ene gies
Re iew
Re iew o T ends and Ta ge s o Complex Sys ems o
Powe Sys em Op imiza ion
Jan Vysocky * and S anisla Misak
ENET Cen e, VSB—Technical Uni e si y o Os a a, 708 00 Os a a, Czechia; s anisla [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 29 Janua y 2020; Accep ed: 25 Feb ua y 2020; Published: 1 Ma ch 2020


Abs ac :
Op imiza ion sys ems (OSs) allow ope a o s o elec ical powe sys ems (PS) o op imally
ope a e PSs and o also c ea e op imal PS de elopmen plans. The inclusion o OSs in he PS is
a big end nowadays, and he demand o PS op imiza ion ools and PS-OSs expe s is g owing.
The aim o his e iew is o de ine he cu en dynamics and ends in PS op imiza ion esea ch
and o p esen se e al pape s ha clea ly and comp ehensi ely desc ibe PS OSs wi h cha ac e is ics
co esponding o he iden i ied cu en main ends in his esea ch a ea. The cu en dynamics and
ends o he esea ch a ea we e de ined on he basis o he esul s o an analysis o he da abase o 255
PS-OS-p esen ing pape s published om Decembe 2015 o July 2019. Ele en main cha ac e is ics o
he cu en PS OSs we e iden i ied. The esul s o he s a is ical analyses gi e ou cha ac e is ics o PS
OSs which a e cu en ly he mos equen ly p esen ed in esea ch pape s: OSs o minimizing he p ice
o elec ici y/OSs educing PS ope a ion cos s, OSs o op imizing he ope a ion o enewable ene gy
sou ces, OSs o egula ing he powe consump ion du ing he op imiza ion p ocess, and OSs o
egula ing he ene gy s o age sys ems ope a ion du ing he op imiza ion p ocess. Finally, indi idual
iden i ied cha ac e is ics o he cu en PS OSs a e b ie ly desc ibed. In he analysis, all PS OSs
p esen ed in he obse ed ime pe iod we e analyzed ega dless o he pa o he PS o which he
ope a ion was op imized by he PS OS, he ol age le el o he op imized PS pa , o he op imiza ion
goal o he PS OS.
Keywo ds:
op imiza ion me hods; ene gy managemen ; ene gy s o age; mic og ids; load con ol;
elec ic ehicles; op imal powe low
1. In oduc ion
Elec ical powe sys em op imiza ion is a popula esea ch opic. Elec ical powe sys em
expe s began o deal wi h he minimiza ion o he ac i e powe loss in elec ical powe sys ems
(PS), and minimiza ion o he PS ope a ion cos s in he 1950s [
1
,
2
]. An impo an miles one in he
pa h o mode n powe sys em op imiza ion sys ems (PS OSs) was de ining he Op imal Powe Flow
(OPF) p oblem [
3
,
4
]. Al hough he basic solu ion o he PS op imiza ion p oblem had al eady been
desc ibed, he low compu ing pe o mance o he compu e s a ha ime did no allow o sol ing
ex ensi e complex op imiza ion p oblems. In he coming decades, he compu ing pe o mance o
compu e s has been inc eased. Now, i is possible o sol e challenging op imiza ion asks o la ge
complex PSs, conside ing many ope a ional cons ain s o he PS [
5
]. Today, PSs a e unde ex ensi e
changes. Con en ional he mal powe plan s, which a e easy o con ol and whose a ed powe s a e in
he o de o hund eds o MW, a e being eplaced by a la ge numbe o small dis ibu ed gene a ion
uni s, whose ope a ional na u e is o en in e mi en ( he uni s using wind o sola ene gy). Mo eo e ,
elec ical powe consume s equi e inc eased quali y o he supplied powe han be o e because
hey use appliances equi ing e y high powe quali y [
6
]. In addi ion o la ge PSs, small isola ed
mic og ids wi h jus a ew powe sou ces and consume s a e being c ea ed oday. New de ices wi h
Ene gies 2020,13, 1079; doi:10.3390/en13051079 www.mdpi.com/jou nal/ene gies
Ene gies 2020,13, 1079 2 o 22
a special ope a ion cha ac e a e being connec ed o PSs, e.g., ba e y ene gy s o ages and elec ic
ehicles. Old analog elec ici y me e s a e subs i u ed wi h new sma elec ici y me e s enabling
eal- ime measu emen . All hese cu en changes in PSs, and he e o o minimize ope a ing cos s
and maximize powe sys em eliabili y, mo i a e PS ope a o s o ins all ad anced powe - low con ol
and communica ion equipmen o hei PSs, and o use comp ehensi e PS OSs o op imal con ol o
hei PSs. Tha is why PS esea che s a e nowadays engaged in c ea ing new PS OSs and imp o ing
he abili ies o he old ones. To accele a e he de elopmen o new PS OSs, hese esea che s o en use
applica ions and unc ion lib a ies o simula e he ope a ion o a PS in a ious ope a ion s a es and o
op imize PS pa ame e s. Such applica ions and unc ion lib a ies a e, e.g., OpenDSS [
7
], G idLAB-D [
8
],
o pandapowe [9].
In his pape , we moni o cu en ends and dynamics o he powe sys em esea ch op imiza ion.
The con en and o m o his e iew pape ha e been chosen wi h espec o he goal o in oducing
young esea che s o cu en ends o he PS ope a ion op imiza ion esea ch a ea. I is impo an o
no e ha he aim o his e iew pape is o p o ide a desc ip ion o he cu en ends and dynamics o
PS OSs, no a desc ip ion o he cu en ends and dynamics o PS OSs which a e based on he OPF o
Uni Commi men op imiza ion p oblem solu ion. Many PS OSs which ha e been analyzed o his
e iew pape a e based on hese wo op imiza ion p oblems, bu he e is also many PS OSs which a e
based on di e en ypes o he op imiza ion p oblem. Speci ically, he OPF and Uni Commi men
op imiza ion p oblems a e no sol ed by he PS OSs which do no obse e powe lows (an example o
such a PS OS is an op imiza ion sys em op imizing powe gene a ion o a dam hyd oelec ic powe
s a ion, which is limi ed only by he maximum and minimum alue o he wa e le el, ou pu wa e
low, and gene a o dynamics and which goal is o maximize p o i [10]).
