Interactions Studies of HVDC-MMC link embedded in an AC Grid

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1 Intertons Studes of HDMM lnk embedded n an A Grd H. Saad, J. Mahseredjan, S. Dennetère, S. Nguefeu Abstrt HD lnk nterconnectons under constructon or planned n France are part of a hghly meshed network. Ths s a relatvely new operatng condton. The mpt of ther operaton and the rsk of abnormal nterton may have an nfluence on the network. The use of voltage source converters (Ss) wth the modular multlevel converter (MM) topology s becomng more attrtve manly due to ther hgher performances and cost. Ths paper analyses the operaton and nterton of MMHD lnks embedded n an grd. Frst a MMHD lnk model sutable for smallsgnal analyss s presented. Ths smallsgnal HD model s then valdated aganst an EMTtype model for systems havng dfferent SR (Shortrcut Rato) values. Modal analyss and parametrc studes are performed n order to study the mpt of the lne connected n parallel wth HD lnk. Keywords: EMTP, HD transmsson, MM, S, Intertons, Modal analyss. S I. INTRODUTION everal HDMM lnk [] projects are currently planned or constructed by RTE (French TSO). One of such projects s the INELFE nterconnecton project, wth a capty of, MW [], between France and Span. HD lnk nterconnectons n France are part of a hghly meshed network. Ths s a relatvely new aspect. Such lnks may have abnormal nterton rsks and also mpt on the performance of the network. In [3] [5], smallsgnal analyss of S statons and modal studes of a grd were presented. In [6], a stablty study between two HD lnks and a comparson between S and L are contrbuted. Studes on a S HD lnk connected n parallel wth an lne are avalable n [7] and [8]. In [9], a study of nterton between a S HD lnk and a STATOM s presented. In ths paper, modal analyss and EMTtype methods are used to study ntertons between HD lnks connected n parallel wth an lne. Theore, unlke prevous artcles, t provdes a complete overvew on the abnormal ntertons that can occur durng small and large dsturbances. There are dfferent smulaton tools for assessng the stablty of electrcal networks. EMT type smulatons are used H. Saad, S. Dennetere and S. Nguefeu are wth Réseau de Transport d'electrcté (RTE), ParsLa Défense, France (emal: han.saad@rtefrance.com). J. Mahseredjan s wth École Polytechnue de Montréal, ampus Unversté de Montréal, 9, ÉdouardMontpett, Montréal (Québec), anada, H3T J4. to evaluate the response of the system subjected to major dsturbances. The models reured for ths type of smulaton must be curate to represent the nonlneartes of the system. EMTtype programs are used to represent curately the electromagnetc transents; they are also well suted to smulate power electroncs devces. For studes related to HD lnks, EMT type models are consdered as erence models for valdatng smplfed models. Although EMT type models can be used to study electromechancal transents, t s generally less effcent n terms of computng tme and t s possble to apply more smplfed methods and models for ths type of phenomenon or for slower dynamc behavor n general. Another approh s based on the small sgnal type analyss [4]. Ths approh s based on the lnearzaton of the model around a set pont of operaton. Theore, the man advantage s the possblty of usng the control theores developed for lnear systems. Small perturbatons around the operatng pont can be appled to study the stablty of the system. Once these lnear state euatons are derved, t becomes possble to analyze the system wth standard tools such as root locus, partcpaton ftor, mode shape, etc. However, snce these lnearzed models are based on smplfcatons, t s mportant to valdate the results wth EMTtype smulatons. For example, t has been shown n [5] that the conclusons drawn from uasstatc analyss are not always n agreement wth the results of smulatons from EMTtype programs. In ths paper, ntertons between the SMM statons embedded n an network are studed. Ths paper begns wth the development of the smallsgnal MMHD lnk model. The model s valdated by comparng t wth an EMT erence model and small sgnal studes are then developed. Fnally, parametrc studes usng EMTPR [6] are presented to evaluate the nfluence of transmsson lnes connected n parallel wth the HD lnk. II. SMALL SIGNAL MODEL Several types of MM models were presented n []. To heve smallsgnal dynamc studes, an average model (AM) of a SMM staton s used. The AM model erred to as the MM Model #4 n [], s shown n Fgure. s the euvalent captor of the MM. L arm and R arm er to the retor and resstance of eh arm. Paper submtted to the Internatonal onference on Power Systems Transents (IPST5) n avtat, roata June 58, 5

