Ci a ion: Dash da , M.; Flah, A.;
Hosseinimoghadam, S.M.S.; Ko b, H.;
Jasi´nska, E.; Gono, R.; Leonowicz, Z.;
Jasi´nski, M. Op imal Ope a ion o
Mic og ids wi h Demand-Side
Managemen Based on a
Combina ion o Gene ic Algo i hm
and A i icial Bee Colony.
Sus ainabili y 2022,14, 6759.
h ps://doi.o g/10.3390/su14116759
Academic Edi o : Thanikan i
Sudhaka Babu
Recei ed: 22 Ap il 2022
Accep ed: 27 May 2022
Published: 31 May 2022
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
sus ainabili y
A icle
Op imal Ope a ion o Mic og ids wi h Demand-Side
Managemen Based on a Combina ion o Gene ic Algo i hm
and A i icial Bee Colony
Masoud Dash da 1,*, Aymen Flah 2,* , Seyed Mohammad Sadegh Hosseinimoghadam 1, Hossam Ko b 3,
El˙
zbie a Jasi´nska 4, Radomi Gono 5, Zbigniew Leonowicz 6and Michał Jasi´nski 6
1Elec ical Enginee ing Depa men , Busheh B anch, Islamic Azad Uni e si y, Busheh 7515895496, I an;
[email p o ec ed]
2Na ional Enginee ing School o Gabès, P ocesses, Ene gy, En i onmen and Elec ical Sys ems,
Uni e si y o Gabès, LR18ES34, Medinine 6072, Tunisia
3Depa men o Elec ical Powe and Machines, Facul y o Enginee ing, Alexand ia Uni e si y,
Alexand ia 21526, Egyp ; [email p o ec ed]
4
Depa men o Ope a ions Resea ch and Business In elligence, W ocław Uni e si y o Science and Technology,
50-370 W oclaw, Poland; elzbie a.jasinska@pw .edu.pl
5Depa men o Elec ical Powe Enginee ing, Facul y o Elec ical Enginee ing and Compu e Science,
VSB—Technical Uni e si y o Os a a, 708-00 Os a a, Czech Republic; adomi [email p o ec ed]
6Facul y o Elec ical Enginee ing, W ocław Uni e si y o Science and Technology, 50-370 W oclaw, Poland;
zbigniew.leonowicz@pw .edu.pl (Z.L.); michal.jasinski@pw .edu.pl (M.J.)
*Co espondence: [email p o ec ed] (M.D.); [email p o ec ed] (A.F.)
Abs ac :
An impo an issue in powe sys ems is he op imal ope a ion o mic og ids wi h demand-
side managemen . The implemen a ion o demand-side managemen p og ams, on he one hand,
educes he cos o ope a ing he powe sys em, and on he o he hand, he implemen a ion o such
p og ams equi es inancial incen i e policies. In his pape , he p oblem o he op imal ope a ion o
mic og ids along wi h demand-side managemen (DSM) is o mula ed as an op imiza ion p oblem.
Load shi ing is conside ed an e ec i e solu ion in demand-side managemen . The objec i e unc ion
o his p oblem is o minimize he o al ope a ing cos s o he powe sys em and he cos o load
shi ing, and he cons ain s o he p oblem include ope a ing cons ain s and execu i e es ic ions
o load shi ing. Due o he dimensions o he p oblem, he simul aneous combina ion o a gene ic
algo i hm and an ABC is used in such a way ha by sol ing he OPF p oblem wi h an ABC algo i hm
and applying i o he s uc u e o he gene ic algo i hm, he main p oblem will be sol ed. Finally,
he p oposed me hod is e alua ed unde he in luence o a ious ac o s, including he ypes o
p oduc ion uni s, he ypes o loads, he uni unce ain y, sha ing wi h he g id, and elec ici y p ices
all based on di e en scena ios. To con i m he p oposed me hod, he esul s we e compa ed wi h
di e en algo i hms on he IEEE 33-bus ne wo k, which was able o educe cos s by 57.01%.
Keywo ds:
mic og id; op imal ope a ion; demand-side managemen ; load shi ing; gene ic
algo i hm; ABC
1. In oduc ion
Today, powe sys em ope a o s ace issues such as signi ican load changes, apid
demand g ow h, and he geog aphical expansion o cus ome s. On he o he hand, due
o he educ ion o ossil esou ces, low ene gy e iciency, and en i onmen al policies,
in es o s a e eluc an o build ossil uel powe plan s and a new challenge has a isen
in ol ing he use o powe gene a ion esou ces o ope a e he powe sys em. The e o e,
hese p oblems ha e inc eased he endency o gene a e powe a he dis ibu ion ol age
le el. The e o e, he app op ia e solu ion is o build small ne wo ks independen o he
main ne wo ks o mic og ids [1,2].
Sus ainabili y 2022,14, 6759. h ps://doi.o g/10.3390/su14116759 h ps://www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2022,14, 6759 2 o 26
The op imal ope a ion o powe sys ems equi es he use o p ope planning, which is
mainly conduc ed in h ee sec ions: long- e m planning, medium- e m planning, and sho -
e m planning. Mic og ids also ha e been planned in hese h ee in e als. In long- e m
planning, each mic og id mus an icipa e he pu chase and ins alla ion o gene a o s by he
load g ow h o ecas . Medium- e m planning should ake in o accoun epai imes, he
main enance o gene a o s and s o age, and uel cos s. Sho - e m planning o mic og ids
is done in one week, one day, and one-hou in e als, and he pu pose o doing so is o
de e mine he ou pu powe o he uni s [3,4].
