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Heida y Yazdi, Seyed Saeid; Rouzbehi, Kuma s; Candela, José
Ignacio; Milimon a ed, Ja a ; Rod íguez, Ped o (2017) Analysis on
impac s o he shun conduc ances in mul i- e minal HVDC g ids
op imal powe - low.
IECON 2017 - 43 d IEEE Annual Con e ence o
he IEEE Indus ial Elec onics Socie y, Beijing, China, Oc . 29 – No .
1, 2017: p oceedings.
[S.l.]: IEEE, 2017. Pp. 121-125 Doi:
10.1109/IECON.2017.8216025
© 2017 IEEE. Es pe me l'ús pe sonal d'aques ma e ial. S’ha de
demana pe mís a l’IEEE pe a qualse ol al e ús, incloen la
eimp essió/ eedició amb ins publici a is o p omocionals, la c eació
de no es ob es col·lec i es pe a la e enda o edis ibució en
se ido s o llis es o la eu ili zació de pa s d’aques eball amb d e s
d'au o en al es eballs.
Analysis on Impac s o he Shun Conduc ances in
Mul i-Te minal HVDC G ids Op imal Powe -Flow
Seyed Saeid Heida y Yazdi*, Kuma s Rouzbehi***, J. Ignacio Candela**
Ja a Milimon a ed*, and Ped o Rod iguez**,***
* Ami kabi Uni e si y o Technology, Teh an, I an
** Technical Uni e si y o Ca alonia, Ba celona, Spain
***Loyola Uni e si y Andalucia, Se ille, Spain
saedheida y@au .ac.i
Abs ac —
This s udy deals wi h impac s o he shun
conduc ances associa ed wi h HVDC cables and VSC-HVDC
s a ions on op imal ope a ion o Mul i-Te minal HVDC (MT-
HVDC). In his s udy, o he i s ime, shun conduc ances a e
in eg a ed o HVDC Op imal Powe - Flow (OPF) p og am ha is
execu ed a he Powe Dispa ch Cen e (PDC) o he MT-HVDC
g id. Wi h he objec i e o losses minimiza ion, op imal e e ence
ope a ion poin s o he VSC-HVDC s a ions a e de i ed. The
ope a ing poin s o he powe con e e s a ions a e adjus ed
based on he calcula ions pe o med in he dispa ch cen e .
CIGRE DCS3 MT-HVDC g id, s uc u ed by CIGRE B4 wo king
g oup, is aken as he es pla o m. Tes esul s ha e e ealed he
op imum ol ages and loss pa e n change. Mo eo e , he indings
a e compa ed wi h he case o neglec ing he shun conduc ances.
Index Te ms—CIGRE DCS3 HVDC g id, dc Op imal powe low,
mul i- e minal HVDC g id.
I.
I
NTRODUCTION
The e olu ion o Mul i-Te minal HVDC (MT-HVDC)
g ids
is mainly because o wo main d i e s: i s ly, hei su iciency
o link mul iple ac ne wo ks ha a e ope a ing a dis inc ac
ol age le els e en a di e en equencies [1], secondly hey
a e sui able o in eg a ing o la ge-scale o sho e wind ene gy
o main ac g ids [2, 3]. In ecen yea s, ex ensi e indus ial and
academic s udies on MT-HVDC g ids ha e been conduc ed [4,
5]. Since 1951, he e has been e idence o up o 180
p edominan wo- e minal poin - o-poin HVDC p ojec s which
ha e been implemen ed wo ldwide [6]. Du ing he las decade,
some HVDC sys ems ha e been ex ended wi h addi ional
powe con e e s a ions o o m he i s ope a ional MTDC
sys ems. By means o he p og ess and ge ing he popula i y o
high-powe Vol age Sou ce Con e e (VSC)s, he p ospec o
he MT-HVDC ne wo ks, comp ised o se e al VSC-HVDC
s a ions has con e ed o a eal oppo uni y.
