Recei ed: 13 Feb ua y 2021 Re ised: 2 July 2021 Accep ed: 20 Augus 2021 IET Gene a ion, T ansmission & Dis ibu ion
DOI: 10.1049/g d2.12295
ORIGINAL RESEARCH PAPER
HVDC g ids s abili y imp o emen by di ec cu en powe sys em
s abilize
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, Pos al Code 6714414971,
I an.
Email: [email p o ec ed].i
Abs ac
High- ol age di ec cu en b eake is among he essen ial componen s o high- ol age
di ec cu en g ids. Such a b eake gene ally needs a di ec cu en eac o o educe he
aul cu en s a e. Howe e , di ec cu en eac o s ha e des uc i e e ec s on he mul i-
e minal high- ol age di ec cu en g id dynamic s abili y, and in such a sys em, despi e
he a ie y o con olle s, he sys em dynamics a e highly sensi i e o he ope a ing poin .
The e o e, addi ional damping con ol will be needed. This pape p oposes a modi ica ion
o be applied o he adi ional d oop con olle o high- ol age di ec cu en g ids o cope
wi h he in luence o hese la ge eac o s, imp o ing he di ec ol age s abili y and dec eas-
ing powe a ia ions in he ansien e en s by in oducing a di ec cu en powe sys em
s abilize . The p oposed me hod o di ec ol age con ol has been in es iga ed h ough
he analy ical model o he sys em. S abili y imp o emen has been s udied ollowing he
applica ion o he p oposed me hod by in es iga ing ze os, poles, and equency esponse
analysis. Mo eo e , a me hod is p oposed o op imal design and op imal placemen o
di ec cu en powe sys em s abilize . The sys em analysis and ime-domain simula ions
demons a e a decen damping imp o emen a ained by he p oposed me hod. All simu-
la ions and analy ical s udies a e conduc ed on Cig é DCS3 es high- ol age di ec cu en
g id in MATLAB/Simulink.
1 INTRODUCTION
The in eg a ion o enewable gene a ions and he elec i ica-
ion o oil and gas pla o ms, as well as he inco po a ion o
di e en elec ici y ma ke s, has esul ed in a eques o new
ansmission sys em solu ions [1]. Ye , high- ol age di ec cu -
en (HVDC) ansmission echnology is used mainly o poin -
o-poin ansmission wi h a sending powe con e e s a ion
and a ecei ing powe con e e s a ion [2,3]. In ecen yea s,
mul i- e minal high- ol age di ec cu en (MT-HVDC) ans-
mission sys ems ha e been p oposed p ima ily o use in o -
sho e wind a ms along wi h he classical sys em [4]. I is iden-
i ied ha he ansien s abili y o such a g id is o se ious con-
ce n unde la ge dis u bances [5] and addi ional con ol ( o p o-
ide adequa e damping o HVDC g ids) would be necessa y [5]
and ol age egula ion has a c ucial ole in he con ol o MT-
HVDC g ids [2].
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s use, dis ibu ion and ep oduc ion in any medium, p o ided he o iginal wo k is
p ope ly ci ed.
© 2021 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
Di e en s a egies ha e been p oposed o con ol and
imp o e he s abili y o HVDC ne wo ks [6]. These s a egies
can be ca ego ized in o wo ypes o con en ional con ol
me hods and ad anced in elligen con ol me hods. In addi-
ion, in e ms o s abili y oscilla ion, hey can be classi ied
in o se e al ca ego ies o powe / equency oscilla ions, sub-
synch onous oscilla ions, and di ec cu en (DC) oscilla ions
[7–10]. Ma hema ical modelling and AC/DC in e ac ion anal-
ysis o HVDC sys ems a e s udied in [11]. The model o a
ol age sou ce con e e -based HVDC (VSC-HVDC) sys em
is ex ac ed in [12], and DC ol age con ol and powe -sha ing
in an HVDC sys em based on d oop con ol a e p oposed in
[13]. The e ec o DC b eake s on he s abili y o he HVDC
sys em is in es iga ed in [14], bu he sys em unde s udy is
VSC based, also he e ec o he p oposed s abilize on he
pe o mance o he d oop con olle is no in es iga ed. Also,
he modelling o o e head ansmission lines and cables in [14]
492 wileyonlinelib a y.com/ie -g d IET Gene . T ansm. Dis ib. 2022;16:492–502.
AZIZI ET AL.493
is based on he π-sec ion model, which is less accu a e han
modelling based on he model equency-dependen model
(FD-π) model [15,16]. Howe e , add essing he p oblem o
oscilla ions in HVDC sys em needs mo e e o ye [14]and
none o hem has in es iga ed a combina ion o d oop con ol
and powe sys em s abilize (PSS) applied o he DC side o
modula mul i-le el con e e s—based HVDC (MMC-HVDC)
s a ions. The p oposed supplemen a y con olle in [17] applied
o he DC side o he VSC con e e and i s pa ame e s uned
by pa icle swa m op imiza ion (PSO) algo i hm conside ing
VSC-HVDC and πline modelling. In [17], he VSC a e age
model is used o con e e modelling and he π-sec ion model
is used o he line modelling.