In a mic og id, he ene gy managemen sys em is esponsible o he op imal ope a ion
o he mic og id in he p esence o p og ammable dis ibu ed gene a ion (DG) uni s,
p obabilis ic DG uni s, in e up ible loads, ene gy s o age uni s, and inal consume s as he
cen al co e [
5
]. In [
6
], he ope a ion o mic og ids equipped wi h enewable esou ces and
powe s o age esou ces is in es iga ed. In [
7
], a sma mic og id is used and i is shown
ha he use o a sma mic og id no only inc eases ene gy e iciency bu also enables
a complemen a y and e ec i e ne wo k ha can imp o e eliabili y and powe quali y.
In [
8
], i is shown ha by ins alling sui able ene gy s o age, changes, and luc ua ions, he
ac i e powe can be s abilized and he mic og id equency can be main ained wi hin he
speci ied limi . In [
9
], a mic og id equipped wi h he ene gy managemen cen e sys em is
in oduced, whose ask is o op imize he ope a ion o he mic og id in bo h island and
g id-connec ed modes. In [
10
], which ocuses on an impo an c i e ion o mee ing he
powe demand wi h he minimum ope a ing cos , he use o an op imal combina ion o
he main g id and mic og id wi h a 24-h planning ho izon is in oduced. In [
11
], economic
planning is used o p oduc ion and load, which equi es managemen o he demand
side. In [
12
], a ma ke s a egy is desc ibed, because wi h he inc easing expansion o
small sou ces o ene gy gene a ion he p oduc ion planning o small uni s ac ing as la ge
gene a ion uni s necessi a es such a ma ke s a egy.
In [
13
,
14
], a Fuzzy-PSO sel -adap a ion algo i hm o powe low in a speci ic mic o-
g id is p esen ed conside ing economic and en i onmen al issues. The esul s indica e
ha wi h he high pa icipa ion o enewable esou ces, he educ ion o pollu ion and
mic og id cos s is se ious and he ene gy exchange be ween he mic og id and he ne wo k
connec ed o i has many bene i s. In [
15
], he au ho s p o ide a mul i-agen sys em o
sma ene gy managemen on he demand side o mic og ids, which includes p edic i e
algo i hms o imp o e sys em managemen . The simula ion esul s show ha he sma
demand-side managemen sys em has me all he design objec i es and has also led o he
e ec i e ope a ion o bounda y condi ions in he mic og id. In [
16
], PSO applica ions o
eal- ime ene gy managemen solu ions o hyb id sys ems a e p esen ed and he esul s
show ha he p oposed me hod can combine a wide ange o solu ions o in eg a e many
objec i es such as educing cos s, inc easing wind u bine e iciency, and educing en i-
onmen al pollu ion. The managemen o mic og id uni s equi es an accu a e economic
model o desc ibe he ope a ion cos s o gene a ing powe . This model con inues o be
disc e e and nonlinea ; he e o e, a s ong and e ec i e op imiza ion ool is needed o
educe ope a ing cos s o a minimum. Va ious algo i hms ha e been used o sol e such
models. Fo example, in [
17
], he p oblem o op imal mic og id managemen based on he
lexible load shaping DSM s a egy as well as he p ice-based and incen i e-based demand
esponse p og ams is sol ed h ough he Black Widow Op imiza ion algo i hm. In [
18
],
he mincon in e io -poin algo i hm is used o he op imal ope a ion o he mic og id
consis ing o pho o ol aics wi h a diesel gene a o unde he p obabilis ic scena io. In [
19
],
he au ho s p o ide a eal- ime p edic i e con ol model o minimize he cos o ope a ion
o he mic og id unde unce ain y. Fu he au ho s discuss he applica ion o algo i hms
in hese e e ences: in [
20
], a Quan um Pa icle Swa m Op imiza ion algo i hm is discussed;
in [
21
], ou heu is ically guided op imiza ion algo i hms; in [
22
], a sel -c osso e gene ic
algo i hm; in [
23
], a wo-le el gene ic algo i hm o sol e mic og id ene gy managemen
p oblem has been implemen ed.
Sus ainabili y 2022,14, 6759 3 o 26
In his pape , by de eloping common me hods in he ope a ion o he powe sys em,
and by conside ing he app op ia e cons ain s, he p oblem o op imal ope a ion o mic o-
g ids along wi h demand-side managemen has been o mula ed. The objec i e unc ion is
o minimize ope a ing cos s and demand-side managemen cos s, and he cons ain s o
op imiza ion include cons ain s on gene a o s and cons ain s on powe balance. Also,
he amoun o load shi ing in e ms o hou s has been conside ed a p oblem a iable, and
o sol e his op imiza ion p oblem, a combined gene ic algo i hm and ABC ha e been
used. The ollowing is he di ision o he a icle: In he second pa , he demand side
managemen is in oduced, in he hi d pa , he objec i e unc ion o he p oblem and
he o mula ion me hod is de ined, and in he ou h pa , he p oblem-sol ing me hod is
p esen ed and in he i h pa , he simula ion esul s o he p oposed me hod a e shown,
Finally, a conclusion is p esen ed in he six h sec ion.
