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o he wo ks.
Con ol S a egy o Dis ibu ion Gene a ion
In e e s o Maximize he Vol age Suppo in he
Lowes Phase Du ing Vol age Sags
An onio Camacho, Miguel Cas illa, Jaume Mi e , Membe , IEEE, L. Ga cía de Vicuña,
Miguel And és Ga nica
Abs ac —Vol age sags a e conside ed one o he wo s
pe u ba ions in powe sys ems. Dis ibu ed gene a ion
powe acili ies a e allowed o disconnec om he g id
du ing g id aul s whene e he ol age is below a ce ain
h eshold. Du ing hese se e e con ingencies, a cascade
disconnec ion could s a , yielding o a blackou . To mini-
mize he isk o a powe ou age, in e e -based dis ibu ed-
gene a ion sys ems can help o suppo he g id by ap-
p op ia ely selec ing he con ol objec i e. Which con ol
s a egy pe o ms be e when suppo ing he g id ol age
is a complex decision ha depends on many a iables. This
pape p esen s a con ol scheme ha implemen s a sma
and simple s a egy o suppo he aul : he maximum
ol age suppo o he lowes phase ol age. The e o e,
he aul ed phase ha is mo e a ec ed by he sag can
be be e suppo ed since his phase ol age inc eases
as much as possible, educing he isk o unde - ol age
disconnec ion. The p oposed con olle has he ollowing
ea u es: a) maximizes he ol age in he lowes phase, b)
injec s he maximum a ed cu en o he in e e , and c)
balances he ac i e and eac i e powe e e ences o deal
wi h esis i e and induc i e g ids. The con ol p oposal is
alida ed by means o expe imen al esul s in a labo a o y
p o o ype.
Index Te ms—G id aul s, Posi i e-nega i e sequence,
Vol age dip, Vol age ide- h ough, Vol age sag, Vol age sup-
po
I. INTRODUCTION
THE high in eg a ion o enewable ene gy sou ces and
dis ibu ed gene a ion (DG) [1] in o he g id has changed
he equi emen s and he ope a ion o powe sys ems [2]. Some
yea s ago, DG sou ces ep esen ed a low con ibu ion o e
he o al ene gy ma ke . A p esen , he o al amoun o non-
con en ional ene gy p oduc ion can achie e up o 50% o he
o al elec ical comsump ion and e en mo e [3], [4]. This new
scena io p esen s a po en ial bene i o e he classical one,
since DG educes ene gy losses and many imes p o ides om
clean and sus ainable ene gy sou ces [5]. Howe e , he massi e
This wo k has been suppo ed by ELAC2014/ESE0034 om he
Eu opean Union and i s linked Spanish na ional p ojec PCIN-2015-
001. We also app ecia e he suppo om he Minis y o Economy and
Compe i i eness o Spain and Eu opean Regional De elopmen Fund
(FEDER) unde p ojec ENE2015-64087-C2-1-R.
A. Camacho, M. Cas illa, J. Mi e , L. Ga cía de Vicuña
and M. A. Ga nica a e wi h he Depa men o Elec onic
Enginee ing, Technical Uni e si y o Ca alonia, 08800 Vilano a
i la Gel ú, Spain (e-mail: an onio.camacho.san i[email p o ec ed];
[email p o ec ed]; jmi e @eel.upc.edu; [email p o ec ed];
miguel.ga nica@a mada.mil.co)
in eg a ion o hose sys ems can comp omise he eliabili y o
he whole sys em, in pa icula du ing ol age sags.
Vol age sags a e one o he wo s pe u ba ions in powe
sys ems cha ac e ized by a sho - ime ol age d op in one
o se e al phases [6]. The main causes a e sho -ci cui s by
unin en ional con ac , ligh nings and equipmen ailu e [7].
Du ing he aul , DG g id-connec ed powe sou ces mus
wi hs and he pe u ba ion and ope a e con inuously. Howe e ,
in o de o p o ec he ins alla ion, when he ol age is low o
a long ime, he powe acili y can be disconnec ed acco ding
o he ol age p o ile and ip imes de ined in g id codes [8]–
[10]. To educe he isk o disconnec ion, app op ia e low-
ol age ide- h ough (LVRT) p o ocols need o be de eloped
o suppo he g id ol ages.
The con en ional LVRT se ices [11]–[15] a e ocused on
medium o big powe plan s abo e a ce ain a ed powe .
The main objec i e o g id codes is o suppo he g id
wi h eac i e powe du ing he aul , and o gua an ee he
con inuous ope a ion o a oid sudden loss o powe gene a ion.
The con ol p oposal o his pape should be unde s ood as a
pa o he new gene a ion o g id codes ha could apply o
any a ed powe gene a ion sou ce, ha is being in e aced
wi h he g id ia lexible powe con e e s, and ied o any
ype o g id impedance (induc i e and esis i e wi h high o
low alues).
Vol age suppo has become a challenging me hod o im-
p o e he g id eliabili y du ing g id aul s. The main eason
o his is he huge amoun o as eac i e powe p o isions
a ailable in in e e -based DG sys ems. How o manage he
cu en injec ed by he DG in o he g id is he main issue
o he new de elopmen o such con ol s a egies. Howe e ,
which s a egy is app op ia e o a gi en ol age sag is a
complex p oblem o be sol ed. This pape p esen s a ol age
suppo con ol scheme ha implemen s one o he simples
objec i es: o maximize he lowes phase ol age. This s a egy
is ai ly jus i ied by he ac ha aising he lowes ol age
could a oid unde - ol age disconnec ion.
