IET Ene gy Sys ems In eg a ion
Resea ch A icle
Inno a i e p ima y equency con ol in low-
ine ia powe sys ems based on wide-a ea
RoCoF sha ing
eISSN 2516-8401
Recei ed on 2nd Janua y 2020
Accep ed on 12 h Feb ua y 2020
E-Fi s on 12 h Ma ch 2020
doi: 10.1049/ie -esi.2020.0001
www.ie dl.o g
Ha old R. Chamo o1 , Felix Ra ael Segundo Se illa2, F ancisco Gonzalez-Longa 3, Kuma s Rouzbehi4,
Hec o Cha ez5, Vijay K. Sood6
1KTH, Royal Ins i u e o Technology, S ockholm, Sweden
2Powe Sys ems and Sma G id Lab a he Zu ich Uni e si y o Applied Sciences, Zu ich, Swi ze land
3Uni e si y o Sou h-Eas e n No way, Po sg unn, No way
4Se ille Uni e si y, Se ille, Spain
5Depa men o Elec ical Enginee ing, Uni e si y o San iago, San iago, Chile
6Depa men o Elec ical and Compu e Enginee ing, Uni e si y o On a io, Ins i u e o Technology, On a io, Canada
E-mail: h [email p o ec ed]
Abs ac : Fu u e plans o in eg a ion o la ge non-synch onous gene a ion and he expansion o he powe sys em in he
No dic coun ies a e a conce n o ansmission sys em ope a o s due o he common in e connec ions and elec ici y exchanges
among hese ope a i e a eas. The expec ed educ ion in he ine ia an icipa es an al e a ion o he equency esponse,
p o oking a high Ra e o Change o F equency (RoCoF) slopes ha can jeopa dise he secu i y o he in e connec ed sys ems.
Since powe gene a ion in he No dic coun ies such as Sweden, Finland and No way is hyd o-domina ed, he e, he au ho s
p opose a no el solu ion o ackle his p oblem including wide a ea measu emen s o moni o and sha e he RoCoF in emo e
a eas wi h lowe ine ia o enhance hei p ima y equency con ol. To demons a e he e ec i eness o he p oposed solu ion,
i s a es benchma k con ol wi h op imised pa ame e s is de eloped and la e compa ed agains he p oposed me hod.
Addi ionally, since he p oposed solu ion is based on measu emen s om emo e loca ions in o de o gua an ee he s abili y o
he sys em he impac o delays in he communica ion channels is also included in he p oblem o mula ion.
1 In oduc ion
The global elec ical sys em is on he cusp o ansi ion due o he
cu en inc ease in enewable in e connec ion o he g id [1]. This
ansi ion is d i en p ima ily due o he echnological de elopmen
o high- ol age di ec cu en and sophis ica ed wide a ea
measu emen sys ems (WAMS) [2, 3]. Howe e , he
implemen a ion o such echnological ad ances is no
s aigh o wa d due o di e en ope a ional challenges ela ed o
WAMS, which is discussed and aced in his b ie . One o he main
issues expec ed om he massi e pene a ion o enewable ene gy
sou ces is he ine ia educ ion [4], which migh esul in la ge
equency de ia ions om he nominal sys em equency unde a
dis u bance [5]. Main aining he equency s abili y wi hin
app op ia e bounda ies and p o iding an adequa e esponse a e o
majo impo ance, since eaching he sys em bounda ies may
p o oke supply in e up ions, which can e en ually u n on lack o
elec ici y, also known as blackou s [6]. T adi ionally, hyd o-powe
plan s a e he i s op ion o con ibu e he mos on equency
con ol in powe sys ems due o i s capabili y o quickly con ol he
wa e lowing in he u bines h ough i s go e no . Hyd o-con ols,
also known as hyd o-go e no s, a e modelled using ans e
unc ions o i s o de composed by gains and ime cons an s [7].
In o de o add ess his challenge and imp o e he hyd o-
go e no 's ac ions, wo g oups o echniques ha e been obse ed in
he li e a u e. The i s g oup co esponds o he use o op imisa ion
me hods and he second o he con olle 's ealisa ion. The e a e
bene i s and d awbacks in bo h di ec ions, which a e b ie ly
desc ibed nex .
E olu iona y algo i hms such as gene ic algo i hms ha e been
applied in [8], in which he d oop go e no con olle has been
op imised. The seconda y equency esponse e o was specially
imp o ed; howe e , he o e shoo , se ling ime and oscilla ion
damping we e no included in he op imisa ion unc ions.
Abdolmaleki e al. [9] uned he d oop gain using pole placemen
o load equency con ol in hyd o-powe plan s. Howe e , e en
hough his shows an imp o emen in he equency esponse, he
op imisa ion unc ion was absen . A ac ional o de p opo ional
in eg al de i a i e (PID) con olle , op imised using he social
spide op imisa ion algo i hm, o seconda y con ol in powe
sys ems inco po a ing dis ibu ed gene a ion, is p esen ed in [10].
In his case, he op imisa ion unc ion in ol ed equency de ia ion
in he connec ed a eas and he esul s demons a ed an
imp o emen in he equency esponse, including a wind powe
model. Howe e , he ine ia was no analysed. A swa m-based
algo i hm, applied o he go e no uning pa ame e s o equency
egula ion, is p oposed in [11]. The compu ing simula ion esul s
we e pe o med o an ac ual hyd o-powe plan ins alla ion.