The s a e-o - he-a wo ks, he challenges, and he u u e ends o OPF esea ch we e desc ibed
in [
11
,
12
]. The Uni Commi men esea ch was desc ibed in [
13
]. In addi ion, [
14
–
17
] also o e some
in e es ing indings.
The pape is s uc u ed as ollows. Sec ion 2desc ibes he p ocess o de ining he cu en dynamics
and ends o PS ope a ion op imiza ion esea ch and p esen s he esul s o his p ocess. Sec ion 3
desc ibes he cha ac e is ics o ele en basic PS-OSs esea ch s eams and p esen s se e al app op ia e
ep esen a i es o hese esea ch s eams. Pape s p esen ed in indi idual subsec ions o Sec ion 3a e
hose ha bes desc ibe he solu ion me hods o PS ope a ion op imiza ion p oblems o gi en esea ch
s eams and which oge he o m an o e all pic u e o gi en s eams o PS-OSs esea ch.
2. Cu en Dynamics and T ends o Resea ch
In o de o analyze he dynamics and ends o PS OSs, 388 pape s ha p esen sys ems op imizing
o he ope a ion o a pa o he powe sys em, and which we e published be ween Decembe 2015 and
July 2019, we e collec ed. The pape s o analysis we e sea ched in he Scopus and Web o Science
da abases. Any pape ound he e which was sui able o his e iew was inse ed in o he e iew’s
pape da abase. In he scope o he e iew’s esea ch, any op imiza ion sys em ela ed o any pa o a
powe sys em was in e es ing ( ega dless o a PS’s ol age le el). As such, wi hin he e iew’s pape
da abase, he e a e pape s p esen ing PS OSs op imizing o he ope a ion o low- ol age ne wo ks
sys ems (e.g., PS OSs op imizing o elec ic ehicle cha ging s a ions) and PS OSs op imizing o he
ope a ion o ansmission ne wo ks sys ems (e.g., PS OSs op imizing he ne wo k powe lows by
se ing he Flexible AC ansmission sys em de ices) a he same ime.
Once all he PS OSs pape s ele an o his e iew had been ound and e iewed, all pape s
in he e iew’s pape da abase we e analyzed in de ail. The aim o his de ailed analysis was o
de e mine whe he he pape p esen s a complex PS OS o no . I a pape did no p esen a complex PS
OS, he pape was emo ed om he e iew’s da abase. I a de ailed analysis showed ha a pape
de ia es om he e iew’s esea ch c i e ia in any way, he pape was also emo ed om he pape
da abase. Once he de ailed analysis was inished, he inal pape da abase was ob ained. The inal
pape da abase con ained 255 pape s ha mee he e iew’s esea ch c i e ia.
Ene gies 2020,13, 1079 3 o 22
Wi hin he de ailed analysis o he inal pape da abase, specializa ions and op imiza ion goals o
indi idual PS OSs we e de ined. Based on he de ined PS OSs’ specializa ions and goals, 11 g oups o
PS OSs we e iden i ied. These 11 g oups (subca ego ies) a e p esen ed in Table 1. A de ailed de ini ion
o each o hese g oups is p esen ed in Sec ion 3.
Table 1. Topics o 11 iden i ied elec ical powe sys em (PS) op imiza ion sys ems (OSs) g oups.
G oup Ma k Name o he G oup
A PS OSs minimizing he p ice o elec ici y/PS OSs educing PS ope a ion cos s
B PS OSs op imizing he ope a ion o enewable ene gy sou ces
C PS OSs egula ing he powe consump ion du ing he op imiza ion p ocess
D PS OSs egula ing he ene gy s o age sys ems ope a ion du ing he op imiza ion p ocess
E PS OSs con olling a special PS ac ion ha dwa e
F PS OSs op imizing he mic og id ope a ion
G PS OSs egula ing he cha ging/discha ging o elec ic ehicles
H PS OSs maximizing he PS ope a ion s abili y
I PS OSs econ igu ing he ne wo k opology du ing he op imiza ion p ocess
J PS OSs inding an op imal PS expansion plan
K PS OSs using he ma ke clea ing du ing he op imiza ion p ocess
A e he PS OSs g oups iden i ica ion, indi idual pape s o he pape da abase we e assigned o
11 pape g oups (indi idual pape g oups a e equi alen o PS OSs g oups p esen ed in Table 1) based
on he specializa ion o goal o he PS OS p esen ed in he pape . Two PS OSs pape s’ assignmen
p ocesses we e pe o med. In he i s assignmen p ocess, a pape was assigned o a ele an pape
g oup based on he main cha ac e is ic o he PS OS p esen ed in he pape . In he second assignmen
p ocess, a pape was assigned o all ele an pape g oups based on all iden i ied cha ac e is ics o he
PS OS p esen ed in he pape . Since in he case o se e al pape s, making a pape assignmen decision
wi hou a doub was impossible, he inal decision o assign hese pape s o he mos app op ia e pape
g oup was bu dened wi h a possible e o o subjec i e decision. Howe e , he numbe o pape s wi h
his unclea assignmen decision was low, so any misassignmen o hese pape s would no ha e a
signi ican impac on he esul s o he s a is ical analysis o he e iew’s pape da abase.