The end in ol age suppo con ol is none heless dedica ed
o mainly induc i e g ids [16]–[20], while low and medium
ol age g ids wi h some inhe en esis i e beha io ha e been
less discussed in he li e a u e [21]–[24]. This s udy p esen s
a con ol scheme ha applies o any ype o g id impedance,
ei he induc i e, esis i e o a combina ion o bo h. Indeed, he
p oposed solu ion is also alid o weak o s i g ids since he
op imal solu ion does no ely on he magni ude o he g id
powe
sou ce
dc-link
in e e il e
LiLoi
C
PCC
L R
g
g id
Fig. 1. Simpli ied scheme o a h ee-phase g id-connec ed dis ibu ed
gene a ion in e e .
impedance, bu on he induc i e/ esis i e a io
p
L
{
R
q
.
Se e al wo ks ha e been p oposed in he li e a u e o
ol age suppo du ing aul s [16]–[28]. Mos o hese wo ks
a e based on symme ic sequences o deal wi h unbalanced
g id ol ages, which has been es ablished as he p e e ed
me hod o de elop ad anced ol age suppo con olle s. The
main ea u es in es iga ed in his esea ch a ea co e : di e en
ol age suppo objec i es [16]–[20], [27], [28], maximum
cu en injec ion du ing he sag [17], [19], [25], [26] and g id
impedance ma ching [22]–[24]. Howe e , none o hese wo ks
joins hese h ee ea u es a he same ime, i.e. imp o ing he
ol age suppo o any ype o g id impedance while injec ing
he maximum a ed cu en . To simul aneously accomplish
hese objec i es, se e al issues need o be add essed i s as
will be shown along he wo k.
Compa ed wi h p e ious s a e-o - he-a con ol s a egies,
he main con ibu ions o he p oposed wo k a e: a) he
o mula ion o a new ol age suppo objec i e o dis ibu ion
gene a ion in e e s du ing g id aul s, b) he con ol scheme
ha gua an ees he maximum inc ease in he lowes phase
ol age, subjec o he cons ain o a sa e cu en injec ion,
and c) he lexibili y o he p oposal o deal wi h induc i e and
esis i e, weak o s i g ids. This me hod has he ad an age
o inc easing as much as possible he lowes phase ol age
in a sa e manne . By conside ing he g id impedance, i is
possible o ex end he ol age suppo ange. Thus, he isk o
unde - ol age disconnec ion is educed.
The pape is o ganized as ollows. Sec ion II o mula es he
p oblem. Sec ion III sol es he p oblem o maximizing he
lowes phase ol age. Sec ion IV deals wi h he impac o he
g id impedance on he pe o mance o he p oposal. Sec ion
V p esen s he expe imen al esul s ob ained in a labo a o y
p o o ype. Finally Sec ion VI concludes he pape .
II. PROBLEM STATEMENT
This sec ion s a s p esen ing he basics o he powe plan
unde con ol, hen he main con olle asks a e enume a ed,
and he ol age suppo concep is b ie ly explained, inally he
con ol objec i es and he p oblem o be sol ed a e p esen ed.
A. Powe Plan
The main objec i e o he p oposed wo k is o maximize he
lowes phase ol age du ing g id aul s. This p oposal applies
o DG in e e s and/o s a ic synch onous compensa o s wi h
ene gy s o age capaci y ha a e in e aced wi h he g id
ia ull-powe con e e s. A gene ic scheme o his kind o
con olled sys ems is p esen ed in Fig.1. In he igu e, he
p ima y sou ce is connec ed o he h ee-phase in e e . In
TASK : Con olle ( k)
1
abc, iabc
= ReadADC()
2
α, β
= Cla ke( abc)
3
iα, iβ
= Cla ke(iabc)
4
α,
β,
α,
β
= SequenceEx ac o
α, β
5i Sag is de ec ed hen
6
i
α, i
β
= Vol ageSuppo
α,
α,
β,
β
7else
8
i
α, i
β
= No malOpe a ion(
)
9
dα, dβ
= PRes
i
α
iα, i
β
iβ
10
Tabc
= SpaceVec o PWM
dα,dβ
Fig. 2. Pseudo-code o he con olle ask.
be ween, a dc-link is needed o balance he powe low om
he sou ce o he g id. The main in e e ’s pa s a e he powe
swi ches and he LCL ou pu il e o educe he swi ching
ha monics. The in e e connec s o he g id a he poin
o common coupling (PCC), which co esponds o he place
whe e he phase ol ages o he di e en ol age suppo
con ols should be compa ed. The g id is modeled as a ol age
sou ce gand an equi alen g id impedance Rand L. I should
be men ioned ha o de eloping he con ol p oposal, he L
{
R
a io need o be known. To his end, wo main me hods can
be bo owed: he knowledge o he nea by elemen s close o
he acili y, o an on-line g id impedance es ima o [29], [30].
In o de o simpli y he s udy, along his wo k i is assumed
ha no local load is ied o he DG in e e . By assuming
his, he heo e ical analysis becomes simple and he con ol
de elopmen can be de i ed in a mo e in ui i e way.