In he amewo k o his eme ging pa adigm, MT-HVDC
g id op imal ope a ion is o high impo ance since i is di ec ly
ansla ed o highe deli e ed powe and hence highe e enue.
In he con ex o MT-HVDC g id wo-laye ed con ol, DC
powe low, DC Op imal Powe Flow (DC OPF) and ene gy
ma ke - ela ed s a egies a e usually add essed a he seconda y
con ol laye . Whe eas, con ol o powe con e e s, di ec
ol ages, and powe sha ing a e assigned o he p ima y con ol
laye . Indeed, app op ia e e e ence se ings a e sen o he
VSC-HVDC s a ions in a p esc ibed ime in e als by he powe
dispa ch con ol cen e o he MT-HVDC g id [7, 8].
Se e al numbe s o esea ch ha e ocused on he designing o
he seconda y con ol laye o minimize ansmission losses [9-
12], and o al ansmission and con e e s losses [13]
conside ing ol age-d oop con ol [14]. I is done by calcula ing
op imum d oop e e ence ol ages. Also, a d oop con ol gain
design me hodology is p oposed in [15] o op imal powe
sha ing among he VSC-HVDC s a ions in o de o maximize
he powe ansmission capaci y. Also, [16] conside ed adap i e
d oop con ol gains acco ding o cable esis ances o minimize
he losses and p e en con e e o e ol age. Mo eo e , [17,
18] p oposed gene azlized d oop con ol amewo k and uni ied
e e ence con olle o onsho e side con e e s o con ol di ec
ol ages and sha e he bu den o dynamic equency esponse
among HVDC con e e s espec i ely.
To he bes o he au ho s knowledge, none o hese s udies is
in es iga ed impac s o he shun conduc ances associa ed wi h
HVDC cables and VSC-HVDC s a ions on he op imal
ope a ion o he MT-HVDC g id. Indeed, hey a e simply
neglec ed in hei modelings. Howe e , hese shun
conduc ances lead o a signi ican change in DC OPF esul s
ha is he ocus o his esea ch.
This pape con ibu es o he s a e o he a by de i ing a
s a ic model o MT-HVDC g id aking conduc ances o HVDC
cables and VSC-HVDC s a ions in o accoun o assess hei
impac s on DC OPF esul pa e n. The op imiza ion esul s
which a e calcula ed a he seconda y con ol laye a e passed
o ol age d oop based p ima y con ol laye . CIGRE DCS3
MT-HVDC g id is selec ed as ou es pla o m in o de o
alida e he claims o his s udy.
This pape is o ganized as ollows: Fo mula ion o DC OPF
and i s sol ing app oach a e p esen ed in sec ions II and III,
espec i ely. Sec ions IV and V d aw he es esul s and main
conclusions espec i ely.
II. FORMULATION
OF
DC
OPF
PROBLEM
The de ini ion o DC OPF p oblem can be inspi ed by he
well-known OPF p oblem o AC powe sys em [19] wi h some
modi ica ions. In ac , he DC OPF can be conside ed as a
simpli ied ype o he AC g ids OPF, since he eac i e powe
does no longe exis in MT-HVDC g ids.
Op imal ope a ion o MT-HVDC g ids can be assessed by
means o se e al echnical, economical and/o o he c i e ions.
Howe e , he p esen s udy ocuses on minimiza ion o he MT-
HVDC g id o al losses (
()
V
) by means o sol ing he DC
OPF p oblem. The DC OPF p oblem is o mula ed by (1)–(5)
assuming n g id side VSC-HVDC s a ions, p in e media y
buses (wi hou gene a ion and loads), and m wind a ms as:
()
T
=VVYV
(1)
()
2
1
++
=
=
¦
VVY
npm
T
ii i
i
P
gV
(2)
()
()
2
11
++ ++
==+
=−
¦¦
YVV
npmnpm
T
ij i j
iji
S
gVV
(3)
whe e
V=
[
V
1
, V
2,
…, V
m+n+p
]
T
and
Y
deno e he MT-HVDC
ec o o buses ol age and admi ance ma ix espec i ely.
