A Multi-Loop Control Technique for the Stable Operation of Modular Multilevel Converters in HVDC Transmission Systems

Transcription

1 Mult-Loop Control Technque for the Stable Operaton of Modular Multlevel Converters n HVDC Transmsson Systems Mad Mehrasa a, Edrs Pouresmael b,c, Sasan Zabh d, Ionel Vechu c, and João P. S. Catalão a,b,e, a C-MST, Unversty of era Interor, R. Fonte do Lamero, 61-1 Covlhã, Portugal b INESC-ID, Insttuto Superor Técnco, Unversty of Lsbon, v. Rovsco Pas, 1, Lsbon, Portugal c ESTI Insttute of Technology, ESTI, F-641, dart, France d ustrala Pty Lmted, errmah, Northern Terrtory, ustrala e INESC TEC and Faculty of Engneerng of the Unversty of Porto, R. Dr. Roberto Fras, Porto, Portugal bstract: mult-loop control strategy based on a sx-order dynamc model of the modular multlevel converter (MMC) s presented n ths paper for the hgh-voltage drect current (HVDC) applcatons. For the ntal analyss of the operaton of MMC, a capablty curve based on actve and reactve power of the MMC s acheved through a part of the sx order dynamc equatons. ccordng to the MMC s control ams, the frst loop known as the outer loop s desgned based on passvty control theory to force the MMC state varables to follow ther reference values. s the second loop wth the use of sldng mode control, the central loop should provde approprate performance for the MMC under varatons of the MMC s parameters. nother man part of the proposed controller s defned for the thrd nner loop to accomplsh the accurate generaton of reference values. lso, for a deeper analyss of the MMC s dc lnk voltage stablty, two phase dagrams of the dc-lnk voltage are assessed. Matlab/Smulnk envronment s used to thoroughly valdate the ablty of the proposed control technque for control of the MMC n HVDC applcaton under both load and MMC s parameters changes. Index Terms Modular multlevel converter (MMC); crculatng currents; passvty control theory; sldng mode control; hgh-voltage drect current (HVDC). I. Nomenclature Indces OLC Outer Loop Controller K a, b, c SMs Sub-Modules J 1, LPF Low Pass Flter bbrevatons DLM Drect Lyapunov Method Correspondng author at Faculty of Engneerng of the Unversty of Porto. E-mal address: catalao@ub.pt (J.P.S. Catalão).

2 KVL Krchhoff's Voltage Law HVDC Hgh-Voltage, Drect Current KCL Krchhoff s Current Law MMCs Modular Multlevel Converters CLC Central Loop Controller PI Proportonal-Integral ILC Inner Loop Controller SLPWM Shft Level Pulse Wdth Modulaton v Rated capactor voltage Varables c S Swtches of the MMCs ul k Q v Lower and upper arms voltages H ( s ) dq ul k Reference values of Reactve power of MMCs Transfer functon v k Output voltages of the MMCs Z Error vector dq vdc dc-lnk voltage E Total saved energy dq u Frst equvalent modulaton functon of k1 the respectve SM stacks u Second equvalent modulaton functon of k the respectve SM stacks v SMs voltages smul k S Tme-varable sldng surface dq Parameters 1/ dq Proportonal gan v ac-sde voltages of the MMCs tdq L Inductance of the MMCs v Reference value of output voltages of the dq MMCs R Resstance of the MMCs v Reference value of dc-lnk voltage L p dc rm s nductance Currents of MMCs k R rm s resstance Crculatng currents of the MMCs C eq Equvalent dc-lnk capactor crk Lower and upper arms currents R dc Equvalent dc-lnk resstance ulk MMCs dc-lnk currents R Inecton resstances dq dc smul k Currents of SMs fac ac-sde frequency dq Reference values of MMCs currents fs Swtchng frequency

3 crdq Reference values of crculatng currents n Numbers of SMs n each arm ldq Load currents C Capactor of SM I avdq verage currents of the MMCs C f Capactor of ac flter Maxmum value of MMCs currents dqmax, Cut-off frequency dqdq max Total harmonc current components of l d q h h 1 loads Integral gan dq / p dq P Inected actve power of MMCs k Postve constant of CLC dq Q Inected reactve power of MMCs Postve constant of CLC crdq P II. Reference values of actve power of MMCs Introducton Postve constant of CLC dq The modular multlevel converter (MMC) topology has been a subect of ncreasng mportance because of ts specal characterstcs such as easy replacement of fault sub-modules (SMs), centralzng the dstrbuted energes, modular structure, very low harmonc components and power losses, and also decreased ratng values [1]-[5]. The MMCs have been wdely utlzed n varous voltage/power levels of growng applcatons such as solar photovoltac [6], large wnd turbnes [7-8], ac motor drves [9-1], hgh-voltage drect current (HVDC) transmsson systems [11-1], dc-dc transformers [13], battery electrc vehcles [14], dstrbuted energy resources (DERs) [15-16], and flexble ac transmsson systems (FCTS) [17]. Many researchers have focused on the control and modellng ssues of the MMCs n varous applcatons n recent years. Reference [18] deals wth the fault condton of the MMC and tres to provde normal performance for the MMCs by the help of an energy-balancng control. bnary nteger programmng based model predctve control for the MMCs s proposed n [19] to optmze the mult-obectve problem wth mnmum computng effort related to the control method whch s the man contrbuton of the paper. closed loop-needless PID controller along wth ncreasng the arm nductance are consdered to evaluate the effects of output voltage and current total harmonc dstorton (THD) response n a modular multlevel converter []. Reference [1] presents a control strategy based on calculatng the dfferental current references to provde desred operaton for the MMCs n HVDC applcatons. Varous dynamc models of the MMCs and ther lmtatons n presentng robust control methods for these converters are nvestgated n []. In ths paper, a complete dervaton of the proposed swtchng state functons wthout losng any crcutal characterstcs of the converter s accomplshed and a swtchng-cycle control approach proposed based on unused swtchng states of the MMCs. modulaton technque s proposed n [3] based 3

