Electri c Machines and Control Vol. 22 No. 1 Jan H APF H H APF APF APF H H APF APF DOI /j. emc TM 72

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1 Electri c Machines and Control Vol. 22 No. 1 Jan H APF H H APF APF APF H H APF APF DOI /j. emc TM TM 46 A X Three-level equilibrium strategy of DC voltage balance control for H-bridge cascaded APF HUANG Hai-hong LIU Ya-yun WANG Hai-xin WEI Ya-kun School of Electrical Engineering and Automation Hefei University of Technology Hefei China Abstract The premise of stable operation for cascaded H-bridge active power filter is that DC voltages are balanced. Due to differences between H-bridge modules imbalance of DC side voltages not only affects the compensation effect but also affects the safe operation of APF. Aiming at the power exchange model between APF and power grid and the characteristics of harmonic current voltage balance among phases was achieved by controlling fifth-order zero-sequence voltage and global voltage stabilization was achieved by controlling the fundamental positive sequence active current. By adding active voltage vector of AC side in each H Bridge the voltage balance is achieved within one phase and finally each DC side voltage is balanced and stable. At the same time the H-bridge cascaded APF compensates harmonic current and reduces distortion rate of the grid current. Validity of the method is verified by simulation and experimental results under low voltage conditions which can provide the basis for the application of the APF to a higher voltage level. Keywords fifth-order zero-sequence voltage voltage balance active voltage vector total harmonic distortion DSP 1990

2 H APF H APF 1-2 APF APF APF H 3-6 APF H APF APF APF 1 H APF Fig. 1 Topology of H-bridgecascaded APF H 2 U dc U dcx x = a b c ΣU dcx U H dcxn H U APF cxn H 6k ± 1 k = H APF APF H 2 Fig. 2 Overall control block diagram of DC voltage balance

3 1 H APF i A = 槡 2 I mn sin nωt + φ n n = 1 6k ±1 k = k ± 1 k = i B = 槡 2 I mn sin nωt + φ n - 2nπ /3 5 n = 1 6k ±1 k = i C = 槡 2 I mn sin nωt + φ n + 2nπ /3 0 A i n = 1 6k ±1 LA 3 k = APF P X = 1 T T U cx i X dt X = A B C 0 6 Fig. 3 3 A Load current of phase A 7 i LA 120 B C 120 i LA 2 i LA = 槡 3 I d π sinωt sin 5ωt sin 7ωt + P A #P B #P C 1 11 sin 11ωt + 1 sin 13ωt ΔP 1 I d APF B = U z5 I m5 cos φ z5 - φ 5-2π / ΔP C = U z5 I m5 cos φ z5 - φ 5 + 2π /3 2 i A = 槡 3 π 1 5 sin 5ωt sin 7ωt sin 11ωt - 1 sin 13ωt APF I m5 > I m7 > I m11 ΔP A = U z1 I m1 cos φ z1 - φ 1 = APF U z5 I m5 cos φ z5 - φ 5 ΔP B = U z1 I m1 cos φ z1 - φ 1 + 2π /3 = 9 U zero = 槡 2 U z5 sin 5ωt + φ z5 U z5 I m5 cos φ z5 - φ 5-2π /3 U X = 槡 2 U m sin ωt - 2kπ /3 X = A B C k = ΔP C = U z1 I m1 cos φ z1 - φ 1-2π /3 = U z5 I m5 cos φ z5 - φ 5 + 2π /3 U z5 φ z5 9 U m APF U z1 I m1 = U z5 I m5 U cx φ z1 - φ 1 = - φ z5 - φ 5 U cx = U X + U LX + U zero 4 APF P A = U m I m1 cosφ 1 + U z5 I m5 cos φ z5 - φ 5 P B = U m I m1 cosφ 1 + U z5 I m5 cos φ z5 - φ 5-2π /3 P C = U m I m1 cosφ 1 + U z5 I m5 cos φ z5 - φ 5 + 2π /3 P A + P B + P C = 3U m I m1 cos φ 1 ΔP A = U z5 I m5 cos φ z5 - φ 5 ΔP A + ΔP B + ΔP C = U z1 φ 1 10 APF I m5 > I m1 APF

