Control Strategy of Cascade STATCOM Based on Internal Model Theory

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1 TEKOMNIKA Indonean Journal of Electrcal Engneerng Vol.12, No.3, March 2014, pp ~ 1694 DOI: Control Strategy of Cacade STATCOM Baed on Internal Model Theory Xa Zhenglong,Sh png, Qanqan School of Informaton and Electrcal Engneerng, Chna Unverty of Mnng and Technology Quan-Shan Dtrct, Xuzhou, Jangu Provnce, PR Chna, pot code: Correpondng author,e-mal: zhenglong.xa@hangruo.com Abtract Internal model control () method enable the ytem to be of good dynamc and teady performance, whch mple, and eay to be mplemented. In alluon to the cacade STATCOM feature of hgh order, ntablty, mult-varable, non-lnearty and tght couplng, the mathematcal model of cacade STATCOM n d-q-0 coordnate wa deduced. Decouplng model of cacade STATCOM wa gven by Internal Model Control prncple, computer mulaton and experment reult were alo gven. Reult how that wth, 3-phae current control method of cacade STATCOM ha good trackng performance and control precon both n a-b-c coordnate and n d-q-0 coordnate, and alo acheve excellent current compenaton reult. Keyword: nternal model control, cacade STATCOM, current control trategy Copyrght 2014 Inttute of Advanced Engneerng and Scence. All rght reerved. 1. Introducton Compared wth the tradtonal SVC, the tatc ynchronou compenator (STATCOM) ha become the development trend, for t fater repone, wder adjutable range and better wave qualty of compenatng current [1-2]. Bede, capactor and reactor ued n cacade STATCOM are maller than thoe ued n tradtonal SVC, whch greatly reduce devce' volume and cot. Artcle [3-5] ponted out that cacade STATCOM had broad applcaton propect, uch a electrc power, metallurgy feld and mnng ndutry. A to the decouplng method of cacade STATCOM mentoned n releaed publcaton, there are two model: one the tate-feedback decouplng; the other the tme decouplng whch an approxmate method. Artcle [6-7] ponted out that the applcaton of tme decouplng wa lmted n practce, becaue t decouplng charactertc were related wth the parameter of power network and the man crcut. Artcle [8-10, 14] are typcal document about tatefeedback decouplng. In artcle [8], the reactve power control trategy baed on nvere ytem control and decouplng control of actve power and reactve power wa degned and realze the dynamc control of phycal prototype, but the repone tme wa not quck. Artcle [9] preented a feedback lnearzaton theory to realze the degn, whch wa proved to be effectve. Artcle [14] derved the current control trategy n d-q-0 coordnate by method of nonlnear, and valdated the method by mulaton, but the actual ue effect need to be teted by project. Baed on artcle [11-16], th paper deduce the mathematcal model of cacade STATCOM n d-q-0 coordnate, and buld mulaton model by computer mulaton oftware MATAB/SIMUINK, at lat verfe the degn by computer mulaton and tet. 2. Mathematcal Model 2.1. Man Crcut Topology Fgure 1 the man crcut topology of cacade STATCOM. repreent the nductance. R repreent power loe. uc () t and c () t repreent voltage and current outputted by cacade STATCOM. () t repreent ytem' current. l () t repreent load current. Receved Augut 25, 2013; Reved September 26, 2013; Aepted October 7, 2013

2 1688 ISSN: a u a la b u b lb c u c lc ca cb R uca R ucb R u Fgure 1. Structure Dagram of Cacade STATCOM 2.2. Mathematcal Model n a-b-c Coordnate Before contructng the mathematcal model of cacade STATCOM, followng aumpton are preented [9-10]: (1) The power ytem treated a balanced. (2) R ued to expre the power lo of flter capactor and flter reactor. (3) ued to expre the nductance of flter reactor. (4) Output voltage of cacade STATCOM drectly proportonal to the um of dc capactor voltage. (5) Snce cacade STATCOM compoed of eventeen-level cacaded nverter ung carrer phae-hftng method, thu only the fundamental component of cacade STATCOM condered, gnorng the harmonc component. Aordng to the above aumpton and the expreon of output voltage generated by ngle phae H-brdge nverter, output voltage expreon of cacade STATCOM can be obtaned by: u ca n( t ) ucb Kudc n( t 2 / 3 ) u n( t 2 / 3 ) (1) K the proportonal coeffcent. the phae angle dfference between the voltage outputted by cacade STATCOM and the ytem voltage. The ytem voltage ymmetrcal three phae voltage, and the real phae voltage expreed by: ua n( t) ub 2US n( t 2 /3) u n( t 2 / 3) c (2) Aordng to Krchhoff' law, the mathematcal equaton of cacade STATCOM expreed by: ca ua uca ca d u u R dt cb b cb cb u c u (3) TEKOMNIKA Vol. 12, No. 3, March 2014:

