JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX
Abs ac —Powe sys ems ace signi ican h ea s om se e e
dis u bances, o en igge ed by ex eme wea he , leading o
widesp ead cascading powe ou ages. Al hough in en ional
con olled islanding (ICI) is an e ec i e las - eso ope a ional
mi iga ion s a egy employed by sys em ope a o s wo ldwide o
p e en comple e cascading blackou s, he impac o la ge-scale
dis u bances, pa icula ly wea he -induced cascading ou ages, on
when and whe e o implemen i is no adequa ely conside ed no
e lec ed in cu en ope a ional decision-making s anda ds and
p ocedu es. This pape p oposes a holis ic cascading-d i en
amewo k ha seamlessly in eg a es ad anced wea he - ela ed
inciden modelling and cascading isk quan i ica ion o high-
impac low-p obabili y (HILP, o ail- isk) e en s wi h a no el
decision-making-based islanding me hod o enhance ope a ional
esilience. The amewo k p o ides a po olio o mi iga ion
ac ions p opo ional o cascading impac s, di e en ia ing be ween
ail- isk e en s and expec ed (“a e age”) e en s ypically
add essed in eliabili y-o ien ed s udies and cu en indus y
p ac ices, while being ailo ed o bo h nea - eal- ime ope a ions
and sho - e m ope a ional planning. The p oposed me hod
in ol es sys em spli ing a ound blacks a uni s while o ming
s able and sel -su icien islands, he eby enhancing sys em
eliabili y and esilience. Implemen ed on he IEEE 39-bus and
IEEE 118-bus sys ems, he s udies demons a e e ec i eness wi h
a signi ican imp o emen in se ed demand ac oss all simula ed
ini ia ing e en s, including up o N-6 con ingencies.
Index Te ms—Cascading-d i en con olled islanding, decision-
making-based mi iga ion s a egies, ope a ional esilience.
I. INTRODUCTION
ORDERN powe sys ems a e inc easingly ulne able o
cascading ailu es d i en by he ising equency o
ex eme wea he e en s. Such ailu es s em om
dependen componen ou ages, o en ini ia ed by se e e
dis u bances and ampli ied by p o ec ion elay ope a ions,
ul ima ely weakening he g id and causing cos ly blackou s
[1].
Mi iga ing such phenomena
equi es emedial ac ions such as
con olled islanding, which complemen s in as uc u e-based
measu es by enhancing ope a ional esilience
[2].
E ec i e
____________________________________
Manusc ip ecei ed: Decembe 21, 2024; e ised: Ap il 23, 2025; accep ed:
Sep embe 19, 2025. Da e o C ossCheck: Sep embe 19, 2025. Da e o online
publica ion: XX XX, XXXX.
This wo k was unded by
H2020
and
Ho izon Eu ope p og am h ough he
p ojec s
“HVDC-based G id A chi ec u es o Reliable and Resilien
WideSp ead Hyb id AC/DC T ansmission Sys ems” (HVDC-WISE) (G an
ID: 101075424),
“Reliabili y, Resilience, and De ense Technology o he
G id” (R2D2) (G an ID: 101075714), and “EUni e sal” (G an ag eemen ID:
864334).
applica ion o such ac ions depends on de ailed modeling o
sys em esponses du ing cascade ini ia ion and p opaga ion.
Cascading ailu e analysis has been widely s udied h ough
a ious app oaches, including opological
[3], s ochas ic
simula ion [4], s a is ical models [5], quasi-s eady s a e (QSS)
[6], dynamic [7], and o he in e dependen models [8]. These
me hods, whe he s ochas ic o de e minis ic, cap u e he
complex mechanisms o cascades. Me ics such as he numbe
o a ec ed elemen s and ope a ed p o ec ion elays a e essen ial
o quan i ying impac s and in o ming mi iga ion s a egies,
including load educ ion and con olled islanding.
Con olled islanding, o in en ional sys em pa i ioning, is a
las - eso emedial ac ion designed o con ine cascading
ailu es and limi blackou se e i y. By isola ing he a ec ed
ne wo k sec ion om he heal hy g id, i supp esses ini ia ing
e en s locally and he eby enhances esilience, pa icula ly
agains wea he - ela ed dis u bances. Fo mula ions o
con olled islanding ypically employ g aph heo y
[9],
clus e ing echniques [10], o
linea /nonlinea p og amming
[11], indi idually o in hyb id o ms. Recen s udies also
inco po a e a i icial in elligence echniques such as gene ic
algo i hms [12], g ey wol –op imized neu al ne wo ks [13],
pa icle swa m op imiza ion [14],
and an colony me hods [15].
The in en ional con olled islanding (ICI) p oblem is inhe en ly
a cons ained combina o ial op imiza ion ask, aiming o
minimize powe low
dis up ion, powe imbalance, load
shedding, ol age and equency de ia ions.
Depending on he ime ame and ype o mi iga ion s a egies
agains he sp ead o an icipa ed o e ol ing e en s, ICI can be
conside ed ei he p e en i e [11], [12]
o co ec i e [16], [17].
P e en i e schemes, implemen ed ahead o an icipa ed e en s,
in ol e ac ions such as gene a o escheduling and demand
esponse. Co ec i e schemes a e applied a e dis u bances and
ely on apid measu es, including load cu ailmen and
equency ese e ac i a ion.
F om a esilience pe spec i e,
se e al s udies ha e ad anced con olled islanding me hods.
Re . [18]
inco po a es ansien s abili y cons ain s,
while
[19]
emphasizes equency s abili y.
Re [12]
de elops a p e en i e
scheme o yphoon e en s using he Ba s model and agili y
S. Hashemi
(co esponding au ho ), B.
V. Venka asub amanian, and M.
Pan eli
a e wi h he Uni e si y o Cyp us, Nicosia 1678, Cyp us (e-mail:
hashemi.seyedsi[email p o ec ed]y;
enka asub [email protected];
pan eli.ma [email protected]).
P. Manca ella is wi h he Uni e si y o Melbou ne, Aus alia and wi h he
Uni e si y o Manches e , UK (e-mail: pie luigi.manca [email protected];
p.manca ella@manches e .ac.uk).
DOI: 10.35833/2024.001371
Cascading-d i en In en ional Con olled Islanding
o Enhancing Powe G id Ope a ional Resilience
Sina Hashemi, Membe , IEEE, Balaji V. Venka asub amanian, Senio Membe , IEEE,
Pie luigi Manca ella, Fellow, IEEE, and Ma haios Pan eli, Senio Membe , IEEE
M
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX
cu es. Da a-d i en de ec ion based on wide-a ea
measu emen s is p oposed in [20], while [21] in oduces a
hyb id op imiza ion app oach balancing dis up ion and s abili y
wi h e icien blacks a alloca ion. A h ee-s age cu se
op imiza ion me hod is p esen ed in [22], and [23] applies
gene ic algo i hms o manage empo a y o e ol ages and
dis ibu ed gene a ion u iliza ion. Finally, [24] p oposes a
mic og id con ol s a egy o enhance esilience h ough
coo dina ed ene gy sha ing and equency suppo .
Ope a ional s anda ds p o ide guidance on managing la ge-
scale dis u bances bu lack explici amewo ks o con olled
islanding. The ENTSO-E Ope a ion Handbook [25], [26]
emphasizes sys em secu i y, inciden con ainmen , and
coo dina ed es o a ion, aligning wi h esilience p inciples.
IEEE S d 1547-2018 [27] speci ies equi emen s o bo h
unin en ional and in en ional islanding, ocusing on s abili y
and DER ansi ions. NERC EOP-011-1 and EOP-011-2 [28],
[29] add ess eme gency p epa edness, while ISO New England
OP-19 [30] p o ides ansmission ope a ion p ocedu es du ing
eme gencies. Howe e , none o hese documen s de ine
con olled islanding s a egies o p e en o mi iga e cascading
ailu es—a c i ical gap o esilience unde ex eme e en s.