2. Demand-Side Managemen
Demand-side managemen gene ally e e s o p og ams ha a ec he elec ici y
consump ion pa e n o subsc ibe s. In o he wo ds, some ac i i ies a e designed by
elec ici y companies o change he amoun o ime o elec ici y consump ion in a way ha
p o ides he necessa y oppo uni y o bene i consume s and e en hemsel es. In gene al,
demand-side p og ams consis o wo main pa s.
Op imal ene gy e iciency: The goal o hese p og ams is o educe ene gy consump ion
pe manen ly, which is usually p o ided by changes in echnology and equipmen o he
inal consume [24,25].
Demand esponse: These p og ams a e one o he new de elopmen s in he ield
o demand-side managemen , which means consume pa icipa ion in imp o ing he
pa e n o ene gy consump ion. This pa ne ship is in esponse o ins an aneous p ice
changes [26,27].
Today, hese p og ams a e conside ed a sui able solu ion o sol e some p oblems
o he de egula ed powe sys em. By de ini ion, demand esponse is he empowe men
o indus ial, comme cial, and esiden ial cus ome s o imp o e he pa e n o elec ici y
consump ion o achie e easonable p ices and imp o e ne wo k eliabili y. In o he wo ds,
demand esponse can change he o m o elec ical ene gy consump ion in such a way ha
he sys em load peak is educed and consump ion is shi ed o non-peak hou s [
28
]. In
gene al, demand esponse me hods can be di ided in o wo gene al ca ego ies, which a e:
elec ici y p ice-based demand esponse p og ams, and incen i e-based demand esponse
p og ams, and Figu e 1show he classi ica ion o demand esponse p og ams.
Figu e 1. Di ision o demand esponse p og ams.
Sus ainabili y 2022,14, 6759 4 o 26
In his pape , among he a ious demand-side managemen p og ams, he load shi ing
p og am has been used o educe peak load and inc ease ne wo k load du ing low load
hou s (ie de-peaking and illing he alley). The e a e also es ic ions on he shi ing
o consump ion ime o each o he loads. Because consump ion ime-shi ing causes
cus ome dissa is ac ion, in his pape , an incon enience unc ion is used o conside he
cos o load shi ing.
3. Fo mula ion o he P oblem
Op imal uni gene a ion planning is o mula ed as an op imiza ion p oblem. In he
op imal ope a ion o a mic og id, on he one hand, he lowes cos is conside ed and on
he o he hand, ope a ion cons ain s and demand-side managemen cons ain s mus be
conside ed. In his issue, he o al gene a ion cos s and cos s o implemen ing demand-side
managemen a e conside ed in objec i e unc ions. The e o e, he objec i e unc ion o he
p oblem o op imal ope a ion o mic og ids can be de ined as Equa ion (1) by conside ing
he demand-side managemen [29].
minF=w1×CF +w2×DC (1)
whe e Fis he o al ope a ing cos s o he mic og id, CF is he o al ope a ing cos s o
he powe gene a ion uni s, and DC is he o al cos o implemen ing he demand-side
p og ams. The coe icien s w
1
and w
2
a e he weigh coe icien s o he cos o ope a ing he
ne wo k and he cos o implemen ing demand-side managemen p og ams, espec i ely.
I hese wo coe icien s a e conside ed as one, he alue o ope a ion cos and demand-
side managemen cos a e conside ed he same. Bu i he goal is o add mo e alue o
consump ion managemen p og ams, he weigh ac o w2can be conside ed la ge [30].
The execu ion o he use- ime shi p og am causes dissa is ac ion among he sub-
sc ibe s. The e o e, he cos o implemen ing he load shi ing p og am in his pape is
modeled as an incon enience unc ion as a hi d-deg ee unc ion acco ding o Equa ion (2)
DC =
m
∑
l=1hAls 3
l+Bls 2
l+Cls li(2)
whe e lis he nume al o loads ha can be shi ed and he coe icien s A,Band Ca e ela ed
o he cos o shi ing o ha load. s
l
is he numbe o hou s o load Ishi ing and mis
he o al numbe o shi able loads. Ope a ing cos s o gene a ion uni s include gene a ion
cos s, s a ing cos s, and main enance cos s. Also, because in he mic og id i is possible o
buy o sell ene gy o he ne wo k, he cos o buying and selling ene gy om he ne wo k is
included in he ope a ion cos unc ion. Equa ion (3) shows he CF ope a ion cos unc ion
in he op imiza ion p oblem [31].
