1
Abs ac --The inc easing amoun o enewable powe gene-
a ion sys ems is a challenging issue o he con ol and ope a ion
o he elec ical ne wo ks. One o he main issues is hei lack o
ine ia, which is becoming a g ea e p oblem as much as he sha e
o he powe plan s based on adi ional synch onous gene a o s
ge s educed. In his ega d he new g id codes ask hese plan s o
p o ide new unc ionali ies such as he equency suppo and
ine ia emula ion.
In his pape , a synch onous powe con olle o g id-
connec ed con e e s is p oposed as a good solu ion o he
enewable gene a ion sys ems wi h ene gy s o age. I p o ides
ine ia, damping and lexible d oop cha ac e is ics. Di e en
om he ai h ul eplica ion o he swing equa ion o synch onous
machines, an al e na i e con ol s uc u e is p oposed, by which
he damping and inhe en d oop slope can be con igu ed
independen ly o mee he equi emen s in bo h dynamics and
equency egula ions. Analysis and expe imen al esul s a e bo h
shown o alida e he p oposed con olle .
Index Te ms--DC-AC powe con e sion, Ine ia emula ion,
Powe gene a ion con ol, Synch onous powe con olle .
I. INTRODUCTION
adi ional gene a ion plan s based on enewable ene gy
sou ces (RES) ac as g id- eeding sys ems, which deli e
he maximum powe om he p ima y sou ce o he g id [1].
As much as he pene a ion o he RES gene a ion plan s
inc eases, he insu icien ine ia in he whole ne wo k could
unde mine i s ope a ing s abili y. The e o e, he con ol
objec i es and dynamics o he g id-connec ed con e e s need
o be adjus ed o ake mo e esponsibili ies in g id suppo ing
issues, such as ine ia emula ion, equency egula ion and
ol age suppo .
The d oop con ol s a egy has been implemen ed in he
con ol o g id-connec ed con e e s as seen in [2]–[6]. E en
hough he ou e d oop loops allow he g id-connec ed
con e e s o adjus he s eady-s a e powe injec ion acco ding
o he demand o he g id, he ansien beha io s o hese
This wo k has been pa ially suppo ed by he Spanish Minis y o
Economy and Compe i i eness unde he p ojec ENE2014-60228-R.
W. Zhang, A. M. Can a ellas, J. Rocabe , A. Luna and P. Rod iguez a e
wi h he Depa men o Elec ical Enginee ing, Technical Uni e si y o
Ca alonia, Ba celona 08222 Spain (e-mail: weiyi.zhang@es udian .upc.edu).
A. M. Can a ellas and P. Rod iguez a e also wi h Abengoa Resea ch,
Abengoa, Se ille 41014 Spain (e-mail: ped o. od [email protected]).
con e e s a e no good enough. The lack o ine ia is s ill a
d awback, which canno be imp o ed by d oop con ol wi hou
jeopa dizing he s able ope a ion o a g id-connec ed con-
e e .
A solu ion o imp o e he dynamics o he con e e s is o
speci y he p ope ies o he g id-connec ed con e e s in such
a way ha i ac s like a synch onous gene a o (SG), as is
p oposed in [7]. I is an app oach ha has been d awing a lo
o in e es s in he ecen yea s. This end is ini ia ed by he
ac ha con en ional g id synch oniza ion algo i hm like
Phase-locked loop (PLL) p esen s no ine ia cha ac e is ics,
and he dynamics o any suppo ing s a egy is a ec ed by he
inhe en dynamics o he PLL. Mo eo e , a PLL migh ha e a
nega i e impac on he con ol pe o mance unde weak ac
g ids [8].
A con ol implemen a ion scheme o he emula ion o SG
is p oposed in [9], in which he loop il e o he con en ional
PLL is modi ied o emula e he ine ia and damping cha ac e -
is ics. O he simila design o p oposals inco po a ing ine ia
and damping in a PLL can be ound in [10] and [11]. Based on
he s a egy in [9]–[11], he ine ia e ec is only linked o he
g id equency, and does no essen ially exis while eac ing o
he powe inpu a ia ions. Then he pe u ba ions in he dc
side will be di ec ly ansmi ed o he ac side wi hou ine ia.
In addi ion, he ine ia e ec does no exis in island ope a ion
based on his ype o design.
Ano he implemen a ion s a egy o emula ing SG is
p oposed and analyzed in [8], in which he PLL is subs i u ed
by an ac i e powe synch oniza ion loop. E en hough his
s a egy has shown ad an ages in he in e connec ion o weak
ac g ids [12], he ine ia and oscilla ion damping a e no
speci ically add essed, and i has o be swi ched o a PLL-
based ec o cu en con ol unde se e e ac aul s.
In [13]–[15], a o que synch oniza ion loop is designed
conside ing ine ia and damping cha ac e is ics. A simila
s a egy is also adop ed in [16]. The au ho s in [17]–[19]
p opose a synch onous powe con olle p esen ing ine ia and
damping cha ac e is ics, and pa icula ly a i ual admi ance
s uc u e is p oposed. The au ho s in [20] and [21] indica e
ha he ine ia can also be implemen ed in he mic og id d oop
con olle , making use o he i s -o de low-pass il e which
is adi ionally used only o damping he measu emen noise.