Mos exis ing s udies [18], [19] e alua e islanding unde a
limi ed se o andom N-k con ingencies, o en neglec ing he
imescales o mi iga ion and he cascading impac s o wea he -
ela ed e en s. As a esul , hei s a egies may be ine icien
unde unce ain condi ions. To add ess his gap, his pape
de elops a holis ic amewo k ha in eg a es eac i e and
p oac i e measu es, ailo ed o e en ype, ope a ing condi ion,
and cascade se e i y. The amewo k combines quan i ica ion,
de ec ion, and mi iga ion o cascading ailu es, iden i ies asse s
ulne able o winds o ms, and e alua es hei impac s o guide
ope a ional esponses. By managing mul iple concu en
ou ages, including e en s up o N-k, he app oach
sys ema ically enhances esilience agains bo h expec ed and
high-impac low-p obabili y (HILP) e en s. Designed o bo h
sho - e m ope a ional planning and nea - eal- ime ope a ion, i
explici ly accoun s o s ochas ic wea he -d i en dis u bances.
Indeed, he no el y o his wo k lies in in eg a ing se e al key
modules and submodules in o a uni ied, p ac ical cascading-
d i en esilience enhancemen amewo k ha enables sys em
ope a o s o make in o med decisions o mi iga ing cascading
impac s—an inc easingly c i ical need in ligh o ecen la ge-
scale blackou s such as he one in he Ibe ian Peninsula. Cen al
o he amewo k is a no el decision-making mechanism ha
le e ages cascade quan i ica ion me ics o de e mine he
app op ia e mi iga ion s a egy, he eby add essing he “when”
aspec o ICI. Building on his, he amewo k in oduces a
newly o mula ed op imiza ion p oblem o ICI—enhanced by
an inno a i e sea ch space educ ion echnique— o deli e
op imal solu ions ha add ess he emaining ICI objec i es o
“whe e” and “how” o execu e sys em pa i ioning e ec i ely,
wi h a pa icula ocus on main aining pos -islanding s abili y.
The main con ibu ions o his wo k a e ou lined below:
• De eloping a holis ic esilience enhancemen amewo k by
cap u ing cascading impac s and enabling zonal es o a ion
h ough he assignmen o blacks a uni s (BSUs) o islands.
• Quan i ying he isks o wea he -induced cascading ailu es,
whe e igge ing e en s a e spa ially co ela ed, by
employing a s ochas ic spa io empo al wea he e en
simula o and QSS cascading ailu e analysis.
• Demons a ing and quan i ying he bene i s o a po olio o
mi iga ion ac ions—enabled by a as , eliable, ule-based
Decision-Making mechanism guided by cascading ailu e
analysis— o enhancing ope a ional esilience, ailo ed o
imescales, ope a ing condi ions, and cascade se e i y.
• P o iding ICI solu ions ha add ess "when", "whe e" and
“how” o island based on cascading impac s, by iden i ying
op imal island ne wo ks a ound cohe en gene a o g oups,
while ensu ing s abili y a e bounda y lines a e opened.
The emainde o his pape is o ganized as ollows: Sec ion
II p esen s a de ailed o e iew o he p oposed me hod,
including he cascading-d i en esilience analysis echnique,
he decision-making mechanism, and he con olled islanding
me hod. Sec ion III del es in o simula ion s udies and esul s
o a la ge se o bo h de e minis ic and s ochas ic
con ingencies. Finally, Sec ion 4 concludes he pape .
II. CASCADING-DRIVEN CONTROLLED ISLANDING
A. P oposed Me hod
Fig. 1 illus a es he p oposed amewo k o he ope a ional
esilience enhancemen s a egy, applicable o bo h sho - e m
ope a ional planning and nea - eal- ime ope a ion. The
amewo k add esses wea he - and non-wea he - ela ed e en s,
pa icula ly HILP dis u bances, h ough decision-making–
based mi iga ion s a egies ha supp ess cascading ailu es. I
suppo s bo h p oac i e and eac i e applica ions, as
ep esen ed by he esilience apezoid cu e [31]. In
ope a ional planning, p e en i e con olled islanding can be
implemen ed hou s ahead using p ojec ed da a, isola ing
ulne able a eas o limi cascade p opaga ion and educe
demand loss. In he nea - eal- ime applica ion, co ec i e
islanding mi iga es e ol ing e en s based on cu en da a. As
shown in Fig. 1, co ec i e islanding ypically esul s in g ea e
deg ada ion, since ea ly e en impac s igge ipping and load
shedding be o e islanding is execu ed. P e en i e measu es, by
con as , educe deg ada ion by allowing ope a o s o
edispa ch gene a ion, adjus opology, and implemen load
educ ion ahead o ime.
Fig. 2 p esen s he lowcha o he p oposed cascading-d i en
ICI me hod, in eg a ing he E en Simula o , Cascading Failu e
Modeling, Cascading Assessmen and Decision-Making, and
In en ional Con olled Islanding in o a uni ied amewo k. This
in eg a ion is a key no el y, enabling ope a o s o make
in o med decisions o mi iga ing cascading impac s. The
p ocess begins wi h esilience assessmen h ough modeling
and quan i ica ion o cascading ailu es. Inpu s include speci ic
ini ia ing e en s o eal- ime ope a ion o wind e en –based
scena ios o sho - e m ope a ional planning. Two me ics a e
employed: Demand No Se ed (DNS) o cha ac e ize cascade
size, and he numbe o a ec ed componen s o indica e g id
in eg i y. Based on hese me ics, he decision-making module
selec s he app op ia e s a egy. I e en s do no p opaga e
unde con olled load educ ion, cu ailmen is applied
p opo ionally ac oss loads; o he wise, con olled islanding is
execu ed. Fo cascading ailu e modeling, he amewo k
employs he AC-CFM me hod [6], which in eg a es AC powe
low and QSS calcula ions o assess sys em pe o mance unde
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
3
Fig. 1. P oposed amewo k o enhancing ope a ional esilience.
Fig. 2. De ailed lowcha o he p oposed cascading-d i en ICI me hod.
dis u bances. Inpu s a e p o ided ei he by he E en
Simula o —gene a ing an icipa ed wea he - ela ed and N-k
con ingency scena ios o sho - e m planning—o by obse ed
ini ia ing e en s in eal- ime ope a ion.
This comp ehensi e se up o he esilience enhancemen
amewo k enables cascade quan i ica ion and suppo s he
selec ion o mi iga ion s a egies, e ec i ely add essing he
h ee key objec i es o ICI: when, whe e, and how o island.
The when is de e mined by he Cascading Assessmen and
Decision-Making Module, which e alua es whe he igge ing
e en s ini ia e a p opaga ing cascade o emain con ained. I
p opaga ion is con i med, ICI is applied o
de ine whe e bounda y lines should be opened and how o
main ain s abili y and sel -su iciency ac oss he esul ing
islands.
Sys em spli ing may be accompanied by gene a ion
escheduling, equency ese e u iliza ion, and load educ ion
wi hin islands expe iencing load–gene a ion imbalance. In his
s udy, he objec i e is o minimize he o al sys em DNS
esul ing om load-gene a ion imbalances, as o mula ed by
Eq. (1). He e, Κ is he se o con olled islands, 𝑁𝑖𝑠𝑙 is he o al
numbe o islands, 𝜁𝑘 is he o al impedance-based dis ance in
island 𝑘, 𝑃𝑙,𝑗 ep esen s he ac i e powe o load 𝑗, and Λ𝑘 is he
se o load buses in island 𝑘. 𝑃𝑔,𝑖 and 𝐹𝑅𝑅𝑔,𝑖 e e o he ac i e
powe and equency es o a ion ese e (FRR) o gene a o 𝑖,
espec i ely. Ω𝑘 deno es he se o cohe en gene a o s in island
𝑘. 𝑍𝑚 is he sho es impedance-based dis ance om bus 𝑚 o
cohe en gene a o g oups (CGGs) o island 𝑘 and is calcula ed
as he smalles leng h o he pa h be ween wo nodes using he
Dijks a algo i hm [32]. The p oblem is cons ained by wo se s
o cons ain s: s uc u al and ope a ional, which a e u he
de ailed in Sec ion II-D-2-b.
min{𝜁𝑘(∑𝑥𝑗𝑃𝑙,𝑗
𝑗 ∈ Λ𝑘 − ∑𝑥𝑖(𝑃𝑔,𝑖+𝐹𝑅𝑅𝑔,𝑖)
𝑖 ∈ Ω𝑘 )}𝑘 ∈ Κ
(1)
𝜁𝑘= ∑ 𝑍𝑚
𝑚 ∈ 𝐵𝑖𝑠𝑙𝑘 (2)
B. Cascading-d i en Resilience Assessmen
This module assesses he esilience o a dis u bed powe
sys em. The dis u bances may include speci ic ini ia ing e en s
ha ha e al eady occu ed o an icipa ed wea he - ela ed
e en s, depending on he imescales o he mi iga i e measu es.
