ALHALIM, S. S. A. e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
Resea ch A icle
CONTROL AND IDENTIFICATION OF SINGLE
MACHINE INFINITE BUS WITH NEURAL
NETWORK FOR SYSTEM STABILITY
Shaimaa Shuk i Abd. ALHALIM1,2,∗, Wissem BAHLOUL2, Mohamed CHTOUROU2, Nabil
DERBEL2
1Depa men o Elec ical Enginee ing, Uni e si y o Technology- I aq, Baghdad, I aq
2Uni e si y o S ax, ENIS, Labo a o y o Con ol & Ene gy Managemen (CEM-Lab), S ax, Tunisia Coun y
shaimaa.s.abdalhalim@uo echnology.edu.iq, [email p o ec ed], [email p o ec ed],
Nabil.de b[email p o ec ed]
∗Co esponding au ho : Shaimaa Shuk i Abd. Alhalim; shaimaa.s.abdalhalim@uo echnology.edu.iq
DOI: 10.15598/aeee. 23i1.240403
A icle his o y: Recei ed Ap 8, 2024; Re ised Aug 12, 2024; Accep ed No 01, 2024; Published Ma 31, 2025.
This is an open access a icle unde he BY-CC license.
Abs ac . This pape deals wi h implemen ing a i i-
cial neu al ne wo ks o he iden i ica ion and con ol
In es iga ing he s abili y and s abiliza ion o a single
machine connec ed o an in ini e bus h ough a ans-
mission line (SMIB) sys em. A i icial Neu al Ne -
wo k (ANN) employs a mul i-laye eed o wa d ne wo k
ained using he Backp opaga ion (BP) algo i hm by
simula ions using MATLAB/Simulink. Weigh coe i-
cien s o he ANN a e de e mined using he Le enbe g-
Ma qua d algo i hm. The p oposed app oach uses wo
ypes o neu al ne wo ks: neu al con olle and neu al
iden i ica ion, neu al ne wo k con ol is a single de ice
on an in ini e bus ins ead o he PID-PSS con olle , o
imp o e he pe o mance o he SMIB sys em, and neu-
al iden i ica ion o emula e he cha ac e is ics o he
single machine in ini e bus (SMIB) sys em These neu-
al ne wo ks model sys em dynamics and nonlinea o
selec ion and con ol pu poses. The p ima y objec i e
is o de elop a neu onal iden i ica ion model ha accu-
a ely equals he cha ac e is ics o he single machine
in ini e bus (SMIB) sys em and a neu o-con olle is
implemen ed o eplace adi ional con olle s such as
Powe Sys em S abilize s (PSS) and Au oma ic Vol -
age Regula o s (AVR). Simula ions a e pe o med o
examine he sys em unde a ious condi ions, e alu-
a ing o o speed de ia ion, s a o ol age, and o o
angle del a.
Keywo ds
Neu o-Iden i ie and Neu o-con olle , Single
Machine In ini e Bus, Au oma ic Vol age Reg-
ula o s, Powe Sys em S abilize s
1. In oduc ion
When an elec ic powe sys em is subjec ed o an ex e -
nal dis u bance, he abili y o eco e i s o iginal ope -
a ional equilib ium and s ay in i s equilib ium s a e is
e e ed o as powe sys em s abili y [1]. The powe
sys em has g own in size and complexi y in ecen
yea s, necessi a ing s ong ins umen s o add ess pe -
inen issues. The gene a o exci a ion sys em’s wo
p ima y pa s he Au oma ic Vol age Regula o (AVR)
and he exci e play an ac i e pa in keeping he s a-
bili y o he powe sys em. I is a de ice ha au oma -
ically egula es he ou pu ol age gene a o o keep i
a a ela i ely ixed alue. This is done by compa -
ing he ol age ou pu wi h a ol age e e ence and,
o he a ia ion (o e o ); making he indispensable
modi ica ion in he cu en ield o ge he ol age ou -
pu nea e o he wan ed alue and con ol he ex-
ci e ou pu , he e minal gene a o ol age is mea-
su ed and compa ed wi h he e e ence ol age. A e
any mal unc ion, he dampe and ield wa e o m a -
emp o dampen he o o swing. The nega i e damp-
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 18
ALHALIM, S. S. A. e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
ing o ques gene a ed by he AVR coun e he damp-
ing sys em [2]. The powe sys em could become un-
synch onized o p oduce undesi able oscilla ions. The
Powe Sys em S abilize (PSS) was ex ended and up-
da ed echnologically o add ess his issue. I p o ides
a damping componen wi h phase and o o speed a i-
a ions, which se es as he p ima y signal gene a o in
he sys em exci a ion, by adding a signal ex a. The e-
o e, ins alling he PSS de ice would imp o e sys em
s abili y [3]. As a esul o his p oblem A i icial Neu-
al Ne wo ks (ANN) echniques we e demons a ed o
become ac i e implemen s o de e mining la ge powe
sys em p oblems and hey could become widely ac ual
when p ope ly connec ed wi h con en ional ma hema -
ical app oache [4]. A i icial Neu al Ne wo ks (ANN)
is a popula solu ion ool because o hei capaci y o
unde s and complex non-linea co ela ions and hei
abili y o handle applica ions wi h a la ge amoun o
his o ical da a [5]. ANN is made up o a ious sim-
ple nodes (neu ons) such as joined o make ei he a
single o mul iple laye s. I is indispensable o s udy
he weigh s ha exis among neu ons [6]. Connec ions
among di e en laye s and connec ions in o he same
laye a e e e ed o as eedback connec ions. The e
a e many a ie ies o Neu al Ne wo ks (NNs). A eed-
o wa d ne wo k is e med by he con inuous o wa d
p opaga ion o inpu and in e media e signals. In his
me hod, he in o ma ion a all imes ge s abou om
he inpu o he ou pu ou o he hidden laye s in a
o wa d di ec ion [7] So, ANN mo e e ec i e gadge
ha u ilizes iden i ica ion and con ol o sys em com-
plex due o he p ope ies o he non-linea cha o
he neu al ne wo ks. When he neu al ne wo k ain-
ing is e y well and enough o gi e esul s, a con olle