Synch onous Powe Con olle wi h Flexible
D oop Cha ac e is ics o Renewable Powe
Gene a ion Sys ems
W. Zhang, S uden Membe , IEEE, A. M. Can a ellas, S uden Membe , IEEE, J. Rocabe , Membe ,
IEEE, A. Luna, Membe , IEEE, and P. Rod iguez, Fellow, IEEE
T
2
The abo emen ioned designs in [13]–[21] inco po a e he
swing equa ion inhe en ly in he powe egula ing loop, hus
he powe synch onizing e ec will be p esen in bo h g id-
connec ed o island ope a ion. Ne e heless, he damping
e ec and he powe - equency d oop slope a e cons ained by
each o he . Due o his, a good pa ame e o he d oop ea u e
may lead o an insu icien damping, and in he o he way
a ound, a p ope damping pa ame e could gi e ise o an
undesi ed d oop slope. On he o he hand, since he d oop
cha ac e is ics is na u ally inco po a ed in he powe egula ing
loop, a ixed powe con ol canno be di ec ly achie ed e en i
i is needed in some applica ions. In [13], he au ho s p opose
o use an addi ional PI con olle wi h a i ual swi ch o adjus
he damping channel o achie e a ixed powe con ol i
needed, bu he o de o he closed-loop ans e unc ion will
inc ease, hus he dynamic analysis and uning o pa ame e s
become mo e complex.
This pape p oposes a synch onous powe con olle wi h
ine ia, damping and lexible d oop cha ac e is ics o g id-
connec ed con e e s. Compa ed wi h he exis ing echniques,
damping and d oop cha ac e is ics a e pa icula ly add essed,
while he ine ia ea u e is main ained. The damping
pe o mance is impo an o he local s abili y and dynamics
o he RES-based gene a ion sys ems. And he d oop
cha ac e is ics is necessa y o ul il he equi ed equency
suppo . The e o e, ins ead o uning a single pa ame e o ind
a good adeo be ween bo h damping and d oop cha ac e -
is ics, a powe loop con olle is p oposed o con igu e
damping and d oop cha ac e is ics sepa a ely. In addi ion, an
explici ela ion among he con olle gains, ine ia, damping
coe icien and d oop slope is gi en, and hus he p oposed
me hod makes a lexible con ol pa adigm possible in which
he con olle gains can be adap i e.
The emaining pa o he pape is o ganized as ollows. In
sec ion II, he mechanism and implemen a ion o he o e all
a chi ec u e o he synch onous powe con olle is in oduced
b ie ly. In sec ion III, he design o he elec omechanical
block is p esen ed and a powe loop con olle is p oposed.
The con ol pa ame e s se ing is shown in sec ion IV. Finally,
in sec ion V and VI, simula ion and expe imen al esul s a e
espec i ely gi en.
II. OVERALL CONTROL STRUCTURE
The p oposed powe loop con olle is based on he gene al
synch onous powe con ol (SPC) a chi ec u e shown in Fig. 1.
This con ol scheme is mainly cha ac e ized by wo blocks, he
elec omechanical block and he i ual admi ance block,
which a e espec i ely desc ibed in [17], [22], [23]. In addi ion
o he con ol scheme shown in Fig. 1, ou e loops can be
added. Depending on he equi emen s o he g id and he
con igu a ion and con ol s a egy a he dc side, he ou e
loops can a y. No mally a Q-V d oop con olle is added o
weak g id suppo and island g id o ming. And conside ing
he limi ed powe ese e om he dc side, an ou e P-Vdc
d oop con ol can also be included as an addi ion o he P-
cha ac e is ics.
Based on he gene al con ol s uc u e, he ine ia can be
essen ially inco po a ed in he elec omechanical con ol loop
by p ope ly designing he powe loop con olle .
As shown in Fig. 1, he powe loop con olle gene a es a
i ual synch onous equency ω, which is hen in eg a ed o a
phase signal θ. Combining he phase signal θ and he
magni ude signal E (gene a ed by he eac i e powe
con olle ), he i ual elec omo i e o ce e will be gene a ed
by he Vol age Con olled Oscilla o (VCO). In his case a PI
con olle is implemen ed in he eac i e powe con ol loop.
The i ual admi ance s uc u e adop ed in [13], [18] is
selec ed as he s uc u e o he inne con ol loops, which is
shown in Fig. 2. I is an emula ion o he ou pu impedance o
SG. This block plays a key ole in load sha ing and p esen s a
na u al ol age magni ude d oop ea u e o g id ol age
suppo .
Fig. 2. Vi ual admi ance emula ing he elec ical cha ac e is ics o synch o-
nous machines.
Compa ed wi h he well-known i ual impedance s uc u e,
Fig. 1. The o e all con ol scheme o synch onous powe con olle
.
3
he i ual admi ance s uc u e emula es he ou pu impedance
wi hou leading o he di icul ies in implemen a ion. The main
ad an ages lay on he e ec i eness o he comple e ange o
ha monic equencies and he simplici y in he inne loop
implemen a ion [18].