4 on a fxed pulse pattern fed nto the SMs to mantan the stablty of the stored energy n each SM, wthout measurng capactor voltages or any other sort of feedback control. It also removes certan output voltage harmoncs at any arbtrary modulaton ndex and any output voltage phase angle. current control desgn for ndependent adustment of several current components and a systematc dentfcaton of current and voltage components for balancng the energy n the arms of an MMC s presented n [4]. In [5], a control strategy based on addng a common zero-sequence voltage to the reference voltages s proposed for balancng the arm currents of the MMCs under unbalanced load condtons. To reach t, a relatonshp between the dc-lnk actve power and ac-lnk average actve power s acheved and then, the dc component of the arm current s calculated through the ac-lnk average actve power n the correspondng phase [5]. In the medum voltage systems, the energy storage can be embedded n MMC that causes several SMs to operate at sgnfcantly lower voltages [6]. In the structure presented n [7], the low-frequency components of the SM s output currents are removed by utlzng the nterfaced batteres through the nonsolated dc/dc converters. Control algorthms proposed n ths paper are developed to balance the state of charge of batteres. compact and clear representaton of dfferental equatons s obtaned for the MMC by ntroducng two nonlnear coordnate transformatons n [8]. In the proposed model, two canddate outputs leaded to the nternal dynamcs of second or thrd order and a quas-statc feedback generates a lnear nput-output behavour. Other dfferent aspects of MMC applcaton n HVDC system such as DC fault and DC sold-state transformers operatng condtons are assessed n the references of [31]-[34]. In many exstng methods, smultaneously havng robustness aganst MMC parameters changes and also havng very good dynamc trackng responses aganst the MMC s load changes have not been consdered n ther desgned control technques. ut, n ths paper, a mult-loop control strategy s amed at provdng a stable operaton of the MMCs n HVDC applcaton under both MMC s arm nductance and resstance parameters varatons and also loads changes as well. Ths the frst feature of the proposed controller that can ncrease the stablty margns of the MMC performance wth exstence of more varatons. ccordng to the acheved sx order dynamc equatons of the MMCs, frstly the outer loop formed by passvty based control technque s ntroduced to enable the convergence ablty of the MMC s state varables for ts reference values n dynamc changes. Then, sldng mode controller s used to prepare the MMCs for stable operaton aganst the MMC s parameters varatons as the central loop of the proposed controller. The nner loop s employed to help other loops have accurate reference values for ts used state varables that as another feature of the proposed controller, can generate nstantaneously the needed references values of both MMCs n varous operatng condtons. lso, a capablty curve s obtaned to specfy the allowable area of the MMC s actve and reactve power generaton n HVDC applcaton and also R and L varatons effects on the curve are evaluated that can provde some control consderatons to understand more about the smulaton results of the MMC s performance. Stablty analyss of dc-lnk voltage s done n fnal part of ths paper. Smulaton results executed by Matlab/Smulnk demonstrate the valdty of the proposed control strategy n all operatng condtons. 4

5 III. The Proposed Dfferental Equaton of MMC Fg. 1(a) shows the proposed HVDC system whch s conssted of two back-to-back MMCs. The ac-sde of the MMC1 comprses ac-system-1, a lne wth nductance of L and resstance of R, a three-phase step-down transformer and the nput nductance and resstance of the MMC1. DC power s produced by MMC1 and then MMC uses ths power to act as an nverter n HVDC structure. The resstance of R dc represents total swtchng loss of MMCs whch s paralleled wth dc lnk. The ac-sde of the MMC conssts of the output nductance and resstance, an ac flter to trap domnant swtchng harmoncs, a load and a three-phase step-up transformer. The employed MMCs are shown n Fg. 1(b). half-brdge converter s the same SM n whch three states are appeared for each SM as: (1) swtch Sul s ON ( k1 S ulk off ), n whch the output voltage of the SM s equal tov sm ul k, () swtch S ul s ON ( k S ulk1 off ) and consequently the SM s voltage becomes zero, and (3) as standby state, both upper and lower swtches are not controlled ( S S ul k1 ul off ) and the capactor of SM s k pre-charged. Two frst states wll be consdered n ths paper. Fg. 1(a) & Fg. 1(b). Proposed sx order dynamc model of MMCs It can be realzed from Fg. 1(b) that the capactor voltages of SM play a key role at generatng dc-lnk voltage. Consequently, to regulate dc lnk voltage, v ul should be accurately controlled. The dynamc equaton based on the MMC s currents can be k acheved by the use of the Krchhoff's voltage law (KVL) for Fg. 1(b) as, dk duk vdc v k L Rk Lp Rpuk vuk dt dt (1) dk dlk vdc v k L Rk Lp Rplk vlk dt dt () The MMC currents based dynamc model can be drven by summng up (1) and () as, L p d k R p L R v u dt k k k 1 (3) where, u k1 can be calculated as, u k 1 v uk v lk (4) 5

6 To properly control the MMC currents for reachng desred values of actve and reactve power sharng, dc-lnk voltage and SM voltages, the swtchng functon of (4) s employed. Next mportant goal s decreasng the crculatng currents of the MMCs whch can be wrtten as, crk uk lk dc (5) 3 The power losses of MMCs, the rpple magntude of capactor voltages and the total MMCs cost are ncreased because of exstng crculatng currents. y subtractng (1) from () and usng (5), the crculatng currents based dfferental equatons can be acheved as (6), dcrk dc v dc L p R pcrk R p u k (6) dt 3 where, u k s defned as, u k v uk v lk (7) ccordng to ponts of and n Fg. 1(b), the connecton amd dc lnk voltage dynamc and MMC s arms currents s gven as, dv v C b, c b, c dc dc eq uk1 uk dt Rdc k a k a dv v C (8) b, c b, c dc dc eq lk1 lk dt Rdc k a k a (9) y summng up (8) and (9) and usng (5), dc lnk voltage dynamc can be wrtten n terms of dc lnk and crculatng currents as (1), dv v C (1) b, c dc dc eq crk dc1 dc dt Rdc ka Notng the swtchng states of SMs, the dynamcs of voltage of SMs for the lower and upper arms can be summarzed as, dv C dt S on ul k1 S sm ul k ul off k1 ulk sm ul k (11) ccordng to (11), and consderng an approprate approxmaton for the operaton of the symmetrcal voltages of capactors of SMs n two arms, dynamc of output voltage of SMs can be deduced through the MMCs or crculatng currents. It leads that the proposed controller effectvely be nvolved n an effectve balanced condton for the SMs capactors n dfferent operatng 6

