ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL

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1 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL 204 Stablty Analy of Unbalanced Dtrbuton Sytem Wth Synchronou Machne and DFIG Baed Dtrbuted Generator Ehan NarAzadan, Student Member, IEEE, Claudo Cañzare, Fellow, IEEE, Danel Olvare, Student Member, IEEE, and Kankar Bhattacharya, Senor Member, IEEE Abtract There are many techncal apect and challenge n dtrbuted generaton (DG) that have not been properly undertood and addreed o far. Dtrbuton ytem cannot be condered a balanced threephae ytem, becaue thee are nherently unbalanced n teadytate operaton. A full characterzaton of the unbalanced ytem wth repect to ytem tablty allow a better undertandng of the dynamc behavour of uch ytem. Th paper preent a comprehenve nvetgaton of the effect of ytem unbalance on the tablty of the dtrbuton ytem wth ynchronou generator (SG) and doublyfed nducton generator (DFIG) baed DG unt at dfferent loadng level. Detaled teadytate and dynamc analye of the ytem are performed. Baed on clacal voltage, mallperturbaton and tranent tablty tude, t demontrated that ytem unbalance can gnfcantly affect the dtrbuton ytem dynamc performance, n way that have not been dcued n the techncal lterature o far. A mple and effectve control trategy baed on an Unbalanced Voltage Stablzer (UVS) alo propoed to mprove the ytem control and the tablty of unbalanced dtrbuton ytem wth SG and DFIG. Egenvalue analye and tmedoman mulaton demontrate the effectvene of the propoed UVS for unbalance condton. Index Term Stablty tude, unbalanced power ytem, dtrbuted generaton, doublyfed nducton generator, voltage control. I. INTRODUCTION SINCE the begnnng of the 990, there ha been gnfcant growth of dtrbuted generaton (DG), drven by envronmental and economc factor reultng n gnfcant penetraton of mall cale generaton at the dtrbuton ytem level. Penetraton of DG n dtrbuton ytem make them actve ytem, ntead of pave. Th can affect the dynamc of the whole power ytem, and epecally of the dtrbuton ytem. Although DG may have ome beneft for the ytem uch a mprovement n ytem relablty, there are many techncal apect and challenge that are tll not properly undertood or addreed. Among the numerou ue aocated wth dtrbuton ytem contanng DG, tablty analy of gnfcant nteret (e.g., [] [3]). Th work wa upported by the NSERC Smart Mcrog Strategc Network (NSMGNet) ( and an NSERC Dcovery grant. E. NazrAzadan, C. Cañzare, and K. Bhattacharya are wth the Department of Electrcal and Computer Engneerng, Unverty of Waterloo, Waterloo, ON, Canada, N2L 3G (emal: enaraza@uwaterloo.ca, ccanzare@uwaterloo.ca, kankar@ece.uwaterloo.ca). D. Olvare wth the Department of Electrcal Engneerng, Pontfcal Catholc Unverty, Santago, Chle (emal: dolvareq@ng.puc.cl). Although ome tablty tude of dtrbuton ytem wth DG have been reported n the lterature, a detaled and ytematc analy conderng dtrbuton ytem under unbalanced condton ha not been uffcently addreed. A majorty of tablty tude reported n the lterature are baed on approache mlar to thoe ued n tranmon ytem, and thu everal mplfcaton, n partcular the aumpton of balanced condton, are appled. However, dtrbuton ytem cannot be condered to be balanced threephae ytem, nce thee are nherently unbalanced n teadytate. A full characterzaton of the unbalanced ytem n tablty analye would allow a better undertandng of t dynamc behavour. Nowaday, n everal countre, many DG are mall ynchronou generator (SG) connected to low voltage dtrbuton ytem [4], [5]. For example, there a gnfcant potental for cogeneraton baed on mall SG from ugarcane faclte n Brazl [4]. Acro Canada, many remote communte operate mcrog uppled motly from deelfred SG [6]. On the other hand, wnd energy one of the mot promng renewable energy ource, wth the demand for connectng wnd generator to dtrbuton ytem beng on the re. Among dfferent type of wnd turbne technologe, doubly fed nducton generator (DFIG) have the larget world market hare of wnd turbne generator [7], offerng everal advantage compared to fxedpeed generator, ncludng t ablty to provde varable peed operaton n a coteffectve way and ndependent actve and reactve power control capablte. Snce the applcaton of thee DG n dtrbuton ytem may reult n dfferent ue uch a electromechancal ocllaton, undertandng the dynamc behavour of SG and DFIG under unbalanced condton n a dtrbuton ytem of nteret to many utlte and g operator. A few reported tude conder the charactertc of dtrbuton ytem n tablty analye takng nto account unbalanced load and lne. In [8], a contnuaton threephae power flow approach n polar coonate preented for voltage tablty analy under unbalanced condton; th approach baed on tatc power flow equaton of a threephae model to obtan PV curve. In [9], voltage tablty tude are preented ung a threephae contraned optmal power flow whch eek to maxmze the loadng factor. Snce thee tude are baed on tatc power flow, the mpact of ytem dynamc on voltage tablty not fully nvetgated.

