A modified droop control structure for simultaneous power-sharing and DC voltage oscillations damping in MT-HVDC grids

Recei ed: 27 Augus 2021 Re ised: 30 Decembe 2021 Accep ed: 21 Janua y 2022 IET Gene a ion, T ansmission & Dis ibu ion DOI: 10.1049/g d2.12427 ORIGINAL RESEARCH PAPER A modi ied d oop con ol s uc u e o simul aneous powe -sha ing and DC ol age oscilla ions damping in MT-HVDC g ids Neda Azizi1Hassan Mo adi CheshmehBeigi1Kuma s Rouzbehi2 1Depa men o Elec ical Enginee ing, Razi Uni e si y, Ke manshah, I an 2Depa men o Sys em Enginee ing and Au oma ic Con ol, Uni e si y o Se ille, Se ille, Spain Co espondence Hassan Mo adi CheshmehBeigi, Tagh-e-Bos an, Uni e si y S ., Ke manshah, I an. Email: [email p o ec ed].i Abs ac Wi h inc easing ene gy demand, he use o enewable ene gy esou ces is inc easing. Renewable ene gy sou ces equi e powe elec onic con e e s o ge in eg a ed in o powe g ids. Mul i- e minal high ol age di ec cu en (MT-HVDC) sys ems a e a p omising solu ion o hei g id in eg a ion. Using d oop-based con olle s a egies in powe con- e e s a ions o MT-HVDC g id, in addi ion, o p o iding powe -sha ing, can suppo he equency o he connec ed AC g ids. Howe e , powe changes lead o di ec ol age de ia ions, he eby dis up ing he s abili y o he MT-HVDC sys em. He e, a new con- ol s uc u e o he d oop con olle o he ol age sou ce con e e (VSC) con olle is p oposed which is named modi ied d oop con olle (M-D oop). This me hod, in addi- ion o powe -sha ing, uses an app op ia e con ol ac ion o p o ide he equi ed ol age s abili y. He e, analy ical s udies o he modi ied con ol s a egy a e epo ed. Mo eo e , h ough a de eloped MATLAB Simulink pla o m, i s pe o mance is e i ied in he e en s o ansien s, consis ing o aul , a iable load, and change in powe gene a ion. 1 INTRODUCTION One o he mos impo an challenges on he oad o mul i- e minal HVDC g id de elopmen is p o ec ing he sys em agains DC aul s. The capaci i e beha iou o HVDC cables and hei ela i ely low impedances leads o a signi ican inc ease in aul cu en s. DC ci cui b eake s (DCCBs) a e one o he mos e ec i e ools o as aul isola ion [1]. Despi e de elop- men s in DCCB echnology, s ill hey need o la ge DC eac o s o educe he a e o ising aul cu en s [2]. Capaci o and DC eac o connec ed o HVDC g id and induc ance and capac- i ance o HVDC ansmission lines make a kind o LC il e , which se iously a ec s he dynamic esponse o DC link ol - age and i s ins an aneous powe in MT-HVDC g id, especially in he long lines [3]. The main con es in con ol o MT-HVDC g ids is di ec ol age egula ion wi h low capaci ance [3]. The a ailable con ol me hods o sol ing his challenge include wo op ions. The i s op ion is based on he cen al con olle and he second op ion is known as he decen alized me hod. In he i s op ion, he en i e sys em is moni o ed h ough an ex e nal communica ions link and he con olle deli e s he This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion-NonComme cial-NoDe i s License, which pe mi s use and dis ibu ion in any medium, p o ided he o iginal wo k is p ope ly ci ed, he use is non-comme cial and no modi ica ions o adap a ions a e made. © 2022 The Au ho s. IET Gene a ion, T ansmission & Dis ibu ion published by John Wiley & Sons L d on behal o The Ins i u ion o Enginee ing and Technology op imal powe low o he sys em’s esou ces and load. The ad an age o his me hod is ha i is op imal, and i s majo disad an age is i s dependence on ex e nal commu- nica ions [4]. In addi ion, he implemen a ion o he p o- posed me hod in he MT-HVDC g id educes ansien ol - age oscilla ions. Howe e , he con ol s a egy o he sec- ond op ion includes me hods such as d oop [5], mas e - sla e [6], and DC bus signalling me hod [7]. In [8], d oop con ol me hods a e p oposed based on he decen alized me hods, bu mos o hem canno