CF = T
∑
=1
I
∑
i=1
C(i, )+MC(i, )+SC(i, )!+
T
∑
=1
[C( )−R( )](3)
whe e C(i, ) is he cos o gene a ing powe o uni ia hou o ope a ion, MC(i, ) is he
cos o main enance and SC(i, ) is he cos o s a ing uni ia hou . Also, C( ) is he cos
o elec ici y pu chased a hou is om he g id, and R( ) is he e enue om ene gy sales
a ha ime. Iis he numbe o powe gene a ion uni s and Tis he s udy ime (T= 24) in
e ms o he hou . He e Ican include a a ie y o gene a ion uni s such as pho o ol aic
(PV) cells, wind u bine (WT), mic o u bine (MT), uel cell (FC), and ba e y (Ba ) wi h a
Sus ainabili y 2022,14, 6759 5 o 26
di e en cos unc ions. The model used o calcula e he wind u bine ou pu powe in
e ms o wind speed acco ding o Equa ion (4) is:
PWT =










0 0 <V<Vci
a·V2+b·V+c∗P Vci <V<V
P V <V<Vco
0Vco <V<∞
(4)
whe e,
P
: a ed powe o wind u bine, V
ci
, and V
co
: minimum and maximum allowable
wind speed; V
and V: a e he nominal speed and he ac ual speed o he wind, espec i ely.
The coe icien s a,band ca e ob ained acco ding o he ca alog in o ma ion o he exis ing
de ice. The powe gene a ed by sola cells depends on he in ensi y o ligh and ambien
empe a u e, which is ob ained acco ding o Equa ion (5):
PPV =PSTC ∗GINC
GSTC
∗(1+k(Tc−T )) (5)
whe e,
PPV
: sola cell ou pu powe a ambien adia ion in ensi y; P
STC
: Maximum
cell gene a ion powe unde s anda d es condi ions;
GINC
: ambien ligh in ensi y;
GSTC
:
Radia ion in ensi y unde s anda d es condi ions, k: Ou pu powe empe a u e coe icien ;
T
c
: cell empe a u e, T
: e e ence empe a u e. Renewable sou ces o WT and PV gene a e
elec ici y h ough wind and sola ene gy ins ead o uel. The e o e, he uel cos o hese
uni s will be ze o. On he o he hand, he in es men cos o cons uc ing hese uni s
is hea y and should be conside ed along wi h he main enance cos s in examining he
mic og id s a us om an economic pe spec i e. Acco dingly, he o al cos o WT and PV
uni s is calcula ed using Equa ion (6):
CRES =
24
∑
=1
PWT, ×AC ×IIn
WT ×IM
WT+
24
∑
=1
PPV, ×AC ×IIn
PV ×IM
PV (6)
whe e
CRES
: cos o enewable uni s, AC: annual cos ac o , I
In
: a io o in es men cos o
gene a e powe o he uni , IM: uni main enance cos .
The ou pu powe o he diesel gene a o (DE) is con olled by he go e no ins alled
on i . The amoun o diesel gene a o uel consump ion (L/h) as a quad a ic unc ion o
gene a ing powe is as Equa ion (7):
CDE =α·(PDE)2+β·PDE +γ(7)
whe e,
CDE
: diesel gene a o uel consump ion cos L/h,
PDE
: diesel gene a o ou pu
powe ;
α
,
β
and
γ
a e cons an coe icien s. Acco ding o Equa ion (8), uel cell e iciency is
he ou pu powe o he inpu uel i bo h a e calcula ed in he same uni .
CFC =CgasFC ∗PFC
µFC
(8)
whe e
CFC
: he cos o uel consumed by a uel cell ($/h);
CgasFC
: he p ice o na u al gas o
eed he uel cell ($/kWh); P
FC
: he ou pu powe o he uel cell;
µFC
: he e iciency o he
uel cell. Acco ding o Equa ion (9), he economic model o a mic o u bine is simila o a
uel cell, excep ha he e iciency o he mic o u bine inc eases wi h inc easing powe .
CMT =CgasMT ∗PMT
µMT
(9)
The cos o elec ici y pu chased C( ) and sold R( ) (Equa ion (3)) is exp essed h ough
Equa ions (10) and (11).
C( ) = Tpp ×Ppp (10)

Sus ainabili y 2022,14, 6759 6 o 26
R( ) = Tsp ×Psp (11)
Tpp
is he a i o pu chasing elec ici y om he g id,
Ppp
is he powe pu chased
om he g id,
Tsp
is he a i o selling elec ici y o he g id and P
sp
is he powe sold
o he g id. The cos o epai ing and main aining uni s is di ec ly ela ed o hei powe
gene a ion. The e o e, he cos o epai and main enance o uni ia hou is exp essed as
Equa ion (12).
MC(i, )=P(i, )×K(i)(12)
whe e
K(i)
is he cos o epai and main enance o uni ipe kW o elec ical powe and
P(i, )
is he ou pu powe o uni ipe hou . The s a ing cos is in ended only o
ossil uel gene a ion uni s. Gi en ha he s a ing cos is only a ibu ed o each pe iod
ha he uni is u ned on, how o calcula e he s a ing cos o uni ia hou is gi en in
Equa ion (13).
SC(i, )=Scos (i)×(U(i, )−U(i, −1)) (13)
whe e
Scos (i)
is he s a ing cos o uni iand
U(i, )
is a bina y a iable ha indica es
he s a us o uni iis on o o a hou . Equali y cons ain s in he p oblem a e he powe
balance cons ain (powe low equa ions) shown in Equa ions (14) and (15).
PG
k−PL
k=
N
∑
i=1
VkVi[Gki cos(θk−θi)+Bkisin(θk−θi)] (14)
QG
k−QL
k=
N
∑
i=1
VkVi[Gki sin(θk−θi)+Bkicos(θk−θi)] (15)
Inequali y cons ain s include uni ou pu powe cons ain s, con ol a iable con-
s ain s, line powe cons ain s, and ol age cons ain s, which a e exp essed in
Equa ions (16)
o (19), espec i ely.