4 80 22 A i A5 φ 5 = APF arctan i d /i q + π /2 I 5 ΔP A ΔP B ΔP C 3 φ 5 I m5 = 1 i 2 d5 + i 2 槡 2 槡 q5 φ 5 = π 2 + arctan i d i i q > 0 q 3π 2 + arctan i d i i q < 0 q π i q = 0 i d > 0 0 i q = 0 i d < 0 14 I m5 φ 5 ΔP D ΔP Q 12 APF U zero Fig. 4 4 Decomposition of fifth-order current vector 8 ABC dq ΔP [ q ΔP ] = 1 2ΔP A - ΔP B - ΔP 5 C 3 [ d 槡 3 ΔP C - ΔP B ] = Fig. 5 Structure diagram of voltage balance among three phases cos φ z5 - φ 5 U z5 I m5 [ - sin φ z5 - φ 5 ] APF 7 U zero = 槡 2 I m5 ΔP q sin 5ωt + φ 5 - ΔP d cos 5ωt + φ H APF dq + 5 PI PR RE U dc_ref = 1 3 ΣU RE dca + ΣU dcb + ΣU dcc 13 I m5 φ 5 7 S z i X dq 4 I 5 A θ dq G z d z 12 d q 8 I 5 i d5 i q5 I 5 4 I 4 5 A 30 db θ 0 = - arctan i d /i q

5 1 H APF 81 c k = e k + Q z c k - N 15 Q z 1 Q z = Fig. 6 6 Structure diagram of total voltage control ΔP xi = 1 T T i X ΔU cxi dt = ΔU dcxi k p 0 n = 1 6k ±1 k = I 2 mn 17 U dcxi < U dcx ΔU dcxi > 0 ΔP xi > 0 A 9 U ca H Fig. 7 7 Repetitive control block diagram Fig. 9 9 Diagram of appending the active voltage vector Fig. 8 8 Bode diagram of repetitive control H 2 H 1 H H ΔU cxi = ΔU dcxi k p i x 16 1 ΔU dcxi = U dcx - U dcxi PI Table 1 System parameters k p i X X = a b c APF /V 380 H

6 s s 450 V Fig Structure diagram of voltage balance within one phase /mh 2 Fig Voltage balance among three phases /μf /V 150 /khz s APF 145 V Ω + 25 mh 2. 1 Matlab /SIMULINK H APF kω 0. 3 s + 13 Fig. 13 Fundamental zero-sequence voltage 0. 3 s 0. 1 s 150 V 14 Fig Voltage balance within one phase s APF 32V APF APF s 0. 2 s s A B C 450 V kω 0. 3 s + 17 APF

1 H APF 83 14 Fig. 14 Voltage balance among three phases 15 Fig. 15 Fifth-order zero-sequence voltage 17 Fig. 17 Load current compensating current and grid current I II B II 40 V APF III 3 0.

7 1 H APF Fig. 14 Voltage balance among three phases 15 Fig. 15 Fifth-order zero-sequence voltage 17 Fig. 17 Load current compensating current and grid current I II B II 40 V APF III s 150 V III B V 0. 3 s V 16 Fig. 16 Change of sum of voltages during phases when abrupt change of load happens 18 Fig. 18 Voltage balance within one phase THD % 3. 23% V III 19 DSP2812 CPLD DSP 158 V 144 V III CPLD 0. 1 s PWM 150 V IV A 10 kω C 47 kω B V kω B 3 IV

84 22 20 2 Table 2 Harmonic current ofpre-compensation and compensation % 5 21. 22 1. 04 7 12. 94 1. 00 11 8. 68 0. 79 13 7. 37 0. 73 17 5. 43 0. 91 19 5. 15 0. 81 Fig.

21 voltage-balancing method of single phase cascaded H-bridge rectifiers J. Electri c Machines and Control 2016 20 5 37.