delibe a e he in lu- ence o he esis ance o cable and e o s o senso gain. Mo eo e , he e is a ade-o be ween ol age egula ion and cu en sha ing in hese me hods. Adap i e o nonlinea d oop is p oposed in [8, 9], in which he ade-o be ween load sha - ing and ol age egula ion is minimal, bu hese me hods also pe o m poo ly when he powe con e e cu en is nega i e o he powe is e e sed. Alongside wi h his me hods, he e a e s a egies include he combina ion o bo h cen alized and decen alized me hods as di e en con ol laye s, which in addi- ion o he ad an ages, include disad an ages o wo me hods [10]. 1890 wileyonlinelib a y.com/ie -g d IET Gene . T ansm. Dis ib. 2022;16:1890–1900. AZIZI ET AL.1891 In DC g ids, he DC ol age has a simila ole as he powe balance sign ha he equency has in AC g ids [11]. Tha is, he DC ol age dynamics a e de e mined by he ene gy s o ed as elec os a ic po en ial ene gy in he capaci o s in he g id [12]. Howe e , con en ional d oops canno inc ease he capaci- ance. The e o e, a new con ol me hod o MMC, called i ual capaci o con ol, is p oposed in [13], which makes i possible o educe he DC g id oscilla ion by simula ing he dynamic esponse o a physical capaci o . To pe o m au oma ic syn- ch oniza ion using he DC-link capaci o dynamics, he au ho s in [14] employed a i ual synch onous con ol, which mimics he synch oniza ion ea u e o a synch onous gene a o . The mos impo an ad an age o his me hod is ha i is ope a ed wi hou a phase-locked loop (PLL), and he e o e a oids ins a- bili y caused by he PLL when connec ing he VSC o a weak g id. The Ine ia Emula ion Con ol (INEC) algo i hm p oposes a me hod o he ine ia emula ion ha uses he ene gy s o ed in he DC-link capaci o o mimic he ine ial esponse o an SG, bu his may need he la ge capaci o s o be added o he sys em. The addi ion o hese capaci o s inc eases cos s and will a ec he dynamics o he con olle s. Combined s a egy is ano he me hod o emula ed ine ia, which u ilizes bo h DC-link capac- i o and wind u bine kine ic ene gy, his me hod is used only in a poin - o-poin HVDC sys em and equi es some modi i- ca ions o ope a e on a DC ne wo k [15]. Though o app o- p ia e ol age egula ion and powe -sha ing, a p ope s a egy is needed o enable he con e e o inc ease DC capaci ance. This pape p oposes a modi ied d oop con olle (M-D oop) ha p o ides capaci ance using he ene gy s o ed in he g id whe e he aul occu ed. The M-D oop can p o ide he capaci- ance equi emen o he HVDC g id wi hou depending on e- quency measu emen and PLL. The con ibu ions o his s udy a e: ∙This pape p oposes a success ul me hod o simul aneous powe -sha ing and oscilla ions o DC ol age damping ∙The p oposed me hod does no equi e inc easing he alue o DC-link capaci o s ∙As he con en ional DC-PSS can only neu alize a small pa o he ol age luc ua ions, while, gi en he p esence o he d oop con olle on he sys em, i has no p ope e ec on he ola ili y o he powe . This s udy shows ha he M-d oop con olle also p o ides a pa o he capaci ance equi ed by he sys em in addi ion o damping o he di ec ol age oscil- la ions. The es o his pape is o ganized as ollows: Con en- ional d oop con olle pe o mance is exp essed in Sec- ion 2. Sec ion 3is buil based on he p oposed con ol s a - egy. The unde s udy ne wo k and i s modelling a e discussed in Sec ion 4. The op imiza ion app oach is in es iga ed in Sec ion 5. Dynamic pe o mance analysis is analysed in Sec- ion 6. Simula ions e i y and con i m he analy ical analy- sis desc ibed in Sec ion 7. Finally, conclusions a e gi en in Sec ion 8. V DC P Ope a ion poin V DC, e P e Ope a ion e g ion Ope a ion egion VDC,min VDC,max Pmax P min αV DC +βP DC +γ=0 FIGURE 1 Gene alized cha ac e is ics o he p oposed d oop con olle VDC PWM V DC P i DC i *DC V DC* M-d oop PCC Powe con olle P * Cu en con olle e c VC L T R T DC BUS V DC C iDC FIGURE 2 Con ol s uc u e o he p oposed con olle o a VSC s a ion 2PERFORMANCE OF A CONVENTIONAL DROOP CONTROLLER Figu e 1demons a es he gene al cha ac e is ics o he d oop con olle . Usually, P* as he ac i e powe e e ence is manipula ed by he ol age d oop con olle (V–P), so, he ac i e powe con ol scheme ac s as pa o he plan o d oop con ol model. The coe icien o he d oop cha ac e is ics can be calcula ed acco ding o he powe low esul s [4, 16] o g id condi ion and s abili y [17]. 