Pmin ≤P≤Pmax (16)
Umin ≤U≤Umax (17)
Pij≤Pmax
ij (18)
Vmin
j≤Vj≤Vmax
j(19)
The shi ing ime o each load is also conside ed in he demand esponse p og am as a
cons ain acco ding o Equa ion (20).
s l≤Tl,l=1, . . . , m(20)
whe e Tlis he pe missible ime o shi he load l h.
I he load shi ime is known, he op imiza ion p oblem p esen ed in his sec ion will
become an op imal powe low (OPF) p oblem. By sol ing he OPF p oblem, he powe
gene a ion o each uni and he powe ecei ed and sen o he global ne wo k will be
calcula ed. In his pape , he ABC algo i hm is used o sol e he OPF p oblem. The e o e,
in he nex sec ion, he combina ion o gene ic algo i hm and ABC has been used o sol e
he p oblem o op imal ope a ion in gene al.
4. P oposed Hyb id Algo i hm
In he p oposed algo i hm, a combina ion o he ABC algo i hm ( o sol e OPF) and
he gene ic algo i hm is used o sol e he p oblem o op imal ope a ion o mic og ids
wi h demand-side managemen . As you can see in Figu e 2, he op imiza ion p oblem
space has di e en dimensions, and due o he dependence o he p oblem on di e en
pa ame e s, in his a icle, we ha e ied o a oid educing compu a ional accu acy and
inc easing compu a ional speed ins ead o using an algo i hm o sol e he p oblem (which
caused complexi y) used a combina ion o ABC and GA algo i hms o sol e he p oblem.
Sus ainabili y 2022,14, 6759 7 o 26
So ha by sol ing he OPF p oblem by he ABC algo i hm and ans e ing he ou pu o
he algo i hm o he GA algo i hm, he p oblem o op imal ope a ion o he mic og id can
be sol ed wi h be e speed and accu acy.
Figu e 2. Gene al space o he p oblem and solu ion me hod.
The ABC algo i hm is based on collec i e in elligence. This algo i hm simula es he
beha io o a bee collec ing ood. In he eal wo ld, bees li e in densely popula ed colonies,
c ea ing a complex social o ganiza ion. This algo i hm uses h ee ypes o bees (employed
bees ( o age bees), onlooke bees (obse e bees), and scou s bees) ha con inuously
imp o e he answe . Ini ial p oduc ion o all candida e esponses is done by scou s bees
( he ini ial popula ion is andomly gene a ed). A e ha , ood nec a is used h ough he
coo dina ed beha io o all ypes o bees. Bees om e e y gene a ion sea ch he space and
ind ood sou ces o di e en quali ies. Obse e bees ake ad an age o sea ch space nea
be e ood sou ces. Bees wi h deple ed ood sou ces a e andomly p oduced in he scou ’s
bees phase. These con inuous cycles o explo a ion and exploi a ion lead o one o he
ollowing wo si ua ions: (1) he inal answe can no longe be sea ched; (2) ood esou ces
ha e been deple ed. Table 1shows he concep s and pa ame e s o he ABC algo i hm.
Table 1. Pa ame e s o ABC algo i hm.
Pa ame e s Desc ip ion
Xm{(xmi,i= 1, . . . , d)} m h o a candida e answe
DNumbe o p oblem dimensions
¯
ymNeighbo hood o Xm
xmi The alue o he a iable m h in he i h
dimension
|P| Popula ion size
lbiThe lowe limi o he i h dimension
µbiThe uppe limi o he i h dimension
φmi Random numbe in he ange (−1, 1)
pmP obabili y o selec ing he eed sou ce o he
employed bee mby he obse e bees
Sus ainabili y 2022,14, 6759 8 o 26
The s eps o implemen ing he ABC algo i hm a e as ollows: The i s s age is he
p oduc ion o he ini ial popula ion. In such a way ha o each bee we ha e like mand
e e y dimension like iwill ha e:
xmi =lbi+ andom(0, 1)∗(ubi−lbi)(21)
In he second s age, he employee bee ac i i y begins. In his case, he en i e sea ch
space is checked. So o e e y bee-like m and e e y andom dimension like iand a andom
bee-like k:
ymi =xmi +∅mi(xmi −xki)(22)
i nessXm=(1
1+ (Xm)i Xm≥0
1+abs Xmi Xm<0(23)
Xm=be e o Xm,Ym(24)
Acco ding o Equa ion (22), he employee bees go o hei ood sou ce and choose
a new ood sou ce in he neighbo hood o he p e ious ood sou ce, and acco ding o
Equa ions (23) and (24), a e he new posi ion o he employee bee m eed sou ce is
ob ained, he alue o he i ness unc ion (objec i e unc ion) is ecalcula ed o i . Now
i he alue o he i ness unc ion o he new answe is be e han he p e ious answe ,
he p e ious answe is disca ded and he new answe eplaces i . O he wise, he p e ious
answe is p ese ed.