Figu e 1shows how many pape s ha e been assigned o each de ined pape g oup in he i s
assignmen p ocess. Figu e 2p esen s he same esul s using he ela i e equency and cumula i e ela i e
equency. Figu e 1shows ha he highes numbe o pape s has been assigned o g oup A (PS OSs
minimizing he p ice o elec ici y/PS OSs educing PS ope a ion cos s, 55 pape s). Howe e , i is impo an
o no e ha g oup A is in ended o he PS OSs pape s which canno be assigned o any o he o he en
pape g oups in he i s assignmen p ocess. Since he h ee la ges pape g oups con ain mo e han
hal o all pape s o he e iew’s pape da abase, he cha ac e is ics o hese h ee pape g oups (g oups
A, B, and C) we e de e mined as he mos equen ly p esen ed in he pape s published in ecen yea s.
The e o e, hese h ee PS OSs cha ac e is ics a e conside ed o be he mains eam o he PS OSs esea ch.
The assigned da abase o pape s, which was c ea ed in he i s assignmen p ocess, was la e
analyzed o he second ime, in o de o ob ain cu en ends o PS OSs esea ch. Fo his eason,
he equency o indi idual PS-OSs cha ac e is ics desc ibed in he pape s o ou da abase was analyzed
o indi idual yea s o he obse ed ime pe iod. Figu e 3p esen s he equency o he indi idual
PS-OSs cha ac e is ics desc ibed in he pape s di ided by he o al numbe o pape s in he obse ed
yea . In his igu e, he colo o g aphs o indi idual PS OSs cha ac e is ics is he same as he colo
o he column o he PS OSs cha ac e is ic in Figu e 1. This igu e shows ha he ela i e equency
o PS OSs g oup A is g adually inc easing, while he ela i e equencies o he o he PS OSs g oups
do no change signi ican ly (due o he small ex en o he s a ic se o indi idual obse ed yea s,
small luc ua ions obse ed in he g aphs o indi idual PS OS cha ac e is ics a e no conside ed o be
signi ican ). The g ow h o he ela i e equency o G oup A can be explained by he idea ha cu en
PS-OSs esea che s y o di e en ia e om olde pape s and s anda d PS-OSs esea ch s eams (i.e., PS
Ene gies 2020,13, 1079 4 o 22
OSs esea ch s eams co esponding o pape g oups B o K). Au ho s o ecen pape s y o c ea e new
PS OSs which sha e he main op imiza ion idea wi h he olde PS OSs (i.e., he minimiza ion o he p ice
o elec ici y o he educ ion o he PS ope a ion cos s). Howe e , in hese ecen PS OSs, unlike in he PS
OSs o he s anda d esea ch s eams, he e is an unusual seconda y op imiza ion a ge de ined o he e
is an unusual PS pa op imized. Rega dless, o he whole obse ed ime pe iod, he claim ha he PS
OSs wi h usual cha ac e is ics (i.e., PS OSs cha ac e is ics co esponding o g oups B o K) ep esen he
majo i y o PS OSs p esen ed in he pape s o ou da abase is s ill alid (In 2019, he ela i e equency
o g oup A was 35.1%, so, in he las yea o he obse ed ime pe iod, he PS OSs wi h mains eam
cha ac e is ics ep esen ed nea ly 2/3 o all PS OSs p esen ed in he pape s o ou da abase).
Ene gies2020,13,xFORPEERREVIEW4o 22

Figu e1.F equencyo indi idualPS‐OSscha ac e is icsdesc ibedinpape so ou pape da abase—
esul so  he i s assignmen p ocess(pape g oupsa ema kedwi h hesamele e sas hepape 
g oupslis edabo e,seeTable1.).

Figu e2.Rela i e equencyandcumula i e ela i e equencyo PS‐OSscha ac e is icsdesc ibedin
pape so ou pape da abase— esul so  he i s assignmen p ocess(pape g oupsa ema kedwi h
hesamele e sas hepape g oupslis edabo e,seeTable1.).
Theassignedda abaseo pape s,whichwasc ea edin he i s assignmen p ocess,wasla e 
analyzed o  hesecond ime,ino de  oob aincu en  endso PSOSs esea ch.Fo  his eason,
he equencyo indi idualPS‐OSscha ac e is icsdesc ibedin hepape so ou da abasewas
analyzed o indi idualyea so  heobse ed imepe iod.Figu e3p esen s he equencyo  he
indi idualPS‐OSscha ac e is icsdesc ibedin hepape sdi idedby he o alnumbe o pape sin
heobse edyea .In his igu e, hecolo o g aphso indi idualPSOSscha ac e is icsis hesame
as hecolo o  hecolumno  hePSOSscha ac e is icinFigu e1.This igu eshows ha  he ela i e
equencyo PSOSsg oupAisg aduallyinc easing,while he ela i e equencieso  heo he PS
OSsg oupsdono changesigni ican ly(due o hesmallex en o  hes a icse  o indi idual
obse edyea s,small luc ua ionsobse edin heg aphso indi idualPSOScha ac e is icsa eno 
conside ed obesigni ican ).Theg ow ho  he ela i e equencyo G oupAcanbeexplainedby
heidea ha cu en PS‐OSs esea che s y odi e en ia e omolde pape sands anda dPS‐OSs
Figu e 1.
F equency o indi idual PS-OSs cha ac e is ics desc ibed in pape s o ou pape
da abase— esul s o he i s assignmen p ocess (pape g oups a e ma ked wi h he same le e s as he
pape g oups lis ed abo e, see Table 1.).
Ene gies2020,13,xFORPEERREVIEW4o 22

Figu e1.F equencyo indi idualPS‐OSscha ac e is icsdesc ibedinpape so ou pape da abase—
esul so  he i s assignmen p ocess(pape g oupsa ema kedwi h hesamele e sas hepape 
g oupslis edabo e,seeTable1.).

Figu e2.Rela i e equencyandcumula i e ela i e equencyo PS‐OSscha ac e is icsdesc ibedin
pape so ou pape da abase— esul so  he i s assignmen p ocess(pape g oupsa ema kedwi h
hesamele e sas hepape g oupslis edabo e,seeTable1.).