may be used ins ead o PSS [8] Adjus di e en ope a -
ing condi ions and ob ain sa is ac o y esul s, o con-
ol di e en ope a ing condi ions and ge e y good
esul s; he ne wo k mus be ained unde di e en
condi ions. The use o backp opaga ion and lea n-
ing ne wo ks leads o con inuous in e e ence p oblems
[9]. The main sugges ion o his wo k is ha u iliz-
ing neu al ne wo k-ins i u ed con olle s and iden i i-
ca ion migh highly become be e he s abili y and
execu ion o SMIB sys ems compa ed o con en ional
con ol echniques. So, i is e y impo an o he
compe i ion o high speed and he abili y o lea n-
ing and gene aliza ion [10]. This new s udy ad ances
wi h comp ehensi e sys em ne wo ks wi hin he SMIB
amewo k, which p e ious esea ch has no ex ensi ely
explo ed. Th ough ca e ul design o he complex in e -
ac ions and dynamics be ween he gene a o and he
in ini e bus, he g id sys em spo s app o ed ol age
s abili y and alle ia ion o e minal damage o ol -
age equipmen . Se e al s udies ha e ocused on his
s udy o NN in powe sys ems [11]. Re e ence [12]
includes he ad anced ansien s abili y assessmen
(TSA) me hod o CNN+GRU, which includes con olu-
ional neu al ne wo ks and ga ed ecu en uni s, and
he ad anced ocal loss (FL) unc ion ha can ap-
ply sel -adap i e changes acco ding o neu al ne wo k
aining and model aining o de ed o guidance.In
e e ence [9] in ends o explica e and explo e he ap-
plica ion o a i icial neu al ne wo ks o enhance he
p obabilis ic ansien s abili y o he elec ic powe
sys em assessmen p ocess. In e e ence [8] o manage
he low- equency oscilla ion ha exis s in he single-
machine in ini e bus sys em (SMIB), a PSS based on
neu al ne wo ks is de eloped in his esea ch. Neu o-
PSS consis s o wo neu ons: Neu o-iden i y, which
simula es powe low, and he Neu o-Con olle , which
gene a es addi ional exci a ion signals. Re e ence [13]
s udy uses mul ilaye pe cep on (MLP) neu ons o o -
e an app oach o de e mining he no malized an-
sien s abili y ma gin. The neu al ne wo ks a e used
o cons uc he in ica e link be ween he inpu and
ou pu a iables. The MLP neu al ne wo k is used
o cons uc he nonlinea mapping ela ionship be-
ween he no malized ansien s abili y ma gin and
he ope a ing ci cums ances o he powe sys em. In
[14] s udy he load ma gin in powe sys ems using a -
i icial neu al ne wo ks (ANN) and gene ic algo i hms
occu s in he publica ion. The load ma gin is an indi-
ca o ha shows how close he sys em is o ins abili y.
Vol age s abili y equi emen s a e o en conside ed in
load ma gin calcula ions; howe e low- equency oscil-
la ion modes wi h slow damping a es can also ha e
an impac on sys em pe o mance. The sugges ed ap-
p oach moni o s he load ma gin by synch onizing da a
om Phaso Measu emen Uni s (PMUs), conside ing
he need o ol age s abili y and small-signal s abili y.
A echnique based on gene ic algo i hms is u ilized o
choose a smalle numbe o buses o he ANN inpu
laye . The ou comes show ha he app oach can be
used o ack he load ma gin in eal- ime. In [15]
he e iew o powe sys ems o ol age s abili y us-
ing a i icial neu al ne wo ks (ANN) is co e ed in his
a icle. The au ho s s ess he need o ol age s abil-
i y e alua ion in main aining he secu e unc ioning o
powe sys ems, pa icula ly in ligh o he ising de-
mand o elec ici y and he sca ci y o a ailable powe
sou ces. In his s udy, se e al line ol age s abili y in-
dices a e in oduced, and he IEEE 9-Bus and IEEE 14-
Bus sys ems a e used o es each o hem. A eal- ime
ol age s abili y moni o ing sys em employing ANN is
also shown, illus a ing he alue o compu ed and es-
ima ed indices in o e elling ol age b eakdown. Ac-
co ding o he esul s, ope a o s can ake he equi ed
s eps o s op ol age collapse mishaps. This pape is
o ganized as ollows Sec ion 2 is a e iew o ecen li e -
a u e on s abili y and con ol o powe sys ems wi h a
compa ison o all me hods o ANN by using con ol
and Iden i ica ion, Sec ion 3, in oduc ion o powe
sys em con ol, Sec ion 4, is me hodology con ained
sys em dynamic modeling, he a chi ec u e o he Neu-
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 19
ALHALIM, S. S. A. e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
al Ne wo k design in SMIB, P ocess o Sys em Iden i-
ica ion, A chi ec u e and aining o Neu al Iden i ie
(NI), de ailed wi h he design sys em con olle , ain-
ing o he Neu al Con olle (NC), Sec ion 5, S udies
and Simula ion Resul s, Sec ion 6 Simula ion and e-
sul s o he Neu al Iden i ie (NI), Sec ion 7, Simula-
ion and esul s o he Neu al Con olle (NC), Sec-
ion8, Simula ion T aining o he Neu al Iden i ie and
Neu al Con olle (NINC) ha will be a compa a i e
plan wi h and wi hou NINC, Sec ion 9, Conclusions
his all esul s.
2. Recen Wo ks
The AVR and PSS applied p ocedu es ha e helped o
gi e no iceably imp o ed s abili y, especially while un-
ning in no mal and mino -dis u bance si ua ions. To
imp o e s abili y condi ions and con ol sys ems unde
ope a ing sys ems, mo e e ec i e con olle pa ame-
e s mus be sough . I is impo an o no e ha ,
as was al eady said, se e al unique op imiza ion ech-
niques ha e been explo ed in he pe inen li e a u e.
