6 4 22 4 ELECTRI C MACHINES AND CONTROL Vol. 6 No. 4 Apr. 22 2 2. 327 2. 3796 TM 464 A 7-449X 22 4-64- 8 Study on the control strategy for single-tuned hybrid active power filters SHI Xiao-jie 2 WANG Zhi-qiang 2 ZHANG Jun-ming QIAN Zhao-ming. College of Electrical Engineering Zhejiang University Hangzhou 327 China 2. Department of Electrical Engineering and Computer Science University of Tennessee noxville 3796 USA Abstract A DC link voltage controller and double loop control strategy with grid current and the fifth harmonic current feedback are proposed to deal with the low compensation precision of the single-tuned parallel hybrid active power filters PHAPFs due to low bandwidth. Specifically the small signal model and transfer function were derived firstly based on the circuit topology of the PHAPF. The double loop controller and the voltage controller were designed. Simulation investigation was done and a prototype was built. Simulation and experimental results verify that the proposed control strategies could not only acquire very high steady-state compensation precision as well as fast dynamic responses but also reduce the cost of the equipment since only two phases of grid current are required to be detected. ey words parallel hybrid active power filters compensation precision current loop voltage loop double closed loop control strategy direct current link voltage control 2-7 - 9 5976 986 985 975-939 2 7
4 65 pulse width modulation PWM 2-3 4-6 MOSFET 主接触器 u S L i S CT u pcc i L L 非线性负载 S ac PT CT R C L d parallel hybrid active i F 接触器 power filter PHAPF C F 7 auto - dis- L F turbance rejection control ADRC 8 - LC IGBTs 和继电器的错误信号 电流采样 PLL 调理电路 CAP A/D PWM 接触器驱动电路 LEM C dc v dc DSP 保护电路 I/O A/D PI 调节器电压采样调理电路 Fig. System configuration of PHAPF APF APF v * AF i Sh v * AF = i Sh 2 khz PWM d - q insulated gate bipolar transistor IGBT d q 2 3 PHAPF PI 3 Z Fh i Sh = i Z Sh Z Lh u Fh Z Sh Z Sh Fh Z Fh Z Sh Z Fh PHAPF u pcch = - i Z Sh Z Lh u Fh Z Sh Z Sh 2 Fh Z Fh = R F sl F / sc F Z Sh = sl S u pcch u S i Sh u pcc u Sh u S L S R F L F C F L ac C F L F v dc C dc active power filter APF Z Sh Z Fh L ac L S 2 LC i Sh u pcch u Sh 3 2 khz R -
66 6 5 Z S 5 = 25 u pcc i F u Sf - u Z F Sh i Lf i Lh Fig. 2 u Sh i Sh Z Sh i Sh Z Fh 2 U AF PHAPF Single-phase equivalent circuits of the PHAPF U AF upcch i Lh i Sh Z Sh u Th i Fh Z Fh i Lh i Sh Z Sh u Sh i Fh Z Fh U AF u pcch (a) 谐波等效电路 (b) 对 i Sh 的等效电路 (c) 对 u Sh 的等效电路 Fig. 3 3 PHAPF Equivalent circuits for harmonics of the PHAPF 2 PHAPF 2. 5 4 4 Fig. 5 Nyquist plot of the system with feedback control low pass filter LPF 2. 2 5 Hz i Sa i Sb i Sc 3 = d - q i d i q i d i q LPF d - q i S Z Fh i Sh = i Z ω 5 = - 5ω Sh Z Lh 4 Fh Z S Z F 电网电流反馈 isa isb isc C dq id iq id LPF iq LPF 驻 id C - dq - cos 棕 t sin 棕 t PLL vpcc isha - ishb - ishc - u ia * u ib * u ic * vdc LPF - v dc * PI DC%voltage control i isa i d5 i Sh Z F s LPF d5 = isb C dq5 i q5 i C i - dq5 Lh Z S s Z F s p amp SRF s inv s delay s q5 isc LPF 5 五次谐波电流反馈 vpcc cos 棕 PLL 5t sin 棕 5t p amp inv s 4 U d V m Fig. 4 Control system for the hybrid active filter inv s = U d /2V m SRF s synchronous rotating frame SRF LC G s jw G s - jw - G s jw SRF s = 6 G s jw G s - jw /G s Imaginary%axis 5-5 - =5 =25 Nyquist%diagram -6-4 -2 2 4 6 Real%axis Z S Z F PHAPF