Acco ding o he elec ical cha ac e is ics o he synch o-
nous machines, he gene a ed ac i e powe can be app oxi-
ma ed o (1), conside ing ha he ou pu impedance o SG is
mainly induc i e.
ΔδP=ΔP
max
(1)
whe e ∆P is he inc emen al gene a ed powe , and ∆δ is he
inc emen al phase-angle di e ence be ween he i ual elec o-
mo i e o ce e and he g id ol age in each phase. The
admi ance gain is exp essed as,
X
EV
=Pmax
(2)
whe e E and V a e espec i ely he RMS alues o e and , and
X he alue o he eac ance p o ided by he i ual
admi ance.
Based on (1), he inne con ol loops can be simply
modeled as an admi ance gain since i has much as e
dynamics compa ed wi h ou e loops. So i a oids he
complexi y in he analysis o powe loop.
III. ELECTROMECHANICAL BLOCK
Acco ding o he con ol scheme shown in Fig. 1, he ac i e
powe egula ing loop can be modeled as shown in Fig. 3,
whe e he powe loop con olle GPLC(s) is designed in his
sec ion. The synch oniza ion mechanism o he SPC-based
con e e is simila o he one o a SG. E en i he g id ol age
angle θg id is unknown, he synch onous angula speed ω can
always be adjus ed o acco dingly shi he load angle δ. In his
way he ac i e powe is egula ed.
+
-
-
+
Powe Loop Con olle
s
1
δ
P
*P
P∆
max
P
θ
g id
θ
ω
)(sG
PLC
Vi ual admi ance
based con e e
Fig. 3. Modeling o ac i e powe con ol loop
As he main ocus o his pape , a powe loop con olle is
p oposed. In he ollowing, he exis ing echniques ha
i ually implemen he swing equa ion o SG a e analyzed
i s , and he bounda ies o he exis ing echniques a e shown.
Then an al e na i e con olle is p oposed, and he
ma hema ical ela ionship be ween he cha ac e is ic
pa ame e s and he con ol pa ame e s is illus a ed.
A. Mechanical Powe Loop Con olle
The SG swing equa ion can be exp essed as (3) in e ms o
powe , o small signals o he o o angula equency ω
a ound he synch onous equency.
ωDJs+ω=PP selecmech )(-
(3)
In (3), Pmech is he inpu mechanical powe , Pelec he ou pu
elec ical powe , ωs he synch onous angula equency, J he
momen o ine ia and D he damping pa ame e . E en hough
he dampe winding o SG can p o ide he damping e ec , i is
ela i ely limi ed. Conside ing his ac , he damping o he
powe loop can be imp o ed and op imized o con ol o g id-
connec ed con e e s. The e o e, he damping e m is
conside ed as well as he ine ia.
Based on he swing equa ion, he o m o GPLC(s) can be
designed as shown in (4), which is e e enced as mechanical
powe loop (MPL) con olle in his pape .
)(
1
)( DJs+ω
=sG
s
PLC
(4)
Acco ding o (4), he esul ing closed-loop ans e unc ion
is ob ained and shown in (5a).
2
2
2
2
)(
nn
n
*
ωs+ξω+s
ω
=s
P
P
(5a)
max
s
JP
ω
D
=ξ2
(5b)
s
max
nJω
P
=ω
(5c)
Equa ion (5a) is gi en in he speci ic o m as an analogy o
he second o de pa ame ic ans e unc ion, o which he
ime esponse is de ined by he pa ame e s ωn and ξ.
Mo eo e , ωn and ξ a e also linked o he damping and ine ia
pa ame e s o he SG swing equa ion h ough (5b) and (5c).
To gua an ee he local s abili y o he sys em, ξ has o be
speci ied g ea e han ze o.
Ins ead o using he momen o ine ia J o designa e he
ine ia cha ac e is ics, he ine ia cons an H is commonly
adop ed, which is de ined in (6), meaning he ime i akes o
accele a e he o a ional speed om ze o o ωs using ull
powe SN [24].
N
s
S
Jω
H= 2
2
(6)
Fo analyzing he dynamics o he powe con ol loop, he
esponse o equency dis u bances also needs o be s udied. In
he modeling, he g id equency can be linked o he g id
phase angle by an in eg a o . Acco ding o Fig. 3, aking ωg as
he a iable while aking P as he unc ion, he associa ed
ans e unc ion (P- esponse) is shown in (7).
2
2
2
)2(
)(
nn
nmax
g
ωs+ξω+s
ξωs+P
=s
Δω
ΔP −
(7)
I is seen om (7) ha he MPL con olle inco po a es an
in insic P- d oop ea u e. I he d oop a io DP is de ined as
(8), which desc ibes he s eady-s a e powe a ia ion caused by
he g id equency change,
kW/hz)0()
1000
2
(=
g
PΔω
ΔP
D⋅
π
(8)
4
hen combining (7) and (8), he in insic d oop a io o he
MPL con olle DP(MPL) is exp essed in (9).
n
max
MPLP
ω
πξP
=D 1000
4
)(
(9)
I is seen ha he MPL con olle b ings abou a con inuous
powe synch onizing beha io as long as he g id equency
de ia es om he nominal alue. Howe e , he d oop a io DP
is cons ained by he ine ia and damping pa ame e s ha leads
o a adeo in he pa ame e s se ing.