2 SR SR v Pa v Pb L arm / v Pc v convc v convabc conv j L arm / v convb conv j e v v / D fault control L arm / R L v conva v convabc I conv a) sde b) sde Fgure : MM Model #4 derved n [] P 4/3 k 6 MA L = 8% Fault MM4L Larm=.5% =mf S km Overhead lne GW 64k 7km D MM4L Larm=.5% =mf S I 4/3 k 6 MA Ltrf = 8% trf e P Fgure : MMHD transmsson system n parallel wth an lne A. MM model The small sgnal model can be found from Fgure and Fgure. The euatons n d frame for the sde are: dd R d vp d vconv d dt L L L () d R vp v conv d dt L L L where L L L and R R R. trf arm trf arm For the sde, the euatons are found from Fgure.b: di e R I () dt L L d e I I conv (3) dt where L L 3, R R 3 and 6 / N. arm Based on (), () and (3), the resultng crcut s presented n Fgure 3. d Pd P R R L convd L conv e.(4) arm I conv L e Fgure 3: smallsgnal model of MM staton R I From Fgure 3, the sde small sgnal model s smlar to a classcal S or 3 level [][] desgn. However, for the sde, dfferences are observed between MM and classcal S, where an euvalent nductance ( L ) and resstance ( R ) are ncluded n the MM model. Based on energy converson: P P I v (4) conv e conv j j ja, b, c n d erence and usng Fgure.b: d v conv d vconv e d I (5) dt e Euaton (5) s not lnear. Usng the frst order Taylor seres, (5) becomes: d e d vconv vconv... dt d e e v v... Pd P d e e v conv d v conv d I e e where the subscrpt denotes ntal values The small sgnal MM model s represented by the lnear euatons (), () and (6). B. Reference change RI to d The d erence frame of the converter staton s synchronzed wth the erence RI (Realnary) network frame by means of a PLL. To take nto count the PLL dynamcs, the varable that represents the phase angle between the two erences must be extrted. It s chosen to algn wth the axs the nary axs I. Theore, the erence change between the network and the staton can be represented as follows [3]. v jv cos jsn v jv (7) d PLL PLL R I By lnearzng euaton (7), we obtan the RI to d erences change: v cos sn d PLL PLL vr... v sn PLL cos PLL v I (8) vr sn PLL v I cos PLL PLL vr cos PLL v I sn PLL The same procedure can be performed to formulate the converson from d to RI erences.. ontrol system MM Model #4 allows neglectng the nternal energy balance []. Theore, the crculatng currents as well as the balancng captor voltages of SMs are neglected n ths study. Only the nner current loops (control) and the outer control are modeled. Furthermore, lnearzaton of the model (6) PLL

3 around a steadystate set pont, allows consderng only the lnear part of the controller. The smplfcatons ntroduced for the smallsgnal model are: Removal of antwndup functons n the loops Lmters and saturatons are suppressed Lnearzaton and smplfcaton of the PLL (Phase Locked Loop) Removal of abcd transformatons The dvson by voltage ( v Pd ) to convert power erence nto current erence s lnearzed. Fgure 4 presents the structure of the control system used for smallsgnal studes. In HD lnks, one staton uses a P control to regulate the tve power of the lnk and the other one control to regulate the voltage. Furthermore, eh staton can ndependently control the retve power (Qcontrol) or voltage ( control). To lnearze the PLL, some loops and components of the nonlnear EMT model must be neglected: the abcd converson, the average freuency estmaton and saturaton blocks. These smplfcatons generate a slght modelng error that wll be evaluated n the next secton. v Pd P P Q Q v P v P PLL Pcontrol control Qcontrol control s v Pd v Pd PLL d d v Pd vp Fgure 4: Small sgnal control system control L LP flter X X LP flter v convd v conv Table and Table present the control gans and flters data respectvely. TABLE : ONTROL ALUES ontrol arable name Tme constant Dampng rato ( ) control, ms.7 Pcontrol control Qcontrol control P Q trl trl trl trl trl ms.7 PLL PLL ms Flter control low pass flter PLL low pass flter TABLE : FILTER ALUES utoff arable name freuency Dampng rato ( ) LP _ Hz.7 LP _ PLL 4.77 Hz.7 The complete smallsgnal staton model s resumed n Fgure 5. v PRI PLL RI d v Pd v conv d ontrol d I PLL, P, Q, d Staton SMM Fgure 5: Staton converter model D. Grd model d RI RI The grd s modeled usng lne mpedances [4] assumng low freuency perturbaton. The general dea s presented as follows: = Z I (9) or usng complex numbers: j R jx I ji () R I R I the smallsgnal mpedance matrx of an network s gven by vr R X... R R X v I X R... X R I () vr R X... R X R v X R... X I R I E. D model One secton has been used to model the. It should be noted that, more sectons wll lead to a better representaton of the. However, n the next secton t wll be shown that ths smplfcaton won t affect the concluson that wll be drven.