B. Con olle
A e p esen ing he main sys em pa s, he con olle unc-
ionali y is b ie ly e iewed. To con ol he plan in Fig. 1,
he in e e is se in cu en -con olled mode. The pseudo-
code ha implemen s he main con olle pa s is p esen ed in
Fig. 2. The con olle ask is ac i a ed each sampling ime,
he i s s ep is o sense he ol ages and cu en s. Then,
by using Cla ke ans o ma ion, he ins an aneous alues in
he α-βdomain a e ob ained. A sequence ex ac o [31] is
needed o decompose he ol age in o he symme ic sequence
coun e pa s (
αand
β o he posi i e sequence, and
α
and
β o he nega i e one). Once he sag is de ec ed, he
p oposed ol age suppo con ol is launched. This pa o
he code will be ully desc ibed in Sec ion III-B. Fo he
case whe e no sag has been de ec ed, he cu en e e ences
a e selec ed based on he con en ional beha io o a cu en -
mode in e e [32], depending on he p oduc ion, desi ed
powe ac o , ope a ional and economic cons ain s. A e
compu ing he e e ence cu en s i
αand i
β, a p opo ional-
esonan con olle compa es he e e ences and he sensed
cu en s o ge he du y cycles o he in e e dαand dβ.
Finally, a space ec o PWM compu es he swi ching imes
o each in e e b anch.
C. Vol age Suppo
Based on he scheme in Fig. 1, he ela ions among he
in e e and he g id ol ages, he injec ed cu en s, and he
g id impedance can be exp essed as
g
Ri
Ldi
d . (1)
whe e he ol age suppo om he g id o he PCC is
∆
g. This ol age inc emen clea ly depends on he
g id impedance as will be shown along his wo k. Indeed, he
main limi a ion o he ol age suppo con ol schemes is he
magni ude o his impedance. Fo weak g ids, highe ol age
suppo e ec s a e ob ained han o s i ones.
Also, as p e iously s a ed, in o de o injec a high-quali y
cu en in o he g id, and o deal wi h unbalanced ol ages, he
me hod o symme ic sequences has become he p e e ed ool
o de elop ad anced ol age suppo con olle s. To u he
de elop he con ol, some magni udes based on he symme ic
sequence heo y a e equi ed. A e ob aining he ins an aneous
ol age sequences
α,
α,
βand
β, he ampli udes o he
posi i e and nega i e sequences a e compu ed as
V
b
p
α
q
2
p
β
q
2(2)
V
b
p
α
q
2
p
β
q
2. (3)
No e ha along he ex , uppe case is used o indica e am-
pli ude a iables while ins an aneous alues a e w i en in
lowe case. Besides, he sag angle be ween he posi i e and
nega i e sequence ϕ, which is needed o de i e he solu ion,
is ob ained as [20]
cos ϕ
α
α
β
β
V
V
(4)
sin ϕ
α
β
α
β
V
V
(5)
ϕ
a an2
p
sin ϕ, cos ϕ
q
(6)
whe e a an2 is he wo-a gumen a c angen unc ion.
Thanks o he use o symme ic sequences, he in e e can
be iewed (when analyzing he ol age suppo e ec s) as
a cu en sou ce injec ing posi i e sequence ac i e I
pand
eac i e I
qcu en s in o he g id. This assump ion is he basis
o he de elopmen o he con ol p oposal, and he de i a ion
o hese ac i e and eac i e cu en e e ences a e he goal o
maximize he lowes phase ol age.
In o de o de ail he p oposed ol age suppo concep , Fig.
3 p esen s he phaso diag am o he phase ol ages o a gi en
ol age sag. The ampli ude o he phases Va,Vband Vcis
gi en in pe uni (p.u.). As shown in he phaso g aph, phase
A ba ely su e s he sag while phase C (in blue colo ) is he
mos a ec ed ol age. In he in e es o cla i y, he angle o
phase C ( he lowes ol age) is selec ed o be 180°. Unde his
conside a ion, he cu en s decomposi ion and he associa ed
angles a e be e app ecia ed in he g aph.
In o de o aise as much as possible he lowes phase
ol age, wo equi emen s a e needed, he i s one is o injec
he maximum a ed cu en o he in e e h ough his phase
(i.e. Ic
Imax), and he second one is ha his phase cu en
0°
30°
60°
90°
120°
150°
180°0°
30°
60°
90°
120°
150°
1p.u.
Ipc
Iqc
Ic
Imax
θ
Va
Vb
Vc
Fig. 3. Vol age suppo concep .
mus be injec ed in a pa icula angle wi h espec o he
phase ol age. This angle is ep esen ed by θ(which has
been a bi a ily selec ed o 60° in he phaso diag am). The
i s equi emen allows o a sa e ope a ion and a be e
u iliza ion o he in e e capabili ies du ing he sag. The
second equi emen is he key poin o maximize he ol age
suppo . Wi hou loss o gene ali y, his injec ed cu en can
be decomposed in o an ac i e Ipc and a eac i e componen
Iqc which a e in-phase and in-quad a u e wi h espec o he
phase ol age espec i ely. Depending on he magni udes o
hese wo cu en s, θwill be modi ied and di e en ol age
a ia ions will be p oduced depending on he g id impedance.
Assuming a mainly induc i e g id, i is clea ha injec ing a
mainly eac i e cu en Iqc will p oduce be e ol age suppo
e ec s on he g id. In such a case θ
90° . On he con a y, o
a mainly esis i e g id, he injec ed cu en should be mainly
ac i e Ipc, and θ
0° . In be ween hese wo ex eme cases,
he bes ol age suppo solu ion o any g id impedance mus
be ob ained, as i will be shown in Sec ion III-A.