A sizable collec ion o gene a o s, ansmission lines,
ans o me s, sa e y equipmen , and o he ela ed com-
ponen s make up an elec ic powe sys em. A powe
sys em’s p ima y unc ion is o gene a e, mo e, and
dis ibu e elec ical ene gy. The sys em’s end use s
can be linked a di e en ol age le els (such as sub-
ansmission, p ima y dis ibu ion, and seconda y dis-
ibu ion), and hey con ol he necessa y gene a ion
needs h ough hei con inually shi ing demand [1] and
[2]. Re e ence ][16] shows how o de elop eed o wa d
and eedback con olle s o disc e e and con inuous-
ime dynamical sys ems using he ideas o ecu en
neu al ne wo ks and ein o cemen lea ning. An ele-
gan ounda ion o sys em iden i ica ion and con ol
design is p o ided by neu al ne wo ks. Neu o con-
olle s o neu al con olle s a e o en c ea ed u ilizing
a eed o wa d- eedback con ol ule, which uses a s a-
bilizing con olle and model compensa ion p o ided
by any neu al ne wo k s uc u e.In [17] esea ch on
he nonlinea con ol o a single-machine in ini e-bus
(SMIB) sys em o s eady-s a e and ansien s abili y
is p esen ed in his publica ion. The esea ch looks a
how he sys em esponds o making a di e ence can
be li e changing. The indings demons a e ha he
me hod p oduces accu a e and eliable in o ma ion on
ansien s abili y. Con ol me hods applied o powe
sys ems o imp o e ansien s abili y a e also include
in he pape . Re e ence [18] s udy looked a how a i-
icial neu al ne wo ks (ANNs) may be used o iden i y
di e en ypes o aul s in elec ic powe sys em ans-
mission lines. The ANN ne wo k a chi ec u e chosen
o each s age o de ec ion was ained and simula ed
using he wo e sions o he pa ame e s. The ind-
ings demons a e ha he sys em expe ienced h ee
line-g ound aul s, h ee line-line aul s, h ee double-
line-g ound aul s, and one h ee-phase aul . Re e -
ence [19] discusses he applica ion o an a i icial neu-
al ne wo k (ANN) neu o con olle o he con ol o
a hyd opowe plan (HPP). The s udy compa es he
pe o mance o he neu o con olle wi h a con en-
ional PID con olle . The neu o-con olle , based on
he NARMA-L2 echnique, o e s as e sys em s abi-
liza ion and be e dynamic pe o mance. The esul s
show ha he neu o-con olle ou pe o ms he PID
con olle in e ms o ise ime, s abili y, and esponse
speed. The s udy highligh s he po en ial o using neu-
ocon olle s in complex non-linea sys ems like HPPs.
In [20] a i icial neu al ne wo k (ANN)–based black-
box modeling s a egy o synch onous gene a o s is
p esen ed in his a icle. The pe o mance o he ANN
is e alua ed in compa ison o o he nonlinea models
a e i has been ained using expe imen al da a om
an ac ual gene a o . The sugges ed ANN model ex-
ceeds he compe i ion and displays g ea accu acy. The
s udy also p o ides a es me hod ha does no call
o ex a ools o disconnec ing he gene a o om he
g id. The issue o oscilla ions in a synch onous gene -
a o connec ed o an endless bus h ough ansmission
lines is co e ed in his a icle. I sugges s using sim-
ula ed annealing (SA) and a i icial neu al ne wo ks
(ANN) as online con ol app oaches o elimina e hese
oscilla ions. Th ough he supp ession o low- equency
oscilla ions b ough on by dis up ions om powe g id
aul s, he con ol echniques y o a oid sys em ins a-
bili y. The simula ion esul s demons a e ha bo h
he SA and NN con olle s success ully inc ease he
s abili y o he synch onous gene a o while sol ing
op imiza ion di icul ies. In [21] he necessi y o an
in elligen exci a ion con ol sys em in powe plan s is
co e ed o main ain he gene a o ’s e minal ol age.
To ge a ound he p oblems o ime delay, nonlinea i y,
and load a ia ions, i sugges s a unique a chi ec u e
u ilizing a neu al con olle . Th ough simula ion, he
sugges ed sys em’s pe o mance is assessed and con-
as ed wi h adi ional con olle s. The bene i s o
he in elligen con olle o e cu en con olle s a e
emphasized. In [22] he cons uc ion o a Simple Neu-
al Ne wo k s abilize (SANN-PSS) o a synch onous
machine in a powe sys em is co e ed in he publi-
ca ion. I highligh s he p oblems wi h con en ional
powe s abilize design based on linea ized models and
sugges s using an a i icial neu al ne wo k o enhance
sys em dynamics and adjus o shi ing ope a ing ci -
cums ances. The a icle discusses he SANN-PSS’s de-
sign and compa ison o a adi ional Lead-Lag PSS, as
well as he ma hema ical model o he powe sys em.