4 67 G s = T n s n T n - s n - T s 7 2. 3 T T 2 T n G s 3-6 τ C dc LC e - τs e - τs C dc APF π /2 delay s = e - τs = e = τs τs τs 2 2 9 inv = 75 τ = μs amp =. 27 增益 /db 2 - -2-3 -4 i Sh%/i Lh( 棕 5=5 棕 ) -5 3 4 注 : 只使用无源滤波器 ;2 电网电流反馈控制 ; 6 Fig. 6 3 电网电流反馈加五次电流反馈控制 2 3 频率 /Hz Filtering characteristics for the load harmonic current i d i q PWM 8 8 a - b - c τs τs 2 2 α - β U k a amp5 - b - c α - β SRF5 s di F u pcc = L F delay s 5 s 4 dt C F i Fdt U k i Sh = i Sh Z F s u Fh u pcc = i Lh Z S s Z F s inv delay s amp SRF s 5 SRF5 s 6 3 7 L ac = 6 3 mh 3% L F = 2. 7 mh. 7% C F = 79. 4 mh Z S Z F 28 ~ 324 Hz 8% U k U ref = U k 7 U ref 9 Ω 3 4 6 5 = 2 Ω U ref U k U ref U d = 2 V U ref L F di Fh dt C F i Fhdt = - U k i Fh Δi Fh = i * Fh - i Fh 2 i * Fh 2 L F dδi Fh dt U ref C F Δi Fhdt = U k - U ref 3 = - L F di * Fh dt - C F i* Fh dt 4 3 U k U ref Δi Fh U k APF i Fh i * Fh i * Fh i * Fh = i Lh 5 α - β
68 6 U k 槡 3 V P I F 槡 3 V P I F s V dc C dc V dc C dc T I G s = U d = 2 V s 2 槡 3 V P I F V dc C dc τs s U d = 5 V Fig. 7 u 琢 /%V 5 U 3(-,,-) 5 U 2(,,-) U 4(,,) U (,-,-) -5 U * d=2v - U * d=2v U * d=9v U 5(-,-,) U 6(,-,) -5-2 - 2 7 u 茁 / %V U k U ref Trajectory of U ref and hexagons formed by U k 8 L F C F L ac ζ ω n L F ζ 槡 3 V P T I I F 槡 3 V P I F ω 2 V dc C n 9 T I V dc C Ud%/% 5 45 4 35 3 25 2 L ac%=5% 5 L ac%=% 5 5 5 2 25 3 35 4 45 5 9 % 2 mh 8. 7% v dcref = 5 V σ. 5 V PI G PI s = P P st I 6 p T i G d s = τs 7 槡 3 V P I F V dc C dc T I τs V total harmonic distortion THD 9 8 I F γ = 9 / ~ 2 Hz V dcref%(s) * 姨 3 vif PI Vdc - Fig. 9 9 C d%(s) sc dc V dc%(s) APF Block diagram of the dc-voltage control 8 dc 槡 dc 槡 V dc 5 V = 9 I F = 7. 5 A PI p =. 4 A /V T I =. 2 s ζ ω n 92. 73 rad /s 3 C F%/% 3. APF 8 C F. Fig. 8 Relationships between a capacitance value of C F and 2 kw a required dc capacitor voltage in the hybrid filter 38 V 5 Hz. 23 mh 2 35 μf 79. 4 μf 25% 2. 7 mh. 7% PHAPF. 7 kva 5 V 3 3 μf 3. 2 Matlab /SIMULIN dc
4 69 APF v dc 5 V PHAPF 5 V 2 kw i Sa v dc 23. 6% THD 26. 6% THD 5. 48% 4. 39%. 7% THD 2. 4% PHAPF ica(5a/div) isa(2a/div) ila(5a/div) ica(5a/div) isa(5a/div) ila(5a/div) (a) 单独使用电网电流反馈 (b) 单独五次电流反馈控制 PHAPF kw PHAPF vdc%/%v Fig. ila(5a/div) isa(2a/div) 6 4 2 8 6 4 2 t(5ms/ 格 ) (a) 负载电流与电网电流 (a 相 ) 波形 t=.35%s, 负载切换..2.3.4.5 t/s (b) 直流电压波形 kw 2 kw i Sa v dc Simulated waveform of i Sa and v dc during load transient kw 2 kw vdc(2v/div) (c) 逆变器直流侧电压 v dc 的建立波形 i La i Sa i Fa v dc Fig. Simulated waveforms of i La i Sa i Fa and the built of v dc THD Table Current THD and harmonics of the simulation in Fig. expressed as the harmonic to 3. % 2. % fundamental current radio % 5 6 5th 7th th 3th 7th 9th THD i La 23. 6 9. 6. 4 4. 2. 5. 9 26. 6 i Sa Fig. a 4. 39. 53. 7. 58.. 2 5. 48 i Sa Fig. b. 7. 47. 65. 72. 64. 6 2. 4 3. 3 2 THD 9. 5% 6. 7% 6. % APF 3 3 5 V 4 5 kw 2 kw PHAPF
7 6 ila(4a/div) isa(4a/div) ica(4a/div) 谐波含量 /% 谐波含量 /% 2 Fig. 2 8 6.2 4.4 2.6.8 9 7.2 5.4 3.6.8 6. 5.49 4.88 4.27 3.66 3.5 2.44.83.22.6 t(ms/ 格 ) (a) 电流 (a 相 ) 波形 总谐波含量为 9.5% 2 6 4 8 22 26 3 34 38 42 46 5 谐波次数 (b) 负载电流 (a 相 ) 频谱 总谐波含量为 6.7% 2 6 4 8 22 26 3 34 38 42 46 5 谐波次数 (c) 电网电流 (a 相 ) 频谱 a Experimental waveforms with the feedback control and the spectrum of i Sa Fig. 4 isa(4a/div) ila(4a/div) ica(4a/div) 谐波含量 /% 4 vdc(5v/div) isa(4a/div) vdc(5v/div) 2.2.98.76.54.32..68.66.44.22 t(ms/div) (a) 电流 (a 相 ) 波形 2 6 4 8 22 26 3 34 38 42 46 5 谐波次数 (b) 电网电流 (a 相 ) 频谱 a Experimental waveforms with the double closed loop feedback control and the spectrum of i Sa (a) 负载增大 (5%kW 2%kW) vdc(5v/div) isa(4a/div) 3 Fig. 3 t(ms/div) (b) 负载减小 (2%kW 5%kW) 5 5 kw 2 kw i Sa v dc Experimental waveform during the start of Fig. 5 Experimental waveform of i Sa and v dc inverter dc link voltage during load transient 5 kw 2 kw