On he o he hand, ega ding he ealisa ion con olle 's
app oach, he au ho s in [12] p oposed a obus con ol based on a
high-gain obse e as an adjus able pa ame e o ob ain an
adequa e dynamic esponse om a dis u bance. A decen alised
con ol signal o hyd o-go e no s has been designed using H∞
con ol in [13], showing he speed esponse du ing di e en
dis u bances. By using a eedback linea app oach, he au ho s in
[14] aimed o design a go e no o deal wi h he ansien s abili y
and o damp he oscilla ions in he sys em used. The au ho s in [15]
p esen ed a obus con ol design o hyd o-go e no s based on
addi ional inne s a es’ eedback signals and his is compa ed wi h
adi ional PI and PID a chi ec u es. In [16], a uzzy PID con ol
s uc u e is designed showing he possibili y o including he
de i a i e e m as an ex a signal in ol ed in he hyd o-go e no
con ol.
These abo e-men ioned con ibu ions show ha op imal
go e no con olle s can be a gene al imp o emen o he p ima y
equency con ol; howe e , his is a p o isional solu ion,
especially when he non-synch onous gene a ion is inc easing
con inuously and he g id dynamics a e changing. The e o e, he
mo i a ion o his esea ch p esen s an inno a i e solu ion using
Ra e o Change o F equency (RoCoF) measu emen s.
T adi ionally, maximum RoCoF is used o igge local p o ec ion
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151
schemes; howe e in his wo k, we make use o he so-called
a e age RoCoF calcula ed o one a ea and hen compa ed wi h
di e en a eas in o de o p o ide ac ions o igge ing a
cen alised con ol scheme. Mo eo e , a powe sys em/powe plan
wi h la ge sys em ine ia will be mo e esilien o equency
dis u bances han a powe sys em wi h smalle sys em ine ia.
Howe e , i he RoCoF ollowing a equency de ia ion has a
s eepe slope, his measu emen can be aken as an ad an age o
imp o e he con olle 's eac ion in ano he /di e en
in e connec ed egion h ough WAMS, imp o ing he gene al
equency esponse in he en i e sys em. The e idence o di e en
RoCoF slopes has been ound in he na ional g id sys em in he UK
and he Ei g id in I eland, whe e geog aphically sepa a ed
equency measu emen s exhibi such beha iou [17, 18]. Such
geog aphic spa seness o ine ia can p o oke u he la ge
equency excu sions and sepa a ion s abili y isks [19].
Ano he example o ine ial equency di e en esponses in
neighbou s ie-line communica ed coun ies is seen in he Cen al
Ame ican egion, whe e powe ou ages in any o he neighbou ing
coun ies cause s ong equency imbalances [20]. This
geog aphical–elec ical misma ch can ac ually p o ide an
inno a i e solu ion o low-ine ia in e connec ed sys ems, he
wide-a ea RoCoF sha ing (WARS). Since he ine ia o a powe
sys em/powe plan a ec s he RoCoF ollowing a sys em e en ,
ano he possible imp o emen o coun e ac he la ge pene a ion o
non-synch onous gene a ion is by adding emo e/supplemen a y
RoCoF measu emen s wi h s eppe slopes o he local ones, he eby
al e ing he con olle 's eac ion acco ding o he low-ine ia
geog aphical zones ha a e in e connec ed. The ela ionship
be ween sys em ine ia and RoCoF can be illus a ed h ough he
swing equa ion shown in
2H×RoCoF = ΔP
(1)
whe e H is he o al ine ia cons an o he sys em (one o se e al
in e connec ed) and ΔP is he o al powe change.
To gi e u he con ex o he wo k in his pape , since as -
esponding hyd o-powe plan s ha e been used o e icien ly and
eliably add non-synch onous gene a ion o elec ic powe sys ems,
many o he go e no s in use in Sweden a e being upg ading
p ocesses om mechanical o au oma ed con olle s [21, 22].
Mo i a ed by his challenge, and he inc ease in non-
synch onous ins alla ions, which educes he ine ia in he sys em,
his pape p oposes a no el app oach o coun e ac such dynamic
changes. A WAMS o sha e he RoCoF signal (WARS) om a eas
wi h s eepe slopes o o he a eas, in o de o in oke a as e
eac ion in emo e hyd o-go e no s, which al oge he con ibu e o
he equency esponse in he cen e o ine ia (CoI) ame. This
WARS me hod is hen compa ed wi h ano he me hod wi h he
op imal hyd o-go e no pa ame e s being ob ained by a simula ed
annealing algo i hm (SAA) op imisa ion me hod. Two di e en
compa a i e signals a e p oposed: (i) he RoCoF a e age alue
ob ained om local and emo e measu emen s and (ii) he
maximum absolu e alue o he local and emo e RoCoF
measu emen s. Mo eo e , he sub-sys ems s abili y and he impac
o he delay in he communica ion channel a e analysed. The
p oposed me hods a e es ed and compa ed in a benchma k sys em
ha emula es he No dic sys em equency esponse.
A p elimina y e sion o his wo k has been published in [23],
whe e a ne wo ked con ol sys em has been p oposed o coun e ac
he non-synch onous gene a ion in eg a ion. This wo k con ains
subs an ial di e ences o he p oposed me hod and new simula ions
ha do no appea in [23]. In con as o [23], his pape ocuses on
using WAMS o sha e he ine ia om low-ine ia a eas in o de o
imp o e he o e all p ima y equency con ol. Mo eo e , he
heo e ical ame and op imisa ion cha ac e is ics a e also gi en.
The pape is o ganised as ollows: in Sec ion 2, he equency
esponse, he pe o mance me ics and he measu emen me ics
a e in oduced. Sec ion 4 p esen s he p oposed me hod o
ein o cing he p ima y equency con ol o coun e ac he
po en ial ine ia educ ion. Sec ion 3 p esen s he pe spec i e o
low-ine ia powe sys ems modelling and es ablishes he es
benchma k sys em. Sec ion 6 p esen s he simula ion esul s
conside ing an agg ega ed model o he No dic sys em, whe e h ee
di e en ope a ional a eas a e in e connec ed. In one o he a eas,
he ine ia has been educed in o de o apply he RoCoF sha ing
me hod and, obse e he impac on he sys em equency con ol,
and he imp o emen by he p esen ed me hod is shown. Finally,
he conclusions and u u e wo k a e gi en.