2 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL There are recent tude of the effect of unbalanced condton on mallperturbaton tablty of SG. Thu, n [0] and [], the effect of unbalanced condton on dampng factor and frequency nvetgated. In [0], a modelbaed approach n the phaor doman for mallperturbaton tablty analy of unbalanced dtrbuton ytem preented, and a model dentfcaton technque for mallperturbaton tablty tude are preented n []. However, n thee paper, the effect of unbalanced condton under hgh loadng level, whch would typcally lead to ntablty, are not tuded. Smplfed model of ynchronou and nducton machne have been developed for tranent tablty tude of unbalanced power ytem [2] [5]. Thee model repreent the fundamental frequency component of the machne behavor and neglect the harmonc component. Baed on thee model, ome author analyze the mpact of DG on tranent tablty. Thu, n [6] and [7], the mpact of nducton generator on tranent tablty tuded, and [8] addree the mpact of DG on tranmon ytem tranent tablty, wheren ncreang the DG penetraton level matched by a reducton n centralzed power generaton, whch conequently reult n a reducton n the total amount of rotatng ma and reactve power upport n the ytem. Mot of the extng tranent tablty tude wth DG conder dfferent fault type under balanced loadng condton. For example, bref tude on tranent tablty analy of a dtrbuton ytem wth elected DG unt baed on the calculaton of crtcal clearng tme (CCT) are preented n [3] and [9]. However, the mpact of load unbalancng on tranent tablty tude ha not been properly tuded. Control and tablty tude of DFIG have been dcued n the lat decade for balanced operaton [20] [24]. However, f voltage unbalance not properly compenated by ytem control, the tator current can be hghly unbalanced even wth a mall unbalanced tator voltage. In uch cae, the man problem that hgh current, torque, and power ocllaton appear at double the electrcal frequency due to the negatve equence component, reultng n dconnecton [25] [27]. Technque have been propoed to mtgate thee ocllaton, baed on the njecton of negatve equence component, conderng rotoe [26] or gde converter [25], [27]. In [28], an approach baed on a dturbance rejecton controller preented to compenate ocllaton ung a feedforwa component of the current controller. In [29], a tandalone DFIG under unbalanced condton tuded, wth the g converter upplyng reactve power to compenate for the unbalanced g voltage. A mall gnal tablty analy of a DFIG wnd turbne preented n [30]. In all thee paper, the effect of unbalanced condton under hgh loadng level, whch would typcally lead to ntablty, are not tuded. Baed on the aforementoned hortcomng dentfed n the extng techncal lterature, comprehenve tude conderng the dynamc behavour of SG and DFIG baed DG under unbalanced condton n dtrbuton ytem are preented here. Th an ue for ome utlte (e.g., Hydro One Remote Communte, n Ontaro, Canada), who have pecal nteret on the tablty analye of unbalanced dtrbuton ytem wth SG and DFIG DG, nce ome of ther feeder preent unbalance a hgh a 25% per phae under certan condton. Therefore, th paper preent, for the frt tme, comprehenve tude on voltage, mallperturbaton, and tranent tablty of unbalanced dtrbuton ytem wth SG and DFIG baed DG. Both dynamc and tatc voltage tablty analye are carred out ung threephae PV curve and maxmum ytem loadablty, and tranent tablty tude are performed ung tme doman mulaton of contngence under varou unbalanced condton, baed on threephae detaled model. Smallperturbaton tablty tude are carred out ung a model dentfcaton approach to compute egenvalue and thu tudy the mpact of load unbalancng n heavly loaded ytem. Fnally, control tratege baed on mple and eay to mplement Unbalanced Voltage Stablzer (UVS) are propoed to mprove the tablty of unbalanced dtrbuton ytem wth DG, ung tmedoman mulaton to demontrate ther effectvene. Hence, the man contrbuton of the paper can be ummarzed a follow: A new applcaton of threephae power flow and dynamc voltage tablty ung tme doman mulaton preented. A tatc threephae power flow wth proper DG model for voltage tablty tude ued to determne maxmum ytem loadblty under varou unbalanced condton. The applcaton of an dentfcaton approach, baed on Prony and StegltzMcBe teraton method, for mallperturbaton tablty tude of unbalanced ytem wth DG propoed. Th method provde a framework for mallperturbaton tablty analy of unbalanced ytem wth DG. A comprehenve evaluaton of voltage tablty, egenvalue analye, and tme doman mulaton for a typcal dtrbuton ytem wth SG and DFIG baeddg preented under varou unbalanced condton. Extng control technque to compenate the negatve mpact of unbalanced operaton of DFIG are demontrated to be neffectve at heavly loaded condton. Furthermore, mple and effectve control tratege baed on voltage unbalance for both SG and DFIG baeddg are propoed to mprove the tablty of the dtrbuton ytem. The mplcty of the propoed UVS make t practcal and relatvely eay to mplement n real ytem. The ret of paper organzed a follow: A bref overvew of the ytem model and the methodology ued for tablty analye under unbalanced condton are preented n Secton II; the propoed unbalanced voltage tablzer control alo dcued n th ecton. In Secton III, comprehenve numercal reult wth dfferent cenaro for a DGloadg ytem are preented and dcued. Fnally, Secton IV hghlght the man contrbuton and concluon of the paper. II. SYSTEM MODELING, ANALYSIS AND CONTROL A. SG and Network Model METHODOLOGY Detaled repreentaton of the SG model ued for the mulaton and tude [3]; hence, threephae tator and rotor wndng n the dqo referenceframe are ued [32]. Snce mall

3 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL SG baed DG are very lkely to have mple Proportonal Integral (PI) voltage regulator, Automatc Voltage Regulator (AVR) Type IV (AC4A) are ued here. Moreover, the type of voltage feedback n the exctaton ytem affect the dynamc behavor of the ytem [33], a typcal voltage feedback repreented by the average value of the voltage magntude for each phae ued n th paper [3]. Lne are modeled a contant coupled mpedance branche, and load are treated a contant mpedance a well. Therefore, the followng loadng factor l defned to model load mpedance Z l ncreae n each phae, whch ncreae the actve and reactve power demand: Z l = Z φ () l where Z φ the baeload mpedance for each phae. A load unbalance factor defned to analyze dfferent cenaro of unbalance a the load vare [0]. Thu, a the mpedance of the load n one phae ncreaed, the load mpedance n another phae decreaed, o that total mpedance of the threephae load reman contant n all cae, a follow: Z al = ( k)z l (2) Z bl = Z l (3) Z cl = ( k)z l (4) where k the load unbalance factor, and Z al, Z bl, and Z cl are the phae mpedance of the load. B. DFIG Model The DFIG modeled ung a clacal and detaled nducton machne model wth a wound rotor [32], and a detaled model of the backtoback ac/ac converter controllng the rotor [34]. Unbalance loadng n DFIG ntroduce negatve equence component n the voltage, current, and flux, whch can reult n gnfcant ocllaton n torque, actve and reactve power