D. Con ol Objec i es
Along his wo k, he con ol o be implemen ed du ing he
sag is based on he ans o ma ion o he unbalanced ol ages
in o he symme ic sequences. Thus, he phase cu en s Ipc
and Iqc need o be ans o med in o he co esponding I
p
and I
q alues, consis ing in he in-phase and in-quad a u e
cu en s ollowing he posi i e sequence ol age V
ins ead
o he phase ol age Vc. The cu en e e ence gene a o o
he symme ic sequences ha achie es his objec i e can be
exp essed as [19]
i
α
I
p
V
α
I
q
V
β(7)
i
β
I
p
V
β
I
q
V
α(8)
whe e i can be seen how he e e ence cu en s i
αand i
β
cause he in e e beha e as a posi i e sequence ac i e and
eac i e cu en sou ce.
I should be highligh ed ha he p oposal deals wi h posi i e
sequence ol ages, being he nega i e sequence uncon olled.
This ac s allows o a simple and easie implemen a ion, p o-
ducing balanced injec ed cu en s, which is o in e es du ing
unbalanced ol age sags. As a d awback, ol age imbalance
canno be mi iga ed wi h he p oposed me hod.
Along his wo k, he lowes phase ol age will be deno ed
as Vxin o de o deal wi h any ol age sag. Fo his pu pose,
he ollowing is de ined
Vx
min
Va, Vb, Vc
u
. (9)
Resuming he main con ol goals, i.e.
1) maximize he lowes phase ol age Vx
2) injec he maximum cu en o he in e e Imax,
he p oblem can be o mula ed as
max
x
P
a,b,c
u
Vx
I
p, I
q
subjec o: Ix
Imax.
(10)
The solu ion elies on inding a combina ion o ac i e and
eac i e cu en s
p
I
p, I
q
q
ha simul aneously maximizes he
lowes phase ol age by injec ing he maximum pe missible
cu en o he in e e Imax. As can be in e ed om (10), he
op imal solu ion comp ises se e al s ages. Fi s , o e alua e
he ol age suppo e ec o an injec ed phase cu en in o a
gene ic R-Lg id o any gi en ol age sag. Then, o ind he
cu en o ol age angle ha maximizes he ol age suppo .
And inally, o ansla e hese exp essions om he phase
alues in o he symme ic sequence alues. These h ee s eps
a e undamen al o de elop he solu ion o (10) as will be
shown in nex Sec ion, and cons i u es he main con ibu ions
o his wo k.
III. PROBLEM SOLUTION
This sec ion will be de o ed o sol e (10). The solu ion is
de eloped in wo s eps: i s ly, he ac i e and eac i e phase
cu en s ha maximizes he lowes phase ol age a e ob ained
and, secondly, he posi i e sequence ac i e and eac i e cu -
en s a e de i ed.
A. Maximiza ion o he Lowes Phase Vol age
P oposi ion 1. Le Ipx be he ac i e phase cu en associa ed
wi h he lowes phase ol age, and le Iqx be he eac i e phase
cu en . Unde his conside a ion, by selec ing
Ipx
Imax
R
a
R2
p
ωL
q
2(11)
Iqx
Imax
ωL
a
R2
p
ωL
q
2(12)
hen he lowes phase ol age Vxis maximized and he injec ed
phase cu en equals he a ed cu en o he in e e Ix
Imax, o a gi en g id equency ω, and o any g id impedance
Rand L.
P oo . The op imal ac i e and eac i e phase cu en s ha
maximize he ol age in he lowes phase a e ob ained by using
he me hod o he Lag ange mul iplie s. The p oblem consis s
in building he Lag ange unc ion Lbased on he objec i e
unc ion and he es ic ion gso ha
L
p
y1, y2, λ
q
p
y1, y2
q
λg
p
y1, y2
q
(13)
whe e λis he Lag ange mul iplie , and y1,y2a e he
dependen a iables.
Using (1) and he g aphical p ojec ion o each phaso as
shown in Fig. 3, he ol age suppo e ec s can be quan i ied.
To his end, he phase cu en is decomposed in o he ac i e
and eac i e pa s. A anging he in ol ed e ms in o a single
equa ion, and a e some ma hema ical manipula ions, he
heo e ical ampli ude o he phase ol age a he PCC side
can be ob ained. As a esul , he PCC ol age is ela ed o he
ol age ampli ude a he g id side, he injec ed cu en s and
he g id impedance as
Vx
ωLIqx
RIpx
b
p
Vgx
q
2
p
ωLIpx
RIpx
q
2(14)
whe e Vxis he ampli ude o he suppo ed phase ol age, Vgx
is he phase ol age a he g id side, and Ipx and Iqx a e he
unknown a iables.
Once he objec i e unc ion o be maximized
p
y1, y2
q
Vx
p
Ipx, Iqx
q
p esen ed in (14) is de i ed, a cons ain should
be included o keep he in e e cu en s sa ely con olled.