The main e o o con ol o DC ol age is o elimina e he
imbalance o powe in ansien condi ions and keep he ol -
age le el wi hin an accep able limi . The e o e, his pape p o-
poses an e ec i e DC- ol age damping con olle as di ec cu -
en powe sys em s abilize (DC-PSS) o imp o e he o e all
sys em di ec ol age/powe s abili y in he p esence o la ge
eac o s. This con olle will ha e signi ican impac s on he g id
s able ope a ion unde g id dis u bances and leads o damping
o low- equency luc ua ions. Also, o in es iga e he e iciency
o he p oposed me hod alongside he o he con olle s, se e al
d oop con olle s a e used in he unde s udy sys em. By u iliz-
ing he p oposed con olle , luc ua ions o ol age and powe
in HVDC g ids a e supp essed. I occu s by injec ing damp-
ing signals in o he d oop con olle loop o he selec ed powe
con e e s a ions in case o ansien e en s. Besides, o achie e
he p ope pe o mance o he DC-PSS, all pa ame e s o DC-
PSS a e op imally uned a he same ime by a mixed-in ege
non-linea op imiza ion p og amming and sol ed by adap i e
pa icle swa m op imiza ion (APSO), which has highe accu-
acy and speed han he usual PSO algo i hm. Besides hese,
he pa icipa ion ac o (PF) me hod is used o selec he mos
app op ia e loca ion o he DC-PSS ins alla ion. Finally, he
e ec s o DC-PSS a e s udied in small-signal modelling and
equency esponse analysis. The main di e ences be ween his
a icle and [17] a e lis ed as ollows. The main pu pose o [17]
is o in oduce a me hod o op imal loca ion o he s abilize
in a VSC-based g id, which used π-model o ansmission line
modelling. Bu he e, he FD-πmodel will be used o ans-
mission line modelling. The au ho s in [17] ha e p oposed a
me hod o imp o e ol age oscilla ions ha is ins alled on he
DC side o he VSC-HVDC, howe e he e DC-PSS will be used
on he DC side o he MMC-HVDC. The p oposed con olle
is compa ed wi h he con olle based on con en ional PI and
d oop, and he esul s o his compa ison a e discussed in de ail.
The PSO algo i hm is used in [17] o op imize he pa ame-
e s, bu he e, he APSO algo i hm is employed o op imize he
pa ame e s.
The main con ibu ions o he cu en s udy a e as ollows:
∙in oducing an e ec i e di ec ol age damping con olle as
DC-PSS applied o he DC side o MMC-HVDC s a ions, o
deal wi h nega i e e ec s o la ge DC eac o s on di ec ol -
age and powe and imp o e he o e all MT-HVDC sys em
di ec ol age/powe s abili y;
FIGURE 1 S uc u e o V-P d oop con olle o an HVDC s a ion
FIGURE 2 The gene al s uc u e o DC-PSS
∙employing di ec ol age/powe s abili y alongside he d oop
con olle o make p ope powe -sha ing while imp o ing
s abili y;
∙ uning o he pa ame e s o DC-PSS by he APSO algo i hm
o elimina e di ec ol age luc ua ions conside ing MMC-
HVDC and FD-πline modelling;
∙selec ing he app op ia e loca ion o he ins alla ion o DC-
PSS.
The emaining sec ions o he pape a e o ganized as ollows.
In Sec ion 2, he p oposed con ol s a egy is p esen ed and
analysed. Sec ion 3discusses he op imiza ion app oach. Small-
signal s abili y analysis is in es iga ed in Sec ion 4. Simula ion
esul s a e epo ed in Sec ion 5.
2PROPOSED CONTROL STRATEGY
Because o he lack o ine ia, he low- equency oscilla o y
modes o HVDC g ids a e less damped ou han hose in AC
powe sys ems. This pape p oposes a me hod, ha du ing
he ansien condi ions, DC ol ages o he HVDC g id will
be con olled by p o iding ansien damping. In his me hod,
V-P d oop con ol is equipped wi h a supplemen a y signal
o imp o e he s abili y o he HVDC g id which is supplied
h ough DC-PSS. As in he AC powe sys em, he PSS imp o es
he dynamic pe o mance o he powe sys em by adding auxil-
ia y signals o he exci a ion sys em [5], a DC-PSS as a damping
con olle in DC sys em, ope a es analogous o a PSS in an AC
sys em and by injec ing an addi ional signal, imp o es he s a-
bili y o he HVDC g id. A gene al con ol s uc u e o such
a con olle is p esen ed in Figu e 1The s uc u e o he p o-
posed DC-PSS is shown in Figu e 2In his s uc u e, he locally
measu ed ol age is used as he inpu ha indica es he powe
balance index in he HVDC g id. This s abilize p oduces an
494 AZIZI ET AL.
auxilia y damping signal in he ou pu ha is p opo ional o
he inpu signal. Con en ional PSS, as a lead-lag compensa o is
mainly designed based on using a linea model and conside ing
one ope a ing poin [5].