3 TEKOMNIKA ISSN: Wth the energy balance theory, dc bu capactor voltage equaton can be obtaned a follow: d 1 2 Cudc () t uca () t ca () t ucb () t cb () t u () t () t dt 2 dudc () t K 2 2 [ ca ( t )n( t ) cb ( t )n( t ) ( t )n( t )] dt C 3 3 Q () t () t () t 0 ca cb dudc () t 3 K [ ca ( t)co( t ) cb ( t)co( t )] dt C 3 The mathematcal model of cacade STATCOM obtaned by: nt d ca ca 2U S 2 A cb cb n( t ) dt 3 u dc u dc 0 (4) R K 0 n( t ) R K 2 A 0 n( t ) 3 3K 3K n( t ) n( t ) 0 C 6 C 2 Equaton (4) the mathematcal model of cacade STATCOM n a-b-c coordnate 2.3. Mathematcal Model n d-q Coordnate Equaton (4) the mathematcal model of cacade STATCOM n a-b-c coordnate, whch the dfferental equaton wth tme-varyng parameter (coeffcent). For t hard theoretcal analy, Equaton (4) tranferred by d-q coordnate tranform a follow: ca ca d d d dt T cb cb dt q dt dt (5) In equaton (5): T 2 2 co( ) co( ) co( ) 2 t t t n( t) n( t ) n( t ) 3 3 Take Equaton (3) to Equaton (5): R d d d 1 ud ucd dt q R q uq ucq Id() R Id() Ud() Ucd() I q() R I q() U q() U cq() (6) (7) Equaton (7) the mathematcal model of cacade STATCOM n d-q coordnate. It eay to ee that current couplng problem not olved, therefore the method of current decouplng needed to realze the control trategy. Control Strategy of Cacade STATCOM Baed on Internal Model Theory (Xa Zhenglong)

4 1690 ISSN: Strategy n d-q Coordnate 3.1. Prncple The tructure dagram of hown n Fgure 2, n whch the nternal model expreed a G ˆ ( ), the controlled object expreed a G(), and the nternal model controller expreed a C (). G ˆ( ) I () C () G () U() I () m I () F() I () m G ˆ () I () C () G () E () U() I () Fgure 2. Dagram of Internal Model Control Fgure 3. Equvalent Feedback Control Block Dagram Fgure 3 the equvalent feedback control block dagram of Fgure 2. In Fgure 3, the equvalent controller F() gven by: ˆ ( ) F()=[1 - C -1 ( ) G ] CIMS ( ) Although there no aumulaton functon n the nternal model controller, t can elmnate the ytem tead-tate error by the tructure. U() and I() repreent voltage and current outputted by cacade STATCOM. In addton to havng mlar vrtue, alo ha many outtandng charactertc uch a follow: (1) can regulate the output error caued by mmatch between G ˆ ( ) and G (). (2) It can realze trackng wthout teady-tate error by ntroducng the correpondng flter expreed a (), and t can alo mprove the robutne of the ytem. The low-pa flter () gven by: () I The dentty matrx expreed a I, the recprocal of cacade STATCOM ytem tme contant Internal Model Decouplng Control The followng et of voltage and current equaton can be obtaned from Equaton (7). ud ucd R d u u R q cq q (8) ud R d u R q q (9) ˆ 1 () G contructed a follow: ˆ 1 ( ) G R R (10) TEKOMNIKA Vol. 12, No. 3, March 2014:

5 TEKOMNIKA ISSN: The current controller, C ( ) gven by: R 0 ˆ 1 R C () G () () R R 0 (11) The tranfer functon can be obtaned from Fgure 3. I () FG () () C () G() () 1 ( )[ ( ) ( )] I 1 FG ( ) ( ) C G Gˆ (12) By combnng equaton (10), the controlled object G() gven by: () ˆ R G G () R 1 (13) The equvalent controller F() can be obtaned from Equaton (11) and Equaton (13). R ( ) [1 ( ) ˆ 1 F S C S G ( )] C ( S ) R (14) I() can be obtaned from Equaton (11), Equaton (12) and Equaton (13). 0 I I I 0 () C () G() () () (15) The d-ax current reference of I () expreed a, and the q-ax current d I () expreed a. () q I can be obtaned from Equaton (15). 0 d d q q 0 (16) Equaton (16) how that the d-q-ax current realze a dynamc thorough decouple. The repone of I to I can be equvalent to the frt-order nerta lnk. The d-q-ax current can be obtaned from Equaton (7) a follow: d ud q R R (17) q uq d R R (18) The voltage outputted by cacade STATCOM expreed a U() can be obtaned from Fgure 3. Control Strategy of Cacade STATCOM Baed on Internal Model Theory (Xa Zhenglong)

6 1692 ISSN: R d d U() F()[ I () I()] R q q (19) The equvalent model of cacade STATCOM decoupled by Equaton (17), Equaton (18) and Equaton (19) hown n Fgure 4. Internal model control alo a clacal PI type control, but the regulatng parameter are only related to mnmal open-loop tme contant. Artcle [10] have already made a detaled reearch on the relatonhp between the open-loop tme contant of cacade STATCOM and the man crcut parameter, the relatonhp of parameter adjutment and the properte of the ytem defnte. The ytem acqure the reference of reactve current expreed a from the control object. The reference of actve current q d acqured from the controller for DC bu voltage regulaton. u dc u dc d ( R) u d 1 R d u u q ( R) u q 1 R q Fgure 4. Internal Model Control of STATCOM 4. Computer Smulaton and Prototype Tral 4.1. Smulaton In order to valdate the correctne of decouplng nternal model control () degn and mathematcal equaton preented n th paper, the mulaton teted of 6-KV, 2.8-MVar, tar-confgured STATCOM wth eght H-Brdge PWM converter n each phae mplemented by Matlab/Smulnk. The nternal model control method adopted n cacade STATCOM n d-q coordnate, and the load three phae ymmetrc load. About 0.1 econd before tartng the devce, the nductance load wth the capacty of 1.44M Var are put nto operaton. About 1.5 econd after tartng the devce, the nductance load wth the capacty of 0.96MVar are put nto operaton, and then the nductance load wth the capacty of 0.72MVar are cut off n 2 econd. Smulaton waveform are hown n Fgure 5 and Fgure 6. For the convenence of comparatve analy, voltage value reproduce at 40 tme. Smulaton waveform before and after compenaton are hown n Fgure 5 under teady tate, uch a ytem voltage u a, ytem current a,load current la,output current of cacade STATCOM ca. (a) Before compenaton of nductve load (b) After compenaton nductve load Fgure 5. Waveform of Grd Voltage, Current and oad Current at Inductve oad TEKOMNIKA Vol. 12, No. 3, March 2014:

TEKOMNIKA ISSN: 2302-4046 1693 Smulaton waveform at udden loadng operaton are hown n Fgure 6. When the load changng, the complete compenaton can be realzed n two power frequency perod.

5 econd (b) Sudden unloadng operaton at 2 econd Fgure 6. Waveform of Grd Voltage, oad Current and STATCOM Current when oad Change 4.2. Prototype Tral Baed on the computer mulaton and the trategy, 6-KV, 2.

7 TEKOMNIKA ISSN: Smulaton waveform at udden loadng operaton are hown n Fgure 6. When the load changng, the complete compenaton can be realzed n two power frequency perod. The reult of computer mulaton hown n Fgure 5 and Fgure 6 prove that nternal model control trategy brng good dynamc and tatc performance. (a) Sudden loadng operaton at 1.5 econd (b) Sudden unloadng operaton at 2 econd Fgure 6. Waveform of Grd Voltage, oad Current and STATCOM Current when oad Change 4.2. Prototype Tral Baed on the computer mulaton and the trategy, 6-KV, 2.8-MVar, tarconfgured STATCOM developed a hown n Fgure 7. Fgure 7. Structure Dagram of Medum Voltage H-brdge Cacade STATCOM Fgure 8. Dynamc Performance of STATCOM Fgure 9. Output Voltage and Current of STATCOM Control Strategy of Cacade STATCOM Baed on Internal Model Theory (Xa Zhenglong)