Nex s ep obse e bees andomly selec a ood sou ce o sea ch. He e he p obabili y
o selec ion o each ood sou ce by he obse e bees is calcula ed by Equa ion (25). The
lowe he i ness unc ion o a ood sou ce, he mo e p obabili y i is o be selec ed.
pm= i Xm
∑|P|
m=1 i Xm(25)
A e each o he obse e bees selec s hei desi ed ood sou ce om he ood sou ces
o he employee bees, hey ly o i and selec a new ood sou ce in hei neighbo hood.
Equa ions (22) o (24) is again used o e alua e he alue o he i ness unc ion o he
new posi ion o he obse e bee ood sou ce. I he new esponse alue o he i ness
unc ion is be e han he p e ious esponse, i is eplaced, o he wise, he p e ious esponse
is p ese ed.
Ano he phase o he ABC algo i hm is he p esence o scou s bee, which allows you
o sea ch o new posi ions ins ead o whe e hey can no longe be sea ched. Tha is, o
each bee m, i i s pe o mance does no imp o e, use Equa ion (21) o econs uc i and
epea he p ocess un il i eaches he bes posi ion.
In his pape , a combina ion o GA and ABC algo i hms is used o imp o e he speed
and accu acy o p oblem-sol ing. Pa o he p oblem space, OPF, is sol ed by he ABC
algo i hm, and i s op imal esponse is conside ed as GA algo i hm genes. In his me hod,
he disciplines (ch omosomes) o he GA algo i hm consis o wo pa s. The i s pa
includes he amoun o shi ing o each load in e ms o hou s and he second pa includes
he op imal esponse ecei ed om he ABC algo i hm. Figu e 3shows an example o
he disciplines o he GA algo i hm. The i s pa o his discipline has m cells, which is
he numbe o manageable loads. In each cell, he numbe s a e be ween 0 and 24, which
indica es he shi ing o he load (s ) in e ms o hou s. The cells o he second pa will
include he minimum gene a ion cos and gene a ion powe o he uni s.
Figu e 3. Gene ic disciplines in he p oposed hyb id algo i hm.
Sus ainabili y 2022,14, 6759 9 o 26
Figu e 4shows a lowcha o he p oposed algo i hm. In his algo i hm, he ini ial
guesses o he shi ing o he load in e ms o hou s a e de e mined andomly. Then, by
ecei ing he ne wo k in o ma ion, he OPF p oblem is o med and sol ed h ough he ABC
algo i hm. By sol ing he OPF p oblem, he op imal amoun o uni p oduc ion is calcula ed,
and also by knowing he numbe o hou s o shi ing each load, he cos o shi ing he
load is calcula ed and he disciplines o he gene ic algo i hm a e o med. Once hese wo
cos s a e known o each GA discipline, he objec i e unc ion and he amoun o he i ness
unc ion o ha discipline a e de e mined. Nex , he disciplines ha ha e a highe alue
om he poin o iew o he i ness unc ion a e selec ed and gene ic ope a o s, including
he c osso e and mu a ion ope a o s, a e applied o hose disciplines. This p ocess is
epea ed un il he inal answe is eached. The condi ion o s opping he algo i hm is no o
change he answe o a la ge numbe o i e a ions.
Figu e 4. Flowcha o he p oposed hyb id algo i hm.
5. Simula ion Resul s
In his sec ion, he p oposed me hod is e alua ed o di e en si ua ions and he esul s
a e p esen ed. An example o he mic og id used in his pape is shown in Figu e 5. Which
is connec ed o he main g id om he PCC poin . This ne wo k has a diesel gene a o , PV
panel, and a ious loads.
Sus ainabili y 2022,14, 6759 16 o 26
p esen s an imp o ed gene ic algo i hm o op imal mic og id powe -sha ing, he bes
answe ob ained he e is $163.6199 . In e e ence [
35
], o op imal economic dispa ch in he
mic og id, he imp o ed ABC algo i hm is used, whe e he bes answe is 162.3335 $. In
e e ence [
36
], he combined algo i hm di e en ial e olu ion and ha mony sea ch a e used
o op imal planning o mic og id uni p oduc ion and cos educ ion, and he bes answe
ob ained he e is $159.2037. In e e ence [
37
], o op imize he ope a ion o he mic og id
and educe he cos , he Adap i e Modi ied Fi e ly Algo i hm has been used, and he bes
answe ob ained he e is 160.4894. Finally, he ou pu o he p oposed algo i hm including
he gene a ion powe o mic og id uni s cos educ ion, and DSM esul s a e shown in
Figu es 13 and 14. Figu e 13 shows he mic og id and main g id gene a ion powe , and
Figu e 14 shows he ne wo k load p o ile changes as a esul o DSM.
1
The bes i ness alue
PSO
GA
ABC
DE-HS
AMFA
GA-ABC
Figu e 12. Con e gence cu e o he p oposed algo i hm.
Figu e 13. Gene a ion powe o mic og id and main g id.

Sus ainabili y 2022,14, 6759 17 o 26
Figu e 14. Ne wo k load changes in 24 h.
5.6. Implemen he P oposed Me hod on he S anda d 33-Bus IEEE Ne wo k
In his sec ion, o con i m he pe o mance o he p oposed me hod, we use he
s anda d 33-bus IEEE ne wo k wi h he p esence o a ious uni s du ing di e en scena ios.