Theassignedda abaseo pape s,whichwasc ea edin he i s assignmen p ocess,wasla e 
analyzed o  hesecond ime,ino de  oob aincu en  endso PSOSs esea ch.Fo  his eason,
he equencyo indi idualPS‐OSscha ac e is icsdesc ibedin hepape so ou da abasewas
analyzed o indi idualyea so  heobse ed imepe iod.Figu e3p esen s he equencyo  he
indi idualPS‐OSscha ac e is icsdesc ibedin hepape sdi idedby he o alnumbe o pape sin
heobse edyea .In his igu e, hecolo o g aphso indi idualPSOSscha ac e is icsis hesame
as hecolo o  hecolumno  hePSOSscha ac e is icinFigu e1.This igu eshows ha  he ela i e
equencyo PSOSsg oupAisg aduallyinc easing,while he ela i e equencieso  heo he PS
OSsg oupsdono changesigni ican ly(due o hesmallex en o  hes a icse  o indi idual
obse edyea s,small luc ua ionsobse edin heg aphso indi idualPSOScha ac e is icsa eno 
conside ed obesigni ican ).Theg ow ho  he ela i e equencyo G oupAcanbeexplainedby
heidea ha cu en PS‐OSs esea che s y odi e en ia e omolde pape sands anda dPS‐OSs
Figu e 2.
Rela i e equency and cumula i e ela i e equency o PS-OSs cha ac e is ics desc ibed in
pape s o ou pape da abase— esul s o he i s assignmen p ocess (pape g oups a e ma ked wi h
he same le e s as he pape g oups lis ed abo e, see Table 1.).
Now le ’s look a he esul s o he second assignmen p ocess. Figu e 4shows how many pape s
ha e been assigned o each de ined pape g oup in his assignmen p ocess. Figu e 5 hen p esen s he
esul s o he same p ocess using he ela i e equency and cumula i e ela i e equency. Since he
Ene gies 2020,13, 1079 5 o 22
minimiza ion o PS ope a ion cos s is he cha ac e is ic sha ed by he as majo i y o PS OSs, g oup A
was no conside ed as pa o he second assignmen p ocess. Figu e 4shows ha he highes numbe
o pape s has been assigned o g oup B (PS OSs op imizing he ope a ion o enewable ene gy sou ces,
73 pape s). Figu e 5shows ha he ou la ges pape g oups amoun o mo e han hal o all pape s in
ou pape da abase (speci ically, hei amoun is 55.6%).
Ene gies2020,13,xFORPEERREVIEW5o 22
esea chs eams(i.e.,PSOSs esea chs eamsco esponding opape g oupsB oK).Au ho so 
ecen pape s y oc ea enewPSOSswhichsha e hemainop imiza ionideawi h heolde PSOSs
(i.e., heminimiza iono  hep iceo elec ici yo  he educ iono  hePSope a ioncos s).Howe e ,
in hese ecen PSOSs,unlikein hePSOSso  hes anda d esea chs eams, he eisanunusual
seconda yop imiza ion a ge de inedo  he eisanunusualPSpa op imized.Rega dless, o  he
wholeobse ed imepe iod, heclaim ha  hePSOSswi husualcha ac e is ics(i.e.,PSOSs
cha ac e is icsco esponding og oupsB oK) ep esen  hemajo i yo PSOSsp esen edin he
pape so ou da abaseiss ill alid(In2019, he ela i e equencyo g oupAwas35.1%,so,in he
las yea o  heobse ed imepe iod, hePSOSswi hmains eamcha ac e is ics ep esen ednea ly
2/3o allPSOSsp esen edin hepape so ou da abase).

Figu e3.Rela i e equencyo PS‐OSscha ac e is icsdesc ibedinpape so ou pape da abase o 
indi idualyea so  heobse ed imepe iod— esul so  he i s assignmen p ocess(pape g oups
a ema kedwi h hesamele e sas hepape g oupslis edabo e,seeTable1.; hecolo o g aphso 
indi idualPSOSscha ac e is icsis hesameas hecolo o  hecolumno  hePSOSscha ac e is icin
Figu e1.).
Nowle ’slooka  he esul so  hesecondassignmen p ocess.Figu e4showshowmanypape s
ha ebeenassigned oeachde inedpape g oupin hisassignmen p ocess.Figu e5 henp esen s
he esul so  hesamep ocessusing he ela i e equencyandcumula i e ela i e equency.Since
heminimiza iono PSope a ioncos sis hecha ac e is icsha edby he as majo i yo PSOSs,
g oupAwasno conside edaspa o  hesecondassignmen p ocess.Figu e4shows ha  hehighes 
numbe o pape shasbeenassigned og oupB(PSOSsop imizing heope a iono  enewable
ene gysou ces,73pape s).Figu e5shows ha  he ou la ges pape g oupsamoun  omo e han
hal o allpape sinou pape da abase(speci ically, hei amoun is55.6%).
Figu e 3.
Rela i e equency o PS-OSs cha ac e is ics desc ibed in pape s o ou pape da abase o
indi idual yea s o he obse ed ime pe iod— esul s o he i s assignmen p ocess (pape g oups
a e ma ked wi h he same le e s as he pape g oups lis ed abo e, see Table 1.; he colo o g aphs o
indi idual PS OSs cha ac e is ics is he same as he colo o he column o he PS OSs cha ac e is ic in
Figu e 1.).
Ene gies2020,13,xFORPEERREVIEW6o 22

Figu e4.F equencyo indi idualPS‐OSscha ac e is icsdesc ibedinpape so ou pape da abase—
esul so  hesecondassignmen p ocess(pape g oupsa ema kedwi h hesamele e sas hepape 
g oupslis edabo e,seeTable1.).