7 condtons. y transformng equatons (3), (6) and (1) nto dq reference frame, the proposed sx order dynamc model of the MMCs n HVDC applcatons can be drven as, L d R L L R L u v dt p d p p d q d 1 d L d R L L R L u v dt p q p p q d q 1 q (1) (13) dcrd Lp Rpcrd Lpcrq ud (14) dt dcrq Lp Rpcrq Lpcrd uq (15) dt dcr 3 vdc Lp Rpcr u Rpdc (16) dt dv v C (17) dc dc eq crd crq cr dc1 dc dt Rdc. Capablty Curve nalyss of MMCs ctve and Reactve Power The MMC s potental n necton of maxmum power s presented n ths secton. ased on Fg. 1(b), the MMCs dc-lnk and the ac sde voltages are related to each other n d-q reference frame accordng to followng equaton, vdcdc vdtd vqtq (18) y consderng Fg. 1(b) and applyng KVL s law to the ac sde of the proposed MMC based HVDC system, the relaton between the output and ac-sde voltages of the MMC n dq reference frame can be acheved as, dd vdt vd L Rd Lq (19) dt d v v L R L dt q qt q q d () y substtutng (19) and () n (18) and also assumng d dq / dt Iav dq, the followng equaton of a crcle s drven as, avd d avq q q LI v LI v LI v LI v 4Rv d R R 4R avd d avq q dc dc (1) The (1) determnes the operaton area of MMC s currents n d-q reference frame. y consderng the MMC s actve and reactve power as P vdd and Q vdq and substtutng n (1), the power curve of MMC n the proposed HVDC system can be obtaned as [9], 7

8 4 avd d d avq d d q LIavdvd vd LIavqvd vqvd Rvdcdcvd Q LI v v LI v v v P R R 4R () The power curve of the proposed MMC based HVDC system n () s drawn n Fg. (a). It can be understood from ths fgure that the maxmum and mnmum amount of the MMC s actve and reactve power are completely dependent on MMC s output parameters and also operaton of the proposed MMC through the proposed controller. ccordng to ths fgure, the center and radus of the power curve are defntely changed by MMC s output parameters, dc lnk specfcatons and also output currents and voltages of MMC n d-q reference frame. Fg. (b) and Fg. (c) show the varous parameters effects of the MMC on the power curve. s can be seen, ncreasng the MMC s resstance (R) causes the power curve to become smaller wth decreasng the radus and center. On the other hand, the scenaro gets nverse when the MMC s nductance (L) ncreases as depcted n Fg. (c). Fg. IV. Control Dscusson In ths secton, the sequent of desgnng process for the proposed mult-loop control technque s dscussed n detal. The general ams of the proposed controller for the MMCs n HVDC applcatons are makng stable operaton under presence of both load and MMC s parameters changes that should be provded through the proposed three control loops.e., outer, central and nner control loops (OLC, CLC, and ILC). OLC s amed at leadng the dynamc errors to attan zero value. The stable operaton of the systems s assured wth the CLC. Fnally, the ILC provdes reference currents for the both MMCs.. The Desgn of Outer Loop Controller (OLC) The outer loop controller s desgned n ths sub-secton to provde the ablty of trackng the reference values of the MMCs state varables for fnal proposed controller wth the exstence of load changes. The Passvty based control technque s used n ths secton. Frstly the proposed sx order dynamc equaton of (1)-(17) s presented as (3), dqdq Tdq X dq Qdq Pdq Odq Ydq (3) dt ll the matrxes used n (3) are presented n ppendx. The proposed error vector of the MMCs s wrtten as, Z Q Q v v dq dq dq d d q q crd crd crq crq cr cr dc dc T (4) To reach an effectve error vector for OLC, the man control ams of regulatng MMC power, dc lnk voltage and ac voltages should be consdered n calculatng ts reference values. Usng (3) and (4), the descrpton of MMC closed-loop error dfferental equaton can be acheved as, dz dq T X Z Q Y P T X Q dt dt dq dq dq dq dq dq dq dq dq dq dq 8 (5)

9 ased on passvty control theory, nectng seres resstances to the MMC closed-loop error dfferental equaton can sgnfcantly enhance the convergence rate of outer loop controller. Eq. (6) s used as seres resstances, R dq Rd Rq Rcrd Rcrq Rcr Rdc 1 (6) The completed closed-loop error dfferental equaton of MMC can be obtaned by addng the term of Rdq Z dq nto the both sdes of (5) as, dz dq T X Z R Z Q Y P T X Q R Z dt dt dq dq dq dq dq dq dq dq dq dq dq dq dq dq dq (7) The desred operaton of outer loop controller can be acheved by Z. Thus, dzdq Tdq X dq Zdq Rdq Zdq (8) dt y applyng (8) nto (7), the proposed state varable error-based equaton of outer loop controller can be obtaned as, dq dq Q Y P T X Q R Z dt dq dq dq dq dq dq dq dq dq (9) Equaton (9) s used to reach the usable modulaton functons of MMCs n outer loop controller as (3). dq P Q Y T X Q R Z dt dq dq dq dq dq dq dq dq dq (3) The Drect Lyapunov control theory s employed to prove that the proposed MMC s closed-loop error dfferental equaton of OLC s stable. Thus, the Lyapunov functon can be defned as, 1 L 1 L 1 1 E Z L z L z L z L z 1 1 L p z cr Ceq z dc p p dq dq d q p crd p crq (31) The error varables of z are the same defned n (4). To prove the globally asymptotc stablty of (31) aganst the undesrable dsturbances, the dervatve of (31) n the state varables traectores should defntvely be negatve. Therefore, 9