As Figu e 2shows, DC-PSS consis s o ou blocks: a
lead compensa o block (wi h T1>T2) o imp o e he speed
esponse and educe he ansien oscilla ion peak, a lag block
(wi h T3<T4) o imp o e s eady-s a e esponse, a gain block
o de e mine he amoun o damping c ea ed by DC-PSS, and a
washou block. The gain alue kDC-PSS de e mines he amoun
o damping c ea ed by DC-PSS. Ideally, he in e es a e is
adjus ed o a alue co esponding o he maximum damping,
howe e , i s alue is usually limi ed by o he conside a ions.
The washou il e block ac s as a high-pass il e wi h a ime
cons an TW ha allows signals co esponding o ol age luc-
ua ions o pass unchanged. The wash il e only allows di ec
ol age luc ua ions o be ansmi ed and il e he s eady-s a e
o se in he ou pu , wi hou allowing he damping con olle o
eac o a dynamic exceeding a ce ain equency h eshold. The
p oposed s abilize on he ac i e powe loop is ed by ol age
de ia ions (ΔV). As is usually he PSS inpu signal in gene a o
sys ems is speed de ia ion, he measu ed local DC ol age in
he DC sys em, is he DC-PSS inpu . As a esul , i s ou pu is
p opo ional o he powe oscilla ions. In he s eady-s a e con-
di ions, an onsho e HVDC s a ion equipped wi h he DC-PSS
beha es simila ly o a con en ional con e e wi h ac i e powe
con ol mode.
3OPTIMIZATION APPROACH
3.1 Objec i e unc ion
Pa ame e s o he p oposed s abilize a e op imally uned a he
same ime by he APSO algo i hm. The objec i e unc ion (1)
de ines he EDC pa ame e as an e o c i e ion [18]. This objec-
i e unc ion calcula es he a ea unde he ol age cu e ollow-
ing oscilla ions and mus be minimized. As shown by (1), ac u-
ally his objec i e unc ion calcula es he e o c i e ion o he
sum o he buses om 1 o n. I means ha EDC o each DC
bus is he egion in he plane ha is bounded by he g aph o
DC ol age and p opo ional o oscilla ions o di ec ol age.
The e o e, by minimizing EDC he oscilla ions can be educed.
In (1), he main eason o include ( ime) as he s udy ime limi ,
in he in eg a ion c i e ion is ha he aul se e i y is conside ed
in he pa ame e op imiza ion and he pa ame e s can be op i-
mized in such a way ha he e ec o DC-PSS o be g ea e in
he ini ial momen s o aul . In his equa ion, n ep esen s he
numbe o busses. Acco dingly, he goal he e is o minimize he
EDC pa ame e as de ined in he ollowing:
EDC =
n
∑
b=1(
∫
0
|||ΔV( )DC (b)( )|||d ).(1)
The ad an age o his objec i e unc ion is ha minimal
dynamic in o ma ion is equi ed o calcula e EDC, and i is
only necessa y o measu e he ol age de ia ion pe bus ins ead
o iden i ying he model pa ame e s equi ed o he DC-PSS
design. Howe e , he p oblem o op imiza ion o he pa ame-
e s equi es special cons ain s ha a e all ela ed o he limi s
o each o he alues and should be aken in o accoun . The
objec i e unc ion, (1), should be minimized conside ing he
maximum and minimum o each pa ame e . The de ini ion o
he objec i e unc ion in his way indica es ha i he e is no
e o o pe u ba ion in he sys em, he alue o his unc ion is
ze o.
3.2 APSO algo i hm
An APSO algo i hm is used o sol e he op imiza ion p ob-
lem. The APSO algo i hm has many ad an ages o e he classic
PSO algo i hm. These ad an ages include a global sea ch ac oss
he sea ch space a a highe con e gence a e [10]. I s de ails
and he solu ion me hodology a e p esen ed and discussed
in [10].
Since upda ing he speed and posi ion o each pa icle is
de e mined based on he objec i e unc ion, i is e y impo -
an o selec he app op ia e objec i e unc ion. The p ocess o
op imizing he pa ame e s he e is summa ized in he ollowing
s eps.