wth a double frequency; hence, a DFIG model that conder the potve and negatve equence component needed to tudy th phenomenon. Th accomplhed ung a threephae gnal n the tatonary αβ referenceframe expreed by the potve and negatve equence component a follow: [ Fα (t) F β (t) ] = [ F α (t) Fα ] (t) F β (t) F β (t) = F αβ ej(ωet) F αβ e j(ωet) where F repreent voltage, current, or flux lnkage; t tme; and ω e electrcal angular frequency. There are two approache for the potve and negatve equence component eparaton under unbalanced condton: eparaton by low pa flter (LPF), and eparaton by a gnal delay cancellaton [27]. In th paper, the potve and negatve equence component eparaton baed on a LPF approach, n whch, a the negatve equence component appear wth the frequency 2ω e n the potve dq referenceframe, and the potve equence appear wth the frequency 2ω e n the negatve dq referenceframe, a LPF can be ued to bypa dc component for both equence. Thu, the tator component (.e., current, voltage, (5) and flux) n the potve and negatve equence αβ referenceframe yeld: F αβ = F dq F dq e j2ωet (6) F αβ = F dq F dq e j2ωet The dax for the potve equence n the dq referenceframe fxed to the potve equence of tator flux rotatng at the peed ω e, whle the dax for the negatve equence rotate at ω e. Baed on two rotatng referenceframe at ω e and ω e, the voltage equaton for the potve and negatve equence at the g de can be wrtten a: v gdq v cdq = (R g jω e L g ) gdq L d gdq g dt v gdq v cdq = (R g jω e L g ) gdq L d gdq g dt where v voltage; current; g the g de; c the converter de; R g g retance; and L g g nductance. Alo, the voltage equaton for the potve and negatve equence at the rotor and the tator de are: [ ] [ [ v L L = m [ v r L m L r ] d dt [ R jl ω e jl m ω e jl m (ω e ω r ) R r jl r (ω e ω r ) ] ] [ r ] r (7) (8) [ ] [ ] [ ] v L L vr = m d L m L r dt ] [ r ] R jl ω e jl m ω e jl m ( ω e ω r ) R r jl r ( ω e ω r ) (9) r where tand for the tator; r tand for the rotor; L tator nductance; L r rotor nductance; and L m mutual nductance. Baed on (8) and (9), the tator output actve and reactve power under unbalance condton can be wrtten a: P = 3 2 [P 0 P n n 2(ω e t) P co co 2(ω e t)] (0) Q = 3 2 [Q 0 Q n n 2(ω e t) Q co co 2(ω e t)] () where P the tator actve power; Q the tator reactve power; and: P 0 v d v q v d v q Q 0 v q v d vq v d P n P co = vq v d v q v d d v d vq v d v q q Q n v d vq v d v q d Q co vq v d v q v q d (2) Snce the electrcal power the um of the power from the equvalent voltage ource jω e ψ and j(ω e ω r )ψ r [26], where ψ tand for flux lnkage, the electrcal torque of the DFIG can be wrtten a: T e = P e /ω r = 3 2 L m L [T e0 T en n 2(ω e t) T eco co 2(ω e t)] (3)

4 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL where T e the electrcal torque; P e the electrcal power; and: T e0 ψ q ψ d ψq ψ d T en = ψq ψ d ψ q ψ rq d T eco ψ d ψq ψ d ψ q rq (4) Note that, nce the negatve equence of tator and rotor component are zero under balanced condton, the n and co ocllatng term for the tator actve and reactve power, and the electrcal toque dappear. The DFIG rotor control baed on the tator fluxorented ynchronou frame n the dqaxe. Thu, the tator flux lnkage can be calculated a follow: dψ dt = v R. (5) The tator flux n the polar form after Clarke tranformaton can be wrtten a: ψ = ψα 2 ψβ 2 (6) ( ) θ = tan ψβ ψ α where the angle θ the ntantaneou locaton of the tator flux. Note that the tranformaton of dq referenceframe to αβ referenceframe n the rotoe baed on ω lp = ω e ω r. The tator actve and reactve power can be ndependently controlled by and rq, repectvely; thu, two PI controller are ued to control the actve and reactve power. From the pont of vew of the reactve power, the DFIG may be n contant power factor (PF) mode, or voltage control mode. A the DFIG can control the reactve power or the output voltage, a PI controller ued to control the output voltage by controllng. The reference current and rq are converted to the αβ and then to the abc referenceframe baed on ω lp. On the gde, two PI feedback controller are ued to decouple current control. Fgure llutrate the DFIG control cheme, where E c the converter dc bu voltage. Under unbalanced condton, there are four degree of freedom for rotor current component,.e., the potve and negatve equence of the rotor current component; thu, dfferent control objectve can be choen. It worth notcng that t not poble to elmnate all ocllaton n the electrcal torque, the actve and reactve power, and the tator current at the ame tme. In th paper, the man objectve to keep the electrcal torque ocllaton at a mnmum for gven actve power and voltage value. Snce and rq are obtaned to control voltage magntude and actve power, repectvely, a hown n Fg., and ubttutng Ten = T eco = 0 n (4), the negatve equence rotor current reference are gven by: [ rq ] [ ψ = q ψ d ψ d ψ q ] [ ψ q ] ψ d rq ψ d ψ q rq (7) If the control target to elmnate the tator actve power ocllaton, accong to (2), the tator current reference are: d q d q = v d v q v d vq v q v d vq v d vq v d v q v d v d vq v d v q P 0 Q 0 P n P co (8) All tmedoman mulaton are carred out n PSCAD/EMTDC [3], whch a commercal tmedoman oftware wth detaled repreentaton of generator, controller, load, and lne. C. Voltage Stablty Stude It common practce to carry out loadablty tude ung PV curve [35]. The contnuaton power flow yeld thee curve for voltage tablty aement by ncreang the ytem loadng level up to a maxmum loadablty pont at whch the ytem become untable. In th paper, both dynamc and tatc analye are carred out ung the PV curve and maxmum loadablty computaton. Statc voltage tablty tude are baed on threephae power flow; n th cae, the tatc maxmum loadablty aocated wth a loadng level at whch there no power flow oluton. Dynamc voltage tablty tude are carred out ung tmedoman mulaton n PSCAD/EMTDC, baed on the detaled dynamc model of DG and ther voltage regulator. Snce the generator operate a a voltage ource to compute the ntal pont for tmedoman mulaton, f the dfference between the teadytate condton and the ntal pont too large, t may lead to numercal ntablty. Thu, the ntal varable of the generator (e.g., termnal voltage phae) are calculated ung a tatc threephae power flow, whch are then ued n PSCAD/EMTDC a the ntal pont for mulaton. Snce the reult of tmedoman mulaton under teadytate condton are needed for loadablty tude, voltage and actve and reactve power hould be n teadytate condton. Hence, the reult of tmedoman mulaton after a long ettlng tme (20 n th paper) are ued to obtan PV curve pont. Threephae power flow calculaton are baed on node voltage and branch current. For each ere element (e.g., tranmon lne, tranformer, etc.) connectng two node, the node voltage and branch current at each end can be repreented by the followng equaton [36]: v a v b v c a b c [ ] [A] [B] = [C] [D] l v a v b v c a b c r = [ABCD] l r (9) where [ABCD] l the threephae equvalent ABCDparameter matrx of the ere element; v a, v b, v c are lnetoground voltage phaor; and a, b, c are lne current phaor. Baed on the πmodel of feeder depcted n Fg.2, the threephae ABCDparameter matrce of the feeder can be calculated a follow: v a v b v c a b c [A] = I 3 2 [Z abc] [Y abc ] (20)