This wo k u ilizes he wind e en modelling de eloped in [33]
o esilience assessmen pu poses, ex ending beyond
de e minis ic N-k (k ∈ [1, 3]) con ingencies.
1) E en Simula o
The E en Simula o gene a es N-k ansmission line
con ingencies de e minis ically (k ∈ [1-3]) o s ochas ically
(k>3). A agili y-based wind e en model is employed o
an icipa e line ou ages om upcoming wea he inciden s. The
esul ing ope a ing condi ions a e hen analyzed using quasi–
s eady-s a e cascading ailu e modeling o sho - e m planning
(see Fig. 2). F agili y cu es, de i ed om s a is ical,
expe imen al, simula ion-based, o expe me hods, de ine he
p obabili y o line ailu e as a unc ion o haza d in ensi y.
Following [33], wind-dependen agili y cu es a e applied o
model line ou ages. Winds o m cha ac e is ics such as gus
speed and adius a e ex ac ed om his o ical da a [34], [35],
and Mon e Ca lo simula ions gene a e a la ge se o s ochas ic
scena ios. By a ying s o m pa ame e s, he simula o cap u es
unce ain y and de e mines line ou age s a us, wi h ipping
decisions based on Eq. (3).
𝐿𝑆(𝑤𝑠𝑡,𝑙)={1 i 𝒫𝑙(𝑤𝑠𝑡)<𝑟
0 i 𝒫
𝑙
(𝑤
𝑠𝑡
)>𝑟 (3)
whe e, 𝑤𝑠𝑡 is he wind in ensi y o wind speed a s ep 𝑠𝑡, 𝒫𝑙 is
he wind-dependen ailu e p obabili y o line 𝑙, and 𝑟 is he
andom numbe gene a ed be ween 0 and 1. The concep o 𝑟 is
in oduced in his p ocedu e o add mo e s ochas ici y o he
model.
2) De ec ion o Uncon olled Ne wo k Spli ing (UNS)
Depending on he se e i y and numbe o concu en
ini ia ing e en s—pa icula ly wea he - ela ed e en s ha a e
spa ially co ela ed and capable o simul aneously dis up ing
nea by ansmission lines—ea ly uncon olled ne wo k
spli ing (UNS), including he isola ion o a leas one load bus,
is e y likely o occu , as concep ually shown in Fig. 3.
Ac i e Islands Ac i e & Blacked-ou
Islands
Da a Cascading-d i en Resilience
Assessmen
Quan i ica ion o
cascading impac s
Implemen a ion o an
Ope a ional Mi iga ion S a egy
Powe Sys em
Sho - e m ope a ional planning
(a ew hou s ahead)
Nea eal- ime ope a ions
To al Demand Se ed
No Mi iga ion S a egies
P e-dis u bance ime
Wi h P oac i e Mi iga ion S a egies
E en
Sho - e m
ope a ional planning
To al Demand Se ed
No Mi iga ion S a egies
ime
Wi h Reac i e Mi iga ion S a egies
E en
Dis u bance p og ess
Nea Real-Time
Ope a ions
•Ne wo k pa i ioning
•Load Reduc ion
•Gene a ion Rescheduling
•Ne wo k pa i ioning
•Load Reduc ion
•F equency Res o a ion Rese e
Cascading Failu e Analysis Module
In en ional Con olled Islanding (ICI)
- Ongoing condi ions wi h
e ol ing e en s
- De e minis ic E en s
- S ochas ic Wea he
E en s
De ec ion o
uncon olled
ne wo k spli ing
Cascading Failu e
Modelling
(AC-CFM)
DNS >
Cascading Assessmen and Decision-Making Module
A e he e
Cascading
E en s?
Yes
No No
Mi iga ion S a egy Module
Yes
No Cascading
Failu es and
No Need o
Mi iga ion
Load
Reduc ion
Iden i ying
CGGs
Con olled
Ne wo k Spli ing
Sho - e m ope a ional planning
Nea - eal- ime ope a ion
MS0
MS2
MS1
Mi iga ion S a egies:
- MS0: No needed
- MS1: Con olled islanding
- MS2: Load educ ion
--------------------------------
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JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX
Fig. 3. De ec ion o UNS caused by ini ia ing e en s.
Algo i hm I:
De ec ion o uncon olled ne wo k spli ing (UNS)
- De ec isola ed bus(es) 𝐵𝑖𝑠𝑜
- i ∃𝐵𝑖𝑠𝑜∈Λ hen
- i ∃𝐵𝑖𝑠𝑜∈𝐵𝐺 hen
- 𝑈𝑁𝑆𝑤𝐺⊆ Mino Subne wo k
- i 𝑁𝑖𝑠𝑙
𝑈𝑁𝑆≥2 (as pe Eq. (4)) hen
- Quan i y 𝐷𝑁𝑆𝑚𝑛 using CFA o he 𝑈𝑁𝑆 and 𝐼𝐷𝑀
𝑚𝑛=1
(ICI may be needed)
- else
- Quan i y 𝐷𝑁𝑆𝑚𝑛 using CFA o he 𝑈𝑁𝑆 and 𝐼𝐷𝑀
𝑚𝑛=0
(No need o ICI bu load educ ion may be needed)
- end i
- else
- Calcula e 𝑃𝐿𝐼𝑠𝑜 (bus(es) wi h load bu wi hou a gene a o )
- end i
- else
- 𝑃𝐿𝐼𝑠𝑜=0 (bus(es) wi h nei he load no a gene a o )
- end i
To de ec UNS and in eg a e i in o he main amewo k, as
illus a ed in Fig. 2, Algo i hm I is de eloped. In his s udy,
UNS e e s o isola ed bus(es) (𝐵𝑖𝑠𝑜), ei he wi hou gene a ion
(𝑈𝑁𝑆𝑤𝑜𝐺) o wi h a leas one gene a o (𝑈𝑁𝑆𝑤𝐺). As 𝑈𝑁𝑆𝑤𝑜𝐺
ine i ably expe iences ou ages, he ocus is on he emaining
ne wo k. Each 𝑈𝑁𝑆𝑤𝐺 is ea ed as a mino subne wo k, while
he es o ms he majo subne wo k—bo h po en ially
equi ing ICI depending on size and cascading se e i y. I 𝐵𝑖𝑠𝑜
con ains bo h load and gene a o buses, i is classi ied as
𝑈𝑁𝑆𝑤𝐺. Since spli ing can agmen he g id in o mul iple
gene a o -con aining segmen s, each 𝑈𝑁𝑆𝑤𝐺 is analyzed
indi idually as a mino subne wo k in Algo i hm I. The
decision-making indica o ( 𝐼𝐷𝑀
𝑚𝑛 ) hen speci ies whe he
con olled islanding is equi ed (1) o no (0).
The numbe o islands (𝑁𝑖𝑠𝑙) is calcula ed using Eq. (4), based
on he numbe o Black-S a Uni s (𝑁𝐵𝑆𝑈) and o al buses (N).
The o mula ion ensu es ha each pa i ioned ne wo k is
su icien ly la ge, de ined as ⌊0.5∙√𝑁⌋ [36], and con ains a
leas one BSU. I numbe o islands in an isola ed subne wo k
(𝑁𝑖𝑠𝑙
𝑈𝑁𝑆) exceeds wo, con olled islanding may be applied, wi h
he decision-making indica o (𝐼𝐷𝑀
𝑚𝑛) se o 1. O he wise, 𝐼𝐷𝑀
𝑚𝑛 is
se o 0, and s abili y mus be p ese ed h ough load educ ion,
equency ese es, o gene a ion escheduling. Mino
subne wo ks wi h ewe han wo islands a e excluded om
con olled islanding, while isola ed buses wi hou gene a ion
expe ience blackou . The algo i hm ou pu s include in e up ed
load om isola ed buses ( 𝑃𝐿𝐼𝑠𝑜), mino subne wo k DNS
(𝐷𝑁𝑆𝑚𝑛), and da a o bo h mino and majo subne wo ks.