10 de L dz L dz dz dz Z L z L z L z L z dt dt dt dt dt dz dz dz L z C z T Z X Z R Z Z dt dt dt dq p d p q crd crq dq d q p crd p crq cr dc dq p cr eq dc dq dq dq dq dq dq dq (3) The error varables based equaton of (8) can be used to demonstrate that the terms generated by necton resstances n (3) are more domnant than other terms. Consequently, (3) can be summarzed as, de dq dt Zdq Rdq Zdq Zdq Rd zd Rq zq Rcrd zcrd Rcrq zcrq 1 cr cr dc dc R z R z (33) The global asymptotcal stablty of the proposed outer loop controller can be guaranteed by (33). The proposed outer loop controllers of both MMCs used n HVDC system can be llustrated n Fg. 3. To regulate the MMCs currents for accurate actve and reactve power sharng, Fg. 3(a) s employed n OLC. On the other hand, to mnmze the MMC crculatng currents, Fg. 3(b) can be used n the global structure of the proposed outer loop controller. Fg. 3 (a) & Fg. 3(b). Desgn of the Central Loop Controller (CLC) In order to desgn a central loop controller wth robust features, sldng mode controller s used n ths sub-secton to make a stable controller aganst MMC parameters changes. tme-varyng sldng surface s consdered as (34), g n 1 d S t, Z k Z dt dq dq dq dq (34) The arbtrary constant values of kdq help CLC have a faster reacton aganst any parameter change. y the help of (34) and also selectng the relatve degree 1 for m and crm, MMCs and crculatng currents can have the reference sldng surfaces of (35) and (36), respectvely as, S 1 t,z z (35) dq dq dq dq dq,z S t z (36) dq crdq cr dq cr dq cr dq The dervatve of the reference sldng surfaces should be consdered to provde the desred moton for MMCs and crculatng currents on the sldng surfaces. Consequently, (37) and (38) can be acheved as, dz d d dq dq dq sgn dq zdq (37) dt dt dt 1

11 dz d d cr dq cr dq crdq sgn cr dq zcr dq (38) dt dt dt Usng the sgn functon and also choosng properly dq and crdq, can lead to mprovng the operaton of central loop controller aganst MMCs parameters. The global structure of the proposed central loop controller for both MMCs and crculatng currents s shown n Fg. 4. Fg. 4(a) & Fg. 4(b) The Lyapunov functon of (39) s ntroduced to evaluate the stablty of the central loop controller performance by consderng the sldng law of (35)-(38) as, J ( Q) zd zq zcrd zcrq zcr (39) The equaton of (4) s acheved by dfferentatng (39) n the traectores of MMCs and crculatng currents as, dj ( Q) dz dz dz dz dz sgn d q crd crq cr zd zq zcrd zcrq zcr zd d sgn zd zq q zq dt dt dt dt dt dt z sgn z z sgn z z sgn z crd crd crd crq crq crq cr cr cr Snce x sgn x z z becomes postve or zero value n each condton, the equaton of (4) s defntely negatve or zero. Thus, accordng to drect Lyapunov method, the proposed sldng mode based loop controller has stable operaton n all ts operatng condtons. C. The Desgn of Inner Loop Controller (ILC) s dscussed, the MMC acts as an nverter and also s responsble to supply nonlnear loads connected to the ac sde of the MMC. The d and q components of nonlnear load currents can be expressed as, (4) I l dq 1dq l dq h h 1 (41) The term of I1dq s the fundamental component of load currents n d and q reference frame that s dependent on the MMC s CC. To specfy the maxmum values of harmonc components of load currents n d-q reference frame are stated as (41), I 1dq n whch MMC s able to supply, the proposed CC can be used. If the total dq 1 (4) l dq h l dq h1 s dq 11

12 LPF-based transfer functon s used n (4) to obtan the harmonc components of load currents n the MMC sde [3]. To perform a precse actve and reactve power sharng of the MMC, extractng properly the harmonc components s very mportant and thus an approprate process of desgnng nner loop controller must be done as shown n Fg. 5(a). Ths fgure s contaned PI controllers as well as LPF n whch ther gans and cut-off frequency should be properly consdered. The process of achevng the MMC1 reference values s llustrated n Fg. 5(b). s shown n Fg. 5(b), to complete the MMC1 reference values, the total reactve power of MMC1 loadsql s used. Fg. 5(a) & Fg. 5(b) V. Convergence Evaluaton and Stablty nalyss In ths secton, the ablty of MMC n load compensaton s nvestgated based on a transfer functon establshed from the Fg. 5(a). Then, the dc-lnk voltage stablty of the proposed model s assessed based on the dynamc equatons obtaned from Fg. 1(b).. The load compensaton capablty analyss of MMC In order to evaluate the capablty of MMC for trackng the reference current components n d-q frame, the rato of dq and dq are defned as the obectve functons. Followng equatons descrbe the relatons between the load current and the maxmum value of currents of the MMC at the fundamental frequency,, dq max ldq ldq dqmax dq s dqmax y combnaton of (43) and the equaton obtaned from Fg. 5(a), followng transfer functon can be acheved, H 3 dqs dq dq dqmax s dqdq dqmax s 1 dq max dq dqmax pdq 1 1dq dqmax pdq dqmax pdq dq dq max s s s 1 pdq dq dqmax dq dq ( s) 3 dq (43) (44) Equaton (44) can be used to specfy approprate values for the utlzed LPF, PI controller gans, and. For a normal operaton, the values of and are almost n the range of and 1, and also the LPF has the cut-off frequency of dq dq max fc fc fs /, whch promses the extracton of the dc part and also low harmonc components from the nonlnear load currents. Consequently, by analysng the transfer functon of (44), the proportonal and ntegral gans of the PI controller (.e.,1/ dq and / ) can be calculated. pdq dq 1