3PROPOSED CONTROL STRATEGY The main con es in con ol o MT-HVDC g ids is di ec ol - age egula ion wi h low capaci ance [3]. This pape sugges s a me hod o p o ide he ansien damp- ing o di ec ol ages o he HVDC g id du ing he ansien condi ions. In his s uc u e, he M-d oop con olle supple- men a y signal is being used ins ead o he con en ional V–P d oop con olle o inc ease he s abili y o he HVDC g id. Figu e 2shows a gene al s uc u e o a p oposed con olle o a VSC s a ion. The con igu a ion o he p oposed M-d oop con olle is e ealed in Figu e 3. Since he measu ed local ol age is known as he powe balance indica o in he HVDC g id, in his s uc u e, he locally measu ed ol age is used as he inpu signal. This M-d oop p o ides an auxilia y capaci ance. In 1892 AZIZI ET AL. FIGURE 3 M-d oop con ol s uc u e A0 Ba-A0 Ba-A1 Cb-A1 Bb-A1 B0 Ba-B0 Ba-B2 Ba-B1 Cb-B2 Cb-B1 Bb-B2 Bb-B4 Bb-B1 B0-C2 B0-D1 C2 D1 Bb-E1 Bb-D1 Bb-C2 DC bipole (+/-400 kV) AC onsho e (380 kV) AC o sho e (145 kV) Cable O e head line FIGURE 4 Cig e DCS3 es MT-HVDC g id addi ion, o il e noises in he measu ed ou pu powe o he V–P d oop con olle , a low pass il e is usually added o he s uc u e. 3.1 Vi ual capaci o con ol Ine ia in an AC sys em is de ined as he sys em’s abili y o p e- en sudden e en s o equency. In gene al, Hsis de ined as he a io o s o ed kine ic ene gy (Ek) and he a ed powe (Sn), as p esen ed in (1): Hs=Ek Sn (1) Ine ia cons an can be de ined as (2)[18]: Hdc =Wk SVSC (2) whe e Wkis s o ed ene gy in capaci o s and SVSC is he a ed powe o VSC. Compa ed o synch onous gene a o s wi h he same capaci y, he Hdc is small. Howe e , his alue can be inc eased by inc easing he capaci ance o he DC link capaci o , bu his inc eases he cos and sho ci cui le el and educes he dynamic cha ac e is ics o he DC bus [19]. The dynamic esponse o a DC capaci o is de ined as (3): CDC VDC dVDC d =Pi−Po=ΔPDC (3) whe e Pois he ou pu powe and Piis he inpu powe . Due o he high speed and lexibili y o he VSC con olle , he addi- ional powe ΔP VSC , conside ing he ange o di ec ol age change, can be ob ained h ough he ac i e powe con ol. ΔP VSC =C i VDC SVSC dVdc d (4) Wi h he pa icipa ion o addi ional powe , he DC link capaci o dynamics change as ollows. CDC VDC dVDC d +C i VDC dVDC d =Pi(pu)−Po(pu)(5) Acco ding o (5), he addi ional powe ΔP VSC ob ained h ough powe con ol can p oduce a i ual capaci o . This capaci o p o ides mo e ine ia o suppo di ec ol age. In his s udy, addi ional powe is ob ained h ough he emaining powe o he sys em a e he powe -sha ing o aul . The ope a ion o he g id con olle s is such ha a e powe - sha ing o a he ime o he aul , he g id may be in a si ua ion whe e he powe e e ence o he con e e s is no a maximum powe . In his case, pa o he g id powe can be s o ed as addi ional powe . 