Switching-Based SVPWM Control for Three-Phase Active Power Filter

Transcription

1 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25), pp Swtchng-Bsed SVPWM Control for hree-phse Actve Power Flter Zhng Menghu *, Cheng Xngong 2, Zong Xju 3, nd Zhng Yong 4 School of Electronc nd Engneerng, nversty of Jnn, Shndong, Jnn, 2522, Chn menghuhppy@63.com Astrct A swtchng-sed SVPWM control method for three-phse ctve power flter s proposed n ths pper. Frst, error model of the swtched system s estlshed. And then, ccordng to the spce voltge vector dgrm nd three-phse supply voltge wveforms, the supply voltge s dvded nto sx sectors. In ech sector, comnton of swtchng susystem s set up ccordng to the requrement of qudrtc stlty conon. Fnlly, the common Lypunov functon s selected nd therefore, the susystem s determned, whch hs mnmum dervtve of Lypunov functon nd meets the conons ove. he vly of the proposed control method s proved wth Mtl/Smulnk nd expermentl results. Keywords: Actve power flter, qudrtc stlty, spce voltge vector control, convex comnton, Lypunov functon, swtched system. Introducton Wth the rpd development of power electroncs technology, more nd more power electronc equpment s for ndustry nd people's dly lves re comng out. At the sme tme, power electroncs produce serous hrmonc polluton prolems to the power grd. As s well-known, the power system hrmonc content s n mportnt ndctor of power qulty. In order to reduce the hrmonc level of power system, growng numer of scholrs hve mde study focusng on ths []. he ctve power flter (APF) plys n mportnt role n hrmonc compenston ncresngly, nd the ssocted control lgorthm s one of the core ssues emerged n the hrmonc compenston. Lnerzton nd unfed modelng s the sc de of nvestgtng APF. In other words, vergng of ech swtchng mode n the tme domn, the correspondng perod verge mode s otned [2-3].Ded-et control [4], one-cycle control [5], the method of current trckng control proposed n [6-7], nd sldng mode vrle structure methods [8] were ll sed on perod verge model. However, APF s typcl nonlner hyrd dynmc system, so we cn get nothng ut the mcro level performnce of APF. Menwhle, nonlner systems of APF cn e dvded nto multple lner dynmc susystems y on-off control. By the dvntge of the swtchng control theory, Zongo Hu nd Wllem ppled swtched lner systems theory to the controlllty nd rechlty of dc-dc converters, nd they mde gret progress [9-]. he control strtegy of sngle phse APF s swtched lner systems ws proposed n [2]. In lterture [3] the swtchng model for APF ws estlshed nd the equvlent dscrete system model ws otned, ut the correspondng clculton process ws very complcted. So method comned swtchng control method wth spce voltge vector control lgorthm ws proposed n ths pper. hree-phse power supply voltge s dvded nto 6 sectors. And then ccordng to the Lypunov functon nd the requrement of qudrtc stlty conon, swtchng rule s proposed to smplfy the lgorthm. Due to the resonle use of zero-vector, swtchng loss decreses sgnfcntly. ISSN: IJSIP Copyrght c 25 SERSC

2 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) 2. Error Model of Actve Power Flter Swtched System he error model of three-phse APF s llustrted n Fgure. s L N c s sc L Lc Nonlner lod L R c c cc S S 2 n S3 S5 S4 S6 + C c Fgure. opologcl Structure of hree-phse APF APF s n prllel wth the nonlner lod nd supples compenston currents to cncel the hrmonc current components from the source current sj (j=,,c). * cj (j=,,c) s the hrmonc current generted y the nonlner lod, nmely the reference current. hrough swtchng the IGBs, APF cn generte compenston current cj (j=,,c) tht trcks * cj (j=,,c) to mke the source current nerly snusodl. L stnds for the flter nductor, R for the totl equvlent resstnce of the flter nductors. he voltge source of APF s. S k Defne swtchng coeffcent: th e p o stv e sw tc h s o n n d th e n e g tv e sw tc h s o ff th e n e g tv e sw tc h s o n n d th e p o stv e sw tc h s o ff he 8 swtchng modes of ctve power flter re shown n le : le. Swtchng Modes of hree-phse APF Swtchng modes S S S c Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ From Fgure, ccordng to Krchhoff Voltge Lw, t cn e otned tht: - 86 Copyrght c 25 SERSC