8 1694 ISSN: The dynamc performance the mportant ndcator of cacade STATCOM. Fgure 8 how the dynamc proce from the tart to the end of compenaton. It alo how that STATCOM can realze fat detecton of current and dynamc compenaton wthn 1.5 power frequency perod, whch content wth above computer mulaton. The waveform of output voltage and current of STATCOM after compenaton n Fgure 9 how that the ytem ha perfect output waveform and good harmonc charactertc. 5. Concluon In th paper, the mathematcal model of STATCOM n both a-b-c coordnate and d-q coordnate developed, and then the computer mulaton model of cacade STATCOM developed baed on theory. The computer mulaton and prototype tral prove that the current decoupled control trategy etablhed n th paper can realze complete decouplng, and brng good dynamc and tatc performance. Acknowledgement Th work wa upported by the Reearch Fund for the Doctoral Program of Hgher Educaton of Chna under grant and by the Key (Key grant) Project of Chnee Mntry of Educaton under grant Reference [1] D Harkrhna, NV Srkanth. Dynamc Stablty Enhancement of Power Sytem Ung Neural-Network Controlled Statc-Compenator. TEKOMNIKA Indonea Journal of Electrcal Engneerng. 2012; 10(3): [2] Al Mohammad, Sajjad Farajanpoer, Saeed Tavakol, SMaoud Barakat. Fluctuaton Mtgaton of Varable Speed Wnd Turbne through Optmzed Centralzed Controller. TEKOMNIKA Indonea Journal of Electrcal Engneerng. 2012; 10(5): [3] Wang Zhaoan, Yang Jun, u Jnjun. Harmonc uppreon and reactve power compenaton. Bejng: Chna Machne Pre. 1998: [4] Hanon DJ, Horwll C, Gemmell BD, et al. A STATCOM-baed relocatable SVC project n the UK for natonal grd. IEEE Power Engneerng Socety Wnter Meetng. New York, USA. 2002: [5] Yu Qangguang, Pe, u Wenhua, et al. Overvew of STATCOM technologe. IEEE Internatonal Conference on Electrc Utlty Deregulaton, Retructurng and Power Technologe. Hong Kong, Chna. 2004: [6] Chaon JR, Tolbert M, McKenze KJ. et al. A unfed approach to olvng the harmonc elmnaton equaton n multlevel converter. IEEE Tranacton on Power Electronc. 2004; 19(2): [7] Poh Chang oh, Holme DGT. Implementaton and control of dtrbuted PWM cacaded multlevel nverter wth mnmal harmonc dtorton and common-mode voltage. IEEE Tranacton on Power Electronc. 2005; 20(1): [8] We Wenhu, u Wenhua, Song Qang, et al. Reearch on fat dynamc control of tatc ynchronou compenator ung cacade multlevel nverter. Proceedng of the CSEE. 2005; 25(2): [9] Zha Xaomng, Zhang Maoong, Sun Janjun. Modelng of cacade D-STATCOM wth decoupled tate varable feedback lnearzaton control. Proceedng of the CSEE. 2010; 30(28): [10] Senke JK. Swtchng Frequency Optmal PWM Control of A Three-level Inverter. IEEE Tranacton on Power Electronc. 2006; 7(3): [11] Geng Juncheng, u Wenhua, Yu Xufeng, et al. Modelng of cacade tatcom. Proceedng of the CSEE. 2003; 23(6): [12] Srukpraert S, Huang AQ, a JS. Modelng, analy and control of cacaded-multlevel converterbaed STATCOM.Proc. IEEE-PES general meetng. Toronto, Canada. 2003: [13] Srukpraert S. The modelng and control of a cacaded-multlevel converter-baed STATCOM. Vrgna, the Unted State & Vrgna Polytechnc Inttute and State Unverty [14] Wang Xuan, n Jayang, Teng etan, Wang Ke, Yuan Meng, et al. Current Control Strategy of Chan Crcut STATCOM n d-q-0 Coordnate. Proceedng of the CSEE. 2012; 32(15): [15] Wang Xuan, Xong Chaoyng, Fu Jan, et al. Dynamc modelng of chan crcut STATCOM. Proceedng of the CSEE. 2012; 32(9): 1-6. [16] Wang Xuan, Fu Jan, Teng etan, et al. Study on current control trategy of chan crcut STATCOM. Proceedng of the CSEE. 2012; 32(12): 1-6. TEKOMNIKA Vol. 12, No. 3, March 2014:

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