Figu e5.Rela i e equencyandcumula i e ela i e equencyo PS‐OSscha ac e is icsdesc ibedin
pape so ou pape da abase— esul so  hesecondassignmen p ocess(pape g oupsa ema ked
wi h hesamele e sas hepape g oupslis edabo e,seeTable1.).
3.MainResea chS eamsinPowe Sys emOpe a ionOp imiza ion
Thes a is icalanalysiso pape sp esen edinSec ion2showed ha  hemains eamo PS‐OSs
esea cha ePSOSswi hcha ac e is icso pape g oupsA,B,C,D,E,andF(acco ding o he i s 
assignmen p ocess, hesesixpape g oupscon ainmo e han80%o allpape so  heda abase).The
ollowingsixsubsec ionso  hissec ionde ail hesemains eamPSOSs.Thelesspopula edpape 
g oups(G,H,I,J,andK)a edesc ibedin helas  i esubsec ionso  hissec ion.Thedesc ip iono 
heselesspopula edpape g oupsislessde ailed han hedesc ip iono  hemos popula edpape 
g oups.O  he o alnumbe o PSOSpape s(255)in he e iew’spape da abase,111PSOSswe e
selec ed o p esen a ionin hispape sec ion.Thepape s ha desc ibed hePSOSmos 
unde s andablywe eselec ed.

Figu e 4.
F equency o indi idual PS-OSs cha ac e is ics desc ibed in pape s o ou pape
da abase— esul s o he second assignmen p ocess (pape g oups a e ma ked wi h he same le e s as
he pape g oups lis ed abo e, see Table 1.).

Ene gies 2020,13, 1079 6 o 22
Ene gies2020,13,xFORPEERREVIEW6o 22

Figu e4.F equencyo indi idualPS‐OSscha ac e is icsdesc ibedinpape so ou pape da abase—
esul so  hesecondassignmen p ocess(pape g oupsa ema kedwi h hesamele e sas hepape 
g oupslis edabo e,seeTable1.).

Figu e5.Rela i e equencyandcumula i e ela i e equencyo PS‐OSscha ac e is icsdesc ibedin
pape so ou pape da abase— esul so  hesecondassignmen p ocess(pape g oupsa ema ked
wi h hesamele e sas hepape g oupslis edabo e,seeTable1.).
3.MainResea chS eamsinPowe Sys emOpe a ionOp imiza ion
Thes a is icalanalysiso pape sp esen edinSec ion2showed ha  hemains eamo PS‐OSs
esea cha ePSOSswi hcha ac e is icso pape g oupsA,B,C,D,E,andF(acco ding o he i s 
assignmen p ocess, hesesixpape g oupscon ainmo e han80%o allpape so  heda abase).The
ollowingsixsubsec ionso  hissec ionde ail hesemains eamPSOSs.Thelesspopula edpape 
g oups(G,H,I,J,andK)a edesc ibedin helas  i esubsec ionso  hissec ion.Thedesc ip iono 
heselesspopula edpape g oupsislessde ailed han hedesc ip iono  hemos popula edpape 
g oups.O  he o alnumbe o PSOSpape s(255)in he e iew’spape da abase,111PSOSswe e
selec ed o p esen a ionin hispape sec ion.Thepape s ha desc ibed hePSOSmos 
unde s andablywe eselec ed.

Figu e 5.
Rela i e equency and cumula i e ela i e equency o PS-OSs cha ac e is ics desc ibed in
pape s o ou pape da abase— esul s o he second assignmen p ocess (pape g oups a e ma ked
wi h he same le e s as he pape g oups lis ed abo e, see Table 1.).
3. Main Resea ch S eams in Powe Sys em Ope a ion Op imiza ion
The s a is ical analysis o pape s p esen ed in Sec ion 2showed ha he mains eam o PS-OSs
esea ch a e PS OSs wi h cha ac e is ics o pape g oups A, B, C, D, E, and F (acco ding o he i s
assignmen p ocess, hese six pape g oups con ain mo e han 80% o all pape s o he da abase).
The ollowing six subsec ions o his sec ion de ail hese mains eam PS OSs. The less popula ed pape
g oups (G, H, I, J, and K) a e desc ibed in he las i e subsec ions o his sec ion. The desc ip ion
o hese less popula ed pape g oups is less de ailed han he desc ip ion o he mos popula ed
pape g oups. O he o al numbe o PS OS pape s (255) in he e iew’s pape da abase, 111 PS
OSs we e selec ed o p esen a ion in his pape sec ion. The pape s ha desc ibed he PS OS mos
unde s andably we e selec ed.
3.1. PS OSs Minimizing he P ice o Elec ici y/PS OSs Reducing PS Ope a ion Cos s
This subsec ion is de o ed o OSs ha ha e he goal o minimize he PS ope a ion cos s o
he elec ici y p ice. Many OSs wi h his goal sol e he so-called economic dispa ch (ED) p oblem.
Fo example, OSs in [
18
–
21
] sol e he eal- ime ED p oblem. In [
21
], a dis ibu ed OS based on a
s a e-based po en ial game is p oposed o he eal- ime ED p oblem in sma g ids. Unde he DC
powe low app oxima ion, he e is he eal- ime ED p oblem wi h coupled ope a ional cons ain s
o mula ed as a cen alized op imiza ion p oblem (cen alized eal- ime ED p oblem). By ea ing
each node in he g id as an agen , cen alized eal- ime ED p oblem is con e ed in o a s a e-based
po en ial game by augmen ing i s objec i e unc ion in he designed game wi h a local augmen ed
Lag ange-like unc ion, leading o a dis ibu ed algo i hm o sol ing his cen alized ED p oblem.
The pape ’s au ho s e eal ha he s a iona y-s a e Nash equilib ium o he s a e-based po en ial
game exac ly iden i ies he global op imum o he cons ained cen alized eal- ime ED p oblem.
