Model Predictive Control of Voltage Source Converter in a HVDC System

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1 Model Predcte Control of Voltage Source Conerter n a HVDC System Mohammad Amn and Marta Molnas Dept. of Engneerng Cyernetcs Norwegan Unersty of Scence and Technology Trondhem-749, Norway mohammad.amn@ntnu.no arx: [cs.sy] 3 Apr 27 Astract Model Predcte Control (MPC) method s a class of adanced control technques most wdely appled n ndustry. The major adantages of the MPC are ts straghtforward procedure whch can e appled for oth lnear and nonlnear system. Ths paper proposes the use of MPor oltage source conerter (VSC) n a hgh oltage drect current (HVDC) system. A MPC controller s modeled ased on the state-space model of a sngle VSC-HVDC staton ncludng the dynamcs of the man ac grd. A full scale nonlnear swtchng model of pont-to-pont connected VSC-ased HVDC system s deeloped n matla/smulnk assocaton wth SmPower system to demonstrate the applcaton of the proposed controller. Index Terms VSC control, HVDC, Model predcte control. I. INTRODUCTION As Voltage source conerter (VSC) ased hgh oltage drect current (HVDC) transmsson system offers many adantages such as ndependent and fast control on acte and reacte power, mprong power qualty, and feedng of remote solated loads []- [3], ts requred the adanced control technques to achee the precse control of acte and reacte power flow to mantan the system stalty, ensure roust operaton, and hgh leels of effcency. A wde range of studes on modelng and control of VSC-ased HVDC systems hae een pulshed n last few years [4]- [7] whch also nclude the small-sgnal stalty analyss [8]- []. Seeral control technque hae een studed and appled n statonery [] and synchronous reference frame [2] to control the three phase power conerter. The VSC operatng wth ector control strategy can perform the ndependent control y means of controllng real d-axs and magnary q-axs current components. Outer loop proportonal ntegral (PI) controller s utlzed to achee dc oltage or acte power control y controllng the d- axs current components, and the ac oltage or reacte power control s acheed y controllng q-axs current components. The controller can e easly tuned from the transfer functon of the conerter dynamcs y applyng symmetrcal optmum and modulus optmum crtera to achee maxmum flatness from the ode plot of the transfer functon [3], howeer stalty prolem arses when t needs to tune the mult-termnal HVDC Identfy applcale sponsor/s here. (sponsors) (MT-HVDC) system. In ths case model predcte control shows great potental to achee desre performance n case of MT-HVDC system. MPC method has een wdely appled n power conerters [4] ecause of hang hgh dynamc performance, smple mplementaton, hgh flexlty y mplementng seeral ojecte functon [5]- [6], and eng capale to drectly manage the ac sgnal wthout frequency transformaton [7]- [8]. In ths paper, MPC method s proposed to control the VSC n a HVDC system. The MPC s ased on the predcton of the system response to a change n control arales n order to attan a mnmum error. It performs followng three steps n each control nteral; ) predct the future ehaor of the system, 2) perform the optmzaton algorthm to calculate the future nputs for hang desred output, and 3) process a certan numer of calculated nputs [2]. The performance of the proposed method s nestgated for lnearzed model of a sngle VSC-ased HVDC system and fnally a swtchng model of pont-to-pont VSC HVDC system s deeloped to demonstrate the applcaton of ths proposed method. II. ANALYTICAL MODELING OF VSC-HVDC SYSTEM The electrcal crcut of an nerter for analytcal modelng s shown n fg. where and R c are the total seres nductance and resstance etween the nerter and pont of common couplng (PCC) and s the dc lnk capactor. s the flter capactance connected at PCC, and R g and are grd resstance and nductance ncludng seres resstance and nductance of the transformer. The dynamc equatons of the nerter n per unt (pu) can e gen y () and (2), flter y (3) and grd y (4) where s ase angular grd frequency; g s grd frequency n pu; oltage and current of these equatons s ndcated n fg. [2], [22]. d L c o ( R c + j g ) L () d dc dc,lne dc (2) d o L o j g o (3) d o o g ( R g + j g ) o (4)