2 Powe sys em p elimina ies
2.1 Powe sys em equency esponse
In he join No dic sys em (Finland, Sweden, No way and Eas
Denma k), he obliga ions o main aining ese es ha e been
ag eed in he Sys em Ope a ion Ag eemen be ween he No dic
ansmission sys em ope a o s (TSOs).
Elec ici y p oduc ion mus be equal o elec ici y consump ion
a all imes. The balance be ween p oduc ion and consump ion is
indica ed by he equency o he elec ici y g id which has a
nominal alue o 50.0 Hz. The ma ke ope a o s plan and balance
hei consump ion and p oduc ion in ad ance, bu in p ac ice he e
a e de ia ions du ing each hou [24].
In a synch onous sys em, in he case o losing a gene a ing uni ,
he equency d ops because o he imbalance be ween gene a ion
and load. Fig. 1 shows he dynamic esponse o he sys em
equency a e disconnec ion o one gene a o o a ypical sys em.
The dynamic esponse is di ided in o wo pe iods: P ima y and
seconda y con ol esponse pe iods. Du ing he i s pe iod, he
ine ial esponse o he spinning machines in he en i e sys em
eac s eleasing o s o ing o kine ic ene gy end o educe he
equency de ia ion. Sys em ine ia is de ined as he o al amoun
o kine ic ene gy s o ed in all he o a ing masses.
The ine ial cons an o an indi idual gene a o can be
in e p e ed as he ime ha gene a o can p o ide ull ou pu powe
om i s s o ed kine ic ene gy, aking alues be ween 2 and 9 s
ypically.
Beyond he ine ial esponse, he equency is s abilised and
hen es o ed o he nominal equency by he equency
con ainmen ese e (FCR) by go e no ac ion and seconda y
con olle s, espec i ely. The FCR ac s as a p opo ional con olle
a oiding la ge equency de ia ions; howe e , due o i s con ol
cha ac e is ic, i e ains a s eady-s a e e o . The ime esponse o
his con ol is gi en in seconds ( ypically <30 s).
The aim o FCR is o s abilise equency dis u bances in he
en i e (in e na ionally) connec ed high- ol age g id, ega dless o
he cause and loca ion o dis up ions. Se e e equency
dis u bances can lead o au oma ic load shedding and in he wo s
case cause a blackou . FCR is used o he cons an con ol o
equency and i can be classi ied in o wo ca ego ies: FCR o
no mal ope a ion (FCR-N) and FCR o dis u bance (FCR-D) [25].
The FCR-N and FCR-D a e momen a ily a ailable ac i e powe
o equency egula ions and a e ac i a ed au oma ically by he
sys em equency. Howe e , FCR-D eac s unde a long
dis u bance and i is associa ed wi h he go e no s ac ion. FCR-N
and FCR-D bo h ha e hei own ma ke . No e ha he one
de eloped in his documen is in he ame o FCR-D [26].
F equency es o a ion ese es e u ns he equency back o i s
nominal alue and also es o es he ese es; i s deployed ime
ame is gi en in minu es.
Fig. 1 Powe sys em equency esponse
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2.2 Pe o mance me ics
Following a dis u bance in he sys em, in pa icula gi en a
nega i e s ep dis u bance such as a sudden load inc ease o
gene a ion d op a = 1, he ollowing me ics a e de ined o
quan i ying he ac ion o he dis ibu ed con ol ac ion:
•Nadi is he maximum dynamic equency de ia ion ollowing
an ac i e powe dis u bance/con ingency. I is domina ed by he
sys em ine ia and go e no s esponse. Employing he op imal
go e no pa ame e s, he equency nadi can be educed.
• Nadi ime is he associa ed ime = 2 o he nadi occu ence.
• Se ling ime = 3 is used o s udy he ansien condi ion and o
ha ing a ime ma k o e alua e he con ol ac ion on he se ling
equency.
The objec i e is o educe he nadi and dec ease he ime
di e ence be ween 2 and 3 o an app op ia e ma gin whe e i is
imp o ing he esponse eac ion and o a oid any oscilla ions in he
esponse.
2.3 Measu emen me ics
In o de o ha e an agg ega ed measu emen o he equency o an
en i e in e connec ed sys em, he CoI is used, which is compu ed
based on he indi idual speeds ωi and he ine ia cons an s o he
synch onous gene a o s Hi.
Assuming he se G o synch onous gene a o s, he exp ession
o compu e he CoI is
ωCoI =Σi∈GHiωi
Σi∈GHi
(2)
In a simila manne , he RoCoF measu emen in he CoI e e ence
is de ined as
dωCoI
d =Σi∈GHi(dωi/d )
Σi∈GHi
(3)
In addi ion, since (2) and (3) co e only a powe sys em sub-
ne wo k (e.g. coun y o egion), hen se e al CoI- e e ed RoCoF
measu emen s should be ga he ed and sha ed om he sub-
ne wo ks in ol ed. Fo ins ance, a powe sys em ne wo k wi h wo
es ablished ope a i e a eas has wo RoCoFCoI measu emen s o be
used. Howe e , i is wo h men ioning ha he alues ha sub-CoI-
e e ed RoCoF sys em migh each depend on he sys em dynamic
con igu a ion, he con ingency magni ude and loca ion, he aul
clea ing ime and he powe sys em con olle s ins alled in he
sys em.
3 Low-ine ia powe sys em modelling
3.1 Non-synch onous gene a ion in eg a ion
The No dic powe sys em (NPS) bases i s powe p oduc ion on
se e al enewable gene a ion sou ces [27]. Base powe demand in
Sweden and Finland is, o a g ea ex en , p o ided by nuclea
p oduc ion; while No way's main sou ce is hyd o-p oduc ion [28].