3.2 M-D oop con olle A design cha ac e is ic o he modi ied d oop con olle is shown in (6), and (7) indica es he alue o he d oop coe icien o his new con olle . Pw=Pw, e −k1(VDC −VDC , e )+k cVDC (6) k c =k2 dVDC d (7) As shown in (6), i he di ec ol age emains cons an , he p oposed d oop con olle con e s o he con en ional d oop con olle , whe e Pwis he nominal alue o powe . P∗ w=Pw, e −k1(VDC , e −VDC )(8) Compa ing (6)wi h(8), Pw=P∗ w+k cVDC (9) Rega dless o he powe losses, i can be said ha he ou pu powe Pou is equal o he injec ed powe Pi. By conside ing he d oop con olle in he sys em, powe changes can be w i en as (10), whe e, Pcis he powe o he AZIZI ET AL.1893 con e e wi hou d oop con olle e ec . Pi=Pou =Pc−kw(Pw−Pw, e )(10) Subs i u ing (9)in o(10) yields: Pi=Pc−kw(P∗ w−Pw, e )−kWk cVDC (11) Acco ding o (3), (12) can be w i en as ollows: CDC VDC dVDC d =Pc−kw(P∗ w−Pw, e ) ⏟⎴⎴⎴⎴⎴⏟⎴⎴⎴⎴⎴⏟ Pin −kWk cVDC −Po (12) Po−Pin =CDC VDC dVDC d −kwk2VDC dVDC d (13) The e o e, he abo e equa ions show ha using powe changes, he d oop con olle can be designed in a way ha o be able o emula e he beha iou o he i ual capaci o . The e o e, he p oposed me hod does no equi e inc easing he alue o DC-link capaci o s. In addi ion, acco ding o (13), i can be said ha he capaci y o he i ual capaci o is equal o (14): C i =kwk2(14) 3.3 E ec s o delays The e a e always delays in MT-HVDC g ids [20]. Usually, in he s uc u e o a d oop con ol, a low pass il e is added o il e noises in he measu ed ou pu powe . Assuming his delay is i s -o de lags wi h a ime cons an Tdand a gain 1/kp has o be eplaced by 1/(1 +Td s) in he small-signal models. 4UNDERSTUDY NETWORK AND ITS MODELING In o de o in es iga e he p oposed con ol s a egy, he g id ha is shown in Figu e 4is selec ed. In his g id 5- e minal bipo- la MT-HVDC g id a e connec ed o ou AC a eas connec ed. The es g id is o med by wo onsho e AC sys ems, wo o - sho e AC sys ems, and i e VSC-HVDC con e e s. I is wo h no ing ha he ypical es g id (Cig e DCS3) has been selec ed only as a selec i e es case, and he p oposed scheme can be easily selec ed in o he VSC-based HVDC g ids. The main goal in he cu en pape is o imp o e he s a- bili y o he DC ol age and educe a ia ions o powe in he s a es o ansien s, and his s anda d g id is selec ed o app o e he pe o mance and app op ia eness o he p oposed con ol me hod. In his pape , ansmission lines a e modelled by he equency-dependen π(FD-π) sec ion modelling [21] ha consis s o mul iple cascaded πsec ions which a e ep esen ed by se ies RL ci cui s, and shun capaci o s C[4]. Eigen alue-based analysis o small signal dynamics in HVDC ansmission sys ems equi es cable models ha a e compa i- ble wi h he display o s a e space. While dis ibu ed pa am- e e models ha calcula e equency-dependen e ec s a e inhe en ly inconsis en wi h he display o s a e space, a yp- ical πmodel can only accu a ely show cable beha iou a a equency. Ins ead, a FD-πmodel, consis ing o a lumped ci cui ep esen a ion wi h mul iple pa allel RL-b anches in each π- sec ion can be u ilized o ep oduce he equency depen- dency o he cable cha ac e is ics in a speci ied equency ange. So, he numbe o sec ions and pa allel b anches a e consid- e ed as ollows: n=10, m=5. Mo eo e , he a ed powe o each con e e is 1000 MW and he a ed ol age is ±320 kV. I is also assumed ha he opology o he unde s udy sys em is a symme ical monopole opology. Acco ding o he esul s ob ained in [22], Ba-B1 has been selec ed as he app op ia e loca ion o M-d oop placemen . 5OPTIMIZATION APPROACH The pa ame e s o he M-d oop con olle mus be adjus ed o dec ease he objec i e unc ion (15). E o = n ∑ b=1(MVb)(15) whe e MVbis he maximum peak o di ec ol age oscilla ions om e e ence alue o n DC bus in aul ime is isible in (15). I should be no ed ha in his pape n=5. This equa ion con i m ha , wi hou any aul o mal unc- ion in he sys em, he E o unc ion will be ze o. In his pape , he pa icle swa m op imiza ion (PSO) algo i hm and gene ic algo i hm (GA) a e employed o de e mine he pa am- e e s o M-d oop based on (15). The op imum pa ame e s a e ob ained wi h 110 epe i ions ollowing ou scena ios include: ▪Case 1: Th ee-phase o g ound in Ba-A0 wi h a du a ion o 15 ms. ▪Case 2: Th ee-phase o g ound in Ba-B0 wi h a du a ion o 15 ms. ▪Case 3: Th ee-phase o g ound in Ba-A0 wi h a du a ion o 10 ms. Op imiza ion esul s o he M-d oop con olle ob ained by PSO and GA a e shown in Table 1. The p ocedu e o op imiza ion o pa ame e s in his pape is exp essed in he ollowing le els. Le el 1. The popula ion is se . 