2 V g Rg PCC ZT R f c c Conerter f VSC Conerter PLL V dc PWM delay ac ac dq dq ld lq ld, ref lq, ref od oq Model Predcte Control ac acte dampng od, AD oq, AD cd + - cq + - cd, ref cq, ref m d m q dq ac Fg. : Oerew of sngle VSC-Conerter staton ncludng the grd dynamcs and MPC controller V o, ac ac dq s V oq V od s g δ V d s V q k p + k s atan2 ε Fg. 2: Oerew of mplemented phase locked loop A. Phase Locked Loop The phase locked loop (PLL) s used to track the actual grd frequency [23]. An nerse tangent functon s used on frst order low-pass fltered output of the q- and d-axs oltage to estmate the actual phase angle error as shown n Fg. 2. Ths phase angle error s the nput to the PI controller for trackng the frequency of the measured oltage. The states of the low-pass flter of the PLL are gen y (5) where P LL s the cut-off frequency of the low-pass flter. d P LL,d = P LL P LL,d + P LL od (5a) d P LL,q = P LL P LL,q + P LL oq (5) The speed deaton, δ P LL of the PLL wth respect to the grd frequency can e defned y (6) where K pp LL and K P LL are the proportonal and ntegral gan of the PI controller; ε P LL s the arale ntroduced to represent the ntegrator state and can e defned y (7). δ P LL = K pp LL arctan d ε P LL ( P LL,q = arctan P LL,d ( P LL,q ) + K P LL ε P LL (6) P LL,d The correspondng phase angle, δθ P LL dfference etween the grd oltage and orentaton of the PLL s represented y (8) and grd oltage represented y ts ampltude ˆV can e transformed nto PLL reference frame as gen y (9). Frequency of the PLan e gen y (). ( ) dδθ P LL P LL,q = δ P LL K pp LL arctan P LL,d + K P LL ε P LL (8) B. State-space realzaton ) (7) g = ˆ g e jδθ P LL (9) P LL = δ P LL + g () The modelng, analyss and control of the system wll e presented n a synchronous reference frame (SRF). The transformaton of the three phase quantty from statonary reference frame to SRF s ased on the ampltude-narant Park transformaton, wth the d-axs algned wth the oltage ector o and q-axs leadng the d-axs y 9. An deal lossless aerage model s assumed for the conerter. Therefore power alance constrant etween dc and ac sde can e gen y dc dc = Ld cd + Lq cq. () In SRF the aerage model of the nerter, oltage oer the flter capactance and current of the grd nductance can e

3 presented y (2)-(3), (4) and (5), respectely. d Ld cd od R c Ld + g Lq (2a) V o, dq AD s AD dq kad V o, dq, AD d Lq cq oq g Ld R c Lq (2) Fg. 3: Implemented acte ac dampng d od d oq d dc dc,lne ( Ld cd + Lq cq ) dc (3) d od d oq Ld od + g oq Lq oq g od od ˆ g cos(δθ P LL ) R g (4a) (4) od + g oq oq + ˆ g sn(δθ P LL ) g od R g (5a) oq (5) The aerage model of conerter presented y (2) and (5) s nonlnear and the nonlnearty preents drect applcaton of classcal lnear analyss technques. Therefore, the model s lnearzed y takng frst-order partal derates n respect to all arales n steady-state operatng pont. The states, nputs and output ector are gen y (6) and resultng state-space matrces are presented y (7). A= R f x = [ ld lq dc od oq od oq u = [ cd cq g dc y = [ ld lq (6) R f Dq C 3,3 R g R g D d Element of A matrx, C 3,3 s as follows. C 3,3 (D d I ld + D q I lq ) V dc D d V dc Dq V dc B = cos(δθ P LL ) lg sn(δθ P LL ) lg ( ) C = ( ) D = (7) The grd oltage s assumed stale and a constant alue and the dc current depends on output current Ld. Neglectng these two arales, the nput ector and B matrx can e wrtten y u = [ cd B = cq Dq D d V dc V dc. (8) The mappng etween nput and output arales can e soled n the Laplace doman y utlzng (9) where matrx G(s) contans small sgnal transfer functons of the VSC conerter at open loop and can e wrtten y (2). Y (s) = [C(sI A) B + D]U(s) = G(s)U(s) (9) C. Acte AC dampng ld (s) =G d (s)v cd + G d2 (s)v cq lq (s) =G q (s)v cd + G q2 (s)v cq (2a) (2) The acte ac dampng s desgned to suppress the LC oscllatons n the flter [24]. There are seeral concepts deeloped for dampng such oscllatons; n ths case the acte dampng, s ased on njectng a oltage component of counter phase wth detected oscllaton n order to produce a cancellaton effect. The oscllaton s frst solated y hgh pass flterng and s then multpled y a gan K AD. The hgh pass flter

4 Vg R g I O L T R T PCC VO I L Rc Vc VSC I dc V dc Rdc Ldc I dc, lne I dc I C V dc dc VSC2 I L V c Rc Lc V O I O R T L T PCC R g Lg Vg Fg. 4: Inestgated pont-to-pont VSC-HVDc system TABLE I: Data used for the pont-to-pont HVDC system Ld (pu) WT=.6.2 WT=.4 WT=.9 Ref current Fg. 5: Performance of the controller for dfferent weght tunng. functon s mplemented y sutractng from measure oltage sgnals a low pass fltered erson of same oltages as shown n Fg. 3. The dampng oltage reference s gen y (2) where ϕ dq s the low pass fltered oltage sgnal of measure oltages sgnal. The correspondng nternal states ϕ d and ϕ q of low pass flter can e gen y (22), where AD s the cut-off frequency of the appled low-pass flter. o,dq,ad = K AD ( ϕ dq + o,dq ) (2) dϕ d = AD ϕ d + AD od (22a) dϕ q = AD ϕ q + AD oq (22) The oltage reference to the conerter can e wrtten cdq,ref (k + ) = cdq (k + ) o,dq,ad (k) (23) III. PROPOSED MODEL PREDICTIVE CONTROL The use of MPC to control the power of a VSC-ased HVDC system s proposed n ths study. The controller s desgned ased on the system presented n state-space form n preous secton. The system s n contnuous tme. It s necessary to conerter t nto dscrete tme snce MPC controller performs all the estmaton and optmzaton calculaton Parameter Value Parameter Value S 2 MVA.5 pu V ac 23 kv R c.5 pu 2π5 rad/s.94 pu Transformer turn rato 23/ V dc 2 kv L T.5 pu dc lne length 75 km R T.27 pu L dc /km 2.65 mh.739 pu R dc /km. Ω R g.52 pu pu n dscrete tme. In dscrete tme t can e wrtten y x(k + ) = A x(k) + B u(k) y(k + ) = C x(k) + D u(k). (24) MPC soles an optmzaton prolem at each control nteral. The solutons determne the nput arales to e used n the next control nteral. A standard cost functon s defned y J(z k ) = p [{w[ Ld,ref (k + k) Ld (k + k)]} 2 = +{w[ Lq,ref (k + k) Lq (k + k)]} 2 ] + ρ ε ε 2 k (25) where k s the current control nteral; p s predcton horzon (numer of nterals); w s the tunng weght; Ld,ref (k + k) and Lq,ref (k+ k) are the predcted alue of reference current at -th predcton horzon step; Ld (k + k) and Lq (k + k) are the predcted alue of output current at -th predcton horzon step; ε k s the slack arale; ρ εk s the constrant olaton penalty weghts and z k s the decson taken y Quadrc Program (QP) and can e gen y z k = [u(k k) T u(k + k) T... u(k + p k) T ε k ] (26) and the nput and output constrants are ound as follows: d,mn () ε k Vmn() d Ld (k + k) d,max () + ε k Vmn() d q,mn () ε k V q mn () Lq(k + k) q,max () + ε k V q mn () d,mn () ε k Vmn() d cd (k + k) d,max () + ε k Vmn() d q,mn () ε k V q mn () cq(k + k) q,max () + ε k V q mn () where =:p and V d mn, Vq mn, Vd mn and Vq mn (27) are the controller constants analogous to the cost functons weghts whch are used for the constrants softenng.