B. Bounda ies o he MPL Con olle
To u he show he es ic ions o he MPL con olle in
pa ame e s uning, he g id equency de ia ion pe cen age ha
ex ac s he ull a ed powe om he con e e is used as he
indica o o he d oop cha ac e is ics, which is ep esen ed by
1/R [25]. The ela ion be ween DP and 1/R is shown in (10).
sP
N
D
S
=
R
ω
π
2
1
(10)
Then he in e ac ion among ine ia, damping and d oop
slope de ined by he MPL con olle is ob ained as w i en in
(11), which is de i ed combining (5c), (6), (9) and (10).
s
pu
Hω
X
ξ
=
R22
1
(MPL)
1
(11)
whe e Xpu ep esen s he pe -uni alue o he eac ance o
i ual admi ance and is exp essed in (12).
max
N
pu
P
S
=X
(12)
Equa ion (11) shows he in e ac ion among H, ξ, Xpu and
1/R. And since he alues o H and Xpu can be p e- ixed
espec i ely conside ing he design equi emen , he challenge
mainly lies in he es ic ion be ween ξ and 1/R.
This es ic ion is isualized in Fig. 4, whe e H is speci ied
o 2, 11 and 20 espec i ely in h ee cases. The g id nominal
equency is se o 50 Hz and Xpu is se o 0.3 o speci y he
model.
0.3 0.5 0.7 0.9 1.1
0
1
2
3
Damping coe icien [p.u.]
D oop slope [%]
H=20
H=11
H=2
Fig. 4. The ela ion be ween he d oop slope 1/R and he damping coe icien
ξ. As shown in Fig. 4, once he damping coe icien ξ is uned
and ixed, he d oop slope will be ixed, oo. Howe e on he
o he hand, he d oop slope needs o be speci ied conside ing
he equency a ia ion o he u ili y g id and he powe
ese e o he gene a ion plan s.
Fo adi ional synch onous gene a o s, a ypical ange o
d oop slope is 4% < 1/R < 5% [25]. Bu o RES-based
gene a ion plan s, 1/R may ha e o be g ea e aking in o
accoun he powe ese e ha is echnically and economically
easible. In he scena ios shown in Fig. 4, 1/R is below 3%. I
1/R is equi ed o be g ea e , ξ has o be educed, which
unde mines he damping pe o mance.
This issue will no exis i he g id is domina ed by he
con e e s con olled wi h he MPL con olle s, since a small
alue o 1/R leads o s onge e ec in opposing equency
de ia ion. Howe e , i he o al gene a ion is domina ed by
adi ional synch onous gene a o s, he equency a ia ion in
he g id can cause equen sa u a ion o low powe quali y
injec ion o he gene a ion uni s ha ha e a small alue o 1/R.
C. Con igu able Na u al D oop Con olle
In o de o achie e a good g id in e ac i e pe o mance in
which he d oop slope can be speci ied independen o he
damping pa ame e , a powe loop con olle wi h ine ia,
damping and lexible d oop cha ac e is ics is p oposed as
shown in Fig. 5.
D oop con ol b anch
∫
+-
x
p
K
++
SG swing equa ion
∫
x
I
K
G
K
+-
P∆
*
ω
Fig. 5. The p oposed powe loop con olle .
O he han he implemen a ion o he swing equa ion o a
SG, a d oop b anch is included in pa allel o con olling he
P- d oop slope in s eady s a e. In his way i adjus s he o se
o he powe ans e unc ion by in oducing a new deg ee o
eedom. The s uc u e o he d oop b anch is de eloped in he
way ha i sha es he same denomina o wi h he ans e
unc ion o he swing equa ion. In his manne he o de o he
powe egula ing loop does no inc ease. In a p ac ical
implemen a ion he in eg a o s in he con olle can be
disc e ized using he Tus in apezoidal me hod o an accu a e
equi alence.
The ans e unc ion o he p oposed con olle is
gene alized as w i en in (13), which is e e ed as
con igu able na u al d oop (CND) con olle in his pape .
G
IP
PLC
Ks+
Ks+K
=sG )(
(13)
Compa ed wi h he MPL con olle , he CND con olle
p o ides an addi ional deg ee o eedom wi hou inc easing
he o de o he powe egula ing ans e unc ion. And i
gi es a na u al P- d oop ea u e which can be con igu ed in-
dependen o he ine ia and damping pa ame e s.
Subs i u ing he powe loop con olle block in Fig. 3 wi h
he exp ession (13), he esul ing closed loop ans e unc ion
5
is shown in (14a). The damping coe icien and na u al
equency a e espec i ely exp essed in (14b) and (14c).