S ep 1. The popula ion is ini ialized. A he cu en posi ion,
he mean dis ance o each pa icle o all he o he pa icles is
calcula ed. The globally bes pa icle is de ined as dg. All di’s
a e compa ed and de e mine he maximum and minimum dis-
ances dmax and dmin. Then, an ‘e olu iona y ac o ’ is calcu-
la ed. Finally, is classi ied in o one o he se e al se s. Also, in
each subpopula ion, a speci ic se o mo ion coe icien s (c1,c
2)
a e used, which o each subpopula ion change adap i ely du -
ing op imiza ion. Finally, he mos op imal solu ion ha is p o-
duced is conside ed. Se e al pa icles a e selec ed as a popula-
ion using a andom p obabili y dis ibu ion unc ion in a space
wi h dimensions co esponding o he numbe o pa ame e s.
The weigh ing o ine ia coe icien o he algo i hm is adjus ed
p opo ionally o he numbe o i e a ions o he algo i hm o
esul in an adap i e algo i hm and ind be e answe s. In addi-
ion, he p ope ies o o he algo i hms such as gene ic algo-
i hms (GAs) a e also used in he algo i hm o ob ain he modi-
ied algo i hm. The balance be ween he global and local sea ch
capabili ies in he PSO algo i hm is shown by ine ia weigh ω,
ha i can be la ge in explo a ion mode and small in exploi a-
ion. Howe e , educing ωo e ime is no necessa ily co ec .
The e o e, (2) can be de ined in such a way ha he alue o
ω( ), acco ding o he ampli ude o changes , ela i ely la ge in
he explo a ion mode and ela i ely small in he con e gence
mode [10].
𝜔( )=1
1+1.5e−2.6 ,∀ ∈[0,1].(2)
Consequen ly, ωadap s o he sea ch en i onmen cha ac e ized
by . This means ha in explo a ion mode, la ge and ωa e
in a ou o global sea ch, and when is small, an exploi a ion
AZIZI ET AL.495
FIGURE 3 Adap i e pa ame e s con ol p ocess
o con e gence mode is de ec ed, and hence, ωis educed o
educe local sea ch.
Figu e 3shows he p ocess o adap i e pa ame e con ol o
s ep 1. The ini ial ωis 0.9. To pull each pa icle o he bes posi-
ion, he c1pa ame e is conside ed, and o push he no ms o
he as e con e gence o he egion, he c2pa ame e is consid-
e ed. Also, gis in he bes posi ion in he neighbou hood. I is
assumed ha he ini ial o bo h o hese alues is 0.2.
S ep 2. In his s ep, a e andomly selec ing a pa icle and
calcula ing he alue o each pa ame e , he minimum and max-
imum limi s o each pa ame e a e checked, and hen he EDC
c i e ion is calcula ed.
FIGURE 4 MMC model including i s con ol s uc u e
S ep 3. The posi ion (pa ame e ) o each pa icle compa es
wi h i s p e ious alue and he be e pa icle is selec ed.
S ep 4. The e olu ion a e and he deg ee o adap i e agg e-
ga ion a e calcula ed and he speed and posi ion in o ma ion o
each pa icle is upda ed.
S ep 5. The c i e ion s ops acco ding o he maximum num-
be o epe i ions o i i a ion o desi ed i ness, i he desi ed
epe i ion ime o i ness does no co espond o he s op c i e-
ion, goes o he p e ious s ep, o he wise, he calcula ed pa am-
e e s a e eco ded as esul s.
4STABILITY ANALYSIS OF HVDC
GRID WITH DC-PSS
4.1 MMC modelling
Figu e 4illus a es he a m swi ching unc ion model o a modu-
la mul i-le el con e e (MMC), o u ilize he s a e-space model
o MMC. This model has he mos applica ions in e ms o accu-
acy and eloci y o calcula ions and i is an app op ia e model
o ansien analysis [19]. Howe e , he de ailed IGBT-based
model o MMC, due o i s e y low compu a ional speed and
high accu acy is used only o in es iga e and es ima e losses.
Also, he a e aged alue model (AVM) MMC model is no used
in ansien DC s udies, since i has an inco ec esponse o
DC side aul s [19]. In his ype o modelling, conside ing he
concep o a hal -b idge con e e swi ching pe o mance, each
MMC a m can be assumed a e age. The dynamics o such a sys-
em can be shown as ollows.
4.1.1 In e nal a iables modelling o MMC
a iables
The MMC con ol sys em shown in Figu e 4consis s o wo PI
con ol loops ha a e modelled by only he sum o he ene gies
and he ze o-sequence ci cula ion cu en as o he in e nal
a iables o he MMC. The agg ega e ene gy is con olled by
a PI con olle in an ex e nal con ol loop. This con olle
496 AZIZI ET AL.
p o ides ze o-sequence ci cula ing cu en e e ence as shown
in (3), whe e, kpw,Σ and kiw,Σ a e he gains o PI con olle .
i∗
c,z=kpw,Σ (w∗
Σ−wΣ)+kiw,ΣkΣ,
d
d kΣ=w∗
Σ−wΣ.