5 Ld, Lq (pu).5 Vac (pu) Fg. 6: d-axs current (upper cure) and q-axs current (lower cure). Intal current reference s.7 pu. At 5 s d-axs current reference steps down for.2 pu and at 25 s steps up for.25 pu. The q-axs current reference keeps pu. (Green sold lne for swtchng model and red dash lne for state-space lnearzed model) IV. RESULT AND ANALYSIS The nestgated pont-to-pont VSC-ased HVDC system s shown n fg. 4. VSC s utlzed to control the acte and reacte power whle VSC2 s used to control the dc lnk oltage and reacte power. The electrcal parameters used for the system are gen n tale I. The conerters are connected to the ac grd through a transformer of 23 kv/ kv as same ratng as conerter. Model predcte control s used n VSC to control the acte and reacte power y controllng the d-axs and q-axs current components of conerter nductor, whle for the VSC2, wdely used decouple PI current control s used for nner current controller and PI controllers are used for outer loop dc oltage control and reacte power control. The MPC controller for VSC s optmzed for the plant model of VSC conerter staton presented n state-space form ncludng the dynamcs of the ac grd. The performance of the controller depends on approprate selecton of control parameters. The control parameters of the MPC nclude the sample tme, T s, Predcton horzon, p, Control horzon, m, Scale factor and tunng weghts. The performance of the modeled controller for dfferent weght of tunng s shown n fg. 5. Ths result s otaned from tme doman response of state-space model. At a lower tunng weghts of.4 t takes longer tme to follow the reference current as shown n fg. 5 y cyan dash-dot cure. When t ncrease the tunng weght to.6, the performance of the system mproes much etter. If t ncreases to much hgher alue, for example here t s ncrease to.9, the tme response ecomes etter, ut t reduces the roustness of the system. The modeled MPC s used to control acte and reacte power y means of controllng the d-axs and q-axs current of the conerter. The performance of the controller s aldated y tme doman response of state-space model and also from Vac (pu) Tme (s).5.5 (a) Tme (s) () Fg. 7: Three phase oltage Instantaneous oltage at nterfacng pont. (a) wthout ac acte dampng, () wth ac acte dampng Vdc (pu) Fg. 8: dc oltage at VSC2 conerter staton from swtchng model full scale nonlnear swtchng model of sngle VSC-HVDC conerter n a pont-to-pont connecton HVDC transmsson

6 Pmeas (pu) Fg. 9: acte power of VSC2 conerter from swtchng model od, oq (pu) Fg. : d-axs and q-axs oltage components at flter capactor connectng pont system. The d-axs and q-axs current from state-space model and swtchng model s shown n fg. 6. The ntal d-axs current reference s set to.7 pu and the q-axs current reference s set to pu. At 5 s, the d-axs current reference steps down for.2 pu and steps up for.25 pu at 25 s. Both state-space model and swtchng model can follow the reference. The hgh frequency components can e remoed y usng approprate dampng constant and cut-off frequency of acte dampng. Fg. 7 shows the mproement of usng ac acte dampng term y remong rpple components. The dc oltage, measured acte power and d-axs and q-axs oltage components of flter capactor of VSC are shown n fg. 8, 9 and, respectely. The dc oltage s always stale for step changng of current and s n nomnal operatng range from.95 to.5 pu. The acte power also