20 5 2016 5 Electri c Machines and Control Vol. 20 No. 5 May 2016 150001 SVPWM DSP DOI 10. 15938 /j. emc. 2016. 05. 005 TM 355 A 1007-449X 2016 05-0028- 09 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 150001 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 2014-11 - 06 51225702 1987 1969 1988 1985
5 0 29 N 1-2 3-4 1 PWM Fig. 1 Three phase bridge PWM inverter circuit 1 1 0 8 PWM 100 110 010 011 001 101 000 111 8 U 1 ~ U 8 2 1 5 6-10 11-12 PWM 13-14 2 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 = 1 2 3 U s θ s 1 SVPWM 6 PWM 1 C O 3 2 1 R L e 2 3
30 20 T c T 0 T 0 4 2 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 000 111
5 31 ( ) t 2k -1 = k - 1 + D k T c 2 t 2k = k - 1 - 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 2 8 5 a ni b ni Fig. 5 a n u - e b n u - e with carrier ratio N c = 15 3 4 N c = 15 Table 4 Analytical value of the typical current harmonics with carrier ratio N c = 15 60 N c ±2 2N c ± 1 3N c ± 2 2 4 4 2 4 13 29 43 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 0. 32 /N m 11 /mwb 52 /khz 8 15 N c = 15 Analytical results of the current harmonics 1 2 4 13 29 43 0 0. 45 0. 65 1. 99 3. 94 0. 99 38. 21 0. 48 0. 69 2. 11 3. 90 0. 99 3 5 DFT 9 DFT x X
32 20 N N sam N sam = T 1 /T sam 6 N sam = 1 876 N sam 1 2 4 13 29 43 7 8 6 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. 875 ms Fig. 8 Simulation results of the high order 1 876 harmonics current amplitude 46 876 7 8 DFT DFT 1 MHz 25 MHz DFT 10 11 1 MHz 12 13 25 MHz DFT
34 20 10 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
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