Conside ing he ins alled capaci y o he h ee coun ies in he
NPS, he di e en sou ces o elec ici y a e shown in Fig. 2. The
con ibu ion by a ious gene a ion sou ces o powe pe coun y is
p o ided in hei espec i e pie cha s, as well as he agg ega ed
sum.
As he Eu opean egion seeks o inc ease i s non-synch onous
gene a ion, se e al coun ies will injec mo e wind powe in he
u u e, hus educing he ope a ional equency esponse capaci y
unde possible imbalances [29]. Conside ing u u e educ ions o
e en o al shu down o he nuclea he mal uni s being eplaced by
enewable ene gies, he equency esponse con ol belongs o
hyd o-powe uni s. Hence, no el me hods a e equi ed o enhance
he equency esponse in powe sys ems wi h low ine ia.
Addi ionally, he cu en and u u e powe sys em
communica ion in as uc u e is based on PMUs along he NPS
[30]. This will enable he applica ion o WAMS o moni o ing he
ope a i e a eas and o ansmi he in o ma ion equi ed o ac i a e
ancilla y se ices o hyd o-go e no s ha can coun e ac he low
ine ia and enhance he equency esponse in ime.
3.2 P ima y equency esponse modelling
The objec i e o a u bine go e ning sys em, ins alled in a
gene a ing uni , is o p oduce a desi ed powe which is pa ly
de e mined by he se alue o he p oduced powe and pa ly by a
con ibu ion o igina ing om he equency con ol [31]. In his
con ex , he la e is o in e es .
Fig. 3 shows a schema ic diag am o he sys em model which
combines he elec o-mechanical p ime go e no , he hyd o-
u bine, he gene a o and load. The go e no de ails a e p o ided
in he expanded schema ic.
The model including he go e ning sys em, he se o and he
u bine i is gi en by
Fig. 2 No dic coun ies powe gene a ion
Fig. 3 Sys em model
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153
ω
˙i=1
Mi
Pi
m−Pi
e−Diωi
P
˙i
m=− 2ki
ωρ
˙i
y+2ki
ω
Ti
ωρi
y−2
Ti
ωPi
m
ρ
˙i
y=1
Ti
pki
ρi
−ρi
y
ρ
˙i
=ki
iρi
c−ki
iRi
pρi
y+ki
pρ
˙i
c−ki
pRi
pρ
˙i
y+ki
dρ
¨i
c−Ri
pρ
¨i
y
ρ
˙i
c=1
Ti
ω e −Ri
ωi−ρi
c
(4)
whe e he cons an s Ti
p, Ti
ω, ki
i, ki
p, Ti
, Ri
p, ki
, Mi, Di s and o he
se o pilo cons an , he wa e ime cons an , he in eg al con olle
cons an , he p opo ional con olle cons an , he ese ime
cons an , pe manen d oop, ine ia cons an , and damping,
espec i ely.
3.3 S abili y analysis
In o de o gua an ee ha he hyd o-go e no s emain s able unde
u u e imp o emen s, i is necessa y o gua an ee a s abili y egion.
Theo em 1: The powe sys em desc ibed by (4) is s able o
ki
p> 0 and ki
i> 0.
P oo : The s abili y o (4) is de e mined by he eigen alues o
A. The oo s o he cha ac e is ic polynomial o A is gi en by
de sI−Ai= 0
∑
j=0
5
ajsj= 0
(5)
Since he hyd o-go e no model used is linea (5), he Rou h–
Hu wi z s abili y c i e ion accomplishes he s abili y p oo (see
Sec ion 8). □
Fig. 4 shows a plo o ki
i e sus ki
p and displays he s abili y
egion o he PI go e no based. ηi s ands o a ec o o k1
iand k1
p
pa ame e s ha a e inside o he s abili y egion Ωs.
4 WARS-based equency con ol
In his sec ion a wide a ea measu emen sys em (WAMS)
a chi ec u e o coun e ac he educ ion o ine ia in powe sys ems
by using WARS measu emen unc ions. Addi ionally, he impac
o he communica ion delay on he s abili y ma gins o he sys em
is shown. These cons i u e he main con ibu ions o his pape .
4.1 Wide-a ea RoCoF sha ing
WAMS a e used o ansmi in o ma ion and accu a e
measu emen s om emo e geog aphical loca ions h oughou he
in ol ed powe sys ems. Fig. 5 ep esen s he concep o he
p oposed me hod based on WAMS. Each agg ega ed powe sys em
a ea is measu ed by a PMU ne wo k spa sed in he sys em, which
a e connec ed o he main phaso da a concen a o (PDC) ia
communica ion channels (shown in dashed lines in Fig. 5) enabling
o ob ain he CoI measu emen by collec ing se e al equency
measu emen s. Mo eo e , in o ma ion om he RoCoF signal is
collec ed and exchanged wi h he equi ed local con olle s
( ypically <0.2 Hz/s wi hin la ge powe ne wo ks) [32].
By exploi ing he ine ia educ ion in one a ea i, caused by he
la ge inc easing enewable ene gy in eg a ion, and assuming a
communica ion channel be ween he o he a eas in he powe
ne wo k, he RoCoF signal is ansmi ed. Since an ine ia
educ ion implies a s eepe declina ion in he RoCoF and as e
eac ion han he local equency in o he egions, sha ing his
measu emen wi h o he egions can imp o e he global equency
esponse in he case o undesi ed dis u bances. As can be seen in
Fig. 5, an a ea is being measu ed and i s espec i e RoCoF is hen
dis ibu ed o he o he a eas (Geni o Genn) and hei con olle s
(Ci o Cn); he sum o hese esul s in he CoI equency. No e ha
Fig. 5 shows only one a ea being measu ed o simplici y.