follows the reference power. The system s workng properly and t shows the great potental of usng MPC controller to control VSC n a HVDC system. V. CONCLUSION In ths paper a MPC controller s proposed for controllng the VSC n a HVDC transmsson system. A pont-to-pont connecton HVDC system s deeloped to demonstrate the applcaton of the proposed MPC controller. The MPC controller s appled to control the d-axs and q-axs current of a VSC n HVDC system and the performance s found to e satsfactory. The performance of the controller depends selecton of optmum control parameters. The sample tme alances etween computatonal effort and controller performance. Small alue of the samplng tme ncreases the computatonal effort when the hgh alue leads to nformaton loss. The alue of the samplng tme should e selected such a way that t can capture the ehaor of the system operatng n the leel wth the fastest dynamcs. A lager alue of predcton horzon, p mproes the stalty of the closed loop system. If the desred response tme of the system s T, then p s selected such that T s equal to p tmes T s (T=pT s ). Smaller alue of control horzon, m allows to compute fewer arale n the QP at each control nteral whch ncrease computaton speed and promotes an nternally stale controller. Another mportant parameter s weght tunng, w defned n the cost functon n (25). The alue of w can e ared from -. Lower alue of w makes the system roust howeer the system shows slower response tme. It s the trade of etween roustness and system response tme. REFERENCES [] Yfan Zhu, The VSC-HVDC electrc power qualty analyss and research, Integraton of Renewales nto the Dstruton Grd, CIRED 22 Workshop, ol., no., pp.,4, 29-3 May 22 [2] Chuny Guo; Chengyong Zhao, A new technology for HVDC startup and operaton usng VSC-HVDC system, Power & Energy Socety General Meetng, 29. PES 9. IEEE, ol., no., pp.,5, 26-3 July 29 [3] Nguyen-Mau, C.; Rudon, K.; Styczynsk, Z.A., HVDC applcaton for enhancng power system stalty, Scence and Technology, 2 EPU- CRIS Internatonal Conference on, ol., no., pp.,6, 6-6 No. 2 [4] Beerten, J.; Cole, S.; Belmans, R., Modelng of Mult-Termnal VSC HVDC Systems Wth Dstruted DC Voltage Control, n Power Systems, IEEE Transactons on, ol.29, no., pp.34,42, Jan. 24 [5] O.A. Gddan, A. Y. M. Aas, G. P. Adam, O. Anaya-Lara, K.L. Lo, Mult-task control for VSCHVDC power and frequency control, n Internatonal Journal of Electrcal Power and Energy Systems, ol. 53, Decemer 23, Pages [6] C. Karawta and U. D. Annakkage, Mult-Infeed HVDC Interacton Studes Usng Small-Sgnal Stalty Assessment, n IEEE Transactons on Power Delery, ol. 24, no. 2, Aprl 29, pp. 998, 29 [7] S. Cole, J. Beerten, R. Belmans, Generalzed Dynamc VSC MTDC Model for Power System Stalty Studes, n IEEE Transactons on Power Systems, ol.25, no.3, August 2, pp [8] M. K. Zadeh, M. Amn, J. A. Suul, M. Molnas, O. B. Fosso, Small- Sgnal Stalty Study of the Cgr DC Grd Test System wth Analyss of Partcpaton Factors and Parameter Senstty of Oscllatory Modes, accepted n PSCC 24, August 8-22, 24, Poland [9] Pnares, G.; Tjernerg, L.B.; Le Anh Tuan; Bretholtz, C.; Edrs, A.- A., On the analyss of the dc dynamcs of mult-termnal VSC-HVDC systems usng small sgnal modelng, PowerTech (POWERTECH), 23 IEEE Grenole, ol., no., pp.,6, 6-2 June 23 [] M. Amn, M. K. Zadeh, J. A. Suul, E. Tedesch, M. Molnas, O. B. Fosso, Stalty analyss of nterconnected AC power systems wth multtermnal DC grds ased on the Cgr DC grd test system, 3rd IET Renewale Power Generaton Conference 24 (RPG 24), Septemer 25-25, 24, Naples, Italy