13 . Dynamc model analyss of the dc-lnk voltage Dynamc model analyss of the dc-lnk voltage s nvestgated to valdate the approprate performance of the proposed HVDC model shown n Fg. 1(b). y applyng KCL s nto the pont, followng equaton can be obtaned [9], dv v C (45) dc dc eq dc1 dc dt Rdc The relatonshp between the MMCs dc-lnk and ac sde voltages s presumed to be: dc v dc v dt d v qt q. Then, (45) can be rewrtten as, dv vdt1d 1 vqt1q 1 vdt d vqt q v (46) dc dc Ceq dt R dc v dc y neglectng the nstantaneous power on mpedances of MMCs, the term vdtd vqtq s approxmately equal tov d d ; and consequently, (46) can be smplfed as, v R P P dvdc dc dc 1 Ceq (47) dt R dc v dc The zero dynamc stablty of (47) s studed to verfy the nternal stablty of the proposed model. The zero dynamc value of dc-lnk voltage s obtaned by dv dc / dt. Therefore, v R P P R v v (48) dc dc dc d d d d Equaton (48) confrms that the desred value of dc-lnk voltage does entrely rely on the accurate control of actve power for the MMCs. In addton to the precse values for the d-component of MMCs currents, the output ac voltages of MMCs requred to be fnely regulated n order to acheve a desred dc-lnk voltage. To plot the phase dagram of the dc-lnk voltage, (47) s rearranged as, dv v dc dc Rdc P1 P vdc a dt R C v bv dc dc dc dc dc 1, dc dc a R P P b R C (49) The phase dagrams for dynamc equaton of the dc-lnk voltage are depcted n Fg. 6. s can be seen, the zero dynamc value of HVDC system dc-lnk voltage s completely stable n both states, whch confrms that the proposed HVDC model reaches a desred dc-lnk voltage n dfferent operaton scenaros. Fg. 6(a) & Fg. 6(b) 13

14 VI. Results and Dscussons The ablty of the proposed mult-loop controller s evaluated n ths secton. For ths, a three-level MMC-HVDC system s consdered based on the proposed model n Fg. 1(a) and s modelled n the Matlab/Smulnk envronment n dscrete-tme mode wth sample tme of s. Strngent and comprehensve smulaton results are provded n ths secton, alongsde a sold mathematcal background, to valdate operaton of the proposed control technque n HVDC power system. Smulaton results are presented n order to confrm hgh performance of the proposed control technque n dc-lnk voltage control, capactor voltage balancng, and crculatng current mnmzaton. In addton, performance of the proposed MMC-based HVDC model n Fg. 1(a) ncludng power and control subsystems are evaluated under varous operatng condtons. System parameters are provded n Table I and the schematc dagram and prncple of the proposed control technque n MMC-HVDC system s shown n Fg. 7. TLE I SIMULTION PRMETERS fac 6 Hz C 5mF fs 1 khz Cf 615µF v 4kV Rdc 4kΩ dc vc 14kV P, Q 15MW,75MVR Lk 5mH Transformer 3kV/13kV ( /Y) power ratng Rk 1Ω load I of MMC1 65MW,-MVR Lk 6mH load II of MMC1 7MW,8MVR Rk.3Ω load I of MMC MW,7MVR n 3 load II of MMC 3MW,MVR Grd Resstance.3 Ω Dead Tme e-6 s Grd Inductance 3 mh HVDC lne Inductance 1 mh Fg. 7. The load varatons based assessment of the proposed control technque Dynamcs and steady state responses of the proposed model ncludng assgned parameter values n table I are evaluated n ths subsecton. The scenaros for evaluaton of OLC and ILC performance durng the load changes are defned as followng. t the begnnng, n the tme nterval of <t<1/ sec, a 65MW-MVR load and a MW+7MVR load are connected to the ac 14

15 sdes of MMC1 and MMC respectvely and the MMCs are supplyng these loads n the steady state operatng condtons. Ths process s contnued up to t=1/ sec where a step load ncrement s occurrng for both MMCs so that n the tme nterval of 1/<t<1 sec, a 7MW+8MVR load and a 3MW+MVR load are added to the pror loads of MMC1 and MMC respectvely. The phase a of the upper and lower swtchng functons of MMCs can be seen n Fg. 8. s t can be observed from ths fgure, the upper and lower swtchng functons of MMC experences a lttle more transent response because of more responsbltes of MMCs n supplyng load varatons. These swtchng functons are employed for SLPWM of MMCs n HVDC system. Fg. 9 shows the dc-lnk voltage of the system, whch s subect to the change of power demand. However as evdent, t s regulated wth mnmum fluctuatons (maxmum.5 kv) around ts nomnal value at 4 kv. In addton, durng the entre processng tme, the SM capactor voltages of both MMCs are kept balanced around ther desred values of v dc / 3 (V dc/n for N=3) wth very low rpples consderng ts response to the power varatons. Fg. 8 Fg. 9 Fg. 1 shows three phase balanced ac voltages of MMCs n the proposed HVDC system n the steady state operatng condton. s shown n ths fgure durng load varatons, the ac voltages of MMCs mantan snusodal waveforms wthout any notceable dstortons. The qualty of the proposed control technque to mnmze crculatng currents of converter arms s demonstrated n Fg. 11. s gven n the fgure, the crculatng currents of MMCs are reduced to small values durng both dynamc and steady state operatng condtons. The dynamc response of the proposed control technque to the step varatons n actve and reactve power commands s shown n Fg. 1. s t can be seen, MMC1 s almost set at the desred values wth 65 MW and - MVR. MMC produces the actve power requred for lne resstances and nonlnear load I and also snks the reactve power generated by the output flter to allow the voltage to settle the desred output voltages as depcted n Fg. 1. Inected actve and reactve power from MMC1 follows the load power varatons, whch confrms merts of the proposed OLC and ILC closed-loop controllers n control of nterfaced MMC n the proposed HVDC model. Fg.1 ndcates the capablty of the proposed control technque to pursue a consecutve ncrement through MMC durng the dynamc operatng condton. s t can be seen, MMC s able to generate requred actve power of addtonal loads wth a short transent tme. Reactve power changes of MMC s proportonal to output flter varatons for reachng a balanced three phase voltage. Fg. 1 Fg. 11 Fg. 1 15