2
2
2
2
)(2
)(
nn
nGn
*
ωs+ξω+s
ωs+Kξω
=s
P
P−
(14a)
n
GPmax
ω
K+KP
=ξ2
(14b)
Imaxn KP=ω
(14c)
E en hough (14a) has a di e en exp ession in he
nume a o compa ed wi h he s anda d second-o de pa a-
me ic ans e unc ion, he denomina o o he sys em is he
same. The e o e, in o de o place he closed-loop poles in he
le hal plain o gua an ee he s abili y, ξ s ill has o be
speci ied g ea e han ze o.
The P- esponse o he CND con olle is shown in (15),
2
2
2
)(
)(
nn
Gmax
g
s++s
Ks+P
=s
Δω
ΔP
ωxω
−
(15)
whe e (16) is ob ained.
I
G
CNDP
K
K
=D 1000
2
)(
π
(16)
Acco ding o (14b), (14c) and (16), by speci ying he
con ol pa ame e s KP, KI and KG, he ine ia, damping and
d oop cha ac e is ics can be espec i ely gi en. Besides, he
na u al equency ωn can be ansla ed o he ine ia cons an H
by combining (5c) and (14c) o equa e he ωn om wo cases.
Op ionally, DP can be se o ze o i he plan is assigned o
ha e a ixed powe con ol.
IV. CONTROL PARAMETERS SETTING
The con ol pa ame e s KP, KI and KG can be clea ly se
acco ding o he inpu o DP, H and ξ. Owing o he explici
link be ween he con olle gains and cha ac e is ic pa ame e s,
he con olle can easily be made adap i e acco ding o he
seconda y con ol, and a lexible con ol pa adigm becomes
possible. In he implemen a ion he algo i hm o calcula ing
he con ol pa ame e s based on (14b), (14c) and (16) can be
embedded in he con e e con olle , bu will only be
ac i a ed when he seconda y commands a e upda ed.
As men ioned in he o me sec ion, DP is he d oop a io
ha needs o be de e mined based on he equency a ia ion
o he u ili y g id and he easible powe ese e. H can be
designa ed conside ing he ine ia cons an o he SG ha has
he same powe le el. And he damping coe icien ξ can be se
conside ing he ypical alue ange
10 <<
x
o c ea e a s able
and unde -damped sys em.
In o de o u he une ξ, he analysis on dynamics is done
based on he ma hema ical ans e unc ions gi en in he
o me sec ion. A uni a y s ep inpu is gi en o he closed loop
ans e unc ion (14a), and he in luence o ξ on he se ling
ime and o e shoo o he ime esponse can be calcula ed.
Then ξ can be adjus ed o mee he equi emen s o he
con e e and he g id.
The analysis on he ela ion be ween ξ and he o e shoo o
he s ep esponse is shown in Fig. 6. Since he o e shoo o he
s ep esponse can conside ably e lec he damping
cha ac e is ics o he sys em, a alue g ea e han 0.7 is
p oposed as he p ope damping alue, which can gua an ee
he o e shoo o he s ep esponse o be smalle han 25%.
010 20 30 40
0
20
40
60
80
Dp [kW/Hz]
O e shoo [%]
xi=0.3
xi=0.5
xi=1.1
xi=0.9 xi=0.7
(a)
010 20 30 40
0
10
20
30
40
50
Dp [kW/Hz]
O e shoo [%]
xi=0.3
xi=1.1
xi=0.7 xi=0.5
xi=0.9
(b)
Fig. 6. The in luence o he damping coe icien ξ on he o e shoo o powe
s ep esponse: (a) H=2 and (b) H=20.
V. SIMULATION RESULTS
Simula ion s udies a e conduc ed o e alua ing he pe -
o mance o he p oposed con olle in cases o g id-connec ed
con e e s connec ing o weak (high-impedance) g ids and
island ope a ions.
A. Pe o mance when In e acing Weak G id
The in luence o sho ci cui a io (SCR) on he maximum
powe gene a ion can be easily shown in (17), which de ines
he pe -uni ou pu powe o a gene a ion uni .
δ
sin=⋅SCRP
pu
(17)
As seen om (17) ha he gene a ed powe will be always
smalle han he a ed powe , when SCR equals o one (which
yields an ex emely weak g id).
The p oposed con ol is able o injec ela i ely mo e powe
o weak g id unde he a ia ion o he powe e e ence,
compa ed wi h he con en ional ec o cu en con ol
accompanied by PLL. This ac is alida ed in Fig. 7. In his
case he SCR o he g id is con igu ed o one.
Fig. 7(a) shows he case when he con en ional ec o
cu en con ol is used, whe e he powe injec ion can be
achie ed un il 0.6 p.u. du ing s eps o powe e e ence based
on he op imal uning. When he p oposed con ol is used, he
powe injec ion can be up o 0.7 p.u. as seen in Fig. 7(b).
6
-20
0
20
Injec ed cu en [A]
0
0.5
1
Ac i e powe [p.u.]
1.5 22.5 3
-0.2
-0.1
0
0.1
0.2
Time [s]
Reac i e powe [p.u.]
1.8 1.82 1.84 1.86 1.88 1.9
-20
-10
0
10
20
2.8 2.82 2.84 2.86 2.88 2.9
-20
-10
0
10
20
(a)
-20
0
20
Injec ed cu en [A]
0
0.5
1
Ac i e powe [p.u.]
