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
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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 ,