1894 AZIZI ET AL. TABLE 1 Op imiza ion esul s o M-d oop con olle ob ained by PSO algo i hms Pa ame e Op imal aluePSO Op imal alueGA Case 1 k11.9 1.83 k24.3 4.51 kw31.5 30.9 kp0.019 0.0188 Case 2 k11.85 1.9 k24.2 4.16 kw30.1 30.2 kp0.024 0.026 Case 3 k11.81 1.85 k24.4 4.31 kw30.8 31.05 kp0.027 0.023 Le el 2. A i s , a pa icle is selec ed and he alue o each pa ame e is calcula ed based on his pa icle. Then, he minimum and maximum limi s o each pa ame e a e checked, and inally, he E o c i e ion is calcula ed a his le el. Le el 3. A his le el, he posi ion (pa ame e ) o each pa i- cle compa es wi h i s p e ious alue, and he be e pa - icle is selec ed. Le el 4. The deg ee o adap i e agg ega ion and he e o- lu ion a e is calcula ed and he speed and posi ion da a o each pa icle is upda ed. Le el 5. In his le el, i he epe i ion o i i a ion o he desi ed i ness co esponds o he s op c i e ion, he c i- e ion s ops acco ding o he maximum numbe o ep- e i ions o i i a ion o he desi ed i ness. O he wise, i goes o he p e ious le el. Le el 6. O he wise, he designed pa ame e s a e e i ied as esul s. In PSO algo i hm, any pa icle has he si ua ion and he speed ha de e mined by Xand V. Then, he nex posi ion and eloc- i y o each pa icle du ing he op imiza ion p ocess is calcula ed acco ding o he cu en eloci y and posi ion and he desi ed indi idual posi ion acco ding o (16)and(17). Vi e +1 i=wV i e i+c1. 1.(Pbes i −Xi e i)+c2. 2.(Gbes −Xi e i) (16) Xi e +1 i=Xi e i+Vi e +1 i(17) whe e, he i h pa icle in he swa m is indica ed by i.i e , shows i e a ion. Ps e eals he bes posi ion o he i h pa icle. Gbes i indica es he bes gene al si ua ion among he swa m. w ep e- sen s he weigh o ine ia and 1and 2a e selec ed as andom numbe s be ween one and ze o. S a End Ini ialize popula ion Selec i s pa icle o popula ion i=1; Check he limi a ion o each pa ame e s Cons ain s iola ed? Calcula e objec i e unc ion (15) All pa icle e alua ed? Selec he bes pa icle wi h minimum objec i e unc ion PSO con e ge? Upda e he popula ion Remo e his pa icle No Yes No Selec a new pa icle se g=0, ω=0.9, c1=0.2, c2=0.2 e olu iona y s a es es ima ion (c1, c2) Run simula ion ile FIGURE 5 Adap i e pa ame e s con ol p ocess In his algo i hm, he upda ed linea ine ia weigh is di ec ly ela ed o he linea dec ease in ine ial weigh (LDW) wi h inc easing epe i ion ime. Howe e , he ela ionships be ween ine ia weigh and epe i ion ime a e no always he same o di e en op imiza ion p oblems. Figu e 5shows he lowcha o he PSO algo i hm o pa ame e s o he con olle . The pa ame e s calcula ed by bo h algo i hms a e almos iden ical, howe e , he PSO algo i hm eaches he inal answe in less ime. 6DYNAMIC PERFORMANCE ANALYSIS In his pa o he pape , he e ec o he p oposed me hod on sys em s abili y will be e alua ed. Gene ally, he linea ized model AZIZI ET AL.1895 Line (m) V I Δu dc(n) Δi dc(n) Δu in l(m) Δi in l(m) Δu dc(1) Line (1) Δu in l(1) Δiin l(1) Δidc(1) FIGURE 6 HVDC g id model in eg a ing line models Δi dc(1) Δi dc(2) Δi dc(n) Δu dc(1) Δu dc(2) Δu dc(n) ΔP *1 ΔP *2 ΔP *n DC G id model Con e e 1 Con e e 2 Con e e n FIGURE 7 Schema ic o a MIMO plan model o he DC ol age con ol in MT-HVDC g id o he sys em in he s a e space o m can be exp essed as (18) [23]. Δx=AΔx+BΔu(18) whe e Δuand Bdeno e he inpu ec o and inpu ma ix espec i ely, Δxand Adeno e he s a e ec o and he s a e space ma ix espec i ely. I is necessa y o men ion, he e, he a e age model o VSC is used o model he powe con e e s and he π-sec ion model is used o model he ansmission lines. The numbe o sec ions o each ansmission line in he π-sec ion model is assumed o be i e o achie e he app op ia e accu acy. I