The sugges ed SANN-PSS ou pe o ms o he sys ems
in e ms o o e shoo , se ling ime, and dependabil-
i y, acco ding o digi al simula ion indings. Pape [23]
examines he use o a i icial in elligence (AI) me h-
ods in he design o powe sys em s abilize s (PSS),
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 20
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including uzzy logic, neu al ne wo ks, and op imiza-
ion algo i hms. I d aws a en ion o he d awbacks o
con en ional con ol sys ems and he ad an ages o em-
ploying AI-based PSS o inc ease sys em pe o mance
and s abili y. The s udy examines se e al AI me h-
ods used in PSS design, such as con olle s based on
a i icial neu al ne wo ks, uzzy logic, and op imiza-
ion.In [24] used he a i icial neu al ne wo ks (ANNs)
o sys em s abili y is co e ed in he publica ion. I
sugges s eplacing adi ional powe sys em s abilize s
wi h a p edic i e con olle based on wo neu al ne -
wo ks. MATLAB and DIgSILENT Powe Fac o y ex-
change da a o ep esen he con ol hie a chy. The
simula ion esul s show how e ec i e he sugges ed
s uc u e. In [25] i is based on a combina ion o Con-
olu ional Neu al Ne wo k (CNN) and G aph A en-
ion Ne wo k (GAT), and his pape shows ha he
mul i- ask ansien ene gy analysis me hod cap u es
ime change p ope ies cap u ed by CNN ime ea u e
ypes, and co ela ions be ween objec s associa ed wi h
he embedded map a e e ched using GAT. To iden i y
he impo an cha ac e is ics a ec ing ansien s abil-
i y and o imp o e powe g id ope a o s’ pe cep ions
o s abili y condi ions, he model u he applies he
Shapley addi i e explana ion (SHAP) me hod. Ma-
e ials indings indica e ha he p oposed model has
s ong opog aphic gene alisa ion, in e p e able analy-
sis, and accu acy. In [26, 27] and [28] he a icle ex-
amines he use o a neu o-con olle in he con ex o
hyd opowe plan con ol, d awing a compa ison wi h
he s anda d PID con olle . The ocus s udied on he
examina ion o dynamics sys em beha io and he o -
mula ion o ma hema ical models. The con olle s a e
simula ed and compa ed using he MATLAB/Simulink
p og am. The indings indica e ha he implemen a-
ion o he neu o-con olle yields supe io ou comes in
e ms o sys em s abiliza ion speed and dynamic pe -
o mance when compa ed o he PID con olle . In
e e ence [29] discuss powe sys em ansien s abili y
imp o emen h ough STATCOM (s a ic synch onous
compensa o ) and neu al ne wo ks. The au ho s p o-
pose an auxilia y con olle o he STATCOM ha
adjus s he shun sensi i i y based on he de ice angle
and speed se e i y The con ol me hod is applied o
a New England 10-machine, 39-bus es sys em, and
simula ion esul s a e shown STATCOM acco ding o
he sys em ope a ion poin o ob ain he c i ical ime
you wan o ix i . The con olle mus adjus he gain
A mul ilaye pe cep on neu al ne wo k-based me hod
is p oposed o speed up he gain es ima ion p ocess
in online applica ions. Simula ion esul s ob ained by
he p oposed me hod a e also p esen ed and discussed.
In gene al, moni o ing he synch onous al e na o has
always been c ucial o he p ope ope a ion o he gen-
e a o . Load angle and o he pa ame e s o SG a ec
al e na o ou pu ; howe e , when he pa ame e is in-
c eased, he powe sys em’s secu i y eaches i s maxi-
mum le el. As a esul , gene a o s a e ope a ed much
below hei s eady s a e s abili y limi o he secu e
unning o a powe sys em. An e ec i e ins umen o
ope a ing and managing powe sys ems, he a i icial
neu al ne wo k (ANN) is p oli e a ing. Weigh uning
o ANN akes a lo o wo k, bu once done co ec ly,
i uns quickly and accu a ely. P e iously, ANNs ha e
been ained ei he online o in a high-dimensional in-
pu space. As a esul , ei he aking a long ime o p o-
duce he con ol signal o using i in associa ed powe
sys ems is a li le unsa e [20].
This pape ’s goal is o in es iga e and hen p o ide
a solu ion o imp o e ansien s abili y and s abiliza-
ion egula ion while emo ing s eady-s a e aul s. I
ocuses on designing wo neu al ne wo ks ( he neu o-
iden i ie and he neu o-con olle ) o nonlinea sys-
ems. Bo h iden i ica ion and con ol a e emphasized.
This objec has wo p incipal objec i es. The i s and
mos impo an objec i e is o sugges neu al iden i-
ica ion o emula e he esul o he gene a o , and
he o he is neu o con olle is applied o eplace a
PSS/AVR wi h a PID con olle (E d) o p o ide a
neu onal iden i ica ion model ha accu a ely emula es
he cha ac e is ics o he single-machine in ini e bus
(SMIB) sys em. I ocuses on designing wo neu al
ne wo ks o nonlinea dynamical sys ems’ s eady-s a e
s abili y and ol age egula ion o nonlinea dynamical
sys ems.
3. Powe Sys em Con ol
Nume ous in e ela ed componen s make up an elec-
ical powe sys em. Se e al o hese pieces a e in-
c edibly nonlinea , and some o hem like synch onous
and induc ion machines, a e made up o a combina ion
o mechanical and elec ical pa s. Thus, he ope a-
ion and con ol o powe sys ems ha e e ol ed in o
complex sys ems wi h a ious uns able p ope ies [30].
These sys ems a e ulne able o a ious in e up ions
because hey di use ac oss such la ge geog aphic e-
gions. Sys ems become conside ably mo e b i le as a
esul o gene a o s wo king unde hese dis u bances
ha ing smalle s abili y ma gins [31]. A wide ange
o issues ha e s a ed o su ace wi h he in oduc-
ion o he connec i i y o massi e elec ical powe ne -
wo ks. Some o hese issues a e caused by he oscilla-
ions (in e -a ea oscilla ions) be ween elec ical powe
subsys ems connec ed o huge ne wo ks [32]. I may
be said ha a sys em is s able i an oscilla ion b ough
on by a dis u bance in he powe sys em quickly s abi-
lizes. I no , he sys em is uns able. An a e age powe
sys em is a mul i a iable sys em ha is in luenced by
a a ie y o de ices wi h a ious dynamic p ope ies.