Mo eo e ,
g
ii
and
g
ij
espec i ely indica e he sum o
conduc ances appea ed be ween bus
i
and g ound and he ne
conduc ance seen be wix buses
i
and
j
. HVDC o e head lines
and cables a e modeled by a lumped ʌ model [20].
Y
is di ided
in o he elemen s in luenced by he shun conduc ances (
Y
P
)
and he emaining pa s (
Y
S
)
. He ea e , losses de ined by (2)
and (3) will be called “shun losses” and “se ies losses”,
espec i ely. They a e quad a ically dependen on bus ol ages
and HVDC lines cu en s espec i ely. The e o e, hey change
in opposi e di ec ions wi h espec o MT-HVDC g id bus
ol age le els. Fo ins ance, as di ec ol age le els inc ease o
educe he cu en s le el (and he e o e se ies losses), he shun
losses inc ease. Hence, he e should be a ade-o de e mined
by he DC OPF ou ine. Se e al equali y and inequali y
cons ain s a e applied o he objec i e unc ion:
()
,0=gVP
(4)
max
,1,,< =!
ii
PP i n
(5)
()
min max
,
,1,,
DC DC i DC
VVV i npm<< = ++!
(6)
max
,,
,1,,
DC k DC k
II k L< =!
(7)
in which
L
deno es he o al numbe o HVDC o e head/cables
inside he sys em. He e,
P
i
,
V
DCi
,
and
I
DC,k
deno e he exchanged
powe by VSC-HVDC s a ion
i
, bus
i
ol age and he amoun
o cu en lowing in he line
k
,
espec i ely. Also,
P
ep esen s
he ma ix o abso bed bus powe s. The DC powe low is
ep esen ed by he equali y cons ain (
()
,=gVP
diag
1
(,.V
.., ) 0
npm
V
++
−=YV P
), and can be expanded as ollows ( o he
case o powe - ol age d oop con ol):
0
,1 1 1
0
,2 2 2
0
,
1
,1
,
()
()
.
()
d0
,..., ) 0
.
i
0
a
.
g(
d oop
d oop
d oop n n n
npm
wind
wind m
kVV
kVV
kVV
VV
P
P
++
ªº
−−
«»
−−
«»
«»
«»
−−
«»
«»
«»
−=
«»
«»
«»
«»
«»
«»
«»
¬¼
YV
(8)
In which
V
i0
and
k
d oop,i
deno es d oop e e ence ol age and
d oop slope o
i
h g id side VSC-HVDC s a ion.
Cons ain s (3)–(5) espec i ely indica e he MT-HVDC g id
limi a ions ha a e associa ed wi h bus ol ages, VSC-HVDC
s a ions ansmi ed powe and he HVDC lines cu en . In (3),
max
i
P
s and o he u mos pe missible ansmi ed powe by he
VSC-HVDC s a ion
i
. In he cons ain (4),
min
DC
V
and
max
DC
V
exp ess he lowe and uppe admissible span o MT-HVDC
g id’s di ec ol ages, espec i ely. Also, he a ed DC cu en
co esponding o he
k
d
ansmission line is ep esen ed by
max
,DC k
I
in (5).
III. DC
OPF
P
ROBLEM
:
S
OLVING
A
PPROACH
The DC OPF p oblem s a ed by (1)–(5) alls in he nonlinea
cons ained op imiza ion ca ego y. Se e al g adien based
sol e s can be u ilized o sol e i as shown below [21]:
()()( ) ()
,,,.,L =+ +
T
VP V qVPI ȜgVP
(9)
In which,
Ȝ
is he o Lag ange mul iplie s ec o o he
equali y cons ain p esen ed by (2),
I
is he DC ansmission
lines cu en ec o . Also, he penal y unc ion co esponding
o he inequali y cons ain s is p esen ed by
q
:
()
() ()
{
}
()
{}
()
{}
min max
max
22
min max
,,
1
22
max max
,,,
,
11
,, . .