Resuming he cu en in phase C om Fig. 3, he es ic ion is
s aigh o wa d since bo h componen s in he phase cu en Ipx
and Iqx a e 90° delayed. Thus, he cons ain can be w i en
as
g
p
y1, y2
q
b
p
Ipx
q
2
p
Iqx
q
2
Imax
0. (15)
Each in ol ed e m in he Lag ange unc ion (13) has been
iden i ied o he p oblem s a ed. To ob ain he op imal solu-
ion, he nex s ep is he compu a ion o he g adien wi h
espec o he in ol ed a iables Ipx,Iqx and λ. Finally,
sol ing he g adien o ze o gi es he op imal solu ion
∇L
p
y1, y2, λ
q
B
L
B
Ipx
,
B
L
B
Iqx
,
B
L
B
λ
0. (16)
De eloping (16), he op imal cu en s
p
Ipx, Iqx
q
ha maxi-
mizes he lowes phase ol age a e (11) and (12).
Al e na i ely, by using igonome ic iden i ies, (11) and
(12) can be ew i en as
Ipx
Imax cos θ(17)
Iqx
Imax sin θ(18)
whe e
θ
a an2
p
ωL, R
q
. (19)
B. Phase Cu en s o Symme ic Sequence Cu en s
P oposi ion 2. Le
s
ϕbe he o a ion angle ha ansla es
he op imal ac i e Ipx and eac i e Iqx phase cu en s in
(17) and (18) o he symme ic sequence coun e pa s I
pand
I
q. Unde such conside a ion he ac i e and eac i e cu en
e e ences in (7) and (8), being he op imal solu ion o (10),
a e
I
p
Imax cos
p
θ
s
ϕ
q
(20)
I
q
Imax sin
p
θ
s
ϕ
q
.(21)
P oo . The p oo is de i ed om igonome ic ela ions
among he phaso s analyzed in Fig. 3. Wi hou loss o gene -
ali y, i can be assumed ha he phase o cu en angle, namely
ϕIx
Vx, equals he impedance angle, i.e.
ϕIx
Vx
θ
0. (22)
By de ini ion,
ϕIx
Vx
ϕVx
ϕIx(23)
is he phase o cu en angle. Based on he phaso analysis, and
con enien ly de eloping he exp essions o he ol age angle
ϕVxand he cu en angle ϕIxas a unc ion o he posi i e
and nega i e sequences, he ollowing ela ion hold [33]
ϕIx
ϕ
ϕx
a an2
p
I
q, I
p
q
(24)
and he angle o he lowes phase ol age can be de i ed by
using di e en me hods, he p oposed one decomposes he
phase ol age in o di ec and quad a u e p ojec ions, based on
he posi i e, nega i e and sequence angle as
ϕVx
a an2
V
sin
p
ϕ
ϕx
q
V
sin
p
ϕx
q
V
cos
p
ϕ
ϕx
q
V
cos
p
ϕx
q
(25)
whe e ϕxindica es he angle
0,
2π
{
3,
2π
{
3
u
associa ed o
he lowes phase ol age as
ϕx:
$
&
%
0,120°
¤
ϕ
240°
ñ
x
a
2π
{
3,0°
¤
ϕ
120°
ñ
x
b
2π
{
3,240°
¤
ϕ
360°
ñ
x
c.
(26)
Equa ion (24) ela es he phase cu en angle ϕIxwi h he
ampli ude o he posi i e sequence ac i e I
pand eac i e I
q
cu en s. This ela ion is he s a ing poin o he de ini ion
o
s
ϕas will be shown below.
Equa ion (25) is de i ed om he igonome ic analysis o
he ol age phaso s in Fig. 3, and i p esen s a use ul me hod
o compu e phase ol age angles ϕVa,ϕVbo ϕVc, based on
he symme ic sequence ampli udes and he sag angle.
Las ly, (26) p esen s a me hod o ack he lowes phase
ol age based on he sag angle in (6). Due o he p ope ies
o symme ic sequences, he sag angle i sel can be used o
iden i y he lowes phase ol age as de ailed abo e. To achie e
his goal, i is equi ed o use he wo-a gumen a c angen
unc ion, in b ie a an2
pq
as p e iously s a ed in (6). This
unc ion helps o ob ain he angle in any o he ou possible
quad an s, be ween he posi i e and he nega i e sequence
ol ages. Thus, allowing o he iden i ica ion o he lowes
phase ol age [20]. The idea behind his ack angle is ha
gene al exp essions can be pa icula ized by using i s alue
ϕx
P
0,
2π
{
3,
2π
{
3
u
.
Using (26) in (24) and (25), and de eloping (23) wi h (22),
he ollowing holds
s
ϕ
ϕVx
ϕx
ϕ(27)
while( ue)
compu e ms
Va, Vb, Vc
0.85p.u?
Vol ageSuppo
pq
No malOpe a ion
pq
e u n
p
i
α, i
β
q
(sag de ec ed)
yes no
i
αi
βi
αi
β
Fig. 4. Flowcha o igge ing he ol age suppo con ol scheme.
Ou e e . gene a o Inne loop
Vol age
Suppo
i
α
i
β
P opo ional
Resonan
dα
dβ
Space
Vec o
Modula o
u1
u6
Plan iα
iβ
α
β
Sequence
ex ac o
α
β
α
β
Fig. 5. Con ol diag am o he p oposed con ol scheme.
which de ines he o a ion angle in (20)-(21) ha cons i u es
he op imal e e ence cu en s.
Based on (11) and (12), and applying igonome ic iden i-
ies o (20) and (21), he abo e exp essions can be ew i en
in e ms o a o a ing ans o ma ion as
I
p
Ipx cos
s
ϕ
Iqx sin
s
ϕ(28)
I
q
Iqx sin
s
ϕ
Ipx sin
s
ϕ(29)
which conclusi ely is he op imal solu ion o (10).