𝑁𝑖𝑠𝑙=min(𝑁𝐵𝑆𝑈,
⌊
0.5∙√𝑁
⌋
) (4)
3) Cascading Failu e Modelling and Quan i ica ion
Resilience assessmen is pe o med using QSS cascading
ailu e modeling, speci ically he AC-CFM me hod [6]. This
as , ecu si e algo i hm simula es he successi e ac i a ion o
p o ec ion mechanisms and models cascades ha may
p opaga e wi hin each island. I inco po a es o e load
p o ec ion (OLP), unde - and o e - equency load shedding
(UFLS, OFGS), unde - ol age load shedding (UVLS), and
gene a o o e /unde -exci a ion limi e s (O/UXL), enabling
eplica ion o s eady-s a e equency and ol age esponses.
The model cap u es powe low edis ibu ion a e componen
ailu es, leading o o e loads and line ipping. Cascade impac s
a e quan i ied h ough me ics such as (DNS and he numbe o
a ec ed elemen s. These esul s in o m he decision-making
module, which selec s he app op ia e mi iga ion s a egy.
C. Decision-Making Mechanism o Cascade Mi iga ion
Building on he cascading-d i en ea u e o he p oposed
amewo k shown in Fig. 2, his module de e mines when o
island based on assessed cascading isks and wha -i analysis.
I e alua es cascade ini ia ion and p opaga ion using wo
me ics: cascade size, measu ed as DNS, and g id in eg i y,
quan i ied by he numbe o ipped elemen s ( 𝑁𝑇𝐸). DNS
e lec s p o ec ion ac ions such as unde ol age and
unde equency load shedding, while 𝑁𝑇𝐸 cap u es e ec s o
o e cu en elay ope a ions and gene a o ipping. Al hough
simple, he mechanism is obus , elying on cu en ope a ing
condi ions and cascading ailu e analysis using AC powe low
and QSS calcula ions. Decisions a e made quickly h ough
h eshold ules de i ed om hese analyses.
Algo i hm II de ines he decision-making mechanism, which
selec s he mos e ec i e mi iga ion s a egy—load isola ion,
con olled islanding, o load educ ion—based on cascade
se e i y. The decision-making indica o (𝐼𝐷𝑀
𝑀𝑆) akes alues o 0,
1, o 2, co esponding o load isola ion, con olled islanding, o
load educ ion, espec i ely. I DNS in ei he he majo
(𝐷𝑁𝑆𝑚𝑛) o mino subne wo ks 𝐷𝑁𝑆𝑚𝑛 (wi h 𝐼𝐷𝑀
𝑚𝑛=1)
exceeds ze o and cascading p opaga ion is con i med (𝑁𝑇𝐸>
0), con olled islanding (MS1) is igge ed. I no p opaga ion
occu s (𝑁𝑇𝐸=0), load educ ion (MS2) su ices o alle ia e
s ess and hal he cascade. These ule-based decisions,
o mula ed in Eq. (5), p ecede he op imiza ion-based
con olled islanding p ocess (Fig. 2). In con olled load
educ ion, he educ ion is p opo ional o each load’s sha e o
he o al connec ed load. O he wise, i con olled islanding is
equi ed, he co esponding op imiza ion p oblem is sol ed.
𝐷𝑒𝑐𝑖𝑠𝑖𝑜𝑛={𝑁𝑜 𝐴𝑐𝑡𝑖𝑜𝑛 , 𝑖𝑓 𝐷𝑁𝑆<𝑃𝐿𝐼𝑠𝑜
𝐿𝑆ℎ, 𝑖𝑓 𝐷𝑁𝑆>𝑃𝐿𝐼𝑠𝑜 𝑎𝑛𝑑 𝑁𝑇𝐸=0
𝐼𝐶𝐼,
𝑖𝑓
𝐷𝑁𝑆>𝑃𝐿𝐼𝑠𝑜 𝑎𝑛𝑑 𝑁𝑇𝐸>0 (5)
Algo i hm II:
Decision-
making o an e ec i e mi iga ion s a egy
- Upda e he da a om he a ailable ne wo k elemen s
- Iden i y he mino and majo subne wo ks using Algo i hm I
- Upda e he o al amoun o 𝑃𝐿𝐼𝑠𝑜 and 𝐷𝑁𝑆𝑚𝑛 a e ini ia ing e en s
- Quan i y 𝐷𝑁𝑆𝑀𝑁 using CFA pe o med o he emaining ac i e ne wo k o
majo subne wo k; (𝐷𝑁𝑆= 𝐷𝑁𝑆𝑀𝑁+𝐷𝑁𝑆𝑚𝑛+𝑃𝐿𝐼𝑠𝑜 )
- i 𝐷𝑁𝑆𝑀𝑁 >0 𝑜𝑟 (𝐷𝑁𝑆𝑚𝑛 >0 𝑎𝑛𝑑 𝐼𝐷𝑀
𝑚𝑛=1) hen
- i any subsequen cascading ou ages occu ed (𝑁𝑇𝐸>0) hen
- Need o hal cascading p opaga ion by pe o ming ICI (MS1) 𝐼𝐷𝑀
𝑀𝑆=1
- else
- Calcula e load educ ion pe bus o con ol he sys em and sa is y
ope a ional cons ain s (MS2) 𝐼𝐷𝑀
𝑀𝑆=2
- end i
- else
- Load in e up ion due o bus isola ion (No cascading occu ed) 𝐼𝐷𝑀
𝑀𝑆=0
- end i
G
GG
G
En i e Ne wo k
Majo
Subne wo k
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
5
D. Mi iga ion S a egy
The mi iga ion s a egies poin ed ou in Algo i hm II, which
in ol e load educ ion and con olled islanding based on he
impac s o ini ia ing e en s and subsequen cascading e en s,
a e de ailed he e.
1) Load Reduc ion
Load educ ion cu ails demand locally o sys em-wide, ei he
h ough ope a o con ol o p o ec ion schemes. Beyond
balancing supply and demand o main ain equency s abili y, i
mi iga es cascading p opaga ion by elie ing s ess om pos -
e en powe low edis ibu ion. When igge ed by he
decision-making module (MS2), load educ ion add esses
load–gene a ion imbalance and line o e loading. Depending on
he imescale, i may be combined wi h gene a ion escheduling
in sho - e m ope a ional planning o equency ese e
u iliza ion in nea - eal- ime ope a ion. Cu ailmen is alloca ed
p opo ionally o each load’s sha e o o al demand. Fo he es
sys em, load educ ion is quan i ied using Eq. (6), which
inco po a es gene a o con ibu ions o he equency
es o a ion ese e (FRR), yielding he o al educ ion o island
k (𝐿𝑅𝑘). In sho - e m ope a ional planning, 𝐹𝑅𝑅𝑔,𝑖 is ze o, bu
𝑃𝑔,𝑖 may change due o gene a ion escheduling. In con as , in
nea - eal- ime ope a ions, 𝑃𝑔,𝑖 emains unchanged, while
𝐹𝑅𝑅𝑔,𝑖 a ies.
𝐿𝑅𝑘=∑ 𝑃𝑙,𝑗
𝑗 ∈ Λ𝑘−∑ (𝑃𝑔,𝑖+𝐹𝑅𝑅𝑔,𝑖)
𝑖 ∈ Ω𝑘 (6)
2) In en ional Con olled Islanding (ICI)
As shown in Fig. 2, his module de e mines whe e and how o
island by o ming s able, sel -su icien islands a ound BSUs.
Using sys em da a and ou pu s om he esilience assessmen
and decision-making modules, i iden i ies bounda y buses and
lines while main aining equency and o o angle s abili y
h ough coo dina ed load and gene a ion con ol.
• Iden i ica ion o Cohe en Gene a o G oups (CGG)
To p ese e o o angle s abili y a e con olled islanding,
cohe en gene a o g oups (CGGs) mus be iden i ied.