..
npm
ii ii
Vi i
i
nL
i i DC k i DC i I k
Pi
ik
VV p VV p
PP p I I p
++
=
==
=− +−
+− + −
¦
¦¦
qVPI
(10)
whe e
min
, i
p
,
max
, i
p
,
max
,Pi
p
, and
,Ii
p
ep esen penal y
ac o s co esponding o he lowe and uppe limi s o di ec
ol age, VSC-HVDC s a ions, and ansmission lines limi s,
espec i ely. In cons ained op imiza ion p oblems, i is a
common p ocedu e o subs i u e he inequali y cons ain wi h
he penal y ac o s, howe e , hese ac o s will be ze o p o ided
ha none o he cons ain s a e iola ed.
DC OPF solu ion can be calcula ed in an i e a i e manne
conside ing ha he de i a i e o he Lag angian unc ion
(
/
∂∂VL
and
/
∂∂ȜL
) should be ze o a he op imum poin :
∂∂∂ ∂
ªº
=++
«»
∂∂∂ ∂
¬¼
qg
Ȝ
VVV V
T
L
(11)
()
,
∂=
∂gVP
Ȝ
L
(12)
The compu ed op imum d oop e e ence ol ages (
00
12
, VV
0
3
and V
) a e applied o he p ima y con ol laye as i is shown
in Fig. 1.
IV. T
EST
R
ESULTS
A) Cig e DCS3 MT-HVDC Tes G id
CIGRE DCS3 MT-HVDC es g id is a bipola (±400 kV) g id
and comp ised o wo o sho e wind powe plan s (m=2), h ee
g id side VSC-HVDC s a ions (n=3), wo in e media y buses
(p=2), eigh HVDC cables and o e head lines (L=8). The DCS3
g id is shown in Fig. 2 and u he da a a e epo ed in [20]. In
his s udy, pe uni esul s a e gi en conside ing 500 MW and
800 kV as base powe and base ol age espec i ely. Onsho e
g id side VSC-HVDC s a ions employ iden ical 60 MW/kV
d oop coe icien s (k
d oop,i
) and 800 kV d oop as he ini ial
e e ence ol ages (V
i0
). Howe e , a se o sui able d oop
e e ence ol ages will be de e mined la e by execu ion o he
DC OPF p oblem. Fo he sake o simplici y, he DC buses o
he DCS3 a e numbe ed as i is p esen ed in Table I.
T
ABLE
I.
DCS3
B
US
N
UMBERS
DC Bus Bb-
A1
Bb-
B1
Bb-
B2
Bb-
B4
Bb-
E1
Bb-
D1
Bb-
C2
Numbe 1 2 3 4 5 6 7
d
sT
e
−
d
sT
e
−
0
1
V
0
k
V
0
n
V
Fig.1. The hie a chal con ol s uc u e o MT-HVDC g id.
Fig. 2. Cig e DCS3 MT-HVDC es g id.
B) Impac s o DC cables and VSC-HVDCs shun
conduc ances on Y ma ix
Pa ame e s o DCS3 MT-HVDC g id disclose ha he
HVDC cables ha e shun conduc ances o 0.048 ȝS/km and
se ies esis ances o 0.0095 /km [20]. Mo eo e , 400 MVA,
800 MVA, and 1600 MVA VSC-HVDC s a ions exhibi 2.5
ȝS, 5 ȝS, and 7.5 μs shun conduc ance espec i ely. Those
a e associa ed wi h hei DC capaci o s. Y
P
and Y
S
can be
w i en in pe -uni as:
729.8246 280.701 0 112.2807 0 0 336.8421
280.7018 898.2456 0 280.7018 336.8421 0 0
0 0 374.2690 374.2690 0 0 0
112.2807 280.7018 374.2690 767.2515 0 0 0
0 336.8421 0 0 673.6842 336.84241 0
0 0 0 0 336.8421 561.4035 224.5614
−− −
−−−
−
=−−−
−−
−−
−
Y
S
336.8421 0 0 0 0 224.5614 561.4035
ª º
« »
« »
« »
« »
« »
« »
« »
« »
« »
−
¬ ¼
(13)
0.007871 0 0 0 0 0 0
0 0.007871 0 0 0 0 0
0 0 0.004800 0 0 0 0
0000000
0 0 0 0 0.006144 0 0
0 0 0 0 0 0.010880 0
0 0 0 0 0 0 0.009280
ªº
«»
«»
«»
«»
=«»
«»
«»
«»
«»
¬¼
Y
P
(14)
(13) and (14) co espond o he se ies and shun losses ha a e
also de ined in (1) espec i ely.