is also assumed ha he p oposed con olle is loca ed on he Cb-B2 bus. Figu e 6displays he cons uc ion o a DC ne wo k wi h ncon e e s and mlines. A schema ic o a plan model o he di ec ol age con ol in he MT-HVDC g id o s abili y in es iga ion in he MT-HVDC g id is shown in Figu e 7. This model can be used o s udies on a mul i-inpu -mul i- ou pu con ol ne wo k (MIMO), and o s udy he closed- loop sys em ollowing g id condi ions. As shown in Figu e 7, he inpu o he con olle s o all con e e s is powe . How- e e , o con e e s equipped wi h a d oop con ol sys em, powe e e ences in DC ol age con ol mode a e used as he manipula ed inpu . Powe changes o con e e s ha a e in ac i e powe con ol mode ac as a dis u bance in DC ol age con ol. Also, he “ e e ence” o powe o each wind a m is he mechanical powe aken by he u bine sys em. Figu e 8illus a es he a e age modelling o a VSC s a- ion. As shown in Figu e 8, he VSC s a ion is modelled as a + - + - PCC * P P * d i q Li * d e d 0 C C i d i sd, sq V s R s L R L sd, sq i d, q e + - d e s i eq u la i dc i a R a L eq C dc u 2 2 i p k ks + 1 1 s Ts+ 1 1 i p k ks + d, q d, q ω FIGURE 8 VSC-HVDC s a ion model including i s con ol s uc u e con olled ol age sou ce on he AC side and con olled cu en sou ce on he DC side behind a capaci o based on he powe balance p inciple commonly used o modula mul ile el con- e e s (MMCs) [24]. The VSC s a ion is ope a ed in a dq synch onous e e - ence ame. Since in he s i AC powe sys em, eac i e powe con ol and qaxis cu en ha e an insu icien e ec on he ac i e powe , meanwhile he q-axis o he ol age o PCC is gene ally kep on ze o by he phase-locked loop (PLL) [25]. Thus, he analy ical model o di ec ol age s abili y s udy ocuses on d-axis ela ed con olle s, because he pu pose o he analysis is no o deal wi h weak sys ems. The dynamics o he sys em linked o he d-axis cu en is shown as ollow: dΔis−d d =𝜔Δis−q+1 Ls Δ d−1 Ls Δ s−d−R Ls Δis−d(19) dΔid d =𝜔Δiq+1 LΔ ed−1 LΔ d−R LΔid(20) whe e Δis employed o he linea ized ope a ing poin , (Rs+jωLs) is he g id impedance, (R+jωL) is equi alen o he impedance o he ans o me and he impedance o he eac o a m, also, ωis he eloci y angula . The sys em dynam- ics o he d-axis il e bus ol age is exp essed as (21). In his pape , he q-axis PCC ol age is p ope ly con olled by he PLL, since, he assump ion is ha he VSC s a ion is connec ed o a s ong sys em. Consequen ly, he small-signal me hod o he in e ing powe o he VSC can be exp essed by way o (22): dΔ d d =𝜔Δ q+1 c Δid−1 c Δisd (21) P=Vdid+Vqiq→ΔP≈ doΔid+idoΔ d(22) The alue o equi alen con e e capaci o Ceq is adop ed o he o al ene gy s o ed in he MMC sub-modules. Laas equi alen a m induc ance is modeled in he DC side gi en by La m =(2/3)L o he a e age model o MMC. I is assumed ha he powe on he AC side is equal o he powe on he DC side in he PCC, he linea dynamic o DC-link capaci ance can 1896 AZIZI ET AL. be exp essed as: dΔueq d =Δila Ceq −Po Cequeqo ΔP+Po Cequeqo2Δueq (23) The subsc ip “o” shows he ope a ing poin . The DC ol age udc ha ac oss Ceq and Lais he ol age o be con olled ol age. To simpli y he sophis ica ed model, a e y small Cocapaci ance has been modeled o enable udc o become a s a e a iable. dΔila d =Δudc La −Δueq La −Ra La Δila Δudc d =− Δila −Δidc Co (24) The dynamic beha iou o he PI con olle s ela ed o he idand ac i e powe con ol is de ined in (25), while he s a e a iables o he in eg a o s a e he xPand xid. dΔxP d =−ki2(ΔP−ΔP∗) dΔxid d =−ki1(Δid−Δid ∗) (25) The e e ence o ican be indica ed in (26), based on he Equa ion (10) and he s uc u e o he ac i e powe con olle . Δid ∗=−kp2[( doΔid+idoΔ d)−ΔP∗]+Δxp(26) The VSC modula ion con ol is shown by a i s -o de ans- e unc ion wi h τas a ime cons an . To acili a e ma hema ical modeling, (27) is used, which causes he AC ol age ed o be con e ed in o a s a e a iable. The dynamics o he s a e a i- able shown in (27). 