7 [] Vasquez, J.C.; Guerrero, J.M.; Saaghe, M.; Teodorescu, R., Modelng, analyss, and desgn of statonary reference frame droop controlled parallel three-phase oltage source nerters, Power Electroncs and ECCE Asa (ICPE & ECCE), 2 IEEE 8th Internatonal Conference on, ol., no., pp.272,279, May 3 2-June 3 2 [2] Wang Yan; Zhao Shu-Zhen; Huangfu Cheng; Ruan Jang-jun, Dynamc Model and Control of Voltage Source Conerter Based HVDC, Power and Energy Engneerng Conference, 29. APPEEC 29. Asa-Pacfc, ol., no., pp.,5, 27-3 March 29 [3] C Bajracharya, M Molnas, JA Suul, TM Undeland, Understandng of tunng technques of conerter controllers for VSC-HVDC,Proceedngs of the Nordc Workshop on Power and Industral Electroncs, (NOR- PIE/28), June 9-, 28, Espoo, Fnland [4] S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodrguez, Model predcte controla smple and powerful method to control power conerters, IEEE Trans. Ind. Electron., ol. 56, no. 6, pp , Jun. 29. [5] P. Cortes, M. Kazmerkowsk, R. Kennel, D. Queedo, and J. Rodrguez, Predcte control n power electroncs and dres, IEEE Trans. Ind. Electron., ol. 55, no. 2, pp , Dec. 28. [6] K. Ahmed, A. Massoud, S. Fnney, and B. Wllams, A modfed statonary reference frame-ased predcte current control wth zero steady-state error for LCoupled nerter-ased dstruted generaton systems, IEEE Trans. Ind. Electron., ol. 58, no. 4, pp , Apr. 2. [7] M. A. Perez, P. Cortes, and J. Rodrguez, Predcte control algorthm technque for multleel asymmetrc cascaded H-rdge nerters, IEEE Trans. Ind. Electron., ol. 55, no. 2, pp , Dec. 28. [8] P. Cortes, A. Wlson, S. Kouro, J. Rodrguez, and H. Au-Ru, Model predcte control of multleel cascaded H-rdge nerters, IEEE Trans. Ind. Electron., ol. 57, no. 8, pp , Aug. 2. [9] Fuchs, A.; Imhof, M.; Demray, T.; Morar, M., Stalzaton of Large Power Systems Usng VSCHVDC and Model Predcte Control, Power Delery, IEEE Transactons on, ol.29, no., pp.48,488, Fe. 24 [2] E. F. Camacho and C. Bordons, Model Predcte Control n the process ndustry, Sprnger-Verlag, London, 995 [2] Blasko, V.; Kaura, V., A new mathematcal model and control of a three-phase AC-DC oltage source conerter, Power Electroncs, IEEE Transactons on, ol.2, no., pp.6,23, Jan 997 [22] Kroutkoa, N.; Hernandez-Aramuro, C.A; Green, T.C., State-space model of grd-connected nerters under current control mode, Electrc Power Applcatons, IET, ol., no.3, pp.329,338, May 27 [23] Kaura, V.; Blasko, V., Operaton of a phase locked loop system under dstorted utlty condtons, Industry Applcatons, IEEE Transactons on, ol.33, no., pp.58,63, Jan/Fe 997 [24] Ole Mo, M. Hernes, K. Ljkelsy, Acte dampng of oscllatons n LC-flter for lne connected, current controlled, PWM oltage source conerters, n Proc. Of th European Conference on Power Electroncs and Applcaton, EPE 23, Toulouse, France, 2-4 Septemer.

Comparison of Reference Compensating Current Estimation Techniques for Shunt Active Filter

Comparison of Reference Compensating Current Estimation Techniques for Shunt Active Filter Comparson of Reference Compensatng Current Estmaton Technques for Shunt Acte Flter R.SHANMUGHA SUNDARAM K.J.POORNASEVAN N.DEVARAJAN Department of Electrcal & Electroncs Engneerng Goernment College of Technology