C) Case s udy (P
Bb-D1
=1.9 pu, P
Bb-C2
=0.9 pu)
The DC OPF esul s a e summa ized in Table II. In o de o
show he conside able impac s o he shun conduc ances, h ee
case s udies a e in es iga ed: 1) powe low wi h cons an 800
kV d oop e e ence ol ages 2) DC OPF p oblem wi hou
conside ing shun conduc ances 3) DC OPF p oblem wi h
conside ing shun conduc ances.
Rega ding he case 2, i s ly he DC OPF p oblem is
o mula ed wi hou aking shun conduc ances in o accoun .
Once he op imum d oop e e ence ol ages a e calcula ed, hey
a e passed o he powe low p oblem (8) which embeds he
T
ABLE
II.
O
PTøMAL
P
OWER
F
LOW
R
ESULTS
Powe Flow Wi h Cons an 1 pu
D oop Re e ence Vol ages
Wi h Op imiza ion, Wi hou
Conside ing o Shun Conduc ances
Wi h Op imiza ion, Wi h
Conside ing o Shun Conduc ances
DC Bus Con ol Mode DC Vol age (pu) Ne Powe (pu) DC Vol age (pu) Ne Powe (pu) DC Vol age (pu) Ne Powe (pu)
Bb-A1 D oop 1.01100-1.05625 1.04270 -1.51592 0.96447 -1.38942
Bb-B1 D oop 1.01040-0.99913 1.04270 -1.23060 0.96418 -1.33413
Bb-B2 D oop 1.00704-0.67658 1.04275 0.01407 0.96417 -0.01345
Bb-B4 In e media e 1.00885 0 1.04272 0 0.96422 0
Bb-C2 P 1.015330.899991.04703 0.90000 0.96909 0.89999
Bb-D1 P 1.017931.900001.04974 1.90000 0.97193 1.89999
Bb-E1 In e media e 1.01416 0 1.04621 0 0.96805 0
Se ies Losses (pu) 0.019920.016320.01913
Shun Losses (pu) 0.048110.051230.04385
To al Losses (pu) 0.068030.067550.06298
impac s o shun conduc ances.
Rega ding he case i s case, he shun losses (0.04811 pu)
a e clea ly supe io o he se ies losses (0.01992 pu).
Pe sis ence o his supe io i y will be discussed in he nex
sec ion ega ding di e en wind powe gene a ions. The e o e,
he DC OPF p oblem ( he Case s udy 3) assigned minimum
pe missible d oop e e ence ol ages o he g id side VSCs
(
0
1
0.95000 puV=
0
2
, 0.95028 pu,V=
0
3
0.96403 puV=
) o
dec ease he shun losses and consequen ly o al losses.
The e o e shun losses a e educed o 0.04385 pu om 0.04811
pu ha shows a % 8.85 loss educ ion.
Mo eo e , while he cu en s lowing inside MT-HVDC
g id a e inc eased as a esul o ol age le el educ ion, se ies
losses shows su p isingly a small dec ease. This is due o
op imal sha ing o he powe among g id side VSC-HVDC
s a ions. In his ega d, he powe s abso bed by Bb-A1, Bb-B1,
and Bb-B2 buses a e a ied o 1.38942 pu, 1.33413 pu, and
0.01345 pu om 1.05625 pu, 0.99913 pu, and 0.67658 pu
espec i ely. Finally, o al losses a e educed o 0.06298 pu
om 0.06803 pu which shows a %7.42 educ ion.