(3)
The in e nal loop PI con olle , con ols he in e nal ci cu-
la ing cu en o he ze o sequence, o o m a co esponding
e e ence ol age alue ∗
c,zin (4). The k dc as he coe icien o
pe o mance o he eed o wa d loop has a numbe be ween
ze o and one, i he con olle has a eed o wa d loop, he alue
o k dc is one and o he wise i is ze o.
∗
c,z=−kpc,z(i∗
c,Σ −ic,z)−kic,z𝜉z+k dc DC ,
d
d 𝜉z=i∗
c,z−ic,z.
(4)
4.1.2 AC side elec ical modelling
The cu en con olle loops and phase-locked loop (PLL), el-
e an o he AC side o he MMC con e e , can be modelled
like he AC side modelling o VSC con e e s [19]. In he ol-
lowing equa ions, ic is he con e e side cu en , iois he g id
side cu en , and ois equi alen capaci o ol age.
d
d ic =−⎛⎜⎜⎜⎝
( a
2+ )𝜔b
La
2+L
+j𝜔g𝜔b⎞⎟⎟⎟⎠
ic +A c −A o,(5)
A=𝜔b
La
2+L
,(6)
d
d o=−j𝜔g𝜔b o+𝜔b
C
ic −𝜔b
C
io,(7)
d
d io=−(j𝜔g𝜔b+ g𝜔b
Lg)io−𝜔b
C
g+𝜔b
C
o,(8)
whe e, 𝜔gis he pe -uni g id equency and La, a,L , ,lg,
g,C a e he esis ances, capaci ance, and induc ances o he
sys em. The AC side cu en s o he con e e a e con olled by
decoupled PI con olle s co esponding o he d and qaxes. The
equa ions o hese con olle s a e de ined by (9–12).
k
o− ∗
AD +kpc (i∗
c −ic )+kic𝛾+jL 𝜔PLL ic ,(9)
d
d 𝛾=i∗
c −ic ,(10)
∗
AD =kAD ( o−𝜑
),(11)
FIGURE 5 PLL linea model
d
d 𝜑=𝜔
AD ( o−𝜑
).(12)
The k as he coe icien o pe o mance o he eed o wa d
loop has a numbe be ween ze o and one, i he con olle has a
eed o wa d loop o o, he alue o k is one and o he wise i
is ze o. Also, ∗
AD is used o elimina e LC oscilla ion. In (8), φis
he s a e o a il e .
4.1.3 PLL s uc u e
Figu e 5exposes he con igu a ion o PLL, which consis s o a
PI con olle . The linea equa ions o PLL a e desc ibed in (13)
and (14).
d
d 𝜃PLL =kp,PLL o,q+xPLL ,(13)
d
d xPLL = o,q.(14)
4.1.4 DC side elec ical modelling
S a e a iables o DC side elec ical modelling a e shown by he
nex equa ions.
d
d DC =𝜔b
Cdc (idc,s−4icz ),(15)
d
d DC , =𝜔
dc, ( DC − DC , ),(16)
whe e he c osso e equency o he low-pass il e is shown
by 𝜔dc . The con ol sys em is such ha he AC powe de ined
by (17)and(18) passes h ough he low-pass il e be o e being
used in he powe con ol loop as shown in (15)and(16).
Pac = o,dic ,d+ o,qic ,q,(17)
d
d Pac,m=𝜔
pac (Pac +Pac,m).(18)
The e e ence cu en i∗
c ,dis de ined by PI con olle o powe
and a DC ol age d oop de e mines he AC powe e e ence as
i is exp essed in (19)and(20).
i∗
c ,d=kpp,ac (P∗
ac −Pac,m)+kip,ac 𝜌, d
d 𝜌=P∗
ac −Pac,m,(19)

AZIZI ET AL.497
FIGURE 6 FD-πmodel o lines
P∗
ac =kd oop ( ∗
DC − DC , )+P e
ac .(20)
Acco ding o he abo e equa ions, he ma ix o s a e a iables
is exp essed in (21) and he inpu ma ix is exp essed in (22).
xj=[ od oq ic ,dic ,q𝛾d𝛾qio,dio,q𝜑d𝜑q DC
PLL ,d PLL,q DC , 𝜌pac,mic,zkΣ𝜉zwz]T,(21)
uj=[ e
DC P e
ac i∗
c ,q||| g|||idc,sw∗
Σ]T
.(22)
The equi alen s a e a iables a e desc ibed as shown in (21).