4 7 6 isa(4a/div) ila(4a/div) ica(4a/div) ica(4a/div) isa(4a/div) ila(4a/div) t(25ms/div) (a) 负载增大 (5%kW 2%kW) t(25ms/div) (b) 负载减小 (2%kW 5%kW) 5 kw 2 kw i Sa i La i Ca CHEN Ruinuo RAFI Youssef LUO An et al. Control strategy of Fig. 6 4 Experimental waveform of i Sa i La and i Ca during load transient 5 kw 2 kw FUJITA H AAGI H. A practical approach to harmonic compensation in power systerms-series connection of passive and ac- 6 23 Salt Lake City Matlab / tive filters J SIMULIN 2 kva /38 V 99 27 6 2-25. 2 25. 3 D. 28. WANG Z XIE C HE C et a. A waveform control technique for high power shunt active power filter based on repetitive control algorithm C / /Conference Proceedings-IEEE Applied Power Electronics Conference and Exposition-APEC February 2-25 2 Palm Springs USA 2 36-366. 2 PENG F Z LAI J S. Generalized instantaneous reactive power theory for three-phase power systems J. IEEE Transactions on Instrumentation and Measurement 996 45 293-297. 3 AAGI H ANAZAWA Y NABAE A. Instantaneous reactive power compensators comprising switching devices without energy storage components J. IEEE Transactions on Industry Application 984 IA - 2 3 625-63. 4. M. 24. 5 WANG Zhiqiang CHEN Guozhu. Study on planar busbar regarding stray inductance minimization and oscillation suppression for high power converter C / /st International Conference on Sustainable Power Generation and Supply SUPERGEN '9 April 6-7 29 Nanjing China 29 5347993. 6. J. 2 2 9 7-2. CHEN Guozhu L Zhengyu QIAN Zhaoming. The general principle of active filter and its application J. Proceedings of the CSEE 2 2 9 7-2. 7. J. 26 9 3 8-22. CHEN Yong ZENG Dongping YU Jiahe. Control scheme for new hybrid active power filters J. Guangdong Electric Power 26 9 3 8-22. 8. J. 25. 39 4 393-396. YANG Jun WANG Yue ZENG Zhidong et al. Design of a kind of three phase hybrid APF J. Journal of Xi'an Jiaotong University 25 39 4 393-396. 9 RAFI Youssef. J. 24. 23 3 23-26. a novel hybrid APF J. Computing Technology and Automation 24 23 3 23-26. AAGI H SRIANTHUMRONG S TAMAI Y. Comparisons in circuit configuration and filtering performance between hybrid and pure shunt active filters C / /Conference Record-IAS Annual Meeting IEEE Industry Applications Society October 2 - USA 23 2 95-22.. IEEE Transactions on Industry Application. D.. 4 WANG Zhiqiang XIE Chuan ZHANG Jing et a. Dynamic DCbus voltage control strategies for a three-phase high power shunt active power filter C / /Conference Proceedings-IEEE Applied Power Electronics Conference and Exposition-APEC February 2-25 2 Palm Springs USA 2 54-52. 5 SHI Xiaojie SHEN Yuwen ZHANG Junming et al. Study on a transformerless hybrid active power filter with high compensation precision and dynamic performance C / /Conference Proceedings- IEEE Applied Power Electronics Conference and Exposition- APEC March 6-2 Fort Worth USA. 2 29-25. 6. J. 28 34 2 74-77. WANG Jianyuan WANG Liping SUN Chengyu. Novel threephase three-wire shunt active power filter J. High Voltage Engineering 28 34 2 74-77.