The p oposed algo i hm is capable o handling bo h equali y and inequali y cons ain s in complica ed
o ms. Du ing op imal solu ion sea ching, he OS conside s cons ain s desc ibed by he ne wo k
lines’ capaci y limi s and he capaci y bounds o local gene a ion uni s and local loads. The pape ’s
au ho s es ed he OS pe o mance by simula ions on he IEEE 9-, 39-, and 118-bus es sys ems.
The esul s o hese es s indica e ha he OS can quickly con e ge o he global op imum e en unde
un eliable communica ion and plug-and-play ope a ions. The OSs in [
22
,
23
] sol e he look-ahead ED
p oblem. An OS in [
24
] sol es he mul iple- imescale ED p oblem using a special s ochas ic sys em.
Ene gies 2020,13, 1079 7 o 22
In [
25
], an OS based on a comp ehensi e wo-s age obus secu i y-cons ained uni commi men
app oach is p esen ed. The OS minimizes he ope a ion cos o he base case while gua an eeing
ha he obus solu ion can be adap i ely and secu ely adjus ed in esponse o con inuous load and
wind unce ain y in e als, as well as disc e e N–K gene a ion and ansmission con ingency secu i y
c i e ia. The OS is equipped wi h igo ously o mula ed co ec i e capabili ies o bo h non-quick-s a
and quick-s a uni s. Speci ically, uni commi men o quick-s a uni s is adap i ely adjus ed in
he ecou se s age o sa is ying secu i y cons ain s unde a ious unce ain ies, which in oduces
mixed-in ege ecou se o he p oposed wo-s age obus secu i y-cons ained uni commi men model.
The p oposed model is sol ed by he combina ion o he modi ied Bende s decomposi ion me hod and
he column-and-cons ain gene a ion algo i hm, which decompose he o iginal p oblem in o a mas e
uni commi men p oblem o he base case and secu i y-checking subp oblems o unce ain ies.
Du ing op imal solu ion sea ching, he OS conside s cons ain s desc ibed by he nodal powe balance,
he maximal ac i e powe supplied ia he e e ence bus, he ne wo k lines’ capaci y limi s, he capaci y
limi s o local he mal uni s, he gene a ion limi s o local wind a ms, o he powe gene a ion uni s’
limi s (minimum on/o ime limi s, s a up/shu down cos limi , and amping up/down limi ), and
many secu i y cons ain s o handling a ious unce ain ies. The pape ’s au ho s es ed he OS
pe o mance by simula ion on he modi ied IEEE 118-bus sys em. The esul s o his es indica e
ha he OS’s op imiza ion app oach is e ec i e. The pape ’s au ho s also pe o med obus ness
pe o mance es s. The esul s o hese es s indica e ha a easonable h eshold on he iola ion o
secu i y checking subp oblems would gua an ee good enough solu ions om an enginee ing poin
o iew, al hough he modi ied Bende s decomposi ion does no p o ide he igh es lowe bound
and may no gua an ee he global op imali y. An OS in [
26
] minimizes he dis ibu ion sys em (DS)
ope a ion cos s while coping wi h high-dimensional unce ain y in a DS wi h high pene a ion o RESs.
The basic me hod o PS ope a ion cos educ ion is a minimiza ion o ac i e powe losses. Fo example,
OSs in [
27
,
28
] minimize he powe losses h ough he ne wo k econ igu a ion. To minimize powe
losses, an OS in [
29
] ins alls dis ibu ed powe sou ces o a ious ypes ac oss he DS. An OS in [
30
]
minimizes he ope a ion cos s consis ing o se e al pa s. This OS op imally dispa ches he ac i e and
eac i e powe o dis ibu ed pho o ol aic gene a ion (PVG), he swi ched capaci o s, and he ol age
egula o s in la ge mul i-phase unbalanced DSs o minimize he ene gy loss, he PVG’s ac i e powe
cu ailmen , and he ope a ions o capaci o s and ol age egula o s, in addi ion o he elimina ion o
he ol age iola ions and he e e se powe low.
3.2. PS OSs Op imizing he Ope a ion o Renewable Ene gy Sou ces
In o de o educe g eenhouse gas emissions om powe gene a ion, he use o enewable ene gy
sou ces (RES) is suppo ed wo ld-wide. The p ice o RES powe plan s’ echnologies has d opped
signi ican ly, so he capaci y o ins alled RES powe plan s is inc easing globally. Since he gene a ion
o sola and wind powe plan s is de ined by a iable wea he and no by he PS ope a o ’s needs,
he OSs need o be used o achie e he e icien use o RES powe plan s and hei powe gene a ion.
I he elec ical ene gy p oduced by a RES powe plan canno be consumed o accumula ed
nea by he RES powe plan si e a he ime o gene a ion, and his ene gy canno be ansmi ed
due o he limi ed PS ansmission capaci y, a PS ope a o cu ails he ins an aneous powe ou pu
o he RES powe plan . This way, he RES powe plan ’s o al powe gene a ion is smalle han i
could be, and he RES powe plan ’s owne s a e sho e in income. OSs p esen ed in [
31
–
35
] help
minimize RES powe plan s cu ailmen and maximize hei o al powe gene a ion, namely he OSs
in [
32
–
34
] op imize he pho o ol aic powe plan ope a ion and he OS in [
35
] op imizes he wind
powe ope a ion. All hese OSs a e pa s o a powe managemen sys em o an economic dispa ch
sys em. The OS in [
35
] is based on an unusual app oach o implemen ing a decen alized mul i-a ea
dynamic ED p oblem o a la ge-scale powe sys em. Usual app oaches a e based on Lag angian
elaxa ion, bu his OS’s solu ion me hod is based on a gene alized Bende s decomposi ion amewo k,
a decomposi ion echnique o sol ing nonlinea p og amming. Since he OS’s algo i hm does no use
Ene gies 2020,13, 1079 8 o 22
he dual elaxa ion, p imal easible solu ions can be ob ained a e only a ew i e a ions. The gene alized
Bende s decomposi ion algo i hm applied he e is modi ied by in oducing a locally op imal cos o
each a ea, which signi ican ly expedi es con e gence. This app oach is applicable o online dispa ch o
mul i-a ea sys ems wi h a hie a chical con ol s uc u e con aining a coo dina o (i.e., whe e each a ea
has a local con ol cen e , and hese local con ol cen e s a e coo dina ed ia an uppe con ol cen e ).