3 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) dc u R L dc u R L dcc u R L N c N c c N c c c () where u N, u N nd u cn represent voltge drop etween ponts,,c nd neutrl pont N, respectvely. In the cse of symmetrcl lod, t holds: u u u (2) N N cn nd u u u u u u u u u N n n N N n n N c N c n n N (3) u u u Susttutng (2-3) nto (), t follows tht: u = S + S + S n N c (4) 3 Susttutng (3-4) nto (2), t follows tht: N N c N 2 S S S c 3 2 S S S c 3 2 S S S c 3 Snce the chnge rte of s much less thn tht of APF output current, we consder s constnt. hen the stte equton of the system s otned: (5) d R 2 S S S c c L 3 L L c d R 2 S S S c c = + + L c 3 L L R cc d 2 c c S S S c c + L 3 L L Ax+ B =, 2,, 8 (6) where x=[ c c cc ] stnds for the stte vrle. Suppose tht x d =[x d x d2 x d3 ] s the reference vlue of compenston current, whch s lso the swtchng equlrum pont. Introduce coordnte trnsformton Δx d =x-x d. So Δx d = s the new swtchng equlrum pont. hen the error model of the swtched system s otned: Copyrght c 25 SERSC 87

4 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) x R 2 S S S R c + x d L R 2 S S S R c = x + + x d 2 L R 2 S S S R c c + x d 3 L = A x + =, 2,, 8 (7) where Δx=[Δ c Δ c Δ cc ] stnds for stte vrle. We cn see tht system mtrx A s fxed nd A < for three- phse ctve power flter. 3. Qudrtc Stlty sed Swtchng Control of the hree-phse Actve Power Flter he mn result of ths pper s s follows: heorem :If there exsts convex comnton λ=[λ λ m ] for m [2,8], such tht: m j j, j D A D G D A D G x D G B d he stte-swtchng control, (8) rg m n t x (9) mkes the equlrum soluton x = of (6) glolly symptotclly stle. Proof: Choose Lypunov functon d V x x x () 2 he dervtve of () cn e otned tht, V x = x x + x x 2 2 = x A x + = x A x + x () where A<, thus Δx AΔx<, m [2-8]. Becuse there exsts convex comnton λ=[λ λ m ] suject to λ =, ccordng to [4], m n x, then V x. he theorem s proved. Corollry : If there exsts convex comnton λ=[λ λ m ] for m [2,8] such tht 88 Copyrght c 25 SERSC

5 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) m j j, j D A D G D A D G x D G B d he stte-swtchng control, (2) t rg m n x c (3) mkes the equlrum soluton Δx d = of (6) glolly symptotclly stle, where: 2 S S S c 3L 2 S S S c 3L 2 S S S c 3L c (4) Proof: Notng tht: x d 2 S S S R c c + x d d 2 R c S S S c + x d 2 d 2 S S S R c c c c + x d 3 d 2S S S d 2S S S c c c c d d d c c c c c d t 3 L d t 3 L d t L d t L d t L = + d 2 S S S R R R c c c d d d c c c c x x x d d 2 d 3 3L d t L d t L d t L = x c + d (5) For ech susystem, d s lwys the sme. hus t cn e otned tht: rg m n rg m n t x x c (6) Corollry s equvlent to theorem wth smplfed clculton process. 4. Swtchng-sed SVPWM Control From (6) t cn e otned, d 2 S S S c c 3L c d 2 S S S c c L R c 3L c c c d 2 S S S c c c 3L (7) Copyrght c 25 SERSC 89

6 voltge( V) Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) Becuse the voltges of L nd R re fr less thn the power supply voltge, they cn e gnored. (7) cn e smplfed s: 2 S 2 S 3 2 c S c As the rght hnd sde of (8) s the reference nput of SVPWM,, nd c cn e regrded s the SVPWM reference nput. Fgure 2 shows the wveform of three-phse power supply voltge, whch s dvded eqully nto 6 sectors. (8) 4 3 A-phse B-phse 2 C-phse degree( ) Fgure 2. Wveform of hree-phse Power Supply Voltge In the ntervl [, 2 ], c s the mnmum of the three-phse voltges. Let S c =. In the sme wy, S = nd S = s set correspondngly n ntervl [2, 24 ] nd [24, 36 ]. he voltge spce vector grph consttuted of,, nd c s shown n Fgure 3. c c 2 ~ 8 6 ~ 2 ~ 6 c 2 c c c 8 ~ ~ 3 3 ~ 36 Fgure 3. Voltge Spce Vector Grph Wthn ntervl [, 6 ], nmely sector, only two rdge legs S ~ S 2 nd S 3 ~ S 4 ct for S c =. he system cn e treted s four swtchng lner susystems I, II, III nd IV n ccordnce wth the evoluton of S, S, S c nd the swtchng modes of ech susystem s lsted n le. For purpose of reducng the swtchng loss, two groups of swtch sequence re chosen, I, III, VII nd I, V, VII. ke the sequence I, V, VII for exmple. When S =, S =, S c = 9 Copyrght c 25 SERSC