4 d v P v Pd I I R L I.3. G G G G Fgure 6: model 5 x 3 From Fgure 6, the small sgnal euatons of the are deduced: d G I I dt d G I I dt dil R I dt L L III. MODEL ERIFIATION () The HD lnk model developed n the prevous secton must be valdated. The nonlnear EMTPR MM Model #4 [] ncludng the complete control system s used as a erence model. Ths model was already valdated aganst a more detaled model (see []). In Fgure, the HD lnk s n parallel wth an overhead lne. The S staton s n Pcontrol and the S staton s n control. To create a small dsturbance n the system, a step change of. pu s appled at t= s on the tve power erence ( P ) of S. For all fgures, a blue sold lne s used for the EMT erence model and a green dotted lne for the smallsgnal model. All smulatons were conducted usng EMTPR software [6]. A. erfcaton wth a strong SR In ths frst test, a hgh SR s consdered for the euvalent Thevenn networks (SR = SR = n Fgure ). The varables of the S staton are compared n Fgure 7. It s observed that there s a dfference n the steady state for the majorty of varables compared between the smallsgnal model and the EMT erence model. The results are slghtly shfted because the steadystate set ponts of the smallsgnal model do not match extly wth the set ponts of the nonlnear EMT model. However, these dfferences have lttle nfluence on the small sgnal studes and the man objectve s to verfy that the oscllatory modes of both models are smlar (whch s the case). PLL x Fgure 7: Smallsgnal model valdaton for SRs = B. erfcaton wth a weak SR For a strong SR, the PLL control (Fgure 4) s undsturbed snce the euvalent source of the network mposes the system freuency. Low SR (SR = SR =.5 n Fgure ) contrbutes to greater dsturbances on the phase angle and the dynamcs of the PLL wll be excted. In Fgure 8 the results at S for the same perturbaton as above, are presented. In ths case more dfferences between the two models on all system varables are notced. As the SR s lower, the varaton on the angle PLL n Fgure 8, s much hgher than n Fgure 7. We can note that the smallsgnal model s able to take nto count the vast majorty of oscllatory modes. However, some hgh freuency oscllatons n v P d (Fgure 8) are not represented n the smallsgnal results. The other dfference between smallsgnal and EMT models les on system dampng rates. The smallsgnal verson underestmates the dampng of oscllatons due manly to the smplfcaton PLL

5 d v P v Pd made n the PLL model. PLL Fgure 8: Smallsgnal model valdaton for SRs =.5 I. MODAL ANALYSIS In ths secton, an egenvalue analyss of the smallsgnal model s presented. The purpose of ths study s to evaluate the mpt of a parallel network on a HD lnk (Fgure ). A. Analytc study Frst, the network mpedance matrx ncludng the parallel lne s found : ZSR Z ZSR ZSR Z SR ZSR Z ZSR Z SR Z ZSR Z (3) ZSR Z SR Z SR Z ZSR ZSR Z ZSR Z SR Z ZSR where Z s the mpedance of the lne n parallel. The dagonal terms of (3), represent the effectve shortcrcut mpedances seen by the S statons. The lne n parallel contrbutes to the reducton of shortcrcut mpedance and conseuently to the ncrease of the SR, snce : Z SR Z Z Z Z Z Z SR SR SR SR (4) Ths mples a better performance of the HD lnk when an lne s n parallel. However, the off dagonals terms are not eual to zero, ndcatng a rsk of nterton between the two converter statons. Note that when Z tends to nfnty, the effect of the parallel lne becomes neglgble and when Z decreases, the rsk of adverse nterton ncreases. B. Partcpaton ftor To study the nfluence of the A lne n parallel on the partcpaton ftor, a small SR (.e, eual to.5) s chosen. HD lnk wth and wthout the lne n parallel are compared. For clarty, modes wth a dampng rate close to are not presented. The partcpaton ftors [4] are presented n Table 3. Table 3 : Impt of Z on partcpaton ftors of HD Mode wthout Z wth Z =.6 pu f=78.6 Hz ; ξ =.867 f=78.6 Hz ; ξ =.867,, I,, I f= 3.6 Hz ; ξ =.7 f= 3.6 Hz ; ξ =.7,, I, I,, I, I f= 6.3 Hz ; ξ =.464 f= 6.3 Hz ; ξ =.464,, I, I,, I, I e e e e f= Hz ; ξ=.634 f= Hz ; ξ =.69 d d d d f= Hz ; ξ =.6 f= 37 Hz ; ξ =.847, d, trl d d d trl trl trl f= 34 Hz ; ξ =.3453 f= 37 Hz ; ξ =.85, d, trl d d d trl trl trl f= 3 Hz ; ξ =.386 f= 3 Hz ; ξ =.44, trl, d LP _, LP _ trl trl d trl trl d d LP _, LP _, PLL trl LP _, LP _ trl f= 4.8 Hz ; ξ =.67 f= 5.5 Hz ; ξ =.57 PLL PLL, e e f= 4 Hz ξ =.354 f= 4 Hz ξ =.59 trl e e PLL, trl e e PLL, f= 4.3 Hz ; ξ =.696 f= 5. Hz ; ξ =.6798 PLL, PLL,,, Q PLL PLL trl trl ) D sde modes The modes, and 3, are related wth the sde