The ma ices ela ed o ∆ DC(j) and ∆idc(j) a e mined o enable
he in eg a ion o he MMC model and he HVDC g id model
[3]asisshownin(23)and(24).
xj=Ajxj+Bdjxdj+[BjG Bj][Δidc(j)
ΔP∗
j],(23)
Δ DC (j)=CjG xj.(24)
4.2 DC ne wo k model
The con en ional π-sec ion model o a line accu a ely shows
he cable beha iou only a a single poin o he equency
domain.
Ins ead, he equency-dependen πmodel can be used o
modelling he beha iou o cables in a speci ic equency ange.
The FD- πmodel consis s o a lumped ci cui wi h pa allel R-L
b anches in each sec ion o he πmodel o he line. The accu-
acy and alidi y o he FD- πmodel a e de e mined by he
numbe o sec ions o he πmodel and he numbe o pa allel
b anches in each sec ion. In he π-sec ion model, he numbe
o sec ions imp o es hype bolic ac o s, bu does no necessa -
ily lead o a good app oxima ion o he ac ual beha iou o he
cable because i does no allow he equency dependence o
he dis ibu ed pa ame e s o be conside ed [15]. In o de o he
modelling o line based on FD-π, i s ly he line is di ided in o n
sec ions. The numbe o sec ions is de e mined by he leng h o
he line and he equency ange o be in e es ed. Then he num-
be o pa allel lines is conside ed and speci ied. Figu e 6shows
he line model based on FD-π[16]. The numbe o he pa allel
b anch is showed by m. Then, he s a e-space model o he j h
FIGURE 7 Closed-loop model o a ypical HVDC g id wi h he
p oposed supplemen a y s abilize
line and he ela ed DC b eaking eac o s:
[x]=[Aline
j][x]+[Bline
j][u],(25)
y=[cline
j][x],(26)
whe e he inpu is DC ol ages a he wo ends and he ou pu
is DC cu en s ou o hem as ou pu :
[x]=[V1V2…Vniin il1…il(n)io]T,(27)
[Y]=[iin iou ]T,[u]=[Vin Vou ]T.(28)
Fo an HVDC g id, he models o DC line (25)and(26)canbe
uni ied o make he s a e-space model o he gene al DC g id
wi h m sepa a e line [14]. To ob ain a p ope inpu ec o o
he line model, V is employed o con e he ec o o he
DC ol ages o MMC e minal and o ob aining a di ec cu -
en om he line model ou pu s, and I is employed o a ain
he di ec cu en ec o o he con e e om he line model
ou pu s, as exposed in (29)and(30)[3].
[VDC (1)⋯VDc(n)]T
=V−1
[Vline(1)
in Vline(1)
ou ⋯Vline(m)
in Vline(m)
ou ]T
,
(29)
[idc(1)⋯idc(n)]T=I−1
[iline(1)
in iline(1)
ou ⋯iline(m)
in iline(m)
ou ]T
.
(30)
4.3 D oop con olle and DC-PSS modelling
Figu e 7shows a closed-loop model o a ypical HVDC g id
wi h a p oposed supplemen a y s abilize . As is shown in Fig-
u e 7 o modelling a d oop con olle and supplemen a y s a-
bilize in con e e s equipped wi h his ype o con olle , i is
su icien o w i e he e e ence powe acco ding o he d oop
gain and in e ms o DC ol age.
498 AZIZI ET AL.
FIGURE 8 Cig é DCS3 es HVDC g ids
4.4 MMC modelling alongside DC ne wo k
modelling
DC g id s a e-space model conside ing he MIMO plan model
o he g id exp essed as:
xG=AGxG+BGΔVDC Δidc =CGxG.(31)
By combing he in es iga i e models o MMCs o all e minals
and he HVDC ne wo k model, he s a e-space model can be
shown in (31)[3]. Whe e xjis he s a e a iable o he j h con-
e e , BGj is he j h column o BG,andCGj is he j h ow o CG,
nis he en i e numbe o he powe con e e s, nGis he numbe
o s a e a iables o xG.
5SIMULATION RESULTS
5.1 Ne wo k unde s udy and i s modelling
Cig é DCS3 es HVDC g id is selec ed o he in es iga ion
o he p oposed con ol s a egy [20]. I should be men ioned
ha he s anda d es ne wo k (Cig e DCS3) is only op ed as
an illus a i e es case and he p oposed s a egy can also be
easily applied o any o he selec ed VSC-based HVDC g ids.
The main goal is o imp o e he di ec ol age s abili y and
dec easing powe a ia ions in he e en s o ansien s and his
s anda d g id is selec ed o con i m he pe o mance and eli-
gibili ies o ou p oposed con ol s a egy. The a ed powe
and ol age o each con e e a e 1000 MW and ±320 kV.