0.5 11.5 22.5 33.5 44.5 5
-0.2
-0.1
0
0.1
0.2
Time [s]
Reac i e powe [p.u.]
2.4 2.42 2.44 2.46 2.48 2.5
-20
-10
0
10
20
4.8 4.82 4.84 4.86 4.88 4.9
-30
-15
0
15
30
(b)
Fig. 7. Ac i e powe s ep esponse o he con e e connec ed o weak g id:
(a) con en ional ec o cu en con ol, (b) he p oposed synch onous powe
con ol.
Compa ing he ime esponse based on hese wo s a egies,
he la e one is ea u ed by an ine ial and mo e damped
esponse in p esence o powe e e ence s eps, which
con ibu es in damping he ansien s.
B. G id Disconnec ion and Island Ope a ion
The p oposed con ol is ea u ed by he capabili y o
eeding an island simila o synch onous machines. As
men ioned be o e, he e e ence o eac i e powe is gi en by
an ou e Q-V d oop con olle .
Based on he con ol scheme in Fig. 1 aided by an ou e Q-
V d oop con olle , he island ope a ion is possible. I is wo h
no ing ha he ac i e powe e e ence will no domina e he
ac i e powe injec ion in island ope a ion, ins ead, he powe
injec ion is de e mined by he i ual admi ance and he P-
d oop cha ac e is ics.
Fig. 8 shows a s udy case whe e a 100 kW and wo 10 kW
con e e s a e connec ed o he g id in pa allel, and se e local
loads o 100 kW.
G id
100 kW VSC3
g id
z
2
P
3
P
Local load 1
Local load 2
10 kW VSC2
10 kW VSC1
1
P
+
-
+
-
+
-
Fig. 8. A s udy case based on h ee pa alleled g id-connec ed con e e s wi h
di e en a ed powe .
Based on (1), (2) and (12), he powe a ia ion o a
gene a ion uni can be exp essed by,
δ∆∆
pu
pu X
P1
=
(18)
Acco ding o (18), he i ual eac ance o each con e e
is se o he same pe -uni alue o a p opo ional load
sha ing.
As an ini ial ope a ion poin , he g id connec ion swi ch is
closed, and he powe injec ion o 3 con e e s a e 8 kW, 7
kW, and 70 kW, espec i ely, co esponding o 0.8 p.u., 0.7
p.u. and 0.7 p.u., and he local load is pa ly ed by he main
g id.
Two e en s a e conside ed in he case s udy. A 1.2 s, a
ailu e in he main g id appea s, while a 1.3 s, he s ep change
o a local load akes place. Fig. 9 shows he esul s.
Rega ding he i s e en , he local ol age is well
main ained when he main g id ailu e occu s, hanks o he
g id o ming capabili y o he p oposed con ol. The local
ol age magni ude d op is calcula ed o be 4.22% as an
accep able alue. As a esponse o his e en , all he 3
con e e s inc ease he powe injec ion, and he inc emen al
powe is all a ound 0.1 p.u. (wi h espec o he a ed powe o
each con e e ). I complies wi h he designa ion o i ual
eac ance. The mino d op o he load powe is due o he d op
o he g id ol age magni ude.
Du ing he second e en , 20% o he local load (local load
1) is swi ched ou . The local ol age is well main ained a e a
sho ansien , and all he con e e s dec ease he powe
7
injec ion p opo ional o hei a ed powe .
-400
-200
0
200
400
G id ol age [V]
-400
-200
0
200
400
Load ol age [V]
6
8
10
Con e e s #1 and #2
ac i e powe [kW]
P
1
P
2
40
60
80
100
120
Con e e s #3
ac i e powe [kW]
P
3
1.15 1.2 1.25 1.3 1.35
60
80
100
Load
ac i e powe [kW]
Time [s]
Fig. 9. The islanding ac ion and load a ia ions o a h ee-po sys em.
VI. EXPERIMENTAL RESULTS
An expe imen al sys em based on a 10 kW g id-connec ed
con e e is buil o alida e he p oposed con olle . The
sys em s uc u e is shown in Fig. 10(a), and a iew o he
se ups is gi en in Fig. 10(b).
LCL- ap il e G id
Isola ion
ans o me
2L - VSC
L
o
L
C
C
o
R
co
L
g
i
abc
abc
dSPACE Acqui ing and Con ol
Sys em
PWM
pulses
dc
bus
(a)
dSPACE 1103
2-L con e e
DC powe sou ce
G id connec ion
il e
Isola ion
ans o me
(b)
Fig. 10. 10 kW Expe imen al sys em: (a) se ups con igu a ion and scheme, (b)
expe imen al se ups.
The dc bus is supplied by a 40 kW Magnapowe dc powe
sou ce, and he ac g id is o med by he Cali o nia Ins umen
egene a i e powe sou ce MX45. The con ol algo i hm is
implemen ed in a dSPACE 1103, and he pa ame e s o he
se ups and he con olle a e shown in Table I.