The na u e o he dis u bance, ope a ing mode, and
sys em a chi ec u e all a ec how ins abili y mani es s
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 21
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Fig. 1: Classi ica ion o powe sys em s abili y.
i sel . The sys em will ypically e u n o no mal op-
e a ing condi ions wi h he help o au oma ed con ols
and/o ope a o in e en ion. Powe sys em s abili y
is ca ego ized, wi h i s ca ego ies and subca ego ies,
in Fig. 1. The classi ica ion o powe sys em s abil-
i y makes i easie o spo ins ances o ins abili y, de-
cide how o e ec i ely handle hem, and use he igh
analysis echniques [33] and [34]. The powe sys em’s
capaci y o e u n o synch onism a e a small dis-
up ion, such as a sligh change in he loads, is known
as small signal s abili y. In his case, he nonlinea
equa ions o he sys em may be linea ized o a poin o
equilib ium. The pe iod o his ype o s abili y ha
is impo an is en o wen y seconds a e a dis u -
bance. In ansien s abili y in es iga ions, he ime
window o in e es is ypically 3 o 5 seconds a e he
dis u bance; howe e , i migh go up o 10 o 20 sec-
onds o la ge sys ems. Vol age s abili y is desc ibed
as a powe sys em’s abili y o keep he ol age le el o
all busba s wi hin an accep able ange unde a ying
ope a ing condi ions. The mos ypical esul o ol -
age ins abili y is loading loss, which is accompanied by
he ipping o ansmission lines and o he elemen s
by hei p o ec i e sys ems, esul ing in cascading ou -
ages. Vol age s abili y may also be classi ied as ei he
a signi ican dis up ion in ol age s abili y o a mino
dis u bance in ol age s abili y, depending on he ype
o dis u bance. This ype o s abili y issue can be clas-
si ied as ei he sho - e m o long- e m, depending on
he pe iod o in e es , which anges om a ew sec-
onds o 10 minu es. The capaci y o a powe sys em o
main ain a s eady equency in he ace o majo supply
and demand imbalances is e e ed o as equency s a-
bili y. I is s a ed i his is a sho - e m o long- e m
phenomenon. Because mo e han one o m o ins a-
bili y may be seen in a powe sys em, he e is some
o e lap be ween he many ypes o ins abili y [33, 34]
and [35].
4. Me hodology
4.1. Sys em Dynamic Modelling
The powe sys em is a highly complex, non-linea sys-
em; hus, when choosing a powe sys em, he s abili y
o he o o angle and gene a o ol age managemen
Fig. 2: Single-line diag am o he powe sys em unde s udy.
should be aken in o conside a ion. Because o his,
he powe sys em has an Au oma ic Vol age Regula o
(AVR) o con ol gene a o ol age and ensu e he s a-
bili y o he powe sys em, as well as a powe sys em
s abilize (PSS) [36] and [37]. This esea ch akes in o
conside a ion he single-machine connec ed o in ini e-
bus (SMIB) powe sys em con igu a ion shown in Fig.
2 [38, 39, 40, 41] and [42]. The synch onous gene a o
model is a se en h-o de de ailed dynamic model, bu
he excessi ely used model hi d o de is s ill a e y
impo an ool o con ol and s abili y analysis once
he gene a o is coupled o he powe sys em, as s a ed
in [33] and [34].
dδ( )
d =ω( )−ω0(1)
dω( )
d =KD
2H[ω( )−ω0] + ω0
2H[P m −P e( )] (2)
dE′
q( )
d =1
T′
do
[E d( )−Eq( )] (3)
In which δ ela es o he o o angle o he gene -
a o , ω he speed de ia ion be ween he synch onism
and he gene a o , Peis he gene a o -deli e ed elec-
ical ou pu powe , The ansien EMF on he q-axis
is dE
′
q, he inpu mechanical powe is Pm, E d is he
inpu ol age exci a ion. The alues o T′
do and KD,H,
deno es he sys em componen s ha co espond o he
exci a ion ci cui ime cons an , dumping o que coe -
icien , and ine ia cons an espec i ely. O he alge-
b aic equa ions a e:
E d( ) = KAEF( )(4)
Eq( ) = Xds
Xds
Eq( )−Xd−X′
d
Xds
Vscosδ( )(5)
Pe( ) = Eq( )Vs
Xds
sinδ( )(6)
V ( ) = 1
Xds (X2
sEq′( ) + X2
sX2
d+ 2XsXdVsEq)
+ ( )cosδ( ))1
2
(7)
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whe e Xs=XT+XL
2,Xds=Xd+Xs,X′
ds= X′
d+Xs. The
e minal ol age magni ude is V ( ),Vsis he ol -
age o he in ini e bus, Xqand Xda e he (q-d-axises)
synch onous eac ance, X′
dis he ansien eac ance
a he d-axis, XLand XTdeno ed o he single-line
eac ance and he ans o me . While he ac i e elec-
ical powe , Pe( ), is genuinely measu e in p ac ice,
he gene a o ’s in e nal ansien ol age. The e o e,
in he sys em dynamic ela ed o Eq. (1), he di e en-
ial o E′
q( )migh be eplace by he elec ical powe
di e en ial (see equa ion (8)):
dPe( )
d =1
T′
do
Vs
X′
ds sin(δ)E d( ) + Xd−X′
d
X′dsXds V2
sωsin2(δ)
Xd−X′
d
X′dsXds V2
sωsin2(δ) + ωco (δ)−Xds
X′ds
1
T′
do Pe( )
(8)
Eq. (1) and (2) p o ide a comp ehensi e desc ip ion
o he o o dynamics, which include a known ine ia
cons an . The con ol ac ion E d ha adjus s he ield
ol age o s abilize he sys em. We can use a combi-
na ion o PID con ol and PSS con ol o achie e his.
Le ’s deno e he PID con olle as uP ID and he ou -
pu o he PSS con olle uPSS. The con ol law o he
combined con ol sys em can be o mula ed as: Whe e
T A and KA deno e, espec i ely, gain cons an o he
exci e ime cons an and he exci e gain cons an and:
U( ) = uP SS +uP ID (9)
Consequen ly, he emphasis o his esea ch is on he
use o neu al ne wo ks o analyze nonlinea powe sys-
ems. The analysis uses a single-machine in ini e bus
(SMIB) model in he powe sys em, which in e aces
wi h a i icial neu ons gene a ed in MATLAB using
he neu al in e ace oolbox. A ime-delayed eed o -
wa d neu al ne wo k is used o cap u e he nonlinea
dynamics o he sys em. No ably, he disc e e model is
impo an o he aining p ocess [25]. Le us conside
a sys em wi h gene al nonlinea discon inui y- ime dy-
namics ep esen ed by:
y(k+1) = y(k).., y(k−n+1), u(k), ..u(k−m+1)(10)
Whe e y and u ep esen scale ou pu and inpu a i-
able espec i ely. The unc ion : Rn→Ris belie ed
o possess di e en ial abili y wi h espec o i s inpu s
The disc e e ime o he hi d-o de model wi h sam-
pling ime Tso he gene a o elec ical and o a ional
dynamics equa ions is ep esen ed as:
δ(k+1) =δ(k)+Ts(11)
ω(k+1) =ωk+Ts1
2H(Pm−Pe−D(ωk−ωs))
(12)
E′
q(k+1) = E′
q+Ts.1
T′
do
[E d(k)−Eq(k)](13)
Whe e:
(k) ep esen s he disc e e ime s ep.