A e de eloping he heo e ical solu ion, (28) and (29), o
he p oblem in (10), a s ep by s ep p ocedu e o implemen his
solu ion is p esen ed. The lowcha o he decision algo i hm
is p esen ed in Fig. 4. In his cha , i can be shown how he
igge ing decision o he whole ol age suppo con olle is
implemen ed. The igge consis s on he compa ison o he
oo mean squa e ( ms) ol ages wi h he common h eshold
ol age o 0.85 p.u. [8], [10]. Whene e he ms ol age
o one o he phases alls below his h eshold, he sag is
de ec ed. Depending on his compa ison, he in e e ope a es
in no mal mode o launchs he ol age suppo con ol scheme
p esen ed in Fig. 5. In his scheme, i can be app ecia ed he
ou e e e ence gene a o , he inne cu en loop, he modula o
and he plan . The de ailed implemen a ion o he e e ence
gene a o is shown in Fig. 6, which p esen s he algo i hm
ha sol es he p oblem a un- ime.
IV. IMPACT OF IMPEDANCE MISMATCHES
This Sec ion de i es an exp ession o quan i y he de ia ions
p oduced in he ampli ude o he minimum ol age due o he
misma ch in he g id impedance es ima ion.
Along he wo k, i has been assumed ha he g id
impedances Rand La e known. Two me hods ha e been
p oposed o no i y he g id alues: a known g id model
FUNC :
i
α,i
β
Vol ageSuppo
α,
α,
β,
β
1θ
a an2
p
ωL, R
q
/* F om known model o es ima o */
2Ipx
Imax cos
p
θ
q
3Iqx
Imax sin
p
θ
q
4V
b
p
α
q
2
p
β
q
2
5V
b
p
α
q
2
p
β
q
2
6cos
p
ϕ
q
α
α
β
β
V
V
7sin
p
ϕ
q
α
β
α
β
V
V
8ϕ
a an2
p
sin
p
ϕ
q
,cos
p
ϕ
qq
9i 120°
¤
ϕ
240° hen
10 ϕx
0/* Lowes phase is A */
11 else i 0°
¤
ϕ
120° hen
12 ϕx
2π
{
3/* Lowes phase is B */
13 else i 240°
¤
ϕ
360° hen
14 ϕx
2π
{
3/* Lowes phase is C */
15 ϕVx
a an2
V
sin
p
ϕ
ϕx
q
V
sin
p
ϕx
q
V
cos
p
ϕ
ϕx
q
V
cos
p
ϕx
q
16
s
ϕ
ϕVx
ϕx
ϕ
17 I
p
Ipx cos
s
ϕ
Iqx sin
s
ϕ
18 I
q
Iqx cos
s
ϕ
Ipx sin
s
ϕ
19 i
α
I
p
V
α
I
q
V
β
20 i
β
I
p
V
β
I
q
V
α
21 e u n
i
α,i
β
Fig. 6. Pseudo-code o he con olle implemen a ion o he ol age
suppo p oposal.
based on he nea by elemen s whe e he powe acili y is
connec ed, and an on-line impedance es ima o . Bo h me hods
ha e inhe en bene i s and d awbacks. Wha e e he me hod
used, a ce ain disc epancy be ween he eal g id alues Rand
L, and he es ima ed alues used o implemen he p oposal
p
Rand
p
Lcould exis .
Assuming ha I
pand I
qin (28)-(29) a e buil based on a
pe ec impedance es ima ion, he ollowing holds
V
x
Vgx
Imax
a
R2
p
ωL
q
2(30)
whe e V
xis he maximum ol age a he PCC ha can be
achie ed wi h he p oposed con ol scheme o he lowes
phase ol age. Howe e , in case o disc epancies be ween he
eal and es ima ed impedance alues (i.e.
p
R
Rand
p
L
L
co esponding o an es ima ed impedance angle
p
θ
θ), he
lowes phase ol age is
Vx
b
V2
gx
I2
max
p
Rsin
p
θ
ωLcos
p
θ
q
2
Imax
p
Rcos
p
θ
ωLsin
p
θ
q
(31)
which co espond o a lowe ol age suppo compa ed wi h
he case whe e he impedance is pe ec ly known. The abo e
exp essions can help o u he unde s and and quan i y he
e ec s o a poo g id impedance es ima ion.
I is wo h men ioning ha he g id model used along
his wo k, made by a ol age sou ce and an equi alen g id
impedance, (see Fig. 1 o de ails), is a simpli ied e sion o
TABLE I
SYSTEM PARAMETERS
Symbol Nominal alue
base powe Sbase 2.3kVA
a ed cu en Imax 10 A(peak)
g id ol age g155 V(l-n, peak)
g id equency ω2π60 ad/s
g id induc ance L5mH
g id esis ance R1.3 Ω
impedance angle θ55
dc-link ol age Vdc 350 V
in e e induc ance Li5mH
il e capaci o C1.4µF
ou pu induc ance Lo2mH
swi ching equency s10 kHz
he eal g id. In a eal powe sys em, AC g id pa ame e s and
loads a e changing dynamically. Thus, a ce ain disc epancy
be ween he eal and he es ima ed g id impedance could
exis s. Howe e , as will be shown in nex Sec ion, a pe ec
g id impedance es ima ion is no eally needed.