16 . The parameter varatons based assessment of the proposed control technque The desgned central loop controller operaton of the MMCs once dealng wth the parameter change s evaluated n ths subsecton. Fg. 13 shows the changes n resstances and nductances of MMCs consdered n ths sub-secton. Fg. 13 Fg. 14 llustrates the upper and lower swtchng functons of the phase a of MMC1 and MMC under parameters changes. For both upper and lower swtchng functons, more transent state can be seen n the mddle of the MMC s parameters changes and more stablty s governed n the other tme nterval of MMC s parameters varatons. The dc-lnk voltage of the proposed HVDC system and SM capactor voltages of MMCs n presence of MMC parameters varatons are depcted n Fg. 15. ased on ths fgure, the reference values can be followed by the proposed controller wth allowable transent response whch verfes the accurate operaton of both desgned CLC and ILC. Fg. 14 Fg. 15 In ths condton, three phase balanced ac voltages can be properly generated by MMCs as shown n Fg. 16. The MMCs crculatng currents are shown n Fg. 17. ccordng to ths fgure, the proposed controller s able to mnmze MMCs crculatng currents wthn acceptable values along wth slght transent responses n the tme of dynamc change. In presence of parameters varatons, the loads of 14MW+45MVR and 35MW+5MVR are suppled through MMC1 and MMC, respectvely as depcted n Fg. 18. s t can be observed from Fg. 18, the actve and reactve power sharng of both MMCs can be accomplshed. However, some slght changes happen for both actve and reactve power of MMCs because of reactve and resstance varatons that are located n acceptable range accordng to Fg. 18. Fg. 16 Fg. 17 Fg

17 VII. Concluson mult-loop control strategy for the stable operaton of MMCs n HVDC system was proposed n ths paper under both load and MMCs parameters varatons. Frstly, a sx-order dynamc equaton was acheved for both MMCs and subsequently a curve based on actve and reactve power of MMC was ntroduced to analyse n depth the MMCs capablty of generatng both powers. ased on ths dynamc model, as the frst advantage, a capablty curve based on MMC actve and reactve power was proposed and the R and L varatons effects on the curve were assessed that could provde some control consderatons to understand more about the smulaton results of the MMC s performance. To desgn the frst loop of the proposed controller, the passvty based control technque was employed to shape OLC for ncreasng the MMCs convergence ablty n dynamc changes. In the next step, to add the robustness feature aganst MMCs parameters changes, the sldng mode controller was consdered to shape the central loop controller. s the second mportant advantage of the proposed controller, the proposed controller was able to smultaneously beng robustness aganst MMC s arm nductance and resstance varatons and also havng very good dynamc trackng responses aganst the MMC s load changes. s the thrd feature of the proposed controller, accurate reference values for MMCs state varables were generated through the nner loop controller usng approprate LPF and regulated PI controllers that could generate nstantaneously the requested references values of both MMCs n all consdered operatng condtons. To further analyse the MMC based HVDC system, the dc-lnk voltage stablty analyss was also carred out. Fnally, to confrm the valdty of the proposed control technque, Matlab/Smulnk was used to acheve strngent smulaton results of MMCs based HVDC system under both load and MMCs parameters changes. cknowledgment Ths work was supported by INSUL'GRID proect, France, by FEDER funds through COMPETE and by Portuguese funds through FCT, under Proects SICT-PC/4/15 - POCI FEDER-16434, POCI FEDER- 6961, UID/EE/514/13, UID/CEC/51/13, UID/EMS/151/13, and SFRH/PD/1744/14. lso, the research leadng to these results has receved fundng from the EU Seventh Framework Programme FP7/7-13 under grant agreement no

18 ppendx ppendx : Q.5 d R Rp R.5R p q Lp Lp L cr p v C dc eq crd dq, Tdq crq X P dq R Rp L Lp L Lp R Rp Rp L p Lp Rp 3 Rp Rdc u d1 vd u q1 v q u, O, Ydq u Rp dc d dq dq uq dc1 dc References [1] Lesncar, Marquardt R. n nnovatve modular multlevel converter topology sutable for a wde power range. In Proc. IEEE ologna PowerTech Conference, 3. [] Mehrasa M, Pouresmael E, korede M, Zabh S, Catalão J P S. Functon-ased Modulaton Control for Modular Multlevel Converters under Varyng Loadng and Parameters Condtons. IET Generaton, Transmsson & Dstrbuton, 17; do: 1.149/et-gtd [3] Fehr H, Gensor, Muller M. nalyss and traectory trackng control of a modular multlevel converter. IEEE Trans. Power Electron 14; 3 (1): [4] Mehrasa M, Hossen S K, Taher S, Pouresmael E, Catalao J P S. Dynamc performance control of modular multlevel converters n HVDC transmsson systems. IEEE Electrcal Power and Energy Conference (EPEC),