(K+1) ep esen s he disc e e nex ime s ep
Ts is he sampling ime.
This esea ch uses neu al ne wo ks wi h wo ypes,
he neu o (iden i ie and con olle ). The a chi ec u e
o he mul i-laye neu al ne wo k, ained using he
backp opaga ion (BP) echnique, is cha ac e ised by a
eed o wa d ne wo k. This ne wo k exhibi s a nonlin-
ea beha iou , as i ope a es wi h inpu s and ou pu s.
The model consis s o weigh pa ame e s and neu ons,
each o which employs a nonlinea sigmoid unc ion.
4.2. Neu al ne wo k design in SMIB
This s udy demons a es he e ec i eness o neu al
ne wo k implemen a ion in single-machine in ini e bus
(SMIB) sys ems. We u ilize wo neu al ne wo ks, iden-
i ie s, and con olle s o cap u e he dynamics o non-
linea sys ems. I ocuses on de eloping app op ia e
models o sys em iden i ica ion and con ol. A eed-
o wa d neu al ne wo k ained wi h a backp opaga-
ion algo i hm can accu a ely ep esen a model o
a nonlinea dynamical sys em. E ec i e aining e-
qui es disc e e modeling. This s udy p esen s wo mul-
ilaye eed o wa d neu al ne wo ks: one o he neu-
al iden i ie and he o he o he neu al con olle .
The mul ilaye neu al sys em includes nonlinea unc-
ions ha cap u e he sys em’s dynamics [17]. In
his wo k, we sugges a Feed o wa d Neu al Ne wo k
(FNN) cons uc ion wi h a Backp opaga algo i hm.
A FNN is one o he modes and ex emely widely
u ilized kinds o a i icial neu al ne wo ks, especially
o asks such as classi ica ion and eg ession. The
s uc u e o an FNN combined wi h backp opaga ion
o aining o ms a undamen al building block in he
ield o neu al ne woWe sugges aining me hods o
neu al ne wo ks, including Feed o wa d Neu al Ne -
wo ks (FNNs), so hey a e c i ical o adjus ing he ne -
wo k’s weigh s o minimize he e o be ween p edic ed
and ac ual ou pu [43]. The Le enbe g-Ma qua d
( ainlm) me hod compa es wi h wo o he me hods
Bayesian Regula iza ion ( ainb ) and Scaled Conju-
ga e G adien ( ainscg) me hods. The neu al ne wo k
p oposed was ained using he aining da a se . Tab.
1 and 2 summa izes he esul s o aining he p o-
posed ne wo k using he h ee aining algo i hms dis-
cussed in his pape . Each en y in he able ep e-
sen s 50 di e en ials, wi h andom ini ial weigh s
aken o each ial o ule ou he weigh sensi i -
i y o he pe o mance o he di e en aining algo-
i hms. The able is shown below o he con ol and
iden i ie . A his ne wo k when aining i , he Le -
enbe g–Ma qua d algo i hm akes he leas alue o
ime on a e age. O he wise, he Scaled Conjuga e G a-
dien Descen algo i hm akes he mos ime on a e -
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age. The Bayesian Regula iza ion-based aining algo-
i hm a ies i s execu ion unc ion mo e o en han he
Le enbe g-Ma qua d algo i hm; hus, i akes longe .
ye , his me hod akes a lo less ime han he Scaled
Conjuga e G adien Descen me hod.
Tab. 1 and 2 explain ha he Le enbe g-Ma qua d
me hod pe o ms be e han all o he aining algo-
i hms calcula ed, in his in es iga ion o he exp es-
sion o speed when aining a neu al ne wo k o ecog-
nize he mul imachine powe sys em.
4.3. Sys em iden i ica ion
The neu o-iden i ie is designed as a mul ilaye eed o -
wa d neu al ne wo k. We u ilize he mul i-laye neu-
al ne wo k wi h a eed o wa d ne wo k ained wi h
he BP algo i hm. This aining algo i hm con ains
a delay componen o inc ease he ne wo k’s capaci y
o ca ch he beha io sys ems’ en a i e aspec s. The
p ocess aining employs disc e e modeling o enhance
he neu al ne wo k o e icaciously lea n and gene alize
he implici pa e ns o he SMIB sys em. The aining
sys em o he Neu o-Iden i ie model is de e mined as
desc ibed in Fig. 3. To ain his NN model, i is neces-
sa y o ha e enough se s o inpu -ou pu pa e ns and
ained a ound s able ope a ing poin s. The aining
p ocedu e o a mul i-laye neu al ne wo k model in cap-
u ing he complex dynamics o powe sys ems ia he
Le enbe g-Ma qua d algo i hm. I is used o ain he
neu al ne wo k e icien ly and is enowned o i s e sa-
ili y and quick con e gence in non-linea op imiza ion
sys em issues. The mul i-inpu mul i-ou pu (MIMO)
model p oposed in ANN u ilizes he mul i-laye neu al
ne wo k wi h a eed o wa d ne wo k ained wi h he
BP algo i hm by ial and e o es . Fo each inpu
sample, pe o m o wa d p opaga ion o compu e he
ou pu s o he ne wo k. So he inpu a iables a e (∆ω,
∆Eq,∆δ,∆Pm,E d) wi h a se o he delay alues o
he inpu laye o he neu al ne wo k and he ou pu
a iables (∆ω,∆δ,∆Eq) o he ou pu laye o he
neu al ne wo k.