STATCOM to enhance power quality and security of rail traction supply Proceeding of Electromotion 2009 C. Lille France IEEE 2009. 2 KUMMAR J AGARWAL P DAS B.

8 Table 2 Harmonic current ofpre-compensation and compensation % Fig Voltage balance among three phases THD Fig Fifth-order zero-sequence voltage Fig. 21 voltage-balancing method of single phase cascaded H-bridge rectifiers J. Electri c Machines and Control Load current grid voltage compensating current and grid current 2 25 THD % 4. 48% 6k ± 1 H APF APF H APF 1 GRUNBAUM R HASLER J P LARSSON T et al. STATCOM to enhance power quality and security of rail traction supply Proceeding of Electromotion 2009 C. Lille France IEEE KUMMAR J AGARWAL P DAS B. Implementation of cascade multilevel inverter based STATCOM J. IETE Journal of Research H J WANG Shunliang SONG Wensheng FENG xiaoyun. One fast 4. STATCOM J GENG Juncheng LIU Wenhua YUAN Zhichang. Research on the voltage unbalance of DC capacitors of cascaded STATCOM Part one mathematical model J. Automation of Electric Power System STATCOM

9 1 H APF 85 J GENG Juncheng LIU Wenhua YUAN Zhichang. Research on the voltage unbalance of DC capacitors of cascaded STATCOM Part two mathematical model J. Automation of Electric Power System J HU Yinghong REN Jiajia WANG Jianze. Unbalanced phenomenon and reason analysis for DC side voltage of cascaded STATCOM J. Automation of Electric Power System MVA J LIU Wenhua SONG Qiang TENG Letian. Balancing control of DC voltage of 50 MVA STATCOM based on cascade multilevel inverters J. Proceedings of the CSEE AKAGI H S INOUE T YOSHII. Control and performance of a transformer-less cascade PWM STATCOM with star configuration J. IEEE Transactions on Industry Applications H APF J LIU Yayun WANG Haixin WEI Yangchao et al. Study of DC voltage balance control for cascaded H-bridge APF J. Journal of Electronic Measurement and Instrument H STATCOM J STATCOM XU Rong YU Yong YANG Rongfeng et al. DC capacitor voltage balance control of H-bridge cascaded STATCOM J. Electric Power Automation Equipment STATCOM J HU Yinghong REN Jiajia SHEN Ke et al. Balancing control of DC capacitor voltage for cascaded H-bridge STATCOM based on voltage redundant states J. Electric Power Automation E- quipment J HUANG Haihong WANG Yu XU Ruobing et al. Three-phase four-wire active power filter with dual-loop repetitive control J. Electric Power Automation Equipment 檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪 OOMMEN T V. Moisture equilibrium in paper-oil systems C. J LIANG Yiming CHEN Yan AO Ming. Gas protection malfunction caused by transformer oil in cold area J. Jilin Electric Power EIC 1983 Proceedings of the 6th Electrical /Electronical Insulation Conference Chicago October C. Piscataway IEEE J WANG Jingyu. Gas protection malfunction caused by low temperature and its preventive measures J. Jilin Electric Power AKBARI A DEHPAHLEVAN S BORSI H. Analyzing dynamic 9. of moisture equilibrium in oil-paper insulation in power transformers for efficient drying C. CEIDP 2006 Proceedings of 2006 IEEE Conference on Electrical Insulation and Dielectric Phenomena Kansas City October Piscataway IEEE 2007.

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u d = R s i d - ωl q i q u q = R s i q + ωl d i d + ωψ 1 u d u q d-q i d i q d q L d L q d q ψ f R s ω i 1 i 5th i th 5 θ 1 θ θ 3 5 5 3 5 018 10 Vol. 3 No. 5 JOURNAL OF HARBIN UNIVERSITY OF SCIENCE AND TECHNOLOGY Oct. 018 150080 Matlab /Simulink DOI 10. 15938 /j. jhust. 018. 05. 011 TM35 A 100-683 018 05-006- 06 Stator Harmonic Optimal