Algo i hm III ou lines his p ocess using gene a o e minal
ol age phase angles om PMUs [11]. Cohe ency is quan i ied
h ough he In aclass Co ela ion Coe icien (ICC), scaled
om 0 o 1, and weigh ed by impedance-based elec ical
dis ances o ensu e spa ial p oximi y and a oid in easible
pa i ions. A K-medoids spec al clus e ing algo i hm [37] is
hen applied o he dis ance-weigh ed ICC (DICC) alues, using
100 samples o 10 ms each wi hin a mo ing window. Elec ical
dis ance is de ined as he minimum equi alen impedance
be ween gene a o s, compu ed ia he Dijks a algo i hm [32].
The DICC o mula ion is gi en in Eq. (7).
𝐷𝐼𝐶𝐶𝑖,𝑗=1−(𝐼𝐵𝐷𝑖,𝑗⊙ (1−𝐼𝐶𝐶𝑖,𝑗)) ,∀ 𝑖,𝑗 ∈𝐵𝐺 (7)
whe e 𝐼𝐵𝐷𝑖,𝑗 e e s o he impedance-based dis ance be ween
each pai o gene a o s (𝑖,𝑗); 𝐼𝐶𝐶𝑖,𝑗 ep esen s he in aclass
co ela ion o he phase angles o each pai o gene a o s; and
𝐷𝐼𝐶𝐶𝑖,𝑗 deno es he dis ance-weigh ed in aclass co ela ion o
gene a o s, anging om 0 o 1, wi h alues close o 1
indica ing g ea e cohe ency. 𝐵𝐺 ep esen s gene a o bus se ,
and ⊙ deno es elemen -wise p oduc ope a ion. 𝐼𝐵𝐷𝑖,𝑗 is
calcula ed by inding sho es leng h 𝕃(ℙ), whe e ℙ deno es
he pa h be ween each pai o gene a o s (𝑖,𝑗) in he
Algo i hm III:
Iden i ica ion o CGGs
- Upda e he da a om he a ailable ne wo k elemen s
- Calcula e he spa se impedance ma ix o he ne wo k 𝑍𝑏𝑢𝑠
- Es ablish impedance-weigh ed g aph o he powe sys em
- o 𝑖 ∈ 𝐵𝐺 do
- o 𝑗 ∈ 𝐵𝐺 do
- i 𝑖≠𝑗 hen
- Calcula e 𝐼𝐵𝐷𝑖,𝑗 by inding he sho es leng h 𝕃(ℙ) among he
pa hs be ween he o igin gene a o node 𝑖 and he des ina ion
node 𝑗 using he Dijks a algo i hm (see Eq. (8))
- Calcula e he in aclass co ela ion (ICC) be ween each pai o
phase angles 𝐼𝐶𝐶𝑖,𝑗
- Calcula e dis ance-weigh ed ICC be ween each pai o phase
angles 𝐷𝐼𝐶𝐶𝐺𝑖𝑗 (see Eq. (7))
- else
- 𝐷𝐼𝐶𝐶𝐺𝑖𝑗 =1
- end i
- end o
- end o
- Iden i y cohe en g oups o gene a o s a ound BSUs using he K-medoids
clus e ing algo i hm based on 𝐷𝐼𝐶𝐶𝑖,𝑗
Algo i hm IV: Cascading-d i en ICI module
- Upda e he da a o he mino and majo subne wo ks
- i 𝐼𝐷𝑀
𝑀𝑆=1 hen
- Iden i y he ma ginal buses
- Run he sub ou ine o Algo i hm III o iden i y CGGs
- while s opping c i e ion is unme do
- Sol e he op imiza ion p oblem subjec o all cons ain s ( ind a
se o decision a iables ha minimizes he objec i e unc ion
while sa is ying all cons ain s)
- end while
- end i
- Iden i y all islands and upda e hei co esponding ne wo ks
- Calcula e he o al alue o DNS o he en i e ne wo k
𝐷𝑁𝑆=∑𝐷𝑁𝑆𝑘𝐼𝑠𝑙
𝑘∈𝛫 + 𝑃𝐿𝐼𝑠𝑜
- e u n DNS, he bounda y lines, he se o buses pe aining o each
island, load and gene a ion alues a each bus
impedance-weigh ed g aph o powe sys em 𝔾=(𝕍,𝔼,𝕎),
wi h 𝕍 ep esen ing he se o e ices, 𝔼 he se o edges, and
𝕎 he weigh s associa ed wi h he edges in he g aph 𝔾.
𝐼𝐵𝐷𝑖,𝑗=min𝕃(ℙ𝑖,𝑗:𝑖 →𝑗), ∀ 𝑖,𝑗∈𝐵𝐺 (8)
This calcula ion is upda ed dynamically a e cascade
quan i ica ion, assessmen , and decision-making, cap u ing
nea - eal- ime changes such as ou ages o impedance a ia ions
o use in ICI op imiza ion. To ensu e BSU p esence, hey se e
as cen al co es in CGG iden i ica ion, and a ailabili y is
echecked wi hin he ICI algo i hm. The numbe o CGGs,
equi alen o he equi ed islands o cascading-d i en
pa i ioning, is de e mined by Eq. (4) (Sec ion II-B-2). The
esul ing se o CGGs is exp essed in Eq. (9).
𝐶𝐺𝐺={𝐺𝐺𝐺𝛾 | 𝛾∈𝛫} (9)
• Con olled Ne wo k Spli ing
The p oposed con olled islanding me hod educes
compu a ional bu den by limi ing sea ch space using elec ical
dis ance. As ou lined in Algo i hm IV, buses close o a CGG
a e di ec ly assigned o ha island and excluded, while ma ginal
buses— hose nea ly equidis an o loca ed a bounda ies—
de ine he educed sea ch space. The sol e hen ope a es on
his subse o iden i y op imal bounda y buses o islanding.
a) Sea ch Space Reduc ion (SSR)
The sea ch space educ ion (SSR) echnique, in oduced he e
o he i s ime in con olled islanding, applies impedance-
based elec ical dis ance o limi possible solu ions. Since
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX
assigning buses a om eac i e powe sou ces can isk
ol age ins abili y, subne wo ks a e i s o med a ound CGGs
using sho es -pa h dis ances. Buses nea island bounda ies a e
hen iden i ied as ma ginal buses, de e mined by hei
maximum impedance-based dis ance o CGGs. These ma ginal
buses de ine he p oblem’s sea ch space (SS), which is explo ed
by an op imiza ion algo i hm o minimize load–gene a ion
imbalance. The p ocess is concep ually illus a ed in Fig. 4.
A e ini ia ing e en s, sys em in eg i y is i s assessed. I
unin en ional spli ing occu s, he isola ed mino subne wo k is
excluded om he islanding s udy, wi h i s decision a iables
se o ze o. Fo he emaining majo subne wo k, bus decision
a iables ake in ege alues om 1 o 𝑁𝑖𝑠𝑙, ep esen ing island
assignmen s. As o mula ed in Eq. (10), buses a e alloca ed o
islands based on hei sho es dis ance o he co esponding
CGG, while ma ginal buses a bounda ies may ake any island
alue om he se 𝛫={1,2,…,𝑘,…,𝑁𝑖𝑠𝑙}. He e, 𝐵𝑖𝑠𝑙𝑘 deno es
he se o buses in island 𝑘 such ha 𝐵𝑖𝑠𝑙𝑘⊂𝐵𝑀𝑚𝑁, and 𝐵𝑀𝑎𝑟𝑔
is he se o ma ginal buses wi h 𝐵𝑀𝑎𝑟𝑔⊂𝐵𝑀𝑚𝑁; 𝐵𝑀𝑚𝑁
deno es he se o buses o he majo and mino subne wo ks.
𝑥𝑖 is he decision a iable o bus 𝑖 ha akes he alue o he
island numbe 𝑘 i i has he sho es dis ance o he CGG o
island 𝑘. The decision a iables o he ma ginal buses a ound
he bounda y o he islands can ake in ege alues om he se
𝐾 ep esen ing he island numbe s (see Fig. 4).
𝑥𝑖={𝑘, 𝑖𝑓 𝑖 ∈ 𝐵𝑖𝑠𝑙𝑘
∈𝐾, 𝑖𝑓 𝑖∈𝐵𝑀𝑎𝑟𝑔
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (10)
As a esul o he p oposed SSR me hod, wo ec o s o he
lowe and uppe bounds o he decision a iables a e
calcula ed, as o mula ed in Eq. (11).