The s udied mic og id p oduc ion uni s include ou DG uni s, wo combined hea and
powe (CHP) uni s, a WT uni , and a PV uni , and he mic og id is connec ed o he main
ne wo k om buses 1, 20, and 29. Figu e 15 shows he modi ied 33-bus IEEE mic og id,
which can sell o buy elec ici y om he elec ici y ma ke . Fou DG uni s a e connec ed
o buses 2, 7, 8, and 25 mic og ids, and hei in o ma ion is p esen ed in Table 9. Whe e
SDc and SUc a e he cos o u ning on and he cos o u ning o , espec i ely, Rup, and
Rdn a e he inc easing and dec easing slope a es o uni p oduc ion, and Pmin, and Pmax
a e he maximum and minimum p oduc ion capaci y o he uni s. In his mic og id, CHPs
a e loca ed in buses 8 and 16, and due o he limi ed capaci y o CHPs, he minimum and
maximum amoun o elec ici y and hea p oduc ion o hese wo uni s, along wi h ixed
coe icien s o a cos unc ion, a e gi en in Table 10. Figu e 16 shows he p edic ed hea load
o subsc ibe s du ing a day. Acco ding o his igu e, he peak hea consump ion (Hmax)
coincides wi h he peak elec ic load.
Table 9. Cha ac e is ics o DG uni s.
Bus Pmin (kW) Pmax (kW) CDG ($/kWH) Rup (kW/H) Rdn (kW/H) SUc ($) SDc ($)
2 50 400 27 200 100 20 25
7 40 500 45 250 250 20 25
8 20 550 35 250 250 50 25
25 50 700 50 700 700 0 0
Table 10. Cha ac e is ics o CHP uni s.
Bus Pmin (kW) Pmax (kW) Hmax (kW h) A B C D E F
8 810 2470 1800 0.0435 36 12.5 0.027 0.6 0.011
16 400 1258 1356 0.0345 14.5 26.5 0.03 4.2 0.031
Sus ainabili y 2022,14, 6759 18 o 26
Figu e 15. The hi d mic og id unde s udy.
Figu e 16. P edic ed hea load demand in a day.
In his sec ion, he pe o mance o he p oposed me hod is implemen ed on he hi d
mic og id in 4 scena ios and he esul s a e compa ed wi h o he op imiza ion me hods.
These ou scena ios a e as ollows:
•
Scena io 1: Wi hou conside ing DSM and wi hou he p esence o CHP uni s in
he mic og id.
•
Scena io 2: Wi hou conside ing DSM and wi h he p esence o CHP uni s in
he mic og id
.
•
Scena io 3: Wi h conside ing DSM and wi hou he p esence o CHP uni s in
he mic og id.
•
Scena io 4: Wi h conside ing DSM and wi h he p esence o CHP uni s in he mic og id.
Fo Scena io 1, he amoun o uni s pa icipa ing and ecei ing elec ical powe om
he main g id is shown in Figu e 17. Acco ding o Figu e 17, he mic og id ends o pu chase
he maximum amoun o load om he main g id h ough bus 1 a peak consump ion. Also,
he p esence o WT and PV uni s wi hin 24 h is accep able p oduc ion. In his scena io, due
o he high e iciency o he PV uni du ing he day om 8 am o 5 pm, i has gene a ed
elec ical powe o he 12 bus. Finally, he maximum p o i o he mic og id in his scena io
is $2185.7133.
Sus ainabili y 2022,14, 6759 19 o 26
Figu e 17. Uni s pa icipa ion a e in supplying elec ic load o scena io 1.
Figu e 18 shows he uni pa icipa ion a es o Scena io 2. In his scena io, due o he
p esence o high-e iciency CHPs in buses 8 and 16, he mic og id ends o sell ac i e powe
o he main g id wi h e enue o $2681.55 and he highes p o i is $5607.0256.
Figu e 18. Uni s pa icipa ion a e in supplying elec ic load o scena io 2.
Figu e 19 shows he pa icipa ion a e o uni s in Scena io 3. In Scena io 3, he mic o-
g id e enue inc eased by $2194.4243 wi h he implemen a ion o DSM, which esul ed in a
p o i o $8.711 compa ed o Scena io 1.
Sus ainabili y 2022,14, 6759 20 o 26
Figu e 19. Uni s pa icipa ion a e in supplying elec ic load o scena io 3.
Figu e 20 shows he pa icipa ion a e o uni s in Scena io 4. In his scena io, due o
he p oduc ion o CHP, he mic og id is mo e inclined o sell elec ical powe o he main
g id. Finally, in his scena io, he mic og id p o i is $5617.706. Acco ding o Figu e 21,
he la ges sha e o hea p oduc ion is ela ed o CHP bus 8 due o i s low p oduc ion cos .
As men ioned in his pape , he ABC algo i hm is used simul aneously o sol e he OPF
p oblem and i s applica ion in he s uc u e o he GA algo i hm o sol e he main p oblem.
Figu e 22 shows he esul s o he ABC algo i hm in sol ing he OPF p oblem, including
he ne wo k ol age p o ile along wi h he ansmission powe o each ne wo k line o
maximum load demand in Scena io 4.
Figu e 20. Uni s pa icipa ion a e in supplying elec ic load o scena io 4.