V. EXPERIMENTAL RESULTS
Based on Fig. 1, a scale-down labo a o y p o o ype has
been buil o check he dynamic and s a ic pe o mance o
he con ol p oposal agains a ime- a ying ol age sag.
A. Labo a o y Se up
The expe imen al se up is made up o an Am el DC powe
sou ce, a Guasch h ee-phase in e e and a Paci ic AC powe
sou ce o ge epe i i e ol age sags. The con olle ask is
implemen ed on a F28M36 Texas Ins umen s digi al signal
p ocesso based on he pseudo-code p esen ed in Fig. 2.
The main sys em pa ame e s a e collec ed in Table I.
F om his able, he nominal alues o he g id impedance
a e R
1.3Ω and L
5mH, being ω
2π60 ad/s. Hence,
he impedance angle is θ
a an2
p
ωL,R
q
55°. I is wo h
men ioning ha he pe uni impedance alues a e R
0.08
p.u. and L
0.12 p.u, which can be conside ed as a weak
g id. Howe e , he me i o he con ol scheme does no ely
on he s i ness o weakness o he g id bu in he L
{
R a io.
This weak g id es -case has been selec ed o highligh he
ol age suppo e ec s and o es he dynamic pe o mance
o he con ol scheme in a wo s case scena io.
B. E alua ion o Dynamic Pe o mance
The es scena io is di ided in o h ee pa s, i s ly he no -
mal ope a ion mode, in which he in e e injec s P
2000W
and Q
0VA in o he g id. Second case co esponds o he
occu ence o he ol age sag, whe e he p oposed ol age
suppo desc ibed in Fig. 6 is launched and he esul s a e
p esen ed below. Finally, he hi d case is he pos - aul s a e,
whe e he in e e comes back o he no mal ope a ion mode
once he aul has been clea ed.
The sag unde es is p esen ed in Fig. 7. The ins an aneous
phase ol ages a e shown in he op, and he ms alues a e
plo ed in he bo om. A
0s, he sag occu s and, a
0.2s,
-150
0
150
Phase
ol ages (V)
ga
gb
gc
-0.05 0 0.05 0.1 0.15 0.2 0.25
(s)
0
50
100
RMS
ol ages (V)
Vga
Vgb
Vgc
Fig. 7. Expe imen al esul s o he ins an aneous and ms phase ol ages o he sag unde es wi hou ol age suppo .
-150
0
150
Phase
ol ages (V)
a
b
c
(s)
0
50
100
RMS
ol ages (V)
Va
Vb
Vc
(s)
0
5
10
15
RMS
di e ence (V)
∆Va
∆Vb
∆Vc
-10
-5
0
5
10
Phase
cu en s (A)
ia
ib
ic
0
5
10
Sequence
cu en s (A)
I+
p
I+
q
0
1
2
Ins an . pow.
(kW,kVA )
p
q
-0.05 0 0.05 0.1 0.15 0.2 0.25
(s)
0
120
240
360
Angles (◦)
ϕ
ϕx
ϕVx
¯ϕ
Fig. 8. Expe imen al esul s o he dynamic pe o mance o he ol age suppo p oposal. F om op o bo om: ins an aneous phase ol ages,
ms ol ages, ms ol age di e ence among no ol age suppo and he p oposed me hod, injec ed phase cu en s, ac i e and eac i e e e ence
cu en s, ins an aneous ac i e and eac i e powe s, and in ol ed angles o he compu a ion o he solu ion.
he aul is clea ed by he p o ec ion de ices. In be ween, he
sag has a dynamic p o ile o es he p oposal agains his
complex aul . I can be seen ha along he es , he h ee-
phase ol ages a e a ec ed, howe e he lowes ol age Vx
conce ns o phase C.
In o de o es he pe o mance o he ol age suppo
con ol, Fig. 8 p esen s he mos impo an signals and mag-
ni udes in ol ed. F om op o bo om, he plo shows he
ins an aneous phase ol ages, he ms phase ol ages, he
ms ol age di e ence be ween he p oposed con ol and he
base- es wi hou ol age suppo , he injec ed phase cu en s,
he e e ences o he ac i e and eac i e sequence cu en s,
ins an aneous ac i e and eac i e powe s, and he angles as
compu ed wi hin he con ol loop.
Compa ing ins an aneous and ms phase ol ages in Fig.
7 (wi hou ol age suppo ), and he ol ages on op o Fig.
8 (wi h ol age suppo ), i is clea ly mani es ed he main
con ibu ion o his wo k: he ol age inc ease o he lowes
phase ol age. The ms compa ison o bo h es s can be be e
app ecia ed in he nex plo , whe e he ms ol age di e ence
wi h and wi hou ol age suppo is p esen ed. Acco ding o
(30), he lowes phase aises app oxima ely 15V independen ly
o he ol age sag p o ile. This is due o he ac ha he
con ol p oposal compu es he op imal solu ion based on he
o a ion angle as p e iously de ailed. I should be poin ed
ou ha his high ol age inc emen is due o he weak g id
scena io. Howe e , o s i g ids, he objec i e o educing he
isk o unde - ol age disconnec ion will be also accomplished
al hough he ol age a ia ion will be less han in he weak
case. The o he phases p esen less ol age inc emen , as
expec ed due o he ac ha he p oposal is in ended o
op imize he lowes phase ol age.