6 egenvalues. These modes are related to the components of the and the MM sde (.e. L and n Fgure 3). Frst, we note that the freuency and dampng ftors do not change cordng to the presence or not of the lne. Based on the partcpaton ftors, we can conclude that mode s related to the L crcut formed by the model. Mode s formed by the nterton between the S nductors ( L ) wth. Fnally, mode 3 s composed of the S components L and. Note that no varables from the sde are partcpatng n the three modes of the sde. However, the opposte s not necessarly true; the perturbaton from the sde can stll ntert wth the sde. Ths can be vewed n mode 9 whch s connected wth the varable ( control of S, trl Fgure ). Theore, for the staton n control, the three resonance freuences from sde should be fltered or blocked by the controller to avod the ncluson of these oscllatons n the control loop. It s theore mportant to choose the gans of the controller adeuately n order to reject these resonances. Ths s already the case, snce the tme constant of control s set to ms. ) A sde modes The egenvalues related to modes 4, 5, 6 and 7 (Table 3) are domnated by the varables related to current: and d trl, d,. The modes 8 and are domnated by PLL, and PLL,. Note that for eh of these modes, when Z s connected n parallel wth the HD lnk (Table 3, thrd column), the varables of the two statons have relatvely hgh partcpaton ftors. When the mpedance of the lne decreases, the partcpaton ftors from the other statons ncrease. Ths mples, theore, a couplng between the two S statons. As a result, a dsturbance from one of the two statons may have an mpt on the other S staton. However, a couplng between two statons varables (.e. ncluson of varables of the two statons n the same modes) does not necessarly mply negatve ntertons. To measure the rsk of ths negatve nterton, the mode shape tool s used.. Mode shape The mode shape evaluates the phase shft angle between the vectors of the complex varables contrbutng to the same mode. The compared vectors of the complex varables must have the same physcal meanng to derve conclusons [4]. When the phase angle between the vectors s close to 8, the rsk of oscllaton s hgh. The domnant varables of the modes 4 ( ), 5 ( ) d, d trl, and 8 (, ) ncludng Z (Table 3, thrd column) PLL, are shown n Fgure 9, Fgure and Fgure respectvely. For modes 4 and 5, we see that the phase angles between the vectors of the two statons are ether n phase or the ampltude of one vector s neglgble compared to the other one. As a result, the rsk of nterton between these varables appears to be neglgble. For mode 8 whch s the PLL, and, PLL, phase dfferences are notceable between the two S statons. However, n the case of the angle s less than PLL, 9 and for the PLL,, the rato between the two ampltudes s relatvely small, theore the rsk of nterton seems to be ute lmted. a) d b) Fgure 9: Mode 4 Table 3 wth Z =.65 pu a) d trl b) trl Fgure : Mode 5 Table 3 wth Z =.65 pu a) PLL b) PLL Fgure : Mode 8 Table 3 wth Z =.65 pu. PARAMTERI STUDY IN EMTPR To valdate the above smallsgnal analyss, a parametrc study s performed usng EMTPR. The parameter varatons of the lne and the HD lnk confguratons are summarzed n Table 4. Table 4: Setup confguraton for parametrc study Parameter Number of confguratons Z 4 confguratons :.,.,. et nfnte (.e. wthout overhead lne) Transt of tve power confguratons : ± MW Staton S n Pcontrol or n control confguratons : Pcontrol or control Staton S : choce between Q and control confguratons : Qcontrol or control Staton S : choce between Q and control confguratons : Qcontrol or control

7 P P P P P P P P A. Small perturbatons A small perturbaton at the P (Fgure ) s made at t = s by applyng a hgh resstve ( kω) three phase to ground fault. A low SRs =.5 s consdered. Actve power results at S are plotted n Fgure. In the results presented n ths secton, the curves wth thck lnes represent the HD lnk smulaton cases wthout the presence of the parallel lne. As for the other confguratons (.e. wth lne), they are represented by thn curves. It s apparent that the hghest perturbaton ampltudes are obtaned wthout the presence of the lne connected n parallel (.e. wthout Z ). Ths confrms the modal analyss presented n secton I.A; addng an lne n parallel ncreases the SR for eh staton and hence the performance of the HD lnk s