Howe e , all o he a eas can be measu ed and he indi idual
RoCoFs can be dis ibu ed o he es o he a eas.
In his applica ion, ini ially a single CoI pe a ea is assumed,
which is ep esen ed by an agg ega ed machine and i s dynamic
con olle . Addi ionally, in o de o obse e he e ec o he RoCoF
sha ing on he CoI, he equency measu emen s o each
agg ega ed a ea a e clus e ed and he o e all equency o he
sys ems can be obse ed as a global CoI. RoCoF a ea
measu emen s a e also de i ed and sha ed o he o he a eas by
communica ion channels.
4.1.1 RoCoF sha ing unc ions: Two unc ions o WAMS
RoCoF measu emen s a e p oposed as ollows:
RoCoFa g =a g(RoCoFs, RoCoFi)
(6)
RoCoFmax =max( RoCoFs, RoCoFi)
(7)
Bo h unc ions (6) and (7) ake he sha ed RoCoF measu emen
( om he RoCoFs ne wo ked a eas) and combine i wi h he local i
measu emen sensed in he espec i e hyd o-go e no . Func ion (6)
is ob ained by he a e age o bo h measu emen s. On he o he
hand, unc ion (7) ob ains he maximum s eepness be ween hose
wo measu emen s. By aking he swing equa ion in (1), bo h
unc ions a e b ie ly analysed in CoI ame as ollows:
2ΣHi
d(ΣiHiωi/ΣiHi)
d = ΣΔPi
2HCoI
dωCoI
d =ΣΔPi
(8)
As an example, by applying he CoI ame o a sys em o wo
masses wi h ine ias H1 and H2, he ollowing exp ession is
ob ained:
Fig. 4 S abili y egion Ωs o he PI go e no based
Fig. 5 Wide-a ea con ol a chi ec u e
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2HCoIT
dωCoIT
d =2H1
dω1
d +2H2
dω2
d
=2H1+H2
H1
H1+H2
dω1
d +H2
H1+H2
dω2
d
= 2 H1+H2
d (H1ω1+H2ω2)/(H1+H2)
d
=2dH1ω1+H2ω2
d
(9)
The esul in (9) coincides wi h he CoI de ini ion. By including he
p oposed a e age sha ed unc ion in one o he a eas, he new CoI
is he ollowing:
2HCoIa g
dωCoITa g
d =2H1
d (H1ω1+H2ω2)/(H1+H2)
d +2H2
dω2
d
(10)
Equa ion (10) shows he dynamic change in he CoI esul whe e
one o he a eas has he weigh ed (a e age) RoCoF ob ained
indica ing he in luence o he unc ion in he local RoCoF and
CoI. No e ha he RoCoF s eepness depends on he ine ia
deli e ed in he sys em. Howe e , he ine ia es ima ion is ou o
he scope o his documen .
Rega ding he second unc ion, he maximum o he absolu e
alue o he RoCoF eac s o he s eepness, he e o e au oma ically
selec ing he RoCoF wi h he highe slope o , in o he wo ds,
anspo ing he RoCoF o he a ea wi h less ine ia. The new CoI
changes as ollows:
2HCoImax
dωCoITmax
d =2H1
dω2
d +2H2
dω2
d
=2dH1ω2+H2ω2
d
=2dω2H1+H2
d
(11)
No e ha (11) compa ed o he common CoI (9) has changed, and
since he RoCoF in he second a ea is s eepe , he dynamic eac ion
p o oked is as e han he a e age unc ion.
4.2 Func ion signals
Fig. 6a shows he equency esponse o wo hypo he ical a eas 1
and 2 a e a load inc easing. Bo h equencies d op
ins an aneously, howe e since each sub-sys em has di e en
ine ia cons an s H1 and H2, he RoCoF esponses a e also di e en
as shown in Fig. 6c. The RoCoF esponses ha e di e en slope
amps as shown in Fig. 6b, whe e he ini ial slope lines ha e been
emphasised o show he espec i e amp decay a he beginning o
he dis u bance which a e sensed by hei espec i e con ol
sys ems (go e no s). When de ec ing an ab up equency d op, he
a e age unc ion be ween he RoCoF measu emen s in ol ed will
gene a e a new RoCoF esponses as shown in he + line in Fig. 6c.
Howe e , when he RoCoF decays as e , he equency slope is
decaying as e he e o e he maximum RoCoF (RoCoF 1 in his
case) unc ion can ha e a bigge impac on he go e no s eac ion
by sha ing i . The selec ion and igge ing o any o hose unc ions
a e au onomously gi en by he slope h esholds ob ained.
Howe e , he RoCoF ma gins depend on he g id code se ings pe
coun y [33].
4.3 Wide a ea measu emen s in as uc u e
Wi h he RoCoF sha ing unc ionali y ins alled, each gene a ing
uni will be able o espond and suppo he sys em du ing
abno mal equency condi ions (FRC-D). The unc ionali y o he
RoCoF sha ing is s aigh o wa d: The gene a ing uni ope a es
no mally a a ixed ou pu se by he egional con ol cen e/TSO
[34]; i he equency goes ou o ange, he gene a ing uni will
espond o a equency change by ei he inc easing/dec easing i s
ou pu , acco ding o i s p ima y equency con ol obliga ion.
The condi ion o ac i a e his con ol om TSO equi es he
knowledge o he indi idual RoCoF measu emen s in he WAMS.
Apa om he PMUs and PDC, ano he key elemen is equi ed
o he RoCoF sha ing applica ion: he de ec ion and ac i a ion o
he RoCoF sha ing mode is made in he local con olle s. The
RoCoF alues om he PMUs a e used as he p ocess alue o he
unc ions ha in e ac wi h he local con olle s. Usually, a
p og ammable logic con olle (PLC) wi h he op imised
pa ame e s and he enable RoCoF sha ing signals unc ion [35].