Nex plo o Fig. 8 p esen s he ins an aneous phase cu en s
ha he in e e injec s du ing he es . Be o e he sag and
when he sag is clea ed, he in e e injec s an ac i e powe
acco ding o he p oduc ion o he powe sou ce. When he sag
is de ec ed, he in e e launches he ol age suppo con ol
o imp o e he ol age p o ile. As can be shown in his g aph,
he injec ed cu en s du ing he sag each he a ed cu en
o he in e e (Imax
10A along he expe imen s). The e o e,
he second objec i e o he p oposal, which consis s in a sa e
cu en injec ion du ing he sag is also accomplished. This
second objec i e no only allows o a sa e in e e ope a ion,
bu also helps o ake ad an age o he as eac ion o in e e -
based powe con e e s when in e aced wi h he g id in on
o sudden pe u ba ions.
A e p esen ing he injec ed phase cu en s, i is wo h
showing he e e ences o he ac i e and eac i e sequence
cu en s. Nex plo o Fig. 8 shows he alues o hese wo
magni udes. The ac i e cu en injec ed be o e and a e he
sag is app oxima ely 8A, and he eac i e cu en is ze o. How-
e e hese alues change du ing he sag so as o gene a e he
app op ia e cu en e e ences ha a e needed o achie e he
abo e men ioned con ol objec i es. The dynamic e olu ion o
hese e e ence cu en s a e due o he dynamic p o ile o he
ol age sag.
Nex plo in he igu e shows he ins an aneous ac i e and
eac i e powe s du ing he expe imen . Be o e he sag, he
in e e injec s 2000W and 0VA , du ing he sag hese alues
e ol e acco dingly o dynamically adap he e e ences o he
op imal solu ion. No e ha he ene gy s o age capaci y o he
in e e allows o egula e he excess/lack o ac i e powe o
he dynamic needs du ing he aul . When he sag has been
clea ed, he p e- aul alues a e kep . As can be app ecia ed in
he plo , du ing he sag bo h magni udes ha e oscilla ions a
wice he g id equency, as expec ed o unbalanced ol age
sags. I should be no iced ha he p oposed me hod can nei he
educe he ol age imbalance no cancel he ac i e powe
oscilla ions, which ha e been selec ed in o he s udies as wo
in e es ing objec i es du ing aul s. This limi a ion is due o he
injec ion o posi i e sequence powe s only, being he nega i e
sequence una ec ed. As a esul , p oblems de i ed om he
oscilla ions in he dc-link ol age should be conside ed, and
o e - ol age in he phase(s) ha do no su e he sag can be
p oduced.
Las plo in Fig. 8 is in ended o p esen he angles compu ed
wi hin he con olle . These angles only ha e a physical
meaning du ing he sag, so he analysis is ocused on his
in e al. F om op o bo om, he sag angle ϕp esen s he angle
be ween he posi i e and nega i e sequence ol ages. The ack
angle ϕxindica es which phase is he lowes one. As can be
obse ed in he sag ol ages, he lowes phase is Vc, hus he
ack angle is 120° du ing he g id aul . The phase ol age
angle ϕVxshows whe e his ol age is loca ed. Al hough i
180º 134º 0º -162º
-100
-50
0
51
107
140
a b c
180º 78º -42º -163º
-10
0
10
iaibic
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
Fig. 9. Time-domain and phaso analysis o ol ages and cu en s.
is close o 120°, he dynamic e olu ion o he ol ages du ing
he sag, makes his ol age angle o change sligh ly depending
also on he ol age sag p og ammed in he expe imen . Finally,
he angle
s
ϕshows he in o ma ion o he o a ion om phase
cu en s o sequence cu en s as heo e ically explained be o e.
C. E alua ion o S a ic Pe o mance
Once he dynamic pe o mance o he con olle has been
p esen ed and discussed, a s a ic analysis has been pe o med
o show addi ional ea u es o he p oposal. Fig. 9 shows he
suppo ed ol ages and he injec ed cu en s in one g id cycle.
The alues ha e been a bi a y collec ed in he middle o
he sag a ime
0.1s. The igu e is di ided in o 2pa s
co esponding o he ime-domain alues (on he igh ) and
he phaso plo s (on he le ). In o de o co obo a e ha
he ol age o cu en angle ma ch he impedance angle θ,
he ime-domain plo s ha e labels indica ing he angle ins ead
o he ime. Fo simplici y i has been assumed a ze o angle
o he ol age o phase A when c ossing he o igin. As i
can be seen in he phaso diag am, he h ee phase ol ages
a e unbalanced and ha e di e en ampli udes. Howe e , he
cu en s ha e he same ampli ude and a e app oxima ely 120°
delayed. As p e iously s a ed, his igu e helps o compu e
he ol age o cu en angle. Taking a look a he labels o
he phase ol age C, i indica es 134°, and he cu en angle
shows 78°, co esponding o a di e ence o 134°
78°
56°
which s ongly ag ees wi h he heo e ical impedance angle
θ
55°. The e o e he p oposed me hod ensu es ha he phase
cu en can be injec ed in a pa icula angle wi h espec o he
lowes phase ol age, in such a way ha he ol age suppo
is maximized.
D. Impac o G id Impedance Misma ches
Las expe imen also deals wi h he s a ic analysis needed
o u he e alua e he op imal solu ion. Se e al es s ha e
been de eloped using a w ongly es ima ed g id impedance,
and he ol age suppo e ec s ha e been epo ed in Fig. 10.