𝑋={𝑥𝑖 | 𝑥𝑖≤𝑥𝑖≤𝑥𝑖 ,𝑖∈𝐵𝑀𝑚𝑁}
𝑋∈[𝑋 ,𝑋] (11)
The p oblem sol e only needs o sea ch he space wi hin
hese bounds o ind an op imal solu ion o he bounda y buses
and he lines connec ing each pai o islands. As illus a ed in
Fig. 4, and assuming h ee islands, he decision a iable ma ix
𝑋 lies wi hin bounds 𝑋 and 𝑋, aking in ege alues om 0 o
3. A alue o 0 deno es an isola ed bus, while o he in ege s
assign buses o he co esponding island based on sho es
dis ance (e.g., 2 o Island 2). Ma ginal bus assignmen s,
bounda y line iden i ica ion, and he op imal pos -islanding
ope a ing poin a e de e mined by sol ing he op imiza ion
p oblem in Eq. (1). The esul ing subne wo ks a e hen upda ed
o e lec he op imal ICI solu ion.
𝑋∈
[
012310⋮12
⋮⋮⋮⋮⋮⋮⋮⋮
032310⋮23
]
→𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑 𝑏𝑢𝑠
→𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠
→𝑖𝑠𝑙𝑎𝑛𝑑 2
→𝑖𝑠𝑙𝑎𝑛𝑑 3
→𝑖𝑠𝑙𝑎𝑛𝑑 1
→𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑 𝑏𝑢𝑠
⋮
→𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠
→𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑏𝑢𝑠
Fig. 4. P oposed sea ch space educ ion concep in ol ing ma ginal o dis an
buses.
b) Cons ain s
• S uc u al Cons ain s
These cons ain s ensu e ne wo k connec i i y and he
assignmen o a leas one BSU o each island, acili a ing he
es o a ion o a blacked-ou island a e a con olled islanding
ailu e. Eq. (12) ensu es ha e e y bus 𝑖 wi h a non-ze o
decision a iable 𝑥𝑖≠0 in he combined majo and mino
subne wo k bus se 𝐵𝑀𝑚𝑁 is assigned o a speci ic island,
he eby main aining connec i i y wi hin he subne wo k o
islands wi hou isola ed buses a e con olled islanding.
|𝐵𝑀𝑚𝑁| deno es he ca dinali y (o size) o he se 𝐵𝑀𝑚𝑁. Eq.
(13) ensu es ha o each 𝛾∈𝛫, he e is a leas one 𝐵𝑆𝑈𝑖 in
𝐺𝐺𝐺𝛾. The bina y a iable 𝑢𝑖,𝛾 akes he alue 1 i 𝐵𝑆𝑈𝑖 is in
𝐺𝐺𝐺𝛾, and 0 o he wise.
∑ 𝑥𝑖/𝑥𝑖
𝑖 ∈ 𝐵𝑀𝑚𝑁 =|𝐵𝑀𝑚𝑁| 𝑖𝑓 𝑥𝑖≠0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖∈ 𝐵𝑀𝑚𝑁 (12)
∑ 𝑢𝑖,𝛾
𝑖 ∈ 𝐵𝑆𝑈 ≥1 ∀ 𝛾∈𝛫 ,
𝑤ℎ𝑒𝑟𝑒 𝑢𝑖,𝛾= {1, 𝑖𝑓 𝐵𝑆𝑈𝑖∈𝐺𝐺𝐺𝛾
0
,
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(13)
• Ope a ional Cons ain s
Ope a ional cons ain s ensu e ha all ope a ing limi s a e
me , including line powe low (Eqs. (14)-(19)), gene a o
ac i e and eac i e powe (Eqs. (17)-(18)), and bus ol age (Eq.
(19)). Du ing op imiza ion, i a cons ain is iola ed, load
educ ion and gene a ion edispa ching a e implemen ed o ind
a easible and op imal solu ion.
𝑃𝑖𝑗(𝑉,𝜃)=𝑦𝑖𝑗[𝐺𝑖𝑗𝑉𝑖2−𝑉𝑖𝑉𝑗(𝐺𝑖𝑗𝑐𝑜𝑠𝜃𝑖𝑗+
𝐵
𝑖𝑗
𝑠𝑖𝑛𝜃
𝑖𝑗
)] ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (14)
𝑄𝑖𝑗(𝑉,𝜃)=𝑦𝑖𝑗[𝑉𝑖𝑉𝑗(𝐺𝑖𝑗𝑠𝑖𝑛𝜃𝑖𝑗−𝐵𝑖𝑗𝑐𝑜𝑠𝜃𝑖𝑗)
−𝐺
𝑖𝑗
𝑉𝑖2 ] ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (15)
(𝑃𝑖𝑗
2+𝑄𝑖𝑗
2)1/2≤𝑆𝑖𝑗 ∀ (𝑖,𝑗)∈ 𝐵𝑙𝑛𝑒 (16)
𝑃𝐺𝑖≤𝑃𝐺𝑖≤𝑃𝐺𝑖 ∀ 𝑖 ∈ 𝐵𝐺 (17)
𝑄𝐺𝑖≤𝑄𝐺𝑖≤𝑄𝐺𝑖 ∀ 𝑖 ∈ 𝐵𝐺 (18)
𝑉≤𝑉𝑖≤𝑉 ∀ 𝑖 ∈ 𝐵 (19)
whe e 𝑃𝑖𝑗, 𝑄𝑖𝑗, and 𝑆𝑖𝑗 deno es he ac i e, eac i e, and
maximum appa en powe low o line 𝑖𝑗, espec i ely, and 𝐵𝑙𝑛𝑒
e e s o he se o wo-end pai buses o lines.
The ol age and eac i e powe cons ain s accommoda e
ol age de ia ions wi hin pe missible ope a ing limi s a pos -
islanding ope a ing poin s, while he objec i e unc ion—
minimizing load-gene a ion imbalance—helps mi iga e
equency de ia ions. Toge he , hese elemen s signi ican ly
con ibu e o ensu ing pos -islanding s abili y and align wi h he
how objec i e o he p oposed cascading-d i en ICI me hod.
III. RESULTS AND DISCUSSION
The IEEE 39-bus sys em (345 kV, 6254.2 MW o al load) is
used o e alua e he p oposed app oach. The op imiza ion
p oblem is sol ed wi h MATLAB’s mixed-in ege nonlinea
oolbox [38] and MATPOWER [39]. Simula ions a e
pe o med on a PC wi h an In el Co e i7 (2.8 GHz, 16 GB
RAM), yielding an a e age compu a ion ime o a ound 15
seconds ac oss all scena ios o he es sys em. Gene a o s a e
assumed o p o ide up o 5% o capaci y as equency
En i eNe wo k Ma ginal buses o
Sea ch Space (SS)
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
7
es o a ion ese es [40], and all ansmission lines a e
conside ed a ailable o de-ene giza ion o enable islanding.
BSUs a e loca ed a buses 32, 36, 37, and 39. The amewo k is
es ed o bo h nea - eal- ime ope a ion, add essing e ol ing
e en s, and sho - e m ope a ional planning, co e ing wea he -
and non-wea he - ela ed scena ios.
A. Nea eal- ime ope a ion unde e ol ing e en s
In his case, h ee lines (1-39, 2-3, and 3-4) a e emo ed as
ini ia ing e en s, ep esen ing an N-3 con ingency. This ou age
se does no cause ea ly bus isola ion o mino subne wo ks
(𝑃𝐿𝐼𝑠𝑜=0 𝑎𝑛𝑑 𝐼𝐷𝑀
𝑚𝑛=0). Cascading ailu e analysis shows
p opaga ion wi h 13 addi ional line ou ages om o e load
p o ec ion (Fig. 5a), esul ing in 2348.2 MW unse ed demand,
including he disconnec ion o buses 3, 12, 18, and 27, and
pa ial load shedding elsewhe e ( 𝐷𝑁𝑆𝑀𝑁 =2348.2). The
cascade is isualized in Fig. 5b using a ee-like g aph, whe e
connec ed and blacked-ou buses a e ma ked in g een and ed,
espec i ely. P o ec ion mechanisms (OL, UFLS, UFGS,
OFGS) a e shown be ween cascade s ages. Two blacked-ou
and h ee uncon olled islands eme ge. Since 𝐷𝑁𝑆𝑀𝑁 >0 wi h
13 cascading ou ages, he decision-making module se s 𝐼𝐷𝑀
𝑀𝑆=
1, equi ing con olled islanding (MS1). Upon ecei ing eal-
ime da a, he algo i hm compu es an op imal solu ion in unde
20 seconds, demons a ing easibili y o nea - eal- ime
ope a ion [41]. Following ICI, h ee islands a e c ea ed by de-
ene gizing lines 14-15 and 26-27 (Fig. 6a). As shown in Fig.