The equency is measu ed in he closes busba /subs a ion o he
gene a ion poin by a PMU and communica ed o he common
PLC.
The PLC execu es he RoCoF block o e e y 100 ms in e al
and uses one o he p oposed RoCoF unc ions measu ed on he
p e ious cycle. I he slope o he equency de ia ion be ween
measu ed and p e ious equency sample when calcula ed o he
o al ime o 1 s is >0.5 Hz hen he sha ing equency mode is
ac i a ed [36]. The common PLC is adjus ing (adjus men is done
by op imal PID con olle gense wise) by inc easing o dec easing
he con ol signals ou pu [37]. The RoCoF alues om he PMUs
a e used as he p ocess alue o he unc ions o modi y he
con olle s. The sys em will be ese o no mal ope a ion mode
when he sys em has been in no mal equency anges ( ypically 1
min) o i au oma ic ese is a disabled sys em which emains in he
eme gency mode un il i is ese om TSO.
TSO can moni o he maximum and minimum a ailable RoCoF
measu emen s. A PID con olle a common physical loca ion (e.g.
a PLC) uses any o unc ions p oposed om emo e and local
eede s and PMU as a p ocess alue om TSO. As a de aul ,
con olle ou pu uses he op imal pa ame e s.
Fig. 6 F equency and RoCoF unc ions
(a) F equency esponse o wo di e en a eas, (b) Ramp angen lines, (c) RoCoF
associa ed
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155
4.4 RoCoF sha ing including communica ion delay
Since he RoCoF sha ing applica ion elies on he communica ion
be ween di e en ope a i e a eas, he delays in he espec i e
communica ion channels need o be e alua ed and measu ed. A
signi ican delay, o e.g. be ween 1.0 and 1.6 s, he RoCoF sha ed
a ea and he ecei e a ea would a ec he pe o mance o he
expec ed esponse and impac on he equency esponse
indi idually and he CoI. Timely p e en i e ac ions equi e he a
p io i knowledge o he delay bounda ies ha he p oposed me hod
and he sys em can a o d. The e o e, a p oo o he delay s abili y
ma gin is calcula ed and gi en in Sec ion 10.
5 Simula ed annealing algo i hm applica ion
SAA is a s ochas ic global op imisa ion algo i hm, which is able o
jump ou om local minimum o achie e he global minimum [38].
In speci ic, SAA could be di ided in o six majo componen s
including
i. cos unc ion,
ii. ini ial condi ion,
iii. mo e gene a ion,
i . p obabili y unc ion,
. cooling schedule,
i. s opping condi ion.
Gi en a cos unc ion, an ini ial solu ion (condi ion) is gene a ed.
Then, in each s ep, he mo e gene a ion unc ion will con ol he
pe u ba ion a ound he cu en solu ion. The p obabili y unc ion
ha is a ec ed by he empe a u e iden i ies he accep ance o a
new s a us. Nex , he empe a u e is cooled down o a chi e a mo e
con ingen accep ance c i e ion o he same p obabili y unc ion;
he e o e, a wo se s a e is ha de o be accep ed in he u u e.
Finally, du ing he SAA p ocedu es, he cos unc ion alue
e en ually con e ges, and he sea ch is e mina ed i he s opping
condi ion is sa is ied. In his pape , he SAA is used o ind he
op imal alues o he unable ki,kp,kd o minimise he se ling ime
s and he ins an aneous equency de ia ion (IFD). The
co esponding pseudo-algo i hm o he applied SAA is p esen ed in
Sec ion 9.
5.1 Op imisa ion p oblem
The o mula ion o op imisa ion p oblem is desc ibed as ollows:
Gi en Ωs
Min s,nadi ,
s . . kp,ki,kd∈ s abili y egion
(12)
whe e Ωs is he s abili y egion o each sys em.
6 S udy cases
6.1 Op imal PID hyd o-go e no benchma k
The op imisa ion p ocess aims o ob ain op imal pa ame e s ha
enhance he p ima y con ol esponse such ha he ime esponse is
minimal and he oscilla ions a e supp essed. These objec i es a e
con lic ing, i.e. he mo e eac ion is eleased o coun e ac he all
o equency, he mo e se e e will be he pos -suppo dis u bance.
Fig. 7 shows he equency esponse e sus ime o h ee cases
wi h low ine ia, high ine ia and low ine ia wi h modi ied
go e no . The igu e also shows he h ee ime zones whe e he
objec i e unc ion is ope a ing. Zone 1 ocuses on minimising he
IFD, Zone 2 looks o a oiding undesi ed oscilla ions along he
s abilisa ion. Finally, Zone 3 aims o ob ain he minimum se ling
ime such ha a as e eac ion will be p o ided.
Ha ing eached he op imal gain pa ame e s in each a ea, he
alues should emain inside he s abili y egion in o de o
gua an ee he s abili y o he sys em. F om he heo em, a
heo e ical egion is shown in Fig. 4. Plane ki
p e sus ki
i encloses a
egion whe e bo h pa ame e s map a s abili y poin . Wi h he
addi ion o he op imal de i a i e con ol pa ame e , a shi in he
egion is a ec ed. The e o e, a ca e ul balance o he pa ame e s is
conside ed in he op imal pa ame e s ob ained. Fig. 8 shows he
ep esen a ion o his shi on he s abili y planes by adding he
de i a i e pa ; he cha ac e is ics wi h h ee di e en alues o he
de i a i e pa ki
d= 0.5, 1 and 2 a e shown.
6.2 Th ee mass a eas
In o de o es he p oposed me hodology, a es sys em was
c ea ed ollowing he pa ame e s in [21]. I ep esen s a No dic
equi alen o equency s udies o med by h ee-mass a eas, as
depic ed in Fig. 9 and concep ually depic ed in Fig. 10 whe e Genn
is he No way (No wegian) sys em, Gens he Sweden (Swedish)
sys em and Gen he Finland (Finnish) sys em.