5 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL UVS Control Target v out v out P out P out Q out rq P out Negatve equence calculaton Ref. PI PI2 rq rq dq dq r r abc r r PWM dq abc PWM v d v q v gd L g L g PI3 PI5 gq gd gd gq gd gq PI4 Ec Ec Rotor Sde Converter G Sde Converter Fg.. Control cheme of the DFIG under unbalanced condton. v a v b v c a b c Fg. 2. Sere element πmodel. Z abc Y abc /2 Y abc /2 ar br cr v ar v br v cr [B] = [Z abc ] (2) [C] = [Y abc ] 4 [Y abc] [Z abc ] [Y abc ] (22) [D] = I 3 2 [Z abc] [Y abc ] (23) where I 3 the 3 3 dentty matrx. Matrce [Z abc ] and [Y abc ] n (20)(23) can be approxmated from the equencereferenceframe dagonal mpedance matrce [Z eq ] and [Y eq ], repectvely, a follow: where [A] = [Z abc ] = [A] [Z eq ] [A] (24) [Y abc ] = [A] [Y eq ] [A] (25) a 2 a a a 2 ; a = 20 (26) SG can be modeled a a pecal cae of ere element connectng the nternal bu voltage to termnal voltage through a ere mpedance. The ere mpedance of a generator n the abc referenceframe can be calculated from the equencereferenceframe mpedance a hown prevouly, where equence mpedance are obtaned from machne parameter [37]. Internal bu voltage are aumed to be balanced, whch modeled ung the followng equaton: e a = e b = e c (27) e a e b e c = 0 (28) It mportant to note that the (27) and (28) alo hold for a negatveequence voltage, and a reaonable tartng pont for varable e a, e b, and e c enure convergence to a potveequence nternal voltage. For modelng PVbue, the power njected by a partcular generator aumed fxed, a follow: [ ] Re va v b v c Load G a b c G = P G (29) Addtonal relaton mpoed by mpedance load are: v a v b = [Z Load ] a b (30) v c c Load where Z Load a dagonal matrx, wth the phaetoground load mpedance n the dagonal. Fnally, the power flow equaton are completed by applyng KCL at each node of the ytem. For mall ytem, th et of nonlnear equaton can be readly mplemented n Matlab [38], and olved wthn reaonable computatonal tme ung the folve functon wth dfferent robut numercal algorthm (e.g., Trutregon and LevenbergMarquat). D. Tranent Stablty Stude There are varou crtera to evaluate the tranent tablty of a ytem. For example, CCT can be ued a an ndex to evaluate the ytem robutne [39]. The CCT repreent the pont beyond whch, the ytem unable to recover t tablty f the fault clearng tme greater than the CCT. When a fault occur n the ytem, the dfference between the actual clearng tme (aumng the ytem table) and CCT may be ued to defne a tranent tablty margn for the ytem. Note that the CCT not uually ued a a tandalone ndex to tudy tranent tablty of power ytem, but t can be ued for comparatve ytem tablty analye a n th paper. Dfferent contngence need to be tuded to determne the wort cae cenaro n the ytem.

6 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL E. SmallPerturbaton Stablty Stude Egenvalue analy of the ytem tate matrx one of the common tool for mallperturbaton tablty tude. In the context of power ytem, everal mplfcaton uch a ytem modelng under balanced condton are appled. Thu, the ytem uually modeled wth nglephae equvalent, o that mallperturbaton tablty analy of a balanced power ytem can be normally carred out by the lnearzaton of the power ytem model around an equlbrum pont. Many commercal program ue phaor model for mallperturbaton tablty tude, and aume a pecfc equlbrum pont under teadytate condton. In the cae of unbalanced condton, equlbrum pont are nontatonary wth repect to the angular velocty of the SG, nce the generator velocty nuodal under teadytate condton; hence, tanda phaorbaed lnearzaton technque are not applcable n th cae [0]. There are two approache for mallperturbaton tablty tude under unbalanced condton: a model baed approach, and a modal etmaton approach [0], [40]. In th paper, mallperturbaton tablty analye are performed ung modal etmaton, n partcular, the Prony method and the StegltzMcBe teraton method [4], [42], baed on tmedoman mulaton. A mentoned n the prevou ecton, PSCAD/EMTDC provde data to analyze the dynamc of the ytem, whch then ued here n an approprate modal etmaton method,.e., StegltzMcBe teraton and Prony, to etmate the ytem egenvalue. In the tude preented n th paper, the generator peed from tmedoman mulaton ued a a gnal for the modal etmaton method. The conventonal Prony method avalable n Matlab ued n th paper [38]. The Prony method utable for tranent tablty tude wth hgh gnal to noe rato (SNR). However, when the ytem become untable, the Prony method cannot follow the gnal properly. In th cae, the StegltzMcBe teraton method ha better performance. Fgure 3 preent a comparon of the meaured data and the etmated gnal by Prony and StegltzMcBe teraton method when the ytem untable. Note that the StegltzMcBe teraton method ft the gnal well, whle the Prony method unable to extract the true pole of the gnal when the ytem untable. Snce the length of the output data of the tmedoman mulaton too long (e.g., pont n a 0 mulaton), t aumed that the gnal dvded n et of 0.5 wndow data, wth each et of data beng then ued n the dentfcaton method to etmate the gnal, gvng a number of pole and zero. Baed on the nature of the gnal and ung meanquareerror, the number of pole wa et to 8 here. F. Propoed Unbalanced Voltage Stablzer When a ytem more heavly loaded, t can become untable a unbalancng ncreae and the crtcal pole cro the magnary axe, a dcued n Secton III. Snce th reult n ocllatory mode, a UVS propoed to mtgate thee ocllaton, ntegratng t wth the generator voltage regulator to provde an auxlary tablzng gnal. Fg. 3. Meaured data and etmated gnal when the ytem untable for the tet ytem dcued n Secton III. Fgure 4 how the propoed UVS for the SG baed DG. Th UVS provde a dampng torque component when the ytem unbalanced; hence, the nput gnal ued here are the voltage magntude n all phae. Thee are then converted to the dqo referenceframe baed on: v d v q v o co(θ) co(θ 20) co(θ 240) = n(θ) n(θ 20) n(θ 240) v a v b v c (3) v 2 d v2 q can be ued to reflect For θ = 0, the tranformaton the degree of unbalance, nce a the unbalance ncreae, the output gnal ncreae a well. The gan K UV S determne the dampng factor provded by the UVS, and the frtoer phae compenaton block provde approprate phae lead to compenate for the phae lag between the voltage regulator nput and the generator electrcal torque. The lmt VUV max S and VUV mn S contran the output gnal, whch an auxlary negatvefeedback gnal for the voltage regulator, due to the fact that by decreang the generator termnal voltage, the load demand decreae, thu reducng the ytem tre a demand and unbalance ncreae. Therefore, tablty can be mproved a the load ncreae wth the propoed UVS. The tunng of the UVS parameter would be mlar to that of the power ytem tablzer n power ytem; thu, the gan K UV S hould be et to guarantee ytem tablty, nce f th gan tuned mproperly, the ytem may be untable, and the tme contant hould be elected to compenate for the phae lag of the ytem. The UVS parameter value ued here are provded n the Appendx. Fgure 5 how the propoed UVS for the DFIG, baed on mlar prncple a the SG UVS. Snce the negatveequence component of termnal voltage are avalable for DFIG control, thee gnal are ued here and then converted to the dq referenceframe. A. Tet Sytem III. RESULTS The dtrbuton ytem n the Kumamoto area n Japan from [43] hown n Fg.6, ued to develop the mplfed tet