TABLE I
KEY EXPERIMENTAL TESTS PARAMETERS
Symbol De ini ion Value
VDC
dc-link ol age [V]
640
Vg
g id phase- o-phase ol age RMS [V]
400
g
g id nominal equency [Hz]
50
SN
nominal powe [kW]
10
sw
swi ching equency [Hz]
10050
ξ
damping coe icien [p.u.]
0.7
R
i ual esis ance [p.u.]
0.1
X
i ual eac ance [p.u.]
0.3
Fo an easy e alua ion and compa ison o he expe imen al
esul s, all he es s a e done conside ing he same alue o he
damping coe icien ξ, which is ixed o 0.7. The i ual
admi ance is designed conside ing he ange o he alues o
synch onous machines [18]. The pe -uni alue o i ual
eac ance is se o 0.3, co esponding o 15.3 mH, while he
pe -uni alue o i ual esis ance is se o 0.1 o su icien
damping, co esponding o 1.6 Ω.
S ep changes o powe e e ence and sweep o g id
equency a e gi en o alida e he dynamic pe o mance o
he p oposed con olle . The sweep o equency is imposed by
p og amming he powe sou ce wi h he equency excu sion
ha may occu in a g id wi h a limi ed amoun o ine ia.
Fo all he equency sweep es s shown in his pape , he
equency changes as: i inc eases om 50 Hz o 49.9 Hz
du ing 0.1 s, and hen a e 1 s, dec eases o 50 Hz aking 0.1
s. The CND con olle is i s implemen ed, and expe imen al
esul s om wo es cases a e shown. In he i s case, a s ep
change in he ac i e powe e e ence om 5 kW o 10 kW is
gi en when he con olle is con igu ed by H=10 s and DP =2
kW/Hz. The injec ed cu en wa e o ms a e shown in Fig.
11(a), whe e he injec ed ac i e and eac i e powe calcula ed
based on he expe imen al da a a e also plo ed. The measu ed
ac i e and eac i e powe is p ocessed by a low-pass il e o
emo e he high equency noise wi hou changing he ou line.
As shown in he esul s, he g id injec ed cu en and powe
change in a amp ins ead o a sha p s ep, showing he ine ia
cha ac e is ics. The ansien esponse wi hou any oscilla ions
also shows a p ope damping o he sys em. And in he s eady
s a e, he injec ed ac i e and eac i e powe is accu a ely
con olled.
In he second case, g id equency a ia ion is gi en. The
powe e e ence is se o 6 kW and 0 kVa , and he con olle
has he same pa ame e s as in he p e ious case. The esul s
a e shown in Fig. 11(b).
As seen om he esul s, he injec ed cu en and powe
oppose he a ia ion o he g id equency, showing a powe
synch onizing beha io . When he g id equency dec eases by
0.1 Hz, he ac i e powe s abilizes a 6.2 kW in s eady s a e,
8
complying wi h he designa ion o DP (2 kW/Hz). The i ual
synch onous equency gene a ed by he powe loop also
shows he ine ia cha ac e is ics as well as an accu a e lock o
he g id equency in s eady s a e.
-20
0
20
Cu en [A]
4
6
8
10
12
Ac i e powe [kW]
0.2 0.4 0.6 0.8 11.2
-2
-1
0
Time [s]
Reac i e powe [kVa ]
1.12 1.14 1.16 1.18
-30
-20
-10
0
10
20
30
0.12 0.14 0.16 0.18
-30
-20
-10
0
10
20
30
(a)
-20
0
20
Cu en [A]
4
6
8
Ac i e powe [kW]
0.5 11.5 22.5
49.8
49.9
50
Time [s]
Synch onous equency [Hz]
0.46 0.48 0.5 0.52 0.54
-30
-20
-10
0
10
20
30
1.56 1.58 1.6 1.62 1.64
-30
-20
-10
0
10
20
30
(b)
Fig. 11. Expe imen al esul s o he CND con olle when H=10 and DP=2: (a)
a s ep in powe e e ence, (b) esponse o g id equency a ia ions.
In con as , he esul s om wo cases when he MPL
con olle is used a e shown in Fig. 12. H is designa ed he
same alue as he p e ious cases as H=10 s.
Fig. 12(a) shows he esponse when a s ep in powe
e e ence is gi en. The MPL con olle leads o a esponse
wi h g ea e se ling ime and less o e shoo .
-20
0
20
Cu en [A]
4
6
8
10
12
Ac i e powe [kW]
20.4 20.6 20.8 21 21.2 21.4
-1.5
-1
-0.5
0
0.5
Time [s]
Reac i e powe [kVa ]
20.46 20.48 20.5 20.52 20.54
-30
-20
-10
0
10
20
30
21.4 21.42 21.44 21.46 21.48
-30
-20
-10
0
10
20
30
(a)
-20
0
20
Cu en [A]
4
6
8
10
12
Ac i e powe [kW]
0.5 11.5 22.5
49.9
49.95
50
Time [s]
Synch onous equency [Hz]
0.82 0.84 0.86 0.88 0.9
-30
-20
-10
0
10
20
30
1.82 1.84 1.86 1.88 1.9
-30
-20
-10
0
10
20
30
(b)
Fig. 12. Expe imen al esul s o he MPL con olle when H=10: (a) a s ep in
powe e e ence, (b) esponse o g id equency a ia ions.