6b, he cascade is con ained, wi h con olled load educ ion o
1287.4 MW and no blacked-ou buses, con i ming ha
con olled islanding e ec i ely hal s p opaga ion and mi iga es
widesp ead ailu es. Fig. 7a shows ime-domain RMS esul s
o gene a o e minal ol age angles be o e islanding, whe e
s able and uns able subne wo ks appea , indica ing gene a o
ins abili y. A e islanding (Fig. 7b), cascading is p e en ed,
and all gene a o s emain s able due o e ec i e CGG
iden i ica ion.
Ano he ins ance o ini ia ing e en s, ep esen ing an ex eme
wea he - ela ed case, conside s ou ages o lines 1-2, 1-39, 2-3,
2-25, 17-18, and 17-27, c ea ing a mino isola ed subne wo k.
Fig. 5. CFA be o e ICI, conside ing he ou age o h ee lines.
Fig. 6. CFA a e ICI, conside ing he ou age o h ee lines.
Fig. 7. Phase angle o gene a o s be o e ICI (a) and a e ICI (b).
Gene a ed by he wind e en simula o wi h s ochas ic N-k
con ingencies (k ∈ [1, 6]), his e en o ms isola ed buses 1, 2,
30 and a mino subne wo k (wi h buses 25–29, 37, 38). As
de ailed in Sec ion II-B-2, since 𝑁𝑖𝑠𝑙<2, his subne wo k is
excluded om con olled islanding and mi iga ed wi h load
educ ion only. The ini ial in e up ion o load due o he Bus 1
isola ion and he sys em DNS be o e ICI implemen a ion a e
𝑃𝐿𝐼𝑠𝑜=97.6 MW and 𝐷𝑁𝑆=2170.35 MW, espec i ely. The
majo subne wo k is hen spli by opening line 14-15, educing
DNS o 726.5 MW (66.5% imp o emen ), as shown in Fig. 8b.
B. Sho - e m ope a ional planning o non-wea he - and
wea he - ela ed ini ia ing e en s
The p oposed amewo k is e alua ed unde ex eme
< 39>
< 1>
< 2>
< 30>
G8
G9
G6
G7
G4G5
G3
G2
< 4>
< 5>
< 6>
< 7>
< 8>
< 9>
< 31>
< 11>
< 12>
< 10>
< 13>
< 32>
< 34> < 33>
< 19>
< 20> < 36>
< 35>
< 23>
< 22>
< 21>
< 14>
< 15>
< 16>
< 24>
< 38>
< 27>
< 17>
< 18>
< 3>
< 25> < 26>
< 28>
< 29>
< BUS #>
< 37> BS Uni
G1
G10
Ini ia ing E en s
Cascading Failu es
Ini ia ing E en s: Lines 1-39, 2-3, and 3-4
Load Isola ion and Reduc ion (%)
100
50
0
Cascading P opaga ion
Node colo s:
ini ial ne wo k s a us
ope a ing s a us
blacked-ou s a us
T ee-Like G aph o Visualizing Cascading Failu es
UFLS OFGS
OFGS
UFLS
EV
OL
OL
OL
OL
ISL
(IEEE 39-bus ne wo k)
< 39>
< 1>
< 2>
< 30>
G8
G9
G6
G7
G4G5
G3
G2
< 4>
< 5>
< 6>
< 7>
< 8>
< 9>
< 31>
< 11>
< 12>
< 10>
< 13>
< 32>
< 34> < 33>
< 19>
< 20> < 36>
< 35>
< 23>
< 22>< 21>
< 14>
< 15>
< 16>
< 24>
< 38>
< 27>
< 17>
< 18>
< 3>
< 25> < 26>
< 28>
< 29>
< 37> BS Uni
G10
Ini ia ing E en s
Bounda y Lines
< BUS #>
G1
Ini ia ing E en s: Lines 1-39, 2-3, and 3-4
Load Isola ion and Reduc ion (%)
100
50
0
Cascading P opaga ion
Node colo s:
ini ial ne wo k s a us
ope a ing s a us
blacked-ou s a us
T ee-Like G aph o Visualizing Cascading Failu es
(IEEE 39-bus ne wo k)
EV
ISL
UFLS OFGS
(a)
(b)
(a)
(b)
(b)
(
a
)
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY, VOL. XX, NO. XX, XX XXXX
Fig. 8. CFA be o e ICI (a) and a e ICI (b), wi h he ou age o h ee lines.
unce ain condi ions, including se e e wea he - and non-
wea he - ela ed e en s. In sho - e m ope a ional planning
s udies o a ew hou s ahead, ope a o s can assess he sys em
unde po en ial and an icipa ed e en s, such as de e minis ic N-
1, N-2, and N-3 con ingencies o ansmission lines, along wi h
a se o s ochas ic scena ios in ol ing wind e en s. This pa o
he s udy in ol es analyzing N-k con ingencies o ansmission
lines (wi h k ∈ [1, 3]) de e minis ically and N-k con ingencies
(wi h k ∈ [1, 6]) s ochas ically, based on 1000 wind- ela ed
s ochas ic e en s. These s ochas ic e en s include 91, 60, and
53 dis inc con ingency se s o N-4, N-5, and N-6, espec i ely.
In his phase o he s udy, ope a o s can eschedule sys em
gene a ion du ing con olled islanding due o su icien ime
be o e e en s, educing eliance on load cu ailmen .
Applying he same ou age scena io as in Sec ion III-A, Table
I compa es p oac i e s a egies (gene a ion escheduling and
load educ ion implemen ed 1 and 2 hou s ahead) wi h eac i e
ones (FRR and load educ ion). The esul s show ha p oac i e
measu es achie e g ea e esilience, as illus a ed in Fig. 1.
Based on gene a o amp a es [42], gene a ion escheduling
inc eases om 696 MW o 1392 MW, while load educ ion
dec eases om 708.9 MW o 12.9 MW when implemen ed 1
and 2 hou s ahead, espec i ely. As e en s app oach, load
educ ion equi emen s ise, bu o e all emain lowe unde
p oac i e s a egies due o simul aneous gene a ion
escheduling. The emaining simula ions assume a 1-hou -
ahead ho izon, wi h u he analysis o mi iga ion s a egies
(MS) o speci ic ex eme wind-d i en e en s. Table II
compa es mi iga ion s a egies (MS0, MS1, MS2) o s ochas ic
ini ia ing e en s in ol ing he loss o 4 o 6 lines (N-k, k ∈ [4,
6]). The decision-making module selec s s a egies based on
DNS and he numbe o ipped elemen s. When DNS=0 ( i s
ow), no mi iga ion is equi ed (MS0). Fo he second case
(lines 13-14, 15-16, 16-21, 16-24), load educ ion o 1673.4
MW (MS2) alle ia es s ess, p e en ing cascading and educing
DNS om 50.2% o 26.8%. In con as , ou ages o lines 5-8, 6-
7, 7-8, and 8-9 igge cascading and se e e ou ages (67.5%),
bu wi h ICI (MS1), DNS imp o es by 81.8%. Fig. 9 illus a es
hese ou comes wi h a hea map compa ing DNS ac oss
s a egies.