mproved. On the other hand, the negatve ntertons between the two statons reman neglgble even when the lne mpedance s low a) S n Pcontrol and rectfer b) S n Pcontrol and nverter c) S n control and rectfer d) S n control and nverter Fgure : Parametrc study for small perturbaton B. Large dsruptons However, these fndngs are vald only for small perturbatons. Indeed, durng major dsruptons nonlnear phenomena may exst; for example, when faults occur, the lmters of control systems may operate and the protecton system can trgger a staton. To assess the mpt of the connecton n parallel wth the HD lnk durng major dsruptons, a sold three phase to ground fault at t= s lastng ms s appled at P (Fgure ). The same confguratons prevously presented n Table 4, are consdered. The results of tve power for S are shown n Fgure a) S n Pcontrol and rectfer b) S Pcontrol and nverter c) S n control and rectfer d) S n control and nverter Fgure 3: Parametrc study for large perturbaton It s notced that several cases of the confguraton ncludng the lne n parallel cause more oscllatons and larger dsturbances compared to the case wthout the lne n parallel. Ths shows that for large transents, the lne n parallel can cause deteroraton of the dynamc performance and negatve ntertons of the HD lnk unlke for the cases nvolvng small perturbatons. To evaluate the mpt of these major dsturbances on overvoltage after fault extncton (around t=. s), the results of the subgroup n whch the staton s n Pcontrol and rectfer mode are shown n Fgure 4. Smlar results can be obtaned for the other 3 subgroups.

8 a) S, Pcontrol and rectfer mode Fgure 4: Parametrc study for large perturbaton on P The oscllatons ncludng the lne n parallel have smaller dampng ftors than the cases wthout lne n parallel. In addton, n some confguratons, the maxmum peak rehes hgher values than n the case wthout the lne n parallel. These peaks can theore exceed the threshold overvoltage of the protecton system, whch can cause the blockng and/or trppng of the HD lnk. The ncrease n the ampltude of voltage after fault extncton s manly due to the retve contrbuton from the other staton. Indeed, the ncluson of the parallel lne allows the transmsson of retve power from S to S and vceversa. Ths means that when a fault occurs close to one staton, retve power wll flow between the two statons. Just after fault clearance, a greater transent occurs because of the response tme of the control loops that wll mantan, for a few tens of ms, the supply of retve power. These large dsturbances can depend on several nonlnear ftors, such as the lnk operaton mode, the saturaton of the control systems, fault rde through capablty, the thresholds of the protecton system, etc. Unfortunately, all these complex ftors cannot be taken nto count through smallsgnal analyss studes. I. ONLUSIONS A HDMM lnk connected n parallel wth an lne was evaluated n ths study. A complete overvew on the abnormal ntertons that can occur durng small and large dsturbances was presented. A smallsgnal analyss model was used to study ntertons n ths system. Ths model was verfed usng nonlnear tmedoman smulatons n EMTP R and the mpt of SR was evaluated. The analyss of egenvalues and mode shapes was used to assess ntertons between dfferent varables of the system. It was found, that durng small perturbatons, the parallel lne can mprove the dynamc performance of the HD lnk and that the rsk of negatve nterton between both HD statons s neglgble. The parametrc studes conducted under EMTPR have confrmed the smallsgnal studes for small perturbatons, but t was found that for large dsturbances, negatve ntertons can occur when an lne s n parallel wth the HD lnk. Theore, t s mportant to perform parametrc studes usng EMTtype models n order to cope wth negatve ntertons. II. REFERENES [] B. Gemmell, J. Dorn, D. Retzmann, and D. Soerangr, Prospects of Multlevel S Technologes for Power Transmsson, n Proc. IEEE Transmsson and Dstrbuton onf. Exp., Mlptas, A, Apr. 8, pp. 6. [] J. Peralta, H. Saad, S. Dennetère, J. Mahseredjan and S. Nguefeu, Detaled and Averaged Models for a 4level MMHD system IEEE Trans. on Power Delvery, vol. 7, no. 3, July, pp [3] G.O. Kalcon, G.P. Adam, O. AnayaLara, S. Lo, K. Uhlen, "Small Sgnal Stablty Analyss of MultTermnal SBased Transmsson Systems," Power Systems, IEEE Transtons on, vol.7, no.4, pp.88,83 [4] B. haudhur, R. 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