On he o he hand, he compa ison o case s udies 1 and 2
exhibi s a di e en endency in DC OPF esul s. Since he
impac s o shun conduc ances a e no conside ed in he DC
OPF p oblem, i assigned d oop e e ence ol ages
(
000
123
1.02691 pu, 1.02988 pu, 1.04289 puVVV
===
) in
o de o maximize he MT-HVDC ol ages while p ese ing
ope a ional cons ain s. In his ega d, se ies losses a e educed
o 0.01632 pu om 0.01992 pu ha shows a %18.07 loss
educ ion. Howe e , he ol age inc ease ends o inc ease he
shun losses om 0.04811 pu o 0.05123 pu ha shows
a %6.48 loss inc emen . Finally, o al loss educ ion is
con ined o %0.7 due o inapp op ia e d oop e e ence ol ages.
D) Impac s o shun conduc ances in di e en wind powe
gene a ion scena ios
The esul s o h ee case s udies de ined in he p e ious
sec ion a e depic ed in Fig. 3 aking di e en wind powe
gene a ions in o accoun . In his igu e, he below and upside
(a) Vol ages o bus Bb-
A1. (b) Vol ages o bus Bb-B1.
(c) Vol age p o iles o bus
Bb-B2.
(d) Vol age p o iles o bus
Bb-D1.
(e) Vol age p o iles o bus
Bb-C2. ( ) T ansmission loss
educ ion (%)
implemen ing op imum
d oop se ings e sus
ixed d oop se ings.
Fig. 3. The esul s o he case s udy 1 (middle planes) and he case s udy 2
( op planes) and he case s udy 3 (bo om planes)
3%E'SX
3%E&SX
3%E'SX
3%E&SX
3%E'SX
3%E&SX
planes s and o he case s udies 3 and 2 espec i ely. On he
o he hand, he middle planes ep esen he case s udy 1.
Clea ly, applica ion o he op imum e e ences wi hou he
e ec o he shun conduc ances will ise he whole MT-
HVDC ol ages and maximizes he o sho e wind a m side
ol ages o educe he se ies losses. Ha ing o sho e wind a m
side ol ages ixed a maximum pe missible alues (i.e., 1.05
pu), g id side ol ages educe as wind powe gene a ion
inc ease since he ol age di e ence be ween MT-HVDC
buses is equi ed o he pu pose o powe low.
On he o he hand, whole MT-HVDC buses ol ages a e
educed o a ound minimum pe missible alues (i.e., 0.95 pu)
aking he e ec o shun conduc ances in o accoun . This
o ien a ion is kep unless in e y high wind powe gene a ions
ha he se ies losses gain supe io i y in con ibu ing o he
ansmission losses. The e o e, DC OPF p oblem ies o
inc ease he MT-HVDC ol age le els in o de o op imize
ansmission losses by making a adeo be ween se ies and
shun losses. The loss educ ion is clea in Fig. 3( ), howe e ,
i is highes in low wind powe gene a ion (i.e., up o %10).
V. CONCLUSION
This s udy analyzed he impac s o he shun conduc ances
associa ed wi h HVDC cables and VSC-HVDC s a ions on
op imal ope a ion o he MT-HVDC g id. These conduc ances
ha can be in e p e ed o he shun losses o he MT-HVDC
g id a e quad a ically dependen on DC bus ol ages. F om he
es pla o m esul s, i was e ealed ha he shun losses a e
dominan in con ibu ing o he o al ansmission losses excep
o e y high wind powe gene a ions. The e o e, he DC OPF
ou ine had a endency o dec ease MT-HVDC g id bus
ol ages o he p oximi y o he minimum pe missible DC bus
ol age. Con e sely, his endency has been changed o
ol age inc emen in e y high wind powe gene a ions since
he MT-HVDC g id se ies losses become dominan .
In es iga ing he impac s o he shun conduc ances on MT-
HVDC g id s abili y is a possible u u e esea ch.
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