22 1 2018 1 Electri c Machines and Control Vol. 22 No. 1 Jan. 2018 H APF 230009 H H APF APF APF H H APF APF DOI 10. 15938 /j. emc. 2018. 01. 011 TM 721. 1 TM 46 A 1007-449X 2018 01-0077- 09 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 230009 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 2016-07 - 29 51177037 1973 1991 1976 DSP 1990
78 22 0 1 1 H APF H APF 1-2 APF APF APF H 3-6 APF H APF 7 8-11 2 8 9 APF APF 1 H APF Fig. 1 Topology of H-bridgecascaded APF 10 11 H 2 U dc U dcx x = a b c ΣU dcx U H dcxn H U APF cxn H 6k ± 1 k = 1 2 3 H APF APF H 2 Fig. 2 Overall control block diagram of DC voltage balance
1 H APF 79 1. 1 i A = 槡 2 I mn sin nωt + φ n n = 1 6k ±1 k = 1 2 3 6k ± 1 k = 1 2 3 i B = 槡 2 I mn sin nωt + φ n - 2nπ /3 5 n = 1 6k ±1 k = 1 2 3 i C = 槡 2 I mn sin nωt + φ n + 2nπ /3 0 A i n = 1 6k ±1 LA 3 k = 1 2 3 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 - 1 5 sin 5ωt - 1 7 sin 7ωt + P A #P B #P C 1 11 sin 11ωt + 1 sin 13ωt - 1 13 ΔP 1 I d APF B = U z5 I m5 cos φ z5 - φ 5-2π /3 8 25 ΔP C = U z5 I m5 cos φ z5 - φ 5 + 2π /3 2 i A = 槡 3 π 1 5 sin 5ωt + 1 7 sin 7ωt - 1 11 sin 11ωt - 1 sin 13ωt + 2 13 2 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 = 0 1 2 3 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 = 0 7 8 U z1 φ 1 10 APF I m5 > I m1 APF
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 ] 11 1. 2 11 APF 7 U zero = 槡 2 I m5 ΔP q sin 5ωt + φ 5 - ΔP d cos 5ωt + φ 5 12 6 12 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
1 H APF 81 c k = e k + Q z c k - N 15 Q z 1 Q z = 0. 97 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 = 1 2 3 I 2 mn 17 U dcxi < U dcx ΔU dcxi > 0 ΔP xi > 0 A 9 U ca0 1 1 2 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 1. 3 10 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
82 22 0. 3 s 0. 04 s 450 V Fig. 10 10 Structure diagram of voltage balance within one phase /mh 2 Fig. 12 12 Voltage balance among three phases /μf 2 200 /V 150 /khz 5 3 13 0. 1 s APF 145 V 37. 5 Ω + 25 mh 2. 1 Matlab /SIMULINK H APF 11 0. 5 0. 8 1 kω 0. 3 s + 13 Fig. 13 Fundamental zero-sequence voltage 0. 3 s 0. 1 s 150 V 14 Fig. 11 11 Voltage balance within one phase 15 0. 1 s APF 32V APF APF 16 0. 2 s 0. 2 s 12 0. 05 s A B C 450 V 0. 5 0. 8 1 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. 4 s 150 V III B 3 170 V 0. 3 s 3 150 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 29. 96% 3. 23% 1 3 19-100 V + 2. 2 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 3 150 V 1. 7 3. 6 5 kω 19 1 18 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. 19 19 Voltage balance among three phases 23 3. 96 0. 65 25 3. 92 0. 76 THD 29. 72 4. 48 4 Fig. 20 20 Fifth-order zero-sequence voltage 21 120 21 Fig. 21 voltage-balancing method of single phase cascaded H-bridge rectifiers J. Electri c Machines and Control 2016 20 5 37. Load current grid voltage compensating current and grid current 2 25 THD 29. 72% 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 2009. 2 KUMMAR J AGARWAL P DAS B. Implementation of cascade multilevel inverter based STATCOM J. IETE Journal of Research 2010 56 2 119. 3. H J. 2016 20 5 37. WANG Shunliang SONG Wensheng FENG xiaoyun. One fast 4. STATCOM J. 2003 27 16 53. 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 2003 27 16 53. 5. STATCOM
1 H APF 85 J. 2003 27 17 35. 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 2003 27 17 35. J. 2011 35 21 96. HU Yinghong REN Jiajia WANG Jianze. Unbalanced phenomenon and reason analysis for DC side voltage of cascaded STATCOM J. Automation of Electric Power System 2011 35 21 96. 7. 50MVA J. 2004 24 4 145. 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 2004 24 4 145. 8 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 2007 43 4 1041. 9. H APF J. 2015 29 12 1836. 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 2015 29 12 1836. 10. H STATCOM J. 2015 35 5 15. 6. STATCOM XU Rong YU Yong YANG Rongfeng et al. DC capacitor voltage balance control of H-bridge cascaded STATCOM J. Electric Power Automation Equipment 2015 35 5 15. 11. STATCOM J. 2011 31 11 33. 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 2011 31 11 33. 12. J. 2016 36 4 40. 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 2016 36 6 40. 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 76 8. 10 OOMMEN T V. Moisture equilibrium in paper-oil systems C. J. 2007 35 4 14. 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 3-6 1983 C. Piscataway IEEE 2016. 2007 35 4 14. J. 2001 29 4 45. WANG Jingyu. Gas protection malfunction caused by low temperature and its preventive measures J. Jilin Electric Power 2001 29 4 45. 11 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 3-6 2006. Piscataway IEEE 2007.