Fig. 12(b) shows he esponse when a ia ion in g id
equency is gi en. The a ia ion o equency is he same as
he case when CND con olle is used. The in insic d oop
cha ac e is ics a e alida ed in Fig. 12(b). When he g id
equency changes om 50 o 49.9 Hz, he injec ed ac i e
powe inc eases om 6 kW and s abilizes a 10 kW. The
pe o mance is cohe en wi h he heo e ical d oop a io, which
is 40.522 kW/Hz. Then as long as he g id equency de ia es
in 0.1 Hz, he powe injec ion o he con e e will change o
9
4 kW (0.4 p.u.), which could be much g ea e han he desi ed
alue. In o de o adjus he d oop a io, he pa ame e ξ, H o
Xpu has o be comp omised.
The ine ia dynamics gi en by he p oposed CND con olle
is alida ed in expe imen al es and shown in Fig. 13. In his
plo he powe s ep esponses unde di e en H a e shown.
00.2 0.4 0.6 0.8
2500
5000
7500
10000
Time [s]
Powe [W, Va ]
H=5
H=10
(a)
00.2 0.4 0.6 0.8
2500
5000
7500
10000
Time [s]
Powe [W, Va ]
H=5
H=10
(b)
Fig. 13. Expe imen al esponses o a s ep change in powe e e ence om 5
kW o 10 kW: (a) DP =20 and (b) DP =0.
E en i he ime esponse will a y when di e en DP is
speci ied, which is seen by compa ing Fig. 13(a) and (b), i can
always be adjus ed h ough adjus ing he ine ia cons an H.
Since he na u al equency ωn is in e sely p opo ional o he
squa e oo o he ine ia cons an H, he ime o esponse is
app oxima ely p opo ional o he squa e oo o H. In Fig.
13(a), he se ling ime o he wo esponses a e calcula ed
544.1 ms and 732.4 ms, espec i ely. And in Fig. 13(b), a e
479.0 ms and 677.5 ms, espec i ely.
In o de o show he e ec o he i ual admi ance in g id
ol age suppo , an unbalanced ol age dip is pe o med, in
which he g id ol age in one phase is educed by 30 V in
RMS. Fig. 14 shows he esul s based on he p oposed
con olle . The unbalanced cu en can be explained by he
eac i e powe injec ion in each phase, which is shown in Fig.
14(b). Fo phase A, whe e he ol age magni ude d ops, he
eac i e powe injec ion is signi ican ly g ea e han he o he
wo phases. I exhibi s ha he implemen ed i ual admi ance
can egula e he eac i e powe injec ion o each phase
ollowing he ol age magni ude. The e o e, he unbalance in
g id ol age can be na u ally diminished. I is wo h no ing ha
his ea u e o unbalanced ol age suppo canno be achie ed
by an ou e Q-V d oop con olle . Mo eo e , i a selec i e
admi ance o nega i e sequence is implemen ed, he le el o
unbalance can be u he diminished.
Mos o he ine ia emula ion con ol elies on he
eplica ion o he swing equa ions o synch onous machines,
which is gene alized as he MPL con olle . Fig. 15 shows he
powe esponse o equency a ia ions o he p oposed CND
con olle compa ed wi h he MPL con olle based on he
expe imen al da a. DP is speci ied o 0, 2 and 4 kW/Hz o he
CND con olle in h ee cases. Fo he MPL con olle , DP
depends on H and ξ.
-200
0
200
Vol age [V]
1.5 22.5 33.5 4
-20
0
20
Time [s]
Cu en [A]
2.95 33.05 3.1
-400
-200
0
200
400
1.95 22.05 2.1
-400
-200
0
200
400
1.95 22.05 2.1
-30
-20
-10
0
10
20
30
2.95 33.05 3.1
-30
-20
-10
0
10
20
30
(a)
0.45
0.5
0.55
Ac i e powe [p.u.]
1.5 22.5 33.5 4
-0.1
-0.05
0
0.05
0.1
Time [s]
Reac i e powe [p.u.]
phase A
phase B
phase C
(b)
Fig. 14. Response in p esence o unbalanced ol age dip: (a) ol age and
cu en p o iles, (b) ac i e powe and eac i e powe in each phase.
I can be seen in Fig. 15 ha he s eady s a e alue o each
esponse based on CND con olle ma ches wi h i s speci i-
ca ion o DP, showing he con igu abili y o he d oop a io. In
addi ion, he ine ia and damping ea u e a e also shown,
whe e he esponses each he s eady s a e in hund eds o
milliseconds wi hou signi ican oscilla ions. The esponses
also show a beha io in opposing he g id equency de ia ion.
A s onge eac ion occu s in he ansien s a e han in he
s eady s a e. And in s eady s a e i keeps suppo ing he g id
acco ding o he designa ion o he d oop a io DP.
In con as , he MPL con olle exhibi s a s onge d oop
e ec ha can be seen om he powe change in Fig. 15. In a
g id wi h low-ine ia gene a ion, he excu sion o g id
equency can be as g ea as ±0.2 o ±2 Hz. Based on he