Mo eo e , i is also assumed ha he sys em has a symme i-
cal monopole opology. I should be no ed ha , in line mod-
elling, he numbe o sec ions o each line and he numbe o
pa allel b anches de e mine he modelling accu acy o each
speci ic equency ange. So, he e, i is assuming ha num-
be o sec ions o model a DC line is n=10 and he num-
be o he pa allel b anch o each sec ion is m=5[15]. See
Figu e 8illus a es he Cig é DCS3 es HVDC g ids.
In his s udy, he ansmission lines a e modelled by FD-π
model [15].
FIGURE 9 The singula alue plo o he closed-loop models wi h all he
DC ol ages and P1*(kd oop1 =0.3; Cb-B2: kd oop2 =0.42)
5.2 Op imal placemen o DC-PSS
The PF analysis is used o selec he p ope loca ion o he DC-
PSS ins alla ion [20].
This me hod can also be applied o iden i y he sui able place-
men o d oop con ol. The singula alue echnique is he
co esponding equency esponse in he sys em wi h mul i-
a iable con ol sys ems and o e s pe cep i e e idence abou
gains among a ious ou pu and inpu [21]. Mo eo e , he
me hod o op imal placemen is wo king o measu e he gain
among he e e ence o powe ela ed o a speci ic MMC e -
minal and di ec ol ages o all he e minals. A plo o singula
alue displays he gains amongs he ou pu and ha o he inpu
ec o in he equency domain [21]. The sui able e minal o
he ins alla ion o DC-PSS is a e minal wi h la ge single alues
in he speci ied equency ange. Figu e 9shows he plo o he
singula alues o he powe se -poin o he selec ed e minals
and ou pu ol age ec o o he closed-loop model wi h da a
om [22].
PF me hod in es iga ion has been accep ed o he selec ed
op imal placemen o PSS in each mul i-machine sys em [23].
Among he i e e minals o he sys em, wo e minals
equipped wi h he d oop con olle we e selec ed as a candi-
da e o DC-PSS ins alla ion. Table 1shows he calcula ed PFs
equi alen o he low- equency poo ly damped modes o he
wo e minals wi h d oop con olle , conce ning he ol age o
he s a ion. Cb-B1 is selec ed as he an icipa ed powe con e e
s a ion o he ins alla ion o DC-PSS, due o i s signi ican pa -
icipa ion in he mos poo ly damped mode. Co esponding o
his me hod, he desi ed powe con e e s a ion o he ins al-
la ion o DC-PSS is Cb-B1.
AZIZI ET AL.499
TABLE 1 Pa icipa ion ac o s o he wo selec ed e minals
F equency (Hz) Eigen alue Cb-B1 Cb-B2
1.96 −12.3 ±0.0132i 0.5679 0.3125
2.16 −13.4 ±0.0131i 0.9679 0.2102
30.7 −17.9 ±30.1i 0.3215 0.2618
35.9 −17.9 ±30.1i 0.2112 0.1894
TABLE 2 Op imal pa ame e s o DC-PSS ound by APSO
Pa ame e Minimum Op imal alue Maximum
KDC 100 123.1 150
T10.01 0.0211 0.1
T20.01 0.01 0.1
T30.01 0.0012 0.1
T40.01 0.01 0.1
5.3 Op imiza ion pa ame e s o DC-PSS
APSO algo i hm is used o op imize DC-PSS pa ame e s in
HVD g id. The pa ame e s T1,T2,T3,T4,andkDC-PSS a e op i-
mized by conside ing he g id s abili y and minimizing he EDC
c i e ion in (1).
Based on he analysis p esen ed in Sec ion 3.2, he p ope
alues o he DC-PSS pa ame e s we e ob ained om he APSO
lis ed in Table 2
Fo obus ness o he solu ions, he ob ained alues o
EDC by employing he calcula ed pa ame e s o he GA and
he APSO algo i hm a e compa ed ollowing se e al aul s.
The esul s o his compa ison a e shown in Table 3As he
able shows, he p oposed APSO algo i hm achie es a be e
esponse han he GA algo i hm, i also has a as e esponse
and ewe epe i ions.
5.4 Dynamic s abili y analysis
The bode plo s o he ans e unc ion be ween ol age e -
e ence j*(s) and he local di ec ol age j(s), which can be
s aigh mined om he MIMO model, wi hou any damping
me hod, wi h d oop con olle , and employing DC-PSS beside
TABLE 3 Compa ison o EDC calcula ed by he pa ame e s ob ained
om wo algo i hm
APSO GA
EDC Rep. EDC Rep.