1 𝜏s[Δ d−𝜔LΔiq+kp1(Δid ∗−Δid)+Δxid ] −1 𝜏s Δed=dΔed d =1 𝜏s (Δed∗−Δed)(27) He e, he e e ence o ol age ∆ed*based on he cu en con- olle cons uc ion is delibe a ed. To achie e he inal space- s a e o mula i is necessa y o eplace ∆id*in (27)wi h(26). The equi alen s a e a iables a e desc ibed as shown in (28). The ma ices ela ed o ∆ dc(j) and ∆idc(j) a e mined o enable he in eg a ion o he VSC model and he HVDC g id model as i shown in (29): xj=[ΔedΔ dΔidΔisd Δxid ΔxpΔueq Δudc Δila] (28) xj=Ajxj+Bdj xdj+[BjG Bj][Δidc(j) ΔP∗ j] Δudc(j)=CjG xj(29) The dominan poles and ze os o he plan model VDC(s)/P*(s) o di ec ol age con ol a e shown in Figu e 9. Figu e 9demons a ions he poles and ze os diag am o he model o small-signal con ol wi h he p oposed con olle and con en ional con olle . As shown in Figu e 9, he unde s udy g id is s able no mally and en i e o ze os and dominan poles a e on he le side o he complex plane. Also, as shown by he di ec ion o he a ows in he igu e, he dominan poles o he sys em, ma ked in blue and co esponding o employing he M-d oop, a e a he away om he o igin coo dina es, indica ing ha he g id using M-d oop has mo e s abili y. Howe e , he p edominan ed poles associ- a ed wi h he con en ional d oop sys em ha e poles close o he o igin o he coo dina es. This igu e shows ha by employ- ing he M-D oop con olle , poles and ze os, mo e a he om he e ical axis. The e o e, i can be said ha he sys em wi h he M-d oop con olle is mo e s able han he sys em wi h a con en ional d oop con olle . Figu e 10 compa es he equency esponse o he sys em wi h he M-D oop con olle and wi h he con en ional con- olle . I is clea ha M-D oop gi es a highe phase ma gin and i is mo e lexible. The e o e, his esul con i ms ha he sys- em wi h he M-d oop con olle is mo e s able han he sys em wi h a con en ional d oop con olle . 7SIMULATION RESULTS In his sec ion, h ee di e en s a egies a e simula ed on he Cig é DCS3 g id o demons a e he ad an ages o he p oposed M-d oop s a egy including con en ional d oop con olle and M-d oop con olle . Th ee scena ios ha a e discussed below consis o educ- ing and inc easing he powe ou pu o he Cb-A1 bus a 3 s and a h ee-phase sho a he AC side o he Cb-A1 bus o 150 ms (3–3.15 s). In hese simula ions, he M-D oop con olle -40 -30 -20 -10 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2x 10 5 Real axis si x a y anigamI M-D oop D oop FIGURE 9 The dominan poles and ze oes o he open-loop TF VDC(s)/P*(s) AZIZI ET AL.1897 -600 -400 -200 0 )Bd (e du i ng aM 10-1 100101102103 -360 -180 0 180 360 540 720 F equency(Hz) )ged ( es ah P M-d oop M-d oop d oop d oop 180 1Hz-10Hz FIGURE 10 F equency esponse o he open-loop TF VDC(s)/P*(s) TABLE 2 Pa ame e s o VSC-HVDC link Pa ame e Value To al numbe o capaci o (N)1 DC capaci o (CDC)7mF Ra ed DC ol age o VSC (VDCo) 1 p.u. Ra ed equency ( o)50Hz Nominal powe 1200 KVA Nominal AC ol age 380 kV Nominal DC ol age 400 kV α1 Β0.03 Γ−0.945 Td(s) 1.1 ms is applied o he Cb-B1 bus con e e assuming he da a a e ol- lowing Table 2. The simula ion esul s o Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 buses a e e ealed. The VSC con olle o he Cb-B1 and Cb-B2 bus is a d oop con olle and he VSC con olle o Cb- C2 and Cb-D1 is a powe con olle . Figu e 11 shows he ou pu di ec ol age and powe o Cb- A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 ollowing he load educ- ion scena io a he Cb-A1. As shown in Figu e 11, by employing he p oposed me hod, he di ec ol age o buses is imp o ed, hey dec ease mo e slowly and he much la ge enhancemen in DC ol age nadi a e ob ained. Because a he momen o sys em change, h ough capaci ance imp o emen , he ene gy s o ed in he DC-link capaci o is used o main ain sys em s a- bili y. In addi ion, his ene gy in addi ion o no a ec