frequency f sam = 25 MHz

8 MHz 25 MHz 3 DFT 5 f sam = 1 MHz 2. Table 5 Comparison of current calculated value and experimental value with sampling frequency f sam = 1 MHz J WU Zhenyu QU Ronghai LI Jian et al. Multi-field coupling rotor design for surface-mounted high-speed permanent magnet machine J. Electric Machines and Control KOLONDZOVSKI Z. Power limits of high-speed permanent-magnet electrical machines for compressor applications. IEEE Transac tions on Energy Conversion D PWM 6 f sam = 25 MHz J. Table 6 Comparison of current calculated value and experimental value with sampling frequency f sam = 25 MHz LI Liyi YU Jikun CAO Jiwei et al. A Universal and New Harmonic Algorithm of Voltage and Current of Permanent Magnet Synchronous Motors Supplied By PWM Inverter J. Proceedings of the CSEE PWM J ZHOU Minglei YOU Xiaojie WANG Chenchen et al. Switching angle calculation and harmonic analysis of current harmonic minimum PWM J. Proceedings of the CSEE HAVA A CETIN N. A generalized scalar PWM approach with 5 1. J WANG Jiqiang WANG Fengxiang BAO Wenbo et al. Rotor design and strength analysis of high speed permanent magnet machine J. Proceedings of the CSEE easy implementation features for three-phase three-wire voltage-. IEEE Transactions on Power Electronics SVPWM source inverters J DFT strategy-an analysis J DSP ics KANCHAN R S BAIJU M R MOHAPATRA K K et al. Space vector PWM signal generation for multilevel inverters using only the sampled amplitudes of reference phase voltages J. IEE Proceedings of Electric Power Applications BIERHOFF M FUCHS F. DC-link harmonics of three-phase voltage-source converters influenced by the pulse width modulation. IEEE Transactions on Industrial Electron- 10 CARRARA G GARDELLA S MARCHESONI M. A new multi-

9 36 20 level PWM method a theoretical analysis J. IEEE Trans on Power Electronics MCGRATH B P HOLMES D G. An analytical technique for the determination of spectral components of multilevel carrier-based PWM methods J. IEEE Transactions on Industrial Electronics PWM SVPWM J CHEN Yao TONG Yibin JIN Xinmin. A novel algorithm of SVPWM harmonic analysis based on PWM rectifier J. Proceedings of the CSEE SVPWM J WU Xiaoxin LIU Wei RUAN Yi et al. SVPWM over-modulation algorithm and its applicationin two-level inverter J. Electric Machines and Control J ZHU Jianlin ZHANG Jianhua GUO Yougui et al. Voltage transfer characteristic and Harmonic analysis of matrix converter under over modulation J. Proceedings of the CSEE

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