7 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL Unbalancng Level Gan Phae Compenaton Max V UVS Z Z2 v abc abc dqo T 2 2 U vd v q TU 2 Mn V UVS Voltage regulator Synchronou machne baed DG Fg. 4. Block dagram of the propoed UVS for an SG baed DG unt. v abc Negatve Sequence Component Clarke PLL dq Low Pa Flter v dq Unbalancng Level 2 2 q v d v Gan Phae Compenaton TU T U 2 Mn V UVS Max V UVS DFIG rotor control Fg. 5. Block dagram of the propoed UVS for a DFIG baed DG unt. ytem depcted n Fg.7. The orgnal ytem ha been ued to tet and compare varou model of everal type of DG [3]. There are varou dtrbuton ytem n Canada, Brazl, and Iran where there a ngle SG or DFIG baed DG, a the cae of the ugarcane faclte n Brazl [4] and remote feeder n Ontaro. Thee ytem can be modeled ung the ytem depcted n the Fg.7, whch contan only one generator. Th ytem alo ueful to better undertand and explan tablty ue aocated wth unbalanced DG, one type of generator at a tme. Thu, the ytem compre a DG unt, feeder and load, all connected to an nfnte bu repreentng the man g. In oer to tudy a contngency n the ytem, hortduraton threephae fault cloe to the load, wth ome mpedance to ground, are mulated. The load modeled a contant mpedance, baed on rated voltage and actve and reactve power. In the bae cae, the actve and reactve power are P Load = 3 MW, and Q Load = Mvar, repectvely. Becaue of the low voltage at the load bu at hgh loadng level, a balanced capactor bank connected at the load bu; the reactve power of the bank for the bae cae Q cap = 0.7 Mvar, and ncreae lnearly wth the loadng factor l. All tet ytem parameter are gven n the Appendx. The man objectve of the gde converter to control Bu Bu2 Bu7 Bu2 Bu3 Bu8 Bu3 Bu9 Bu4 Fg. 6. Kumamoto, Japan dtrbuton tet ytem from [3]. Bu4 Bu0 Bu5 Bu5 Bu Bu6 Bu6 Fg. 7. Smplfed tet ytem. the dc lnk voltage by controllng gd. The DFIG aumed to be n peed control at.2 p.u,.e., the rotor peed et externally, a the large nerta of the wnd turbne reult n low change of the rotor peed. In th cae, the capactor at the load et at Q cap = 2.7 Mvar. To tart the mulaton, the rotoe converter frt et n PF control mode and at t = the controller wtched to voltage control, otherwe the ytem untable. B. Voltage Stablty Analy The DG and lack bu (man g) are aumed to hare the njected power nverely proportonal to the lne mpedance Z and Z 2 a the load ncreaed, conderng lmt on DG actve power. Table I how the comparon of the maxmum actve power loadablty, and loadng factor for dfferent unbalanced condton obtaned wth threephae power flow and tmedoman mulaton (TDS) for the SG baed DG. Table II how the maxmum loadablty and the voltage magntude n phae a, b, and c for dfferent realtc unbalanced condton for the SG. Oberve from Table I and II that when the ytem unbalancng ncreae, the maxmum loadablty of the ytem decreae. Alo, the dfference between the maxmum loadng factor obtaned from the tatc and dynamc tude,.e., threephae power flow and TDS, repectvely, are becaue of the effect of detaled modelng of generator and voltage regulator on TDS. The ytem become untable due to egenvalue crong the magnary axe, a dcued n detal n Secton IIID, whch cannot be oberved n power flow tude. Fgure 8 llutrate the voltage magntude at the load under balanced and unbalanced condton, and Fg.9 depct the PV curve under balanced and unbalanced condton for k = 20% for the SG. Oberve that the voltage magntude n phae b cloe to the voltage magntude for the balanced condton, and the voltage magntude of phae c and a are greater and le than that of phae b, repectvely, a expected. The voltage magntude n phae c relatvely hgh, whch due to the capactor bank. Note that nce the load are modeled baed on contant mpedance, the maxmum power for the ytem doe not necearly correpond to the maxmum loadng factor, due to the actve and reactve power beng proportonal to the quare of the voltage and the loadng factor. It worth notcng that the maxmum loadablty of the ytem wll be lmted n practce by voltage lmt, whch would requre addtonal compenaton equpment. Alo, the voltage dfference for all phae may be compenated by perphae capactor bank. Table III how the maxmum loadablty and the voltage magntude n phae a, b, and c for dfferent realtc un

8 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL TABLE I MAXIMUM ACTIVE POWERS AND LOADING FACTORS FOR DIFFERENT UNBALANCED CONDITIONS FOR STATIC THREEPHASE POWER FLOW AND TIMEDOMAIN SIMULATIONS WITH SG. k(%) Maxmum loadng factor (p.u.) Maxmum actve power loadablty (p.u.) TDS Threephae PF TDS Threephae PF TABLE II MAXIMUM ACTIVE POWER AND VOLTAGE MAGNITUDE IN ALL PHASES FOR DIFFERENT UNBALANCED CONDITIONS WITH SG. k(%) Maxmum actve power loadablty (p.u.) V a(p.u.) V b (p.u.) V c(p.u.) Voltage Magntude (p.u.) Total actve power loadng (p.u.) Fg. 9. PV curve wth SG for k = 20%. Voltage Magntude (p.u.) V balanced Va Vb Vc V balanced Va Vb Vc Loadng Factor Fg. 0. Load voltage magntude veru loadng factor wth DFIG for k = 5%. balanced condton of the dtrbuton ytem wth DFIG. Oberve that when the ytem unbalancng ncreae, the maxmum loadablty of the ytem decreae, and the voltage magntude dfference n phae a, b, and c wth repect to the voltage magntude n balanced condton ncreae. Fgure 0 how the voltage magntude at the load under balanced and unbalanced condton for k = 5% wth DFIG, and Fg. depct the PV curve under balanced and unbalanced condton. Oberve that the voltage magntude n phae b cloe to the voltage magntude for the balanced condton, and the voltage magntude of phae c and a are greater and le than that of phae b, repectvely, a expected. C. Tranent Stablty Analy Threephaetoground fault of hortduraton and cloe to the load are condered a contngence for the SG. The mulaton tme 20, and the fault occur at t = 3. Table IV llutrate the CCT of the tet ytem wth the SG and the DFIG for dfferent value of k for the bae loadng factor (.e., l = p.u.). Oberve that the CCT decreae a the unbalance ncreae, decreang by 30% for the SG and 95% for the DFIG a k ncreae from 0% to 25%. Snce the power ratng of the SG and the DFIG are dfferent, the correpondng CCT are not comparable wth each other. It hould be noted that, a the load ncreaed, t wa oberved that the CCT remaned unchanged, due to the fact that the DG at t maxmum power output at bae load. Fgure 2 and 3 depct the tranent behavor of the SG at Voltage Magntude (p.u.) V balanced Va Vb Vc Total Actve Power Loadng (p.u.) Voltage Magntude (p.u.) V balanced Va Vb Vc Loadng Factor Fg. 8. Load voltage magntude veru loadng factor wth SG for k = 20%. Fg.. PV curve wth DFIG for k = 5%. TABLE III MAXIMUM ACTIVE POWER AND VOLTAGE MAGNITUDE IN ALL PHASES FOR DIFFERENT UNBALANCED CONDITIONS WITH DFIG. k(%) Maxmum actve power loadablty (p.u.) V a(p.u.) V b (p.u.) V c(p.u.)