19 [5] Ilves K, ntonopoulos, Norrga S, Nee H-P. Steady-state analyss of nteracton between harmonc components of arm and lne quanttes of modular multlevel converters. IEEE Trans. Power Electron 1; 7(1): [6] lexander, Thathan M. Modellng and analyss of modular multlevel converter for solar photovoltac applcatons to mprove power qualty. IET Renewable Power Generaton 15; 9(1): [7] Debnath S, Saeedfard M. New Hybrd Modular Multlevel Converter for Grd Connecton of Large Wnd Turbnes. IEEE Trans. Sustanable Energy 13; 4 (4): [8] Zhang Y, Ravshankar J, Fletcher J, L R, Han M. Revew of modular multlevel converter based mult-termnal HVDC systems for offshore wnd power transmsson. Renewable and Sustanable Energy Revews In Press, Corrected Proof, valable onlne 8 February 16. [9] ntonopoulos, ngqust L, Norrga S, Ilves K, Harnefors L, Nee H-P. Modular Multlevel Converter C Motor Drves wth Constant Torque From Zero to Nomnal Speed. IEEE Trans. Industry pplcatons 13; 5 (3): [1] ntonopoulos, ngqust L, Harnefors L, Nee H-P. Optmal Selecton of the verage Capactor Voltage for Varable- Speed Drves Wth Modular Multlevel Converters. IEEE Trans. Power Electron 14; 3 (1): [11] Nam, Lang J, Dkhuzen F, Demetrades G D. Modular Multlevel Converters for HVDC pplcatons: Revew on Converter Cells and Functonaltes. IEEE Trans. Power Electron 14; 3 (1): [1] M Mehrasa, E Pouresmael, S Zabh, JC Trullo Caballero, JPS Catalão. novel modulaton functon-based control of modular multlevel converters for hgh voltage drect current transmsson systems. Energes 16; 9 (11): [13] Gowad I, dam G, hmed S, Hollday D, Wllams. nalyss and Desgn of a Modular Multlevel Converter wth Trapezodal Modulaton for Medum and Hgh Voltage dc-dc Transformers. IEEE Trans. Power Electron 15; 3 (1): [14] Quraan M, Yeo T, Trcol P. Modular Multlevel Converters for HVDC pplcatons: Revew on Converter Cells and Functonaltes. IEEE Trans. Power Electron 15; do: 1.119/TPEL [15] Soong T, Lehn P W. Internal Power Flow of a Modular Multlevel Converter wth Dstrbuted Energy Resources. IEEE Journal of Emergng and Selected Topcs n Power Electroncs 14; (4): [16] Pouresmael E, Mehrasa M, Shokrdehak M, Rodrgues E M G, Catalão J P S. Control of Modular Multlevel Converters for Integraton of Dstrbuted Generaton Sources nto the Power Grd. In Proc. SEGE 15; 1-6. [17] Du S, Lu J. Study on DC Voltage Control for Chopper-Cell-ased Modular Multlevel Converters n D-STTCOM pplcaton. IEEE Trans. Power Delvery 13; 8 (4): [18] Debnath S, Jangchao Q, ahran, Saeedfard M, arbosa P. Operaton, Control, and pplcatons of the Modular Multlevel Converter: Revew. IEEE Trans. Power Electron 14; 3 (1):

20 [19] Dsfan V R, Fan L, Mao Z, Ma Y. Fast model predctve control algorthms for fast-swtchng modular multlevel converters. Electrc Power Systems Research 15; 19: [] Gebreel, Xu L. Power qualty and total harmonc dstorton response for MMC wth ncreasng arm nductance based on closed loop-needless PID controller. Electrc Power Systems Research 16; 133: [1] Jangchao Q, Saeedfard M. Predctve Control of a Modular Multlevel Converter for a ack-to-ack HVDC System. IEEE Trans. Power Delvery 1; 7 (3): [] ergna G, Garces, erne E, Egrot P, rzande, Vanner J-C, Molnas. Generalzed Power Control pproach n C Frame for Modular Multlevel Converter HVDC Lnks ased on Mathematcal Optmzaton. IEEE Trans. Power Delvery 13; 9 (1): [3] Wang J, urgos R, oroyevch D. Swtchng-Cycle State-Space Modelng and Control of the Modular Multlevel Converter. IEEE Journal of Emergng and Selected Topcs n Power Electroncs 14; (4): [4] Ilves K, ntonopoulos, Norrga S, Nee H-P. New Modulaton Method for the Modular Multlevel Converter llowng Fundamental Swtchng Frequency. IEEE Trans. Power Electron 1; 7 (8): [5] La X, Songa Q, Lua W, La Q, Raob H, Xub S. Zero-sequence voltage necton control scheme of modular multlevel converter supplyng passve networks under unbalanced load condton. Electrc Power Systems Research 15; 11: [6] Moon J W, Gwon J S, Park J W, Kang D W, Km J M. Model Predctve Control Wth a Reduced Number of Consdered States n a Modular Multlevel Converter for HVDC System. IEEE Trans. Power Delvery 14; 3 (): [7] Vasladots M, Rufer. nalyss and Control of Modular Multlevel Converters Wth Integrated attery Energy Storage. IEEE Trans. Power Electron 14; 3 (1): [8] arnklau H, Gensor, Rudolph J. Model-ased Control Scheme for Modular Multlevel Converters. IEEE Trans. Industral Electron 1; 6 (1): [9] Mehrasa M, Pouresmael E, Zabh S, Catalao J P S. Dynamc Model, Control and Stablty nalyss of MMC n HVDC Transmsson Systems. IEEE Trans. Power Delvery 17; 3 (3): [3] Pouresmael E, Mehrasa M, Catalao J P S. Multfuncton Control Strategy for the Stable Operaton of DG Unts n Smart Grds. IEEE Trans. Smart grd 15; 6 (): [31] L R, Fletcher, J E. novel MMC control scheme to ncrease the DC voltage n HVDC transmsson systems. Electrc Power Systems Research 17; 143: [3] L R, Fletcher J E, Xu L, Wllams W. Enhanced Flat-Topped Modulaton for MMC Control n HVDC Transmsson Systems. IEEE Transactons on Power Delvery 17; 3(1):

21 [33] L R, Xu L, Yao L, Wllams W. ctve Control of DC Fault Currents n DC Sold-State Transformers Durng Rde- Through Operaton of Mult-Termnal HVDC Systems. IEEE Transactons on Energy Converson 16; 31(4): [34] L R, Xu L, Hollday D, Page F, Fnney S J, Wllams W. Contnuous Operaton of Radal Multtermnal HVDC Systems Under DC Fault. IEEE Transactons on Power Delvery 16; 31(1):