The pa ame e s o each a ea, including he de aul go e no
se ings be o e uning (kp, ki, kd), and he powe p oduc ion in he
sys em a e shown in Tables 1 and 2, espec i ely. Addi ionally, he
Fig. 7 Powe sys em equency esponse: Op imisa ion egions
Fig. 8 S abili y egion Ωs o a go e no PID based: ki
d a ia ion
Fig. 9 Th ee mass a eas: block diag am
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1-a ea agg ega ed model ha ep esen s he en i e equency model
sys em is shown. No e ha he de aul pa ame e s do no con ain
he de i a i e con olle cons an .
As a benchma k, he op imal pa ame e s de i ed using SAA
[39] ha e been used o e alua e he WARS me hod. The op imal
pa ame e s o he con olle s ob ained om he SAA a e gi en in
Table 3.
6.2.1 F equency esponse: By applying he SAA, he op imal
go e no pa ame e s a e ound o be based on he c i e ia
es ablished in he benchma k. Fig. 11 shows he ime- esponse
compa ison be ween he pa ame e s ob ained by he SSA and he
me hods p oposed in each a ea o he sys em. Addi ionally, he CoI
esponse is also gi en. As can be seen in Figs. 11b and c, bo h
esponses in No way and Finland eac ed as e compa ed o he
op imal case in Fig. 11a. The op imal esponse in Sweden
emained he same since i is he one wi h educed ine ia and
sha ing i s RoCoF measu emen h ough he unc ions o he o he
ope a i e a eas. By sha ing he RoCoF, he equency esponse is
d as ically imp o ed, educing he o e shoo and se ling ime.
Addi ionally, he CoI esponse o he wo me hods p oposed in
Fig. 11d is shown. Op imal esponse has been imp o ed
signi ican ly by he RoCoF sha ing in he o he wo a eas since wo
o hem ha e been imp o ed indi idually.
Table 4 shows he pe o mance me ics compa ison be ween he
SAA op imal pa ame e s and he applica ion o bo h unc ions
(a e age and maximum) ollowing he RoCoF measu emen s. The
op imal SAA applica ion has clea ly imp o ed he esponse o he
de aul sys em. Howe e , wi h he applica ion o he p oposed
me hod unc ions he ela i e se ling ime and Δ ha e been
educed in he o e all sys em esponse.
6.2.2 F equency esponse wi h he delay e ec : Fig. 12 shows
he a ia ion o he communica ion delay τ e sus de i a i e
con olle gain kd in No way and Finland sys ems. A la ge alue in
he de i a i e con olle gain is less sensi i e o he communica ion
Fig. 10 WARS ep esen a ion
Table 1 Hyd o-go e no pa ame e s
Pa ame e Agg ega ed model Sweden Finland No way
kp1.6 0.25 0.08 1.27
ki0.175 0.0417 0.0133 0.141
ep0.133 0.236 1.25 0.236
Ty0.2 0.2 0.2 0.2
Tω1.01 1.4 1.4 0.7
M9.68 4.65 1.93 3.25
D0.517 0.246 0.087 0.184
Table 2 Powe p oduc ion pe coun y
P oduc ion Sweden No way Finland
MW 11,620 17,825 2028
Wkin 112,605 81,177 48,187
Table 3 Ob ained con olle pa ame e s by SAA
Plan ki
pki
iki
d
Sweden 0.56 0.07 1.85
No way 0.8 0.05 2.34
Finland 0.07 0.02 1.05
Fig. 11 Th ee a eas equency esponse wi h RoCoF sha ing
(a) F equency esponse: SAA op imal case, (b) Sha ing RoCoF measu emen : a e age
unc ion, (c) Sha ing RoCoF measu emen : max unc ion, (d) F equency esponse: CoI
Table 4 Pe o mance me ics compa ison
Nadi ime Se ling ime Δ
base 12.85 46.83 33.98
a g 12.89 38.90 26.01
max 13.03 34.62 21.59
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157
delay in he con ol signal since i s eac ion has a la ge eac ion in
a ime ame. Howe e , i is clea ha an in e up ion o he signal
o a consis en delay will b ing he sys em o an uns able egion.
E en hough he ope a i e a eas whe e he RoCoF measu emen s
ha e been sha ed ha e a simila delay s abili y egion, i is
obse ed ha Finland has a la ge c i ical in luence in he
de i a i e con olle (Fig. 12b).
Ha ing ound he maximum possible delay in he sha ed RoCoF
signals in he espec i e ope a i e a eas, he impac o such a delay
is shown in Fig. 13. Bo h a e age and maximum unc ions and CoI
equency esponse a e clea ly a ec ed by he communica ion
delay comp omising no only he pe o mance me ics, bu he
indi idual esponses also. Since in he scena io p oposed, No way
has bigge ine ia cons an , i is less a ec ed, con a y o Finland,
whose esponse becomes oscilla o y o ou o ange o an adequa e
esponse. Addi ionally, he op imal esponse ob ained is also
a ec ed.
6.2.3 RoCoF sha ing and delay impac on he
ine ia: Addi ionally, he a ia ion o he ine ia Mi pa ame e o
he No wegian and Finnish a eas is shown in Figs. 14 and 15,
espec i ely. In gene al, as educing he ine ia, he sys em ole a es
a smalle delay wi hin he con ol ac ion s abili y egion, implying
ha he con ol ac ion accep s a lowe delay in he in o ma ion
p opaga ion.
7 Conclusions
The in eg a ion o la ge amoun s o non-synch onous gene a ion in
in e -connec ed powe sys ems is a conce n as i leads o a
educ ion in he ne ine ia o he o e all sys em. The deg ada ion
in he ine ia al e s he equency esponse and p o okes di e en
RoCoF slopes in he in e connec ed sys ems.