9 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL Fg. 2. Tranent behavor of SG at k = 25% before CCT. Fg. 3. Tranent behavor of SG at k = 25% after CCT. TABLE IV CCT OF THE TEST SYSTEM AT BASE LOAD (l = P.U.) FOR A THREEPHASETOGROUND FAULT. k(%) CCT of the tet ytem wth the SG () CCT of the tet ytem wth DFIG () a loadng factor l =.5 p.u. and k = 25% for the tuded fault before and after the CCT. Oberve that the ytem table for a clearng tme 0.2, and untable for clearng tme greater than 0.2. D. UVS Impact on SG Two cenaro are condered to analyze the effect of unbalanced condton on mallperturbaton tablty for the SG, a follow: ) Effect of Unbalancng at Bae Load: In the frt cenaro, the load at the bae cae (.e, l = p.u.), and the ytem perturbed wth a hortduraton threephae fault at t =, o that the crtcal ytem mode can be obtaned ung the dentfcaton approach. Th ued to tudy the ytem tablty under varou unbalanced condton at low loadng level, demontratng the mpact of unbalancng on the table TABLE V DAMPING FACTORS AND FREQUENCY OF OSCILLATIONS FOR DIFFERENT UNBALANCED CONDITIONS. Pole Dampng factor (%) Frequency (rad/) k= 0%.09 j k=5%. j k=0%.2 j k=5%.3 j k=20%.4 j k=25%.6 j ytem. Table V llutrate the dampng factor and frequency of the crtcal pole at the bae load for dfferent unbalanced condton. Note that a k ncreae, the frequency decreae, whle the dampng factor ncreae; mlar obervaton were reported n [0] and [40]. 2) Effect of Unbalancng on Hgh Loadng Level: In the econd cenaro, the ytem load ncreaed cloe to t maxmum value (l = 2.2 p.u.), and the machne then connected at t = 0.5. Th ued to tudy the tablty of the ytem for varou unbalance condton at hgh loadng level, demontratng how unbalancng lead the ytem to ntablty. Fgure 4 llutrate the crtcal pole of the SG peed for varou level of unbalanced condton. Oberve that, beyond k = 5%, the crtcal pole croe the magnary ax and thu the ytem experence a Hopf bfurcaton wth.9 Hz

10 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL Imagnary Ax k=% k=2% k=3% k=4% k=5% k=6% k=7% Generator Speed (p.u.) Wthout UVS Wth UVS Real Ax Fg. 4. Zeropole map of SG peed around crtcal unbalanced condton. Imagnary Ax =0.5 =0.4 =0.3 =0.2 =0. Wthout UVS Real Ax Fg. 5. Crtcal pole of SG peed aocated wth the ocllatory mode wth and wthout UVS. frequency. For a loadng level of 2.2 p.u. and unbalancng of k = 25%, the ytem untable a the crtcal pole of the SG peed move to the rght de of the magnary ax. Th can be corrected by ntroducng the propoed UVS. Thu, Fg.5 how the effect of UVS on the crtcal pole for dfferent K UV S value. Note that a the gan of UVS ncreae, the crtcal pole move to the left de of the magnary ax and the ytem become more table. Fgure 6 llutrate the generator peed wth and wthout UVS at l = 2.2 p.u., k = 25%, and K UV S = 0.2, when the machne connected, howng that the generator peed uffcently damped and the ytem become table wth the UVS. E. UVS Impact on DFIG In oer to compare extng control tratege and the propoed UVS for the DFIG, the followng cenaro are tuded for k = 5% and l =.5 p.u.: S: Th the clacal control balanced approach, whch doe not take nto account the poblty of unbalanced voltage. In th cae, the ynchronou referenceframe algned wth the tator flux and ha no negatve equence njecton Tme () Fg. 6. Tranent behavor of SG peed wth and wthout UVS. S2: Th cae baed on lmtng the electrcal torque ocllaton n (7); thu, the negatve equence component are adjuted to lmt the electrcal torque. S3: Th cae baed on lmtng the tator actve power n (8); thu, the negatve equence rotor current are adjuted to lmt the tator actve power ocllaton. S4: Th the ame a S wth the UVS added. S5: Th the ame a S2 wth the UVS added. S6: Th the ame a S3 wth the UVS added. The output actve and reactve power are et at P out = MW, and Q out = 0 Mvar, repectvely. Baed on dfferent control target, Fg.7 depct the mulated reult wth the varou control tratege for PF control mode. The control wa ntally et to S and changed to S2 at t = 2, and then to S3 at t = 3, repectvely. Durng the mulaton, the gde converter wa enabled, then the DFIG tator wa energzed, and fnally the machne wa connected at t = 0.5 ; thu, the DFIG n teadytate after. Snce the tranent behavour of the tartng proce not the focu of th paper, th proce not hown n any of the plot. Oberve that when the controller et to S, the negatve equence component of rotor current reference are zero; hence, the actve and reactve power, electrcal torque, tator voltage and current all contan gnfcant ocllaton at 20 Hz, whch may damage the DFIG. In the rotor de, the current contan both the fundamental component of the rotor mechancal frequency mnu the tator frequence (f r f ) and the harmonc component of (f f r ). At t = 2, the control n S2 actvated, reultng n the torque ocllaton beng reduced over 90% compared to S; however, the power ocllaton ncreae. On the other hand, when the control n S3 actvated, the oppote take place,.e., the torque ocllaton ncreae but the power ocllaton decreae. Fgure 8 llutrate the reult of the DFIG wth voltage control, but wthout UVS. In th cae, the reference voltage et at.03 p.u. to operate the ytem wthn the voltage lmt. Oberve that the ytem become untable for S2 and S3, wherea t wa table under balanced condton; hence, the voltage unbalance lead to ntablty. Fgure 9 depct the reult of the DFIG n voltage control mode wth UVS. Thu, S5 take place at t = 2, and S6