Fig. 3: Block diag am o aining he neu o-iden i ie .
4.4. A chi ec u e and aining o NI
We u ilize he mul i-laye neu al ne wo k wi h a eed-
o wa d ne wo k ained wi h he BP algo i hm. So,
he neu o-iden i ie is composed o wo hidden laye s
and h ee ou pu neu ons, and he numbe o hidden
neu ons will be cons an in la e lea ning ials he ac i-
a ion unc ion o he hidden laye is ha o a sigmoid
and he linea o inpu and ou pu , he ou pu o he
neu on a each laye by exp ession he ollowing:
a(k)(id)
i= Xw(k)(id)
ij a(id)(k−1)(14)
In which is he ac i a ion unc ion. In o de o
aining p ocedu e o a mul i-laye neu al ne wo k
model in cap u ing he complex dynamics o powe
sys ems. The neu al model has been ained a ound
some s able ope a ing poin s and a e aining ails,
he be e op ion a i icial o da a se equi es
a e 16 inpu s based on he numbe o delays, wo
hidden laye s, each ha ing 10 neu ons, he algo-
i hm o backp opaga ion is u ilized o ain he
neu o-iden i ie . The Neu o-Iden i ie is placed in
pa allel wi h he sys em and has he ollowing inpu :
[∆ω, ∆ω(k −1),∆ω(k −2),∆ω(k −m),..., ∆Eq,∆Eq
(k −1),∆Eq(k −2),∆Eq(k −m),..., ∆δ, ∆δ(k −1),∆
δ(k −2),∆δ(k −m),Pm,..., u(k),u(k −1),..., u(k −n)].
Whe e ∆ωis he gene a o speed de ia ion, ∆Eqa
q-axis componen o he s eady-s a e in e nal em
p opo ional o he ield winding sel - lux linkages, ∆δ
o o angle, u(k) is he ou pu o he neu o con olle
(gene a o inpu and neu o-iden i ie inpu ) and i is
e e ed o [E d], i is no ed ha Pmis he inpu me-
chanical powe , and E d he inpu exci a ion ol age.
The mul i ou pu o he iden i ie is he p edic ed
(∆ωspeed de ia ion, ∆δ o o angle, ∆Eq). This
model is a comp ehensi e nonlinea amewo k ha
accoun s o he in e connec ed nonlinea ela ionship
be ween he ou pu o he plan and p e ious alues o
bo h plan inpu s and ou pu s. The backp opaga ion
algo i hm egula es he ne wo k o he weigh s o
educe he e o among he ac ual sys em esponses
and he p edic ed ou pu s. One eason o choosing
di e en alues o ime s eps is ha a hi d model
o he sys em is su icien o s udy he ansien
s abili y. Ano he eason is ha mo e ime delay
means mo e compu a ion p e ious s udies ha e shown
ha di e ences in ime delays a e la ge o such
p oblems [44]. The cos unc ion used o he NI is:
Ji=1
2Pi(ei(k))2=1
2Pi(∆ω(k)−∆bω(k))2+
∆δ(k)−∆b
δ(k)2+∆Eq(k)−∆c
Eq(k)2
(15)
The lea ning a e o his da a se o 0.01 o con ol
he s ep size h ough weigh upda es, and he da a un-
de s udy is ypically di ided in o; T aining da a ypi-
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Tab. 1: S a is ical compa ison o di e en aining algo i hms o he iden i ie .
T aining Algo i hm A e age
Time (s)
Maximum
Time (s)
Minimum
Time (s)
S anda d
De ia ion
Le enbe g
Ma qua d 7.1867 13.803 0.05 4.0405
Scaled Conjuga e
G adien Descen 78.344 151.38 0.063 42.796
Bayesian
Regula iza ion 41.364 82.677 0.06 23.997
Tab. 2: S a is ical compa ison o di e en aining algo i hms o he con ol.
T aining Algo i hm A e age
Time (s)
Maximum
Time (s)
Minimum
Time (s)
S anda d
De ia ion
Le enbe g
Ma qua d 0.1246 0.147 0.08 0.074
Scaled Conjuga e
G adien Descen 0.23 0.353 0.082 0.5165
Bayesian
Regula iza ion 0.494 0.862 0.092 0.5165
Fig. 4: E olu ion o he mean squa e lea ning e o s o NI.
cally comp ising 70%, alida ion da a ypically makes
15% and es Da a makes 15%, also measu ed he pe -
o mance in exp ession o mean squa ed e o . The e o-
lu ion o hese mean squa e lea ning by he Le enbe g-
Ma qua d algo i hm and he bes alida ion pe o -
mance is an a e age o 5.5727e-06 a epoch 603 a Fig.
4.
4.5. Sys em con olle
In a single machine in ini e bus (SMIB) sys em, he
main componen s include a synch onous gene a o ,
powe sys em s abilize (PSS), exci a ion sys em, u -
bine and go e no sys em, and load dynamics. The
synch onous gene a o is esponsible o con e ing me-
chanical ene gy in o elec ical ene gy [44]. The PSS
helps in s abilizing he sys em by adjus ing he gen-
e a o ’s exci a ion le el. The exci a ion sys em egu-
la es he e minal ol age and eac i e powe ou pu o
he gene a o . The u bine and go e no sys em main-
ain he o o speed a he desi ed le el. Finally, load
dynamics e e o he beha io o loads connec ed o
he sys em ha may cause luc ua ions in he powe
ou pu . These componen s collec i ely con ibu e o
he unc ioning and s abili y o he SMIB sys em [45].
The ole o he neu o-con olle in egula ing sys em
pa ame e s is essen ial o achie ing s abili y and op-
imal pe o mance in he single-machine in ini e bus
sys em. Va ious aining me hods can be employed o
he de elopmen o a neu o-con olle in he con ex
o a SMIB. One app oach is he supe ised lea ning
echnique. So, his wo k ole o he Neu o-Con olle
is applied o eplace a PSS/AVR and PID con olle o
p o ide E d. The neu o- con olle is also design om a
mul ilaye eed o wa d neu al ne wo k. We u ilize he
mul i-laye neu al ne wo k wi h a eed o wa d ne wo k
ained wi h he BP algo i hm.