7 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) R x L L R L L R c x L L d x d 2 d 3 (9) When S =, S =, S c = 2 R + x R R c + x + x 2 d 2 d 3 d (2) When S =, S =, S c =, R + x R 2 R c + x d + x 3 d 2 d 3 (2) We fnd tht λ +λ 2 +λ 3 =(λ (,), =,2,3) s lwys true whch cn derve λ =, whose expnded form s: r 2 R + x d 2 x d L L R + 3 x d r R + x d 2 2 x d 2 L L R + 3 x d 2 (22) We cn otn, x x 2 R R Rx Rx d d d d 2 R x 2 2 R x d d 2 (23) stsfyng the formul (8) nd (2), the conon of theorem nd corollry, respectvely. In the sme wy, three swtchng susystems meetng the conon of theorem nd corollry cn e otned for ll other sectors, shown n le 2. Copyrght c 25 SERSC 9

8 L/A Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) le 2. Swtchng Modes nd Swtchng Functons of hree-phse APF n Ech Sector Intervl Swtchng modes S S S c ~6 Ⅰ > > c Ⅴ Sector Ⅶ 6 ~2 > > c Sector 2 2 ~8 > c> Sector 3 8 ~24 c> > Sector 4 24 ~3 c> > Sector 5 3 ~36 > c> Sector 6 Ⅰ Ⅲ Ⅶ Ⅰ Ⅲ Ⅳ Ⅰ Ⅱ Ⅳ Ⅰ Ⅱ Ⅵ Ⅰ Ⅴ Ⅵ 5. System Smulton nd Expermentl Verfcton In order to verfy the performnce of the proposed control method, Mtl/Smulnk s used to smulte the system. he prmeters of ths smulton system re gven s follows, R=.5Ω, L=2mH, C=68μF, System voltge s 38V/5Hz, the reference dc sde voltge * =75V. In order to verfy the dynmc response performnce, we dopt two three-phse uncontrolled rectfers s the nonlner lods. lods re R=25Ω, C=6μF nd R=Ω, L=mH, respectvely. When t=.5s, we put the second uncontrolled rectfer nto operton Fgure 4. Nonlner Lod Current L he hrmonc component of lod current s prtculrly hgh s shown n Fgure 4. It s ovous tht there s serous dstorton of current nd the HD s 24.3%. Fgure 5 shows the wveform of phse-a supply current fter compenston. he ner snusodl supply current shows tht most of the hrmonc currents hve een compensted successfully. ht s to sy, the compenston current cn trck the chnge of lod current hrmonc components. We cn see from Fgure 6 tht the HD s only.28%. 92 Copyrght c 25 SERSC

9 /V c c*/a s/a Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) Fgure 5. Supply Current s fter Compenston Fgure 6. Spectrum Dgrm of Supply Current s fter Compenston Fgure 7 shows the process tht compenston current of APF trcks the chnge of lod current hrmonc components. 5 c c* Fgure 7. he Compenston Current c rckng Commnd Current c * Fgure 8 shows the wveform of -sde output voltge Fgure 8. -sde Output Voltge Fgure 9 shows the Lypunov functon chngng over tme. We cn see from the fgure tht the system s stle t.2s. Copyrght c 25 SERSC 93

10 swtchng drvng sgnls voltge(v) s/a L/A V(x) Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) 5 x Fgure 9. Lypunov Functon V(x) he wveforms of the lod current L nd the system current s under sltton lod re shown n Fgure nd Fgure, respectvely. We cn see from the fgures tht n the cse of lod chngng, APF controlled y the method proposed n ths pper hs good hrmonc compenston effect Fgure. Wveform of the Lod Current L nder Sltton Lod Fgure. Wveform of the System Current s nder Sltton Lod he Drver sgnls for swtches S, S, S c re shown n Fgure 2. It s shown tht when c s the mnmum, S c =. It s to sy tht only two rdge legs swtch, whle t requres three rdge legs to swtch [4]. So the numer of swtchng needed n the control strtegy proposed n the present pper s less. Swtchng loss then decreses drmtclly. 5-5 c.5 Sc.5 S.5 S Fgure 2. Drver Sgnls for Swtches 94 Copyrght c 25 SERSC

11 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) For further verfyng the vly of the proposed control strtegy n ths pper, n expermentl pltform s set up. ype of IGB s CM3dx of Mtsush. ype of DSP s MS32F28335 of exs Instruments. ype of FPGA s EP3CE44C8N of Alter. Swtchng rules re relzed y DSP. he mn functon of FPGA s protecton of hrdwre crcut, fult detecton, control of A/D nd so on. We dopt two three-phse uncontrolled rectfers s the nonlner lod. lods re R=25Ω, L=mH nd R=25Ω, L=mH, respectvely. he crcut prmeters of the experment re the sme wth smulton. Fgure 3 nd Fgure 4 show the mn crcut nd controller of APF. Fgure 3. he Mn Crcut of APF Fgure 4. he Controller of APF he wveforms of A-phse lod current L, compenston current c nd supply current s re shown n Fgure 5. Fgure 5. he Wveforms of L, c nd s Fgure 6 shows the hrmonc nlyss of three- phse supply current. Due to the lmtton of hrdwre, the smplng perod of expermentl prototype s lrger thn the smplng perod of smulton. herefore, the hrmonc components of supply current fter compenston re not s low s the hrmonc components of smulton. We cn see from Fgure 6, the three-phse HD re 2.9%, 2.9%, 2.8%, respectvely. Copyrght c 25 SERSC 95