11 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL 204 Fg. 7. Tranent behavour of DFIG wth varou control tratege for PF control mode: (a) tator actve power; (b) tator reactve power; (c) electrcal torque; (d) voltage magntude of the load. Fg. 9. Tranent behavour of DFIG wth varou control tratege for voltage control mode wth UVS: (a) tator actve power; (b) tator reactve power; (c) electrcal torque; (d) voltage magntude of the load. baed on detaled tmedoman mulaton of contngence; and mallperturbaton tablty tude were performed baed on dentfcaton method. The PV curve howed that the loadablty of the ytem decreaed a unbalancng ncreae, and from the pont of vew of tranent tablty, the tmedoman mulaton demontrated that the ytem wa le table a unbalancng ncreaed; another nteretng reult wa that, a the ytem load ncreaed, the crtcal pole croed the magnary axe and the ytem became untable a unbalancng ncreaed. An unbalanced voltage tablzer wa propoed to mprove the tablty of the ytem, demontratng the effectvene of the tablzer by egenvalue analye and tmedoman mulaton. Fg. 8. Tranent behavour of DFIG wth varou control tratege for voltage control mode wthout UVS: (a) tator actve power; (b) tator reactve power; (c) electrcal torque; (d) voltage magntude of the load. APPENDIX Table VI preent the ytem parameter ued n th paper, aumng a mple decoupled mpedance lne model. The SG data were extracted from [3]. Table VII how the DFIG parameter. The SG voltage regulator, PI controller, and UVS parameter are hown n Table VIII, IX, and X, repectvely. occur at t = 3. Note that the ytem now table and the electrcal torque ocllaton are reduced, wth the bet overall ytem performance beng oberved for S5. Th demontrate the clear advantage of ntroducng the propoed UVS for unbalanced ytem operaton. IV. CONCLUSIONS Th paper concentrated on the tablty analye of SG and DFIG baed DG n the context of dtrbuton ytem under unbalanced condton. Voltage tablty analye were performed baed on PV curve obtaned from both power flow and dynamc tude; tranent tablty tude were carred out TABLE VI SYSTEM PARAMETERS. S bae (MVA) 0 Voltage ratng (kv) 2.4 Lne mpedance (Z ) (p.u.) j 0.2 Lne mpedance (Z 2 ) (p.u.) 0.35 j 2. ACKNOWLEDGMENT The author would lke to thank Dr. Rodrgo Andrade Ramo from the Unverty of So Paulo, Brazl, for h nghtful comment and uggeton.

12 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL TABLE VII DFIG PARAMETERS. Power ratng (MVA).77 Voltage ratng (kv) 0.69 Stator/rotor turn rato R (p.u.) R r (p.u.) L (p.u.) L r (p.u.) 0.8 L m (p.u.) H (ec) 4.55 TABLE VIII SG VOLTAGE REGULATOR PARAMETERS. Maxmum regulator voltage (p.u.) 6 Mnmum regulator voltage (p.u.) 0 Regulator gan 78 Regulator pole (ec) 0 Regulator zero (ec) Tme contant of the feld crcut T d (ec) TABLE IX PI CONTROLLERS PARAMETERS. P I P I 2 P I 3 P I 4 P I 5 Proportonal gan Integral tme contant (ec) TABLE X UVS PARAMETERS. SG DFIG K UV S 0.2. T U (ec) T U2 (ec) VUV max S (p.u.) VUV mn S (p.u.) REFERENCES [] M. Reza, J. G.Slootweg, P. H. Schavemaker, W. L. Klng, and L. V. der Slu, Invetgatng mpact of dtrbuted generaton on tranmon ytem tablty, n Proc. IEEE Power Tech Conference, Bologna, Jun [2] A. M. Azmy and I. Erlch, Impact of dtrbuted generaton on the tablty of electrcal power ytem, n Proc. IEEE PES General Meetng, Jun [3] E. NarAzadan, C. Canzare, and K. Bhattacharya, Modelng and tablty analy of dtrbuted generaton, n Proc. IEEE PES General Meetng, Jul [4] S. Granvlle, P. Lno, F. Ralton, L. A. Barroo, and M. Perera, Recent advance of ugarcane boma cogeneraton n brazl, n Proc. IEEE PES General Meetng, Jul [5] M. Wang and J. Zhong, Development of dtrbuted generaton n chna, n Proc. IEEE PES General Meetng, Jul [6] M. Arraga, C. A. Cazare, and M. Kazeran, Renewable energy alternatve for remote communte n northern ontaro, canada, IEEE Tran. Sutanable Energy, vol. 4, no. 3, pp , 203. [7] T. Ackermann, Wnd Power n Power Sytem. NJ: Wley: Hoboken, [8] X.P. Zhang, P. Ju, and E. Handchn, Voltage tablty analy n unbalanced power ytem by optmal power flow, IEEE Tran. Power Syt., vol. 20, no. 3, pp , Aug [9] D. Laura and P. Varlone, Contnuaton threephae power flow: A tool for voltage tablty analy of unbalanced threephae power ytem, Proc. IET Gen., Tran. and Dt., vol. 53, no. 3, pp , May [0] R. H. Salm and R. A. Ramo, A modelbaed approach for mallgnal tablty aement of unbalanced power ytem, IEEE Tran. Power Syt., vol. 27, no. 4, pp , Nov [], A framework for analyzng the mallgnal dynamc performance of unbalanced power ytem, n Proc. IEEE PES General Meetng, Jul. 20. [2] R. G. Harley, E. B. Makram, and E. G. Duran, The effect of unbalanced network and unbalanced fault on nducton motor tranent tablty, IEEE Tran. Energy Conver., vol. 3, no. 2, pp , 988. [3] E. B. Makram, V. O. Zambrano, R. G. Harley, and J. C. Balda, Threephae modelng for tranent tablty of large cale unbalanced dtrbuton ytem, IEEE Tran. Power Syt., vol. 4, no. 2, pp , 989. [4] R. G. Harley, E. B. Makram, and E. G. Duran, The effect of unbalanced network on ynchronou and aynchronou machne tranent tablty, Elect. Power Syt. Re., vol. 3, no. 2, pp. 9 27, 987. [5] E. B. Makram, V. O. Zambrano, and R. G. Harley, Synchronou generator tablty due to multple fault on unbalanced power ytem, Elect. Power Syt. Re., vol. 5, no., pp. 3 39, 988. [6] V. Akhmatov, Analy of dynamc behavour of electrc power ytem wth large amount of wnd power, Ph.D. dertaton, Techncal unverty of Denmark, Lyngby, Denmark, [7] A. P. Grlo, A. d. A. Mota, L. T. M. Mota, and W. Freta, An analytcal method for analy of largedturbance tablty of nducton generator, IEEE Tran. Power Syt., vol. 22, no. 4, pp , [8] M. Reza, Stablty analy of tranmon ytem wth hgh penetraton of dtrbuted generaton, Ph.D. dertaton, Delft Unverty of Technology, Delft, Netherland, [9] I. Xyng, A. Ihchenko, M. Popov, and L. van der Slu, Tranent