The OS’s decen alized solu ion me hod aims o p ese e he decision independence o each a ea while
conduc ing mul i-a ea dynamic ED bu does no aim o compe e wi h he cen alized solu ion me hods
in compu a ional e iciency. Since he decen alized me hod p esen ed in his pape is de eloped o
mul i-pe iod mul i-a ea dynamic economic dispa ch, i can be applied o day-ahead hou ly powe
dispa ch o in a-hou look-ahead powe dispa ch o a mul i-a ea sys em. Du ing op imal solu ion
sea ching, he OS conside s cons ain s desc ibed by he easibili y-cu s limi , he op imali y-cu s limi ,
and he locally op imal cos o each a ea subp oblem. The pape ’s au ho s es ed he OS pe o mance
by simula ions on a eal la ge-scale powe sys em in China, which is a ou -a ea egional powe sys em
wi h a o al wind-powe -plan ins alla ion capaci y o 18 GW.
While he elec ical ene gy p oduced by he i s gene a ion o RES powe plan s was supplied
o he PS a a cons an subsidized p ice, in some coun ies wi h a o able condi ions o he RES
powe plan s ope a ion, he e a e cu en ly RES powe plan s unde cons uc ion which will p oduce
ene gy o be sold a local ene gy ma ke s [
36
]. To maximize RES powe plan s owne s’ p o i s
on he ma ke s, some OSs use o e ing s a egies. Such OSs a e p esen ed in [
37
–
39
]. In [
37
,
38
],
op imal day-ahead o e ing s a egies o wind a ms equipped wi h ene gy s o age sys ems a e
p esen ed. The op imiza ion me hod used in [
38
] desc ibes and e alua es an in eg a ed s a egy o
he day-ahead o e ing while accoun ing o he op imal ope a ion o an ene gy s o age sys em a he
balancing s age, whe e he eal- ime ope a ion policy o he s o age is modeled wi h linea decision
ules. Op imal decision ules and day-ahead o e s a e ob ained join ly. The op imiza ion p oblem
is ansla ed in o a s ochas ic op imiza ion p oblem whe e a ade-o is made be ween he expec ed
p o i maximiza ion and he isk-a e sion. Subsequen ly, disc e iza ion and linea iza ion me hods a e
employed o e en ually ob ain he solu ion o such s ochas ic op imiza ion p oblems. This OS neglec s
he deg ada ion cos s o he ene gy s o age sys em. I uses an assump ion o being a p ice- ake in some
Eu opean elec ici y ma ke s. The OS also quan i ies he alue o he esidual ene gy o he ene gy
s o age sys em. Fu he mo e, a sensi i i y analysis is ca ied ou o analyze he in luence o p ice
unce ain y and empo al co ela ion o wind powe gene a ion on p o i s. Du ing op imal solu ion
sea ching, he OS conside s cons ain s desc ibed by he limi o he esidual ene gy o indi idual
ESSs a each in e al, he ESS cha ging and discha ging powe limi s, he wind powe gene a ion
cu ailmen limi , and he limi o wind- a m in eg a ion capaci y. The pape ’s au ho s es ed he OS
pe o mance by wo case s udies which we e based on ealis ic da a om he No d Pool ma ke and
wind a ms in Denma k. In hese case s udies, he pape ’s au ho s used 100 scena ios. The esul s o
hese case s udies indica e ha he OS’s s a egy is mo e e ec i e han o he exis ing s a egies.
An o e ing s a egy in [
39
] agg ega es a ew wind powe plan s o one i ual powe plan .
Ope a ion coo dina ion o a RES powe plan wi h a ully-con olled powe sou ce is an app op ia e
way o inc ease he ope a ional capabili y o he RES powe plan . OSs in [
40
–
42
] also use such
ope a ion coo dina ion. The OS in [
40
] coo dina es he ope a ion o hyd opowe plan s wi h he mal
powe plan s and he OS in [
41
] coo dina es ope a ion o wind a ms and pumped-hyd o s o age.
To maximize he o al ene gy p oduc ion o a RES powe plan , i is also necessa y o educe he powe
losses o he powe plan . To minimize wind a m’s powe losses, OSs in [
43
–
45
] op imize he design
o hei in e nal cable ne wo ks.
3.3. PS OSs Regula ing he Powe Consump ion Du ing he Op imiza ion P ocess
Ano he PS’s pa which can be in ol ed in he op imiza ion p ocess is he loads. Indi idual loads’
powe consump ion has an in e mi en cha ac e , simila o he in e mi en cha ac e o sola o wind
powe plan s’ powe gene a ion. Howe e , a load’s powe inpu is p ima ily de ined by he cu en
Ene gies 2020,13, 1079 9 o 22
needs o he consume , no by cu en wea he condi ions. Fo some ypes o elec ical appliances,
he use may need o un an appliance o a ce ain ime pe iod (e.g., 2 h a day), bu he pa o he day
he appliance is unning does no a ec he appliance’s u ili y. Then, PS ope a o s can shi appliances
o such ypes o a ious pa s o day o achie e a powe balance h oughou he day and minimize he
magni ude o he PS’s consump ion peak. Powe consume s ecei e inancial compensa ion o pay a
lowe elec ici y p ice o allowing he PS ope a o o se he ope a ion ime o hei appliances.
To se he ope a ion ime o each shi able load op imally, he load shi s a e con olled by OSs.