In his pape , an app oach o coun e -measu e he educ ion o
ine ia in powe sys ems is p oposed: a no el WAMS based on
RoCoF sha ing (WARS) o enhance he p ima y equency
esponse. Addi ionally, wo unc ions o he RoCoF sha ing
me hod a e p oposed and compa ed. The me hod imp o es he
indi idual equency a ea's esponse and he CoI esponse.
Mo eo e , i is analysed he impac o he ine ia a ia ion and he
delay on he RoCoF sha ing showing he egions o s abili y whe e
he me hod can be ope a ed.
Fu he s udies equi e he me ge o he so-called syn he ic
ine ia wi h he sha e RoCoF and he applica ion o la ge powe
sys ems; addi ionally, a s udy o obus con ol echniques in
delayed dynamical sys ems.
Fig. 12 S abili y delay egions o he RoCoF sha ed a eas
(a) Communica ion delay: RoCoF sha ing o No way, (b) Communica ion delay:
RoCoF sha ing o Finland
Fig. 13 Delay impac on he p oposed RoCoF sha ing unc ions
(a) Delay impac : a e age unc ion, (b) Delay impac : max unc ion
Fig. 14 Communica ion delay and ine ia a ia ion in pe cen age: RoCoF
sha ing o No way
Fig. 15 Communica ion delay and ine ia a ia ion in pe cen age: RoCoF
sha ing o Finland
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8 Rou h–Hu wi z s abili y p oo
F om G s he e ms o he cha ac e is ic polynomial a e ob ained
and Rou h–Hu wi z's c i e ion is applied o es ablish he s abili y
bounda ies. Le ai be he cha ac e is ic polynomial coe icien s and
le bi, ci, di and ei be he Rou h–Hu wi z's coe icien s. Then, he se
Ωs is de ined by he ollowing cons ain s p oblem:
Ωs=∀ki
p,ki
i:
max u:ki
p+ki
i
s. . g1:a5> 0
g2:a4ki
p> 0
g3:a3ki
p,ki
i> 0
g4:a2ki
p,ki
i> 0
g5:a1ki
p,ki
i> 0
g6:a0ki
i> 0
g7:b1ki
p,ki
i> 0
g8:c1ki
p,ki
i> 0
g9:d0ki
p,ki
i> 0
g10:e0ki
i> 0
g11:ki
p>0
g12:ki
i> 0
(13)
9 Used SAA pseudo code
See Fig. 16.
10 Delay s abili y p oo
A delay ime τ has been in oduced hough he be ween he sha ed
RoCoF and he local RoCoF measu emen e lec ed in he
de i a i e con ol ac ion e e eed o Fig. 3. This addi ion implies
modi ica ion in he sys ems neu al delay di e en ial equa ion
(NDDE) sys em ep esen a ion [40]. The s a e a iable ρi
is
de ined as
ρ
˙i
=ki
iρi
c−ki
iRi
pρi
y+ki
pρ
˙i
c−ki
pRi
pρ
˙i
y+ki
dsρ
^
˙
i
c−Ri
pρ
^
˙
i
y
(14)
The gene al s uc u e o a linea sys em is desc ibed by NDDEs
wi h τ≥ 0 is
x
˙i −∑
k=1
q
Bikx
˙i −kτ=Ai0xi +∑
k=1
q
Aikx −kτ,τ≥0
(15)
Ha ing q= 1 and x
^i=xi −τ, he NDDE s uc u e in he s a e
space is gi en by
x
˙i −Bi1x
^
˙
i=Ai0xi +Ai1x
^i,τ≥0
(16)
Ai1=
0 0 0 0 0
00 0 0 0
0 0 0 0 0
ki
dRi
Ti
1
Ti
+Di
Mi
−ki
dRi
Ti
Mi
−ki
dRi
p
Ti
2
ki
dRi
pki
Ti
p2
ki
d
Ti
2
00 0 0 0
(17)
Bi1=
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
000−ki
dRi
pki
Ti
p0
00 0 0 0
(18)
The cha ac e is ic polynomial o sys em (16) is hen
p3s,e−τs= de sI−Bi1e−τs−Ai0−Ai1e−τs,τ≥0
(19)
The neu al pa o he sys em is equi ed o be s able:
x−Bi1x
^=0
(20)
Equa ion (20) is s able o τ≥ 0 i and only i ρNs< 1. Now,
Ns=Bi1 and ha ing he delay τ in ol ed, hen
ρNs= max λ1, …, λ5=ki
dRi
pki
Ti
p<1
(21)
F om (21) he maximum ole ance limi o ki
d is ex ac ed as
ki
d<Ti
p
Ri
pki
(22)
F om (21), he delay ma gin is gi en by
τi
s=in τ:p s,e−τis= 0, o as∈ ℂ
¯> 0
(23)
Wi h n= 5, q= 1 and Bi0= 0 is ha ing k= 0, 1, …, 2:
Hk=∑
j=max 0, k−1
min k,1
Aik−j⊗Bi1−j
⊤+Bik−j⊗Ai1 − j
⊤
(24)
Qk=
I⊗Ai1−k
⊤−Hk,k= 0
Ai0⊕Ai0
⊤−Hk,k= 1
Aik− 1 ⊗I−Hk,k= 2
(25)
Ma ices U and V, as well as Ξz, a e gi en by
U=I0
0Q2
(26)
V=0 I
−Q0−Q1
(27)
Ξz=I−Bi1z−1 Ai0+Ai1z
(28)
Fig. 16 Algo i hm 1: SAA pseudo code
IET Ene gy Sys . In eg ., 2020, Vol. 2 Iss. 2, pp. 151-160
This is an open access a icle published by he IET and Tianjin Uni e si y unde he C ea i e Commons A ibu ion-NonComme cial-NoDe i s
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