ing he M-d oop con olle pe o mance in powe -sha ing will inc ease he o e all sys em s abili y. Ou pu DC ol age and DC powe o all busses include Cb- A1, Cb-B2, Cb-B1, Cb-C2, and Cb-D1 ollowing load inc eas- ing scena io a he Cb-A1 is shown in Figu e 12.Asshown 1.005 1.01 1.015 ) u.p( 1 A-bC -1000 0 1000 Cb-A1(MW) -500 0 500 Cb-B1(MW) 1 1.005 1.01 ) u . p (2 B -b C -800 -700 -600 Cb-B2(MW) 1.005 1.01 1.015 1.02 )u.p(2C -bC con en ion M-d oop 400 450 500 550 Cb-C2(MW) 3 4 5 1 1.02 1.04 Time(s) (a) )u.p(1D-bC 3 4 5 900 950 1000 Time(s) (b) Cb-D1(MW) 1.005 1.01 1.015 ) u.p(1B-bC FIGURE 11 (a) DC ol age and (b) powe o Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 ollowing 250 MW educing wind a m 2 gene a ion in Figu e 11, wi h he con en ional me hod, he di ec ol age o buses, will shock and has keen sha p peaks, om he ini ial alue o he inal alue. Because wi h he p oposed me hod, he ene gy s o ed in he DC-link capaci o is used o main ain sys- em s abili y wi hou any a ec ing he pe o mance o he d oop con olle . The simula ion esul s ollowing he p e ious scena io abou educing powe p oduc ion o he Cb-B2 bus a e shown in Figu e 13 and Figu e 14. The esul s o his bus also con i m ha he s abili y o di ec ol age o Cb-A1 and Cb-C2 can be imp o ed by using delay il e compa e M-D oop wi hou delay il e , due o lack o d op and a sudden inc ease in bus ol age. In addi ion, Figu e 14 shows ha using M-d oop, bus powe oscilla ions a e also educed and do no change ab up ly. How- e e , he sys em wi h i ual capaci o and delay il e simul a- neously has less oscilla ion and i s damping is mo e apid. Figu e 15 shows he di ec ol age o Cb-A1, Cb-B2, and Cb- B1 p o iles du ing a h ee-phase sho ci cui o he g ound a he AC side o he Cb-A1 bus o 150 ms (3–3.15 s). As shown in Figu e 15, wi h he M-d oop me hod, he di ec ol age and powe o buses ha e smalle oscilla ion han wi h con en ional d oop and each s abili y as . Because wi h he p oposed me hod, he ene gy s o ed in he DC-link capaci o is used o main ain sys em s abili y wi hou any a ec ing he pe o mance o he d oop con olle . 1898 AZIZI ET AL. 1.01 1.015 1.02 ) u .p(1A-bC -700 -600 -500 -400 -300 Cb-A1(MW) 1.01 1.015 1.02 )u.p(1 B -bC -500 0 500 Cb-B1(MW) 1 1.005 1.01 1.015 ) u .p( 2 B- b C -800 -750 -700 -650 Cb-B2(MW) 1.01 1.015 1.02 )u.p(2C-bC 300 400 500 600 Cb-C2(MW) 3 4 5 1.01 1.015 1.02 1.025 Time(s) (a) ) u .p ( 1D- b C 3 4 5 900 950 1000 Time(s) (b) Cb-D1(MW) M-d oop con en ional FIGURE 12 (a) DC ol age and (b) powe o Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 ollowing 250 MW inc easing wind a m 2 gene a ion 1.01 1.012 1.014 1.016 1.018 )u.p(1A-bC 2.5 33.5 44.5 5 -700 -600 -500 -400 Time(s) )u.p ( 1A-b C wi h delay w/o delay FIGURE 13 DC ol age and powe o Cb-A1 ollowing 250 MW educing wind a m 2 gene a ion In addi ion, he equency o he AC side o Cb-A1 bus is shown in Figu e 16. This igu e shows he equency p o iles du ing a h ee phase sho ci cui o he g ound a he AC side o Cb-A1 bus o 150 ms (3–3.15 s). As shown in Figu e 16, wi h he M-d oop me hod, he equency oscilla ions can be e damp han wi h con en ional d oop and each s abili y as . 1.01 1.015 1.02 1.025 )u. p (2 C - b C 2.5 33.5 44.5 5 350 400 450 500 550 Time(s) )WM(2C-bC wi h delay w /o delay FIGURE 14 DC ol age and powe o Cb-C2 ollowing 250 MW inc easing wind a m 2 gene a ion 0.995 1 1.005 1.01 1.015 1.02 1.025 ).u.p ( 1B-bC -400 -200 0 200 400 600 Cb-B1(MW) 3 4 5 0.995 1 1.005 1.01 Time(s) (a) ).u.p(2B-bC 3 4 5 -800 -700 -600 -500 -400 Time(s) (b) Cb-B1(MW) M-d oop con en ional FIGURE 15 (a) DC ol age and (b) powe o Cb-B1 and Cb-B2 ollowing a h ee-phase sho ci cui o he g ound 8 CONCLUSIONS One o he main con es s in con ol o HVDC g ids is di ec ol age egula ion. This pape p oposed a new con ol s uc- u e o he d oop con olle called he M-d oop con olle ,