OSs in [
46
,
47
] schedule he ope a ion ime o loads o educe PS’s peak powe consump ion and
o la en he load p o ile. The OS in [
47
] op imally schedules he g oup o household appliances
connec ed o a mic og id. To achie e op imal scheduling, he OS ca ego izes he appliances in o
lexible and non- lexible de e able loads, acco ding o hei elec ical componen s. The OS uses a
dynamic scheduling algo i hm whe e use s can sys ema ically manage he ope a ion o hei elec ic
appliances. The OS algo i hm sol es wo mul i-objec i e op imiza ion p oblems. The i s one a ge s
he ac i a ion schedule o non- lexible de e able loads and he second one deals wi h he powe p o iles
o lexible de e able loads. These mul i-objec i e op imiza ion p oblems a e sol ed by using a as
and eli is mul i-objec i e gene ic algo i hm (speci ically Non-domina ed So ing Gene ic Algo i hm
II). Du ing op imal solu ion sea ching, he OS conside s cons ain s desc ibed by he limi ed lexibili y
o local shi able loads (indi idual loads a e limi ed by he o al ene gy demand o comple e hei ask).
The pape ’s au ho s es ed he OS pe o mance by he simula ion o he collabo a i e sys em ha
consis s o 40 mic og ids egis e ed in he p og am o he load cu e la ening. In his simula ion,
e e y egis e ed mic og id includes one lexible de e able load (e.g., wa e hea e ) and a non- lexible
de e able load (e.g., dishwashe ). The esul s o his es indica e ha he OS‘s scheduling app oach
can each a e y la load cu e.
OSs in [
48
–
51
] op imize PS’s powe lows using he esiden ial demand- esponse se ice.
Speci ically, he OS in [
48
] con ols he powe consump ion o domes ic hea pumps in esponse
o a PS equency, and he OS in [
49
] con ols a g oup o hea ing, en ila ion, and ai -condi ioning
loads. The OS in [
51
] combines he cen alized and decen alized app oach. The OS sol es a
cen alized op imiza ion p oblem o he independen sys em ope a o o minimize he social cos , i.e.,
he consume s’ discom o cos and supplie s’ gene a ion cos , subjec o he powe ne wo k ope a ing
cons ain s. The OS’s decen alized ene gy ading algo i hm sol es a decen alized op imiza ion
p oblem o main ain he p i acy o he consume s and supplie s in he demand esponse p og am.
This decen alized algo i hm sea ches o he con ol signals ha he independen sys em ope a o
sends o he local en i ies. In esponse, he consume s and supplie s ob ain hei op imal load and
gene a ion le els, espec i ely. The pape ’s au ho s show ha , unde some speci ic con ol signals
om he independen sys em ope a o , he decen alized algo i hm con e ges o he unique solu ion
o he OS’s cen alized p oblem. Du ing op imal solu ion sea ching, he OS conside s cons ain s
desc ibed by he limi ed lexibili y o local shi able loads (indi idual loads a e limi ed by hei demand
a ia ion in indi idual ime slo hs, and hei o al ene gy demand o comple e hei ask) and he
minimal and maximal alue o ac i e powe gene a ed by indi idual local gene a o s. The pape ’s
au ho s es ed he OS pe o mance by he simula ion on he IEEE 40-bus powe sys em. The esul s o
his es indica e ha he OS can dec ease bo h he consume s’ and he gene a o s’ cos s and he OS’s
algo i hm is as e han algo i hms based on a cen alized app oach.
Some pape s p opose an op imum load con ol and schedule sys em which con ols many loads
o a ious ypes loca ed in a ious loca ions as one la ge agg ega e load. Such sys ems a e p esen ed,
o example, in [
52
–
54
]. When op imizing PS ope a ion using he load con ol, echnically, he easies
load-con ol me hod is o con ol la ge compac loads, because his ype o con ol allows changing
PS’s o al powe consump ion by hund eds o MW, e en when con olling only a small numbe o
loads. This ype o load con ol is used, o example, in OSs [
55
], [
56
] which con ol he powe demand
o la ge indus ial consume s. The OS in [
56
] enables cemen plan s o p o ide he powe egula ion o
he load ollowing wi h he suppo o an onsi e ene gy s o age sys em. OSs in [
57
,
58
] hen ocus on
Ene gies 2020,13, 1079 16 o 22
o he educ ion o he PS ope a ion cos s). Howe e , in hese new PS OSs, unlike in he PS OSs o
he s anda d esea ch s eams, an unusual seconda y op imiza ion a ge is de ined o he e is an
unusual PS pa op imized. Taking a close look a he indi idual PS OSs p esen ed in he pape s o ou
da abase, we see a g owing in e es in he impac o unce ain ies on he solu ion o he op imiza ion
p oblem. The impac o unce ain ies on he solu ion o he op imiza ion p oblem is in es iga ed
mainly in PS OSs wo king wi h enewable ene gy sou ces (especially PS OSs wo king wi h wind
powe plan s deal wi h unce ain ies e y o en [37,38,40,42]).
In he u u e, i would be in e es ing o analyze new ends in PS OSs’ op imiza ion algo i hms.
Some ecen pape s p esen ed new op imiza ion algo i hms based on biologically inspi ed op imiza ion
s a egies (e.g., op imiza ion algo i hms based on he Sine Cosine Algo i hm [
130
], Pa icle Swa m
Op imiza ion [131], o Flowe Pollina ion Algo i hm [132]).
Au ho Con ibu ions:
Concep ualiza ion, J.V.; me hodology, J.V. and S.M.; alida ion, S.M.; o mal analysis, J.V.;
in es iga ion, J.V.; w i ing—o iginal d a p epa a ion, J.V.; w i ing— e iew and edi ing, S.M.; supe ision, S.M.
All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This pape was suppo ed by he ollowing p ojec s: This pape was suppo ed by he ollowing p ojec s:
SP2020/129 S uden s G an Compe i ion; TACR TN01000007, TK02030039 and TJ02000157, Czech Republic.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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