Fu he mo e, sys em eliabili y and esilience a e quan i ied
using he expec ed alue o DNS (EDNS) and Condi ional
Value-a -Risk (CVaR) a he 95% con idence le el [43]. This
analysis aims o demons a e he e ec i eness o con olled
islanding in mi iga ing he impac o bo h expec ed e en s
( he eby dec easing he mean alue o DNS) and he e ec s o
unexpec ed ail- isk e en s ( esul ing in a educ ion o he
condi ional alues o DNS). Fo his pu pose, a 95% con idence
le el o DNS (CVaR95%) is conside ed o he a e age DNS
among he wo s 5% o e en s. Table III compa es EDNS and
CVaR be o e and a e mi iga ion o de e minis ic N-k (k ∈ [1,
3]) con ingencies, showing a leas 45.6% imp o emen in
EDNS and 32.9% in CVaR o N-3 cases. A simila analysis o
1000 s ochas ic wind- ela ed scena ios up o N-6 demons a es
u he bene i s. As illus a ed in Fig. 10, con olled islanding
shi s he DNS p obabili y dis ibu ion le wa d, educing
EDNS om 1249.83 MW o 650.98 MW and CVaR om
4426.86 MW o 3241.87 MW, he eby lowe ing blackou isk
TABLE I
PREVENTIVE ICI COMPARED TO CORRECTIVE ICI
Type o S a egy
P oac i e (P e en i e ICI)
Reac i e
(Co ec i e ICI)
Hou s ahead 1 2
Remedial ac ions Gen.
Resch. LR Gen.
Resch. LR FRR LR
P (MW) 696 708.9 1392 12.9 117.5 1287.4
TABLE II
RESULTS OF DIFFERENT MITIGATION STRATEGIES
Sc.
k
in
(N-k)
Lines
DNS in MW (%)
Imp.
MS
Be o e
ICI
A e
ICI %
1
4
14-15, 16-17,
17-18, 17-27 0 0 MS0
2 13-14, 15-16,
16-21, 16-24
3140.8
(50.2)
1673.4
(26.8)
0 MS2
3 5-8, 6-7, 7-8,
8-9
4223.6
(67.5)
767
(12.3)
81.8 MS1
4
5
4-5, 6-11, 7-8,
8-9, 13-14
3298.9
(52.7)
1444.7
(23.1)
56.2 MS1
5 3-4, 5-6, 14-15,
15-16, 22-23
320
(5.1)
0 MS0
6
6
2-3, 3-4, 3-18,
17-18, 17-27,
26-27
761
(12.2) 0 MS0
7
4-14, 6-11,
10-11, 10-13,
13-14, 14-15
2171.2
(34.7)
894.3
(14.3) 58.8 MS1
Fig. 9. Compa ison o cascading impac s ac oss a ious scena ios using
di e en mi iga ion s a egies.
< 39>
< 1>
< 2>
< 30>
G8
G9
G6
G7
G4G5
G3
G2
< 4>
< 5>
< 6>
< 7>
< 8>
< 9>
< 31>
< 11>
< 12>
< 10>
< 13>
< 32>
< 34> < 33>
< 19>
< 20> < 36>
< 35>
< 23>
< 22>< 21>
< 14>
< 15>
< 16>
< 24>
< 38>
< 27>
< 17>
< 18>
< 3>
< 25> < 26>
< 28>
< 29>
< 37>
G1
G10
Mino Subne wo k
: BS Uni
: Ini ia ing E en s
: Cascading Failu es
< BUS #>
: Isola ed Bus(es)
: Wind T ajec o y
Mino Subne wo k
< 39>
< 1>
< 2>
< 30>
G8
G9
G6
G7
G4G5
G3
G2
< 4>
< 5>
< 6>
< 7>
< 8>
< 9>
< 31>
< 11>
< 12>
< 10>
< 13>
< 32>
< 34> < 33>
< 19>
< 20> < 36>
< 35>
< 23>
< 22>< 21>
< 14>
< 15>
< 16>
< 24>
< 38>
< 27>
< 17>
< 18>
< 3>
< 25> < 26>
< 28>
< 29>
< 37>
G1
G10
: BS Uni
: Ini ia ing E en s
: Bounda y Lines : Isola ed Bus(es)
< BUS #>
: Wind T ajec o y
Be o e MS A e MS
1
2
3
4
5
6
7
Scena io No.
Cascading Impac s unde Di e en Scena ios and Mi iga ion S a egies
26.8
12.3
23.1
14.3
50.2
67.5
52.7
34.7
0
20
40
60
80
100
0
5.1
12.2
Cascading Se e i y (%)
MS0
MS2
MS1
MS1
MS0
MS0
MS1
(b)
(
a
)
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
9
TABLE III
EXPECTED DNS AND CVAR FOR DETERMINISTIC EVENTS
Con.
DNS be o e
mi iga ion (MW)
DNS a e
mi iga ion (MW)
Imp o emen (%)
EDNS CVaR EDNS CVaR EDNS CVaR
N-1 753.11 4736.68 320.48 1975.3 57.45 58.3
N-2 1317.49 4407.28 654.1 2860.3 50.35 35.1
N-3 1745.98 4669.37 948.85 3133.24 45.65 32.9
Fig. 10. PDF cu es o DNS o s ochas ic con ingencies.
Fig. 11. Cascading ailu e analysis o he IEEE 118-bus sys em unde ini ia ing
e en s wi hou con olled islanding.
and enhancing esilience.
To demons a e scalabili y, he p oposed me hod is applied o
he IEEE 118-bus sys em unde concu en ou ages o lines 49-
54, 59-60, 59-61, and 59-63. As shown in Fig. 11, hese e en s
igge widesp ead cascading and se e e blackou s. Figs. 12 and
13 plo sys em equency and ol age agains cascade
gene a ion numbe s, whe e each gene a ion ep esen s a s age
o p opaga ion in ol ing ipping, load shedding, o gene a o
disconnec ion. Resul s show ol age and equency collapse in
blacked-ou islands, while su i ing islands s abilize nea
nominal alues. Fig. 14 u he illus a es cascading impac s
h ough a node-b anch g aph, whe e pu ple dashed lines
indica e winds o m-exposed elemen s, ed solid lines ep esen
ini ia ing ou ages, and ed dashed lines show subsequen
cascading ailu es. Fu he mo e, sys em pe o mance imp o es
ma kedly wi h he p oposed con olled islanding me hod. As
shown in Figs. 15–18, cascading impac s a e g ea ly educed,
and all islands s abilize wi h ol age and equency nea
nominal alues. The o al compu a ional ime, including
cascading ailu e analysis, decision-making, and islanding
compu a ion, is 16.4 seconds. Fig. 19 compa es sys em
esilience using he apezoid cu e, showing se ed load ising
om 121.4 MW o 3960.6 MW—a 90.5% imp o emen .
C. Compa a i e analysis and alida ion o ICI
To benchma k pe o mance, he p oposed con olled
islanding me hod is compa ed wi h he classical spec al
clus e ing me hod (SCICI) [44], which models he g id as a
weigh ed g aph. While compu a ionally e icien , SCICI
Fig. 12. Sys em equency o he IEEE 118-bus sys em unde ini ia ing e en s
wi hou con olled islanding.
Fig. 13. Vol age p o ile o he IEEE 118-bus sys em unde ini ia ing e en s
wi hou con olled islanding.
Fig. 14. Visualizing cascading impac s on he IEEE 118-bus sys em unde
ini ia ing e en s wi hou con olled islanding.
Fig. 15. Cascading ailu e analysis o he IEEE 118-bus sys em unde ini ia ing
e en s wi h con olled islanding implemen ed.
ascading ail e nalysis s sys e i n lled slanding nde ni ia ing en s
: ini ial ne wo k s a us wi h k bus
: he sys em wi h k buses du ing cascading p opaga ion
: he sys em wi h k ac i e buses a e CFA
#k
#k
#k
: he sys em wi h k blacked-ou buses a e CFA
#k
Cascading Failu e Analysis o IEEE 118-bus sys em
wi hou Con olled Islanding unde Ini ia ing E en s
Cascading gene a ion no.
0
10
20
30
40
50
60
70
80
90
100
Wind T ajec o y
: ini ial ne wo k s a us wi h k bus
: he sys em wi h k buses du ing cascading p opaga ion
: he sys em wi h k ac i e buses a e CFA
#k
#k
#k
Cascading Failu e Analysis o IEEE 118-bus sys em
wi h Con olled Islanding unde Ini ia ing E en s
0
10
20
30
40
50
60
70
80
90
100
Cascading gene a ion no.
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been edi ed. Con en will change p io o inal publica ion.