4.6. A chi ec u e o NC
The ne wo k has mul iple laye s and is eed- o wa d.
The expec ed ol age a ins an (k+1) in he u u e,
he eal ol age a he end, and he gene a o de ia-
ion speed make up i s inpu . The neu al con olle
emi s he ac ual ene gy ha exci es he machine. The
NN con olle akes as i s inpu s ei he he delayed al-
ues o he neu al ne wo k’s ou pu s ei he he con ol
signal o he sys em ou pu o bo h. The ne wo k is
ained o ep oduce he gi en a ge (con ol signal).
In his case, he di e ence be ween he NN ou pu and
he e e ence is used o adjus ing weigh s du ing ain-
ing. We u ilize he mul i-laye neu al ne wo k wi h a
eed o wa d ne wo k ained wi h he BP algo i hm.
So, he neu o con olle s a e composed o one hidden
laye and one ou pu neu ons and wi h h ee inpu s
(ω(k) , δ (k) ,Eq(k)) numbe o hidden neu ons will be
cons an in la e lea ning ials he ac i a ion unc ion
o he hidden laye is ha o a sigmoid and he linea
o inpu and ou pu linea . A chi ec u e o he neu al
con ol sugges ed in Fig. 4 he ou pu o he neu on a
each laye by exp ession he ollowing:
a(k)(co)
i= Xw(k)(co)
ij a(co)(k−1)(16)
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4.7. T aining o he NC
Fig. 5: S uc u e o Neu al con olle .
A simula ion app oach is employed o assess he pe -
o mance o a neu o-con olle in egula ing SMIB
sys em is shown in Fig. 5. NC is designed as a
mul i-laye eed o wa d neu al ne wo k ained using
he Le enbe g-Ma qua d backp opaga ion algo i hm
( ainlm) me hod. Wi h h ee inpu , wel e hidden
laye , and one ou pu laye . The NC cascades wi h he
aining o he NI du ing his pa he inpu o he NC
a e ( o o speed de ia ion (ω), load angle (δ), and s a-
o ol age (Eq)and ou pu is o gene a e he con ol
signal E d, i is hen sen o he neu o iden i ie , which
compa es i o he a ge . The desi ed con ol signal
is calcula ed h ough he neu o-iden i ie by compa -
ing i wi h he desi ed esponse o he sys em h ough
he neu o-iden i ie . Simula ions a e conduc ed using
MATLAB/Simulink, wi h he neu o-con olle eplac-
ing (PSS) and (PID) con olle s o Au oma ic Vol age
Regula o (AVR) con olle s. The objec i e unc ion
used o ain he neu o o he con olle is gi en by:
J(k) = 1
2Xk
1(yd(k+ 1) −y(k+ 1)) (17)
The g adien descen o he e o o he ne wo k
weigh s is a unc ion o he back-p opaga ion me hod
as ollows:
wi(k+ 1) = wi(k)−ε∂J(k)
∂wi(k)(18)
∂J(k)
∂wi(k)=∂J(k)
∂E d( )
∂E d( )
∂wi(k) (19)
Whe e εis he lea ning a e o his da a se o 0.01
o con ol he s ep size h ough weigh upda es, and
he da a unde s udy is ypically di ided in o; aining
da a ypically comp ising 70%, alida ion da a ypically
makes 15% and es da a makes 15% also, measu ed
he pe o mance in exp ession o mean squa ed e o .
The e olu ion o hese mean squa e lea ning by he
Le enbe g-Ma qua d algo i hm and he bes alida-
ion pe o mance is an a e age o 1.2748e-07 a epoch
200 a Fig. 6. This sec ion p esen s simula ion esul s
ob ained h ough a specialized lea ning app oach o
neu al ne wo ks. To de elop a neu al ne wo k con-
olle , he ini ial s ep in ol es de ining app op ia e
ne wo k a chi ec u e by speci ying he numbe o laye s
and neu ons in each laye . Following se e al lea ning
ials, he numbe o hidden neu ons emains cons an ,
and he a chi ec u e ha yields he ewes e o s is cho-
sen. Fo he hidden laye , he sigmoid ac i a ion unc-
ion is commonly employed, while he inpu and ou pu
laye s ypically u ilize he linea ac i a ion unc ion.
Fig. 6: E olu ion o he mean squa e lea ning e o s o NC.
5. S udies and Simula ion
Resul s
In his pa , he pe o mance and eliabili y o he sys-
em con olle shown in Fig. 2 is assessed using a single
gene a o linked ia a ans o me o an in ini e num-
be o buses. The assumed alues o he ol age exci-
a ion a e as ollows:
E dmin = −4p.u.and E dmax = 4p.u.
The sys em ope a es a a s eady s a e and becomes
esul as ollow:
δ0= 55.1 deg, Eq0= 1.57p.u., E d0= 1.82p.u.,
Pe0= 0.75p.u., Pm0= 0.75p.u., V 0= 1p.u., Vs=
1p.u.,
Te= 0.7516 pu and ωm= 1 (p.u).
This esul was ob ained by using a s eady-s a e
condi ion design o (SMIB) by using sol e ypes
o Simulink wi h he ollowing choices: sol e (ode4
Runge-Ku a), ype ( ixed s ep) and he p ima y sam-
ple ime (10-4 s). A s eady s a e (be o e aul ) and
he ansien s abili y based on a h ee-phase sho ci -
cui applied a he sys em o he in ini e bus wi h he
compa ison o he sys em esponses cases, which a e
desc ibed as ollows:
The sys em is exposed o a h ee-phase sho ci cui
aul ha occu ed nea he in ini e bus a = 3m s and
clea ed a 100ms by he disconnec ion o he aul ed
and he esul shows he o o speed de ia ion (ω),
load angle (δ), and s a o ol age (Eq) is shown in Fig.
7(a, b, c) espec i ely.
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 26