22 R L R R L s1 L s1 vabcs1 vabc1 v abct v 1 abct v abc v abcs Ls R s P Q l1 l1 s 1 P Q 1 1 ac Flter P Q s P Q l l (a) dc1 dc + ua1 SM1 ub1 SM1 uc1 SM1 uc SM1 ub SM1 ua SM1 ua1 S ua11 S ua1 C v smua1 v ua1 - L R a1 a R L v at1 b1 v R dc v v dc v abc1 bt1 c1 v b at v abc v bt ct1 v c ct + v la1 SMN L p R p L R p p SM1 SMN SM1 L p R p SMN SM1 L p R p SMN L p R p L R p p SM1 SMN SM1 L p R p SMN SM1 L p R p v ua - + v la SMN SMN SMN SMN SMN SMN - la1 lb1 lc1 dc1 dc lc lb la - (b) Fg. 1. Schematc dagram of the MMC-HVDC system. (a) Sngle-lne dagram model and (b) crcut dagram of the back-to-back MMC.

23 LIavdvd vd LIavqvd vqvd 4Rvdcdc vd Q VR LI v v LI v v v 4R, Q R R max avd d d avq d d q r P mn c P max P W Q mn r r r 1 3 c c c Increased change of R Q VR (a) r r r 3 1 c c c Increased change of L Q VR r 1 r 3 r 3 r 1 r 3 P W r 1 P W (b) (c) Fg.. (a) Power curve of MMCs (b) R and L changes effects on MMCs power curve. 3

24 L Lp s R Rp / d R d u d1 abc abc abc / dq abc / dq d q L.5L p L.5L p L Lp s R Rp / q R q v d v q u q1 (a) 1/ Lps Rp crd - + R crd u d cr abc cr abc crd abc / dq L p cr abc abc / dq 1/ Lps Rp abc / dq L p crq - + crq cr R crq 1/ L ps Rp R cr + cr v dc u q R p dc - u (b) Fg. 3. The proposed outer loop controller for (a) MMCs currents (b) MMCs crculatng currents 4

25 dq dq dq 1 s 1 s dq zdq dq zdq dq z dq crdq crdq crdq 1 s 1 s crdq zcrdq crdq zcrdq crdq z crdq Fg. 4. The Proposed Central Loop Controller for (a) MMCs currents (b) MMCs crculatng currents. ldq / s dq dqmax s dq pdq / dqs dq dq / dq abc abc dq (a) v dc v dc d1 s / s pd1 d1 Q q1 / v l1 d1 s / s pq1 q1 q1 (b) Fg. 5. The Proposed Inner Loop Controller for (a) the MMC reference currents (b) the MMC1 reference currents. 5

26 dv dc dt dv dc dt a a t a a b a t a b Fg. 6. The phase dagrams of the dc-lnk voltage (a) a> and (b) a<. r crabc r ulabc r dc dc ulabc crabc r ldq r crdq r v abcs r dq r abc r labc v dc labc abc v abcs dq crdq ldq r v dqs r r uabc 1 u abc uabc 1 u abc v dqs r dq r u dq 1 r u dq u dq 1 u dq dq crdq r crdq Fg. 7. lock dagram of the proposed control technque for the MMC-HVDC system n Fg. 1. 6

27 4 u ua u la Tme[s] (a) 4 u ua u la Tme[s] (b) Fg. 8. The upper and lower swtchng functons of phase a of (a) MMC1 (b) MMC, under load changes. 7

28 v dc (kv) dc-lnk & SM s voltages of MMCs v sma1(1-6) (kv) v sma(1-6) (kv) v sma(1-3) v sma1(1-3) v sma1(4-6) v sma(4-6) Tme[s] Fg. 9. MMCs dc-lnk and Sub-Module s voltages wth load changes. 4 ac-sde voltages of MMCs v abc1 (kv) v abc (kv) Tme[s] Fg. 1. MMCs ac voltages wth load changes. 8

29 Crculatng currents of MMCs crabc1 (k) crabc (k) Tme[s] Fg. 11. MMCs Crculatng currents wth load changes. P,P l &P f (MW) Q,Q l &Q f (MVR) P 1 (MW) ctve and reactve power of MMCs, Load & ac flter 8 6 P l P 4 P f Q 1 (MVR) Q l Q Q f Tme[s] Fg. 1. ctve and reactve power of MMCs, load, and ac flter wth load changes. 9

30 .6.5 MMC 1 1 MMC1.4 MMC1 8 MMC Tme[s] (a) Tme[s] (b) Fg. 13. Parameters changes for (a) the resstance of MMCs (b) the nductance of MMCs. 3

31 4 u ua1 u la Tme[s] (a) 4 u ua u la Tme[s] (b) Fg. 14. The upper and lower swtchng functons of phase a of (a) MMC1 (b) MMC, under MMC parameters changes. 31

32 dc-lnk & SM's voltages of MMCs v dc (kv) v sma1(1-6) (kv) v sma(1-6) (kv) v sma(1-3) v sma1(4-6) v sma1(1-3) v sma(4-6) Tme[s] Fg. 15. MMCs dc-lnk and SM s voltages wth parameters changes. 4 ac-sde voltages of MMCs v abc1 (kv) v abc (kv) Tme[s] Fg. 16. MMCs ac voltages wth the parameters changes. 3

33 Crculatng currents of MMCs crabc1 (k) crabc (k) Tme[s] Fg. 17. MMCs crculatng currents wth parameters changes. 33

34 P,P l &P f (MW) Q,Q l &Q f (MW) P 1 (MW) Q 1 (MVR) ctve and reactve power of MMCs, load & ac flter P P l P f Q Q l Q f Tme[s] Fg. 18. ctve and reactve power of MMCs, load, and ac flter wth parameters changes. 34