Th ee-phase sho ci cui 0.091 83 0.098 100
Dec easing load 0.283 79 0.297 100
Inc easing load 0.287 81 0.296 100
FIGURE 10 Roo locus and bode plo s o he j(s)/ j*(s) ans e
unc ion wi h kd oop =0.3 om a single con e e
d oop, a e illus a ed in Figu e 10 This plo shows ha he DC-
PSS and d oop con olle wo k a he esonan equency, bu i
is clea ha DC-PSS gi es a highe bandwid h, which imp o es
he ansien esponse and educes he amoun o mu a ion.
Besides, his igu e shows ha DC-PSS gi es a highe phase
ma gin a low equency. The e o e, he designed compensa o
will p o ide mo e p ope damping o he sys em.
5.5 In es iga ion o he p oposed DC-PSS
o he unde s udy ne wo k
In his sec ion, he p oposed DC-PSS on he HVDC es sys em
is examined. As men ioned be o e in his s udy Cig é DCS3 is
selec ed and MATLAB/SIMULINK is used o he simula ions.
Responses o he DC ol age and DC powe o VDC-Cb-A1,
VDC-Cb-B2, VDC-Cb-B1 and PDC-Cb-A1, PDC-Cb-B2, PDC-
Cb-B1 unde 200 MW educing o gene a ion in wind a m
2 and du ing aul happening o 10 ms (3–3.01 s) in Cb-A1
bus wi h d oop con olle a Cb-B1 and Cb-B2 (kd oop =0.3,
kd oop =0.2) ollowing wi h and wi hou DC-PSS is shown as
ollows. Howe e , despi e he DC-PSS on he Cb-B1 and he
use o powe luc ua ions o educe ol age luc ua ions, he
powe o his bus inc eases sligh ly in he ini ial momen s o
he aul .
5.6 Reducing o gene a ion
Figu e 11(a) shows ha he p esence o DC-PSS along wi h
d oop con olle educes he oscilla ion o ol age a he ins an
o gene a ion dec ease and inc eases he speed o ge ing he
s eady-s a e condi ion. Fu he mo e, Figu e 11(b) illus a es
ha he damping o ol age luc ua ions has led o a educ-
ion o powe oscilla ions and inc eases he speed o ge ing he
s eady s a e o powe .
500 AZIZI ET AL.
FIGURE 11 F equency, DC ol age and DC powe o Cb-A1, Cb-B2 and
Cb-B1 ollowing 200 MW educing o gene a ion in wind a m 2. (a)
F equency and di ec ol age o Cb-A1, Cb-B2 and Cb-B1. (b) Powe o
Cb-A1, Cb-B2 and Cb-B1
5.7 Faul incidence a Cb-A1
Figu e 12 shows VDC-Cb-A1, VDC-Cb-B2, and VDC-Cb-B1
p o iles du ing aul occu ence o 10 ms (3–3.01 s) in Cb-A1
bus. The aul a Cb-A1, esul ed in a 70% ol age d op. Since
i is e ealed om Figu e 12 h oughou he aul , he DC-PSS
has been able o minimize he ol age peak and s abilize he bus
FIGURE 12 The DC ol age o Cb-A1, Cb-B2, and Cb-B1 ollowing a
aul happening a Cb-A1
ol age as e and i means ha he peak o ol age has been
imp o ed.
Figu e 12 con i ms ha wi hou DC-PSS, he peak ol age
may be la ge, so ha i goes ou o ange and he p o ec ion sys-
em en e s ope a ion. In addi ion, his igu e shows ha unde
he same condi ion p oposed, he me hod wi h DC-PSS a e
elimina ion o he aul has been able o b ing back he alue
o he ol age o he p e ious alue wi h a smalle peak and
less oscilla ion. The compa ison o he simula ion esul s in Fig-
u e 12 shows he damping imp o emen by he p oposed DC-
PSS.
Figu es 11(a) and (b) in addi ion o displaying ol age and
powe luc ua ions, show ha he damping signal does no a ec
he pe o mance o he d oop con olle and does no p e en
i s p ope ope a ion. This means ha , despi e he washou il e ,
he injec ion signal is applied only a he pe iod o dis u bances.
Figu e 11(a) also shows ha he use o DC-PSS has an e ec on
he equency and DC-PSS can also imp o e equency oscil-
la ions. Because in he weak sys ems, usually i he equency
d ops each below 0.98 pu (o 49 Hz in 50 Hz powe sys ems)
he load shedding will be ac i a ed. As can be seen om Fig-
u es 11(a) and (b) he p oposed me hod no only educes he
oscilla ions bu also does no enable load shedding.
Addi ional signals om DC-PSS will educe powe luc ua-
ions and cause a as e dec ease in powe luc ua ions.
Table 4shows he imp o emen o he damping by he esul s
o he analy ical s udy, i DC-PSS is on Cb-B1. The impac o
DC-PSS in Cb-B1 on he oscilla ing equency and he damping
a io ζo he closed-loop MIMO model o he poo ly damped