tablty analy of a dtrbuton network wth dtrbuted generator, IEEE Tran. Power Syt., vol. 24, no. 2, pp , May [20] P. Ledema and J. Uaola, DFIG model for tranent tablty analy, IEEE Tran. Energy Conver., vol. 20, no. 2, pp , Jun [2] Y. Le, A. Mullane, G. Lghtbody, and R. Yacamn, Modelng of the wnd turbne wth a DFIG for g ntegraton tude, IEEE Tran. Energy Conver., vol. 2, no., pp , Mar [22] D. Xang, L. Ran, P. Tavner, and S. Yang, Control of a DFIG n a wnd turbne durng g fault e through, IEEE Tran. Energy Conver., vol. 2, no. 3, pp , Sep [23] J. Morren and S. de Haan, Rde through of wnd turbne wth DFIG durng a voltage dp, IEEE Tran. Energy Conver., vol. 20, no. 2, pp , Jun [24], Shortcrcut current of wnd turbne wth DFIG, IEEE Tran. Energy Conver., vol. 22, no., pp , Mar [25] O. GomBellmunt, A. JunyentFerre, A. Sumper, and J. BergaJan, Rdethrough control of a DFIG under unbalanced voltage ag, IEEE Tran. Energy Conver., vol. 23, no. 4, pp , Dec [26] L. Xu and Y. Wang, Dynamc modelng and control of DFIGbaed wnd turbne under unbalanced network condton, IEEE Tran. Power Syt., vol. 22, no., pp , Feb [27] Y. Zhou, P. Bauer, J. Ferrera, and J. Perk, Operaton of gconnected DFIG under unbalanced g voltage condton, IEEE Tran. Energy Conver., vol. 24, no., pp , Mar [28] T. K. A. Brekken and N. Mohan, Control of a doubly fed nducton wnd generator under unbalanced g voltage condton, IEEE Tran. Energy Conver., vol. 22, no., pp , Mar [29] R. Pena, R. Caena, E. Ecobar, J. Clare, and P. Wheeler, Control ytem for unbalanced operaton of tandalone DFIG, IEEE Tran. Energy Conver., vol. 22, no. 2, p , Jun [30] L. Yang, Z. Xu, J. Otergaa, Z. Y. Dong, K. Wong, and X. Ma, Ocllatory tablty and egenvalue entvty analy of a DFIG wnd turbne ytem, IEEE Tran. Energy Conver., vol. 26, no., pp , Mar. 20. [3] PSCAD/EMTDC ver 4.2 Uer Manual, Mantoba HVDC Reearch Centre Inc., Wnnpeg, Mantoba, Canada. [32] P. Kundur, Power Sytem Stablty and Control. New York: McGraw Hll, 994. [33] R. H. Salm and R. A. Ramo, Analyzng the effect of the type of termnal voltage feedback on the mall gnal dynamc performance of ynchronou generator, n Proc. IREP Symp. Bulk Power Sytem Dynamc and Control, Aug. 200.

13 ACCEPTED TO IEEE TRANSACTIONS ON SMART GRID, APRIL [34] N. Mohan, T. M. Undeland, and W. Robbn, Power electronc: converter, applcaton, and degn. New York: Wley, [35] Voltage tablty aement: Concept, practce and tool, IEEE/PES Power Sytem Stablty Subcommttee, Tech. Rep., Aug [36] W. H. Kertng, Dtrbuton Sytem Modelng and Analy. CRC Pre, [37] M. Z. Kamh and R. Iravan, Unbalanced model and powerflow analy of mcrog and actve dtrbuton ytem, IEEE Tran. Power Del., vol. 25, no. 4, pp , Oct [38] MATLAB, The MathWork Inc. [39] A. G. Expoto, A. J. Conejo, and C. Canzare, Electrc Energy Sytem, Analy and Operaton. CRC Pre, [40] R. H. Salm, R. A. Ramo, and N. G. Breta, Analy of the mall gnal dynamc performance of ynchronou generator under unbalanced operatng condton, n Proc. IEEE PES General Meetng, Jul [4] H. Ghaem, Onlne montorng and ocllatory tablty margn predcton n power ytem baed on ytem dentfcaton, Ph.D. dertaton, Unverty of Waterloo, Waterloo, Canada, [42] K. Stegltz and L. E. McBe, A technque for the dentfcaton of lnear ytem, IEEE Tran. Autom. Control, vol. AC0, pp , 965. [43] S. L, K. Tomovc, and T. Hyama, Load followng functon ung dtrbuted energy reource, n Proc. IEEE PES Summer Meetng Meetng, Jul Kankar Bhattacharya (M 95, SM 0) receved the Ph.D. degree n electrcal engneerng from the Indan Inttute of Technology, New Delh, Inda, n 993. He wa n the faculty of Indra Gandh Inttute of Development Reearch, Mumba, Inda, durng , and then the Department of Electrc Power Engneerng, Chalmer Unverty of Technology, Gothenburg, Sweden, durng He joned the E&CE Department of the Unverty of Waterloo, Waterloo, ON, Canada, n 2003 where he currently a full Profeor. H reearch nteret are n power ytem economc and operatonal apect Ehan NarAzadan (S ) receved h M.Sc. degree n Electrcal Engneerng from the Amrkabr Unverty, Tehran, Iran, n 2009, and currently purung the Ph.D. degree n Electrcal Engneerng at the Unverty of Waterloo, Waterloo, ON, Canada. H reearch nteret are n modelng, control, and tablty ue n mcrog. Claudo A. Cañzare (S 86, M 9, SM 00, F 07) receved the electrcal engneer dploma from the Ecuela Poltécnca Naconal (EPN), Quto, Ecuador, n 984 and the M.S. and Ph.D. degree electrcal engneerng are from the Unverty of WconnMadon n 988 and 99, repectvely. He ha held varou academc and admntratve poton at the Electrcal and Computer Engneerng Department of the Unverty of Waterloo, Waterloo, ON, Canada, nce 993, where he currently a full Profeor, the Hydro One Endowed Char, and an Aocate Drector of the Waterloo Inttute for Sutanable Energy (WISE). H reearch actvte concentrate n the tudy of tablty, optmzaton, modelng, mulaton, control, and computatonal ue n power ytem wthn the context of compettve electrcty market and mart g. Dr. Cañzare ha been the recpent of varou IEEEPES Workng Group awa and hold and ha held everal leaderhp appontment n IEEE PES techncal commttee and ubcommttee. He a regtered Profeonal Engneer n the provnce of Ontaro and a Fellow of the Royal Socety of Canada and of the Canadan Academy of Engneerng. Danel E. Olvare (S ) wa born n Santago, Chle, and receved the B.Sc. and the Engneer degree n electrcal engneerng from the Unverty of Chle n Santago n 2006 and 2008, repectvely. He fnhed h Ph.D. tude n Electrcal and Computer Engneerng at the Unverty of Waterloo, Waterloo, ON, Canada, n January 204. H reearch nteret nclude modelng, mulaton, control and optmzaton of power ytem n the context of mart g.