12 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) Fgure 6. Hrmonc Anlyss of hree-phse Supply Current Fgure 7 shows the dynmc responses to lod chngng suddenly. After short tme trnsent process, the APF cn compenste hrmonc current stedy. 6. Conclusons Fgure 7. Dynmc Responses to Arupt Lod Chnge A swtchng-sed SVPWM control method for three-phse ctve power flter s proposed n ths pper. hree-phse power supply voltge s dvded nto 6 sectors. And then ccordng to the Lypunov functon nd the requrement of qudrtc stlty conon, swtchng rule s proposed to smplfy the lgorthm. Due to the resonle use of zero-vector, swtchng loss decreses sgnfcntly. Acknowledgment hs work ws supported y the ntonl Nturl Scentfc Founon of Chn (Grnted No. 279), the Independent Innovton Specl Projects of Shndong Provnce (Grnted No. 22CX332), nd the Nturl Scence Founon of Shngdong Provnce (Grnted No.ZR2EEM24). References [] Z. Y. L nd L. F. Shen An LCL-APF Drect Power Control Approch Bsed on Non-Hrmonc Detecton echnology, Power System echnology, vol. 36, no. 2, (22), pp [2] J. Le nd Q. R. Jng, he nlyss of hysteress current control strtegy of three-phse four-wre APF sed on the unfed mthemtc model, Proceedng of the CSEE, vol. 27, no., (27), pp [3] J. M. Chen nd F. Lu, Pssvty-sed controller for three phse four-wre APF, Automton of Electrc Power Systems, (26). [4] Y. M. L nd W. M. M., Applcton of dedet control n seres ctve power flter, Automton of Electrc Power Systems, vol. 25, no. 4, (2), pp [5] H. D. Bttst nd R. J. Mntz., Hrmonc seres compenstors n power systems: ther control v sldng mode, IEEE rnsctons on System Control echnology, vol. 8, no.2, (2), pp [6] W. P. Zhou, Z. G. Wu nd L. X, Current trckng performnce optmzton control for three-phse three-wre ctve power flter, Proceedngs of the CSEE, vol. 24, no., (24), pp Copyrght c 25 SERSC

13 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) [7] S. Fukud nd. Yod, A novel current-trckng method for ctve flters sed on snusodl nternl model for PWM nverters, IEEE rns on Industry Applctons, vol. 37, no. 5, (2), pp [8] H. H. ng nd C. W. L, Modelng nd Control of Sngle Phse Actve Power Flter Bsed on Swtched Lner System, Power System echnology, vol. 3, no. 3, (27), pp [9] Z. B. Hu, B. Zhng nd W. H. Deng, Controlllty nd rechlty of - converters s swtched lner systems, Proceedngs of the CSEE, vol. 24, no. 2, (24), pp [] Z. B. Hu nd B. Zhng, heoretcl nlyss nd expermentl verfcton of one cycle control feslty for oost pfc converter, Proceedngs of the CSEE, vol. 25, no. 2, (25), pp [] L. Wllem nd K. De, Dgtl optml reduced-order control of pulse-wh-modulted swtched lner systems, Automtc, vol. 39, no., (23), pp [2] Y. F. Zhng, X. G. Cheng nd X. J. Zong, Nonlner swtchng control of sngle-phse ctve power flter, Power System Protecton nd Control, vol. 39, no.8, (2), pp [3] C. W. L, nd H. H. ng, Modelng nd Qudrtc Optml Control of hree-phse APF Bsed on Swtched System, Proceedngs of the CSEE, vol. 28, no. 2, (28), pp [4] B. Polo nd S. Wllm, Qudrtc stlzton of swtched ffne system out nonequlrum pont, Amercn Control Conference, (24), pp Author Menghu Zhng ws orn n 988, she receved B.Eng. degree n electrcl engneerng from nversty of Jnn, Jnn, Chn, n 2. She s currently pursung the M.S. degree n nversty of Jnn, Jnn, Chn. She s mjor n control engneerng. Copyrght c 25 SERSC 97

14 Interntonl Journl of Sgnl Processng, Imge Processng nd Pttern Recognton Vol.8, No. (25) 98 Copyrght c 25 SERSC