Sus ainabili y 2022,14, 6759 21 o 26
Figu e 21. Pa icipa ion o CHP uni s in bases 8 and 16 o p o ide hea load in scena io 4.
Figu e 22.
OPF esul s wi h ABC algo i hm, (
a
) Vol age p o ile, (
b
) Line ansmission powe changes
o scena io 4.
Figu e 23 shows he mic og id load a ia ion cu e wi h DSM implemen a ion o
Scena io 4. In his pape , ins ead o cu ing and shedding he load, he load shi ing
echnique is used o manage he cos o he mic og id. In addi ion, c i ical loads a e
conside ed non-shi able loads and he mic og id is esponsible o supplying he load.
He e, as shown in Figu e 23, load6, and load7 a e conside ed non-shi able loads and will
no pa icipa e in he DSM p og am. As you can see in Figu e 23, he mic og id loads wi h
shi ing we e able o peak sha ing and smoo h he mic og id load p o ile compa ed o he
case wi hou DSM (Figu e 23 ).

Sus ainabili y 2022,14, 6759 22 o 26
Figu e 23. (a– ) Mic og id load a ia ion cu e in 24 h wi h DSM implemen a ion o scena io 4.
Finally, Table 11 summa izes he s a us o he p oposed me hod in di e en scena ios.
Whe e income, cos , and p o i o mic og ids wi h and wi hou DSM can be seen in ou
scena ios. He e income is he esul o he sale o elec ici y, he cos o he sum o DC
and CF, and p o i is he di e ence be ween he wo amoun s. As you can see, wi h he
implemen a ion o DSM and he p esence o a a ie y o uni s in he mic og id o scena io
4, he maximum p o i is ob ained. In Table 12 and Figu e 24, he pe o mance o he
p oposed me hod is compa ed wi h he e e ence me hods [
38
,
39
]. As you can see, he
p oposed me hod was able o educe cos s by 57.01% and imp o e by 32.01% compa ed o
he s anda d GA algo i hm.
Table 11. The esul s o p o i and cos o mic og ids in di e en scena ios.
Scena ios Coe icien s Income ($) Cos ($) P o i ($)
W1W2
Scena io1 1 0 7492 5306.29 2185.7133
Scena io2 1 0 7956.636 2349.38 5607.2560
Scena io3 1 1 7185.814 4991.39 2194.4243
Scena io4 1 1 7898.686 2280.98 5617.7067
Sus ainabili y 2022,14, 6759 23 o 26
Table 12. Compa ison o he esul s o he p oposed GA-ABC algo i hm.
Algo i hms Cos ($) Cos Reduc ion (%)
GA algo i hm 3979.71 25
GA-ABC algo i hm 2280.98 57.01
Analy ic Hie a chy P ocess (AHP)—Swa m
in elligence [38]2713.10 48.87
Imp o ed quan um pa icle swa m
op imiza ion (IQPSO) algo i hm [39]2616.53 50.69
1
The bes i ness alue
Figu e 24. Con e gence cu e compa ison o he p oposed GA-ABC algo i hm.
6. Conclusions
In his pape , he op imal ope a ion o mic og ids along wi h he implemen a ion o
DSM p og ams was modeled as an op imiza ion p oblem. The objec i e unc ion used in
his op imiza ion p oblem is o minimize cos s including he cos o ope a ing he mic og id
and he cos o implemen ing DSM p og ams o educe cus ome dissa is ac ion. He e, o
sol e he op imiza ion p oblem, a hyb id algo i hm including a gene ic algo i hm and ABC
is used. All he cons ain s we e included in he op imal powe low p og am and he load
shi ing cons ain s we e included in he gene ic algo i hm. The esul s ob ained om he
implemen a ion o his hyb id algo i hm in h ee sample ne wo ks showed ha , i s ly, he
implemen a ion o he DSM p og am (load ime shi ) educes he cos o ope a ing he
en i e mic og id. Second, wi h he inc ease o he weigh ac o o he DSM, he numbe
and hou s o load shi ing ha e dec eased and as a esul , he ope a ing cos has inc eased.
I was also ound ha he ins an aneous p ice o elec ical ene gy can ha e a g ea impac
on he p oblem o op imal ope a ion o he mic og id. Finally, o con i m he pe o mance
o he p oposed me hod, i was implemen ed on he IEEE 33-bus ne wo k in di e en
scena ios and he esul s we e compa ed wi h AHP and IQPSO algo i hms, especially i
compa ing he inancial eedback o his algo i hm aces he imp o ed gene ic algo i hm
whe e he ob ained alue is $2280.98, and wi h a s anda d GA algo i hm gi es a alue
o $3979.71. Wi h o he AHP and IQPSO Algo i hms, he bes answe ob ained he e is
$2713.10 and $2616.53 which dec eased by 48.87% and 50.69%, espec i ely, al hough i had
a good pe o mance, wi h he p oposed me hod, we we e able o educe by 57.01% and
Sus ainabili y 2022,14, 6759 24 o 26
imp o e by 32.01% compa ed o he s anda d GA algo i hm. Finally, he design ea u es
a e as ollows:
•
P o ide shi ing load ins ead o cu ing and shedding load and supply o c i ical load
by mic og id.
•
Imp o ed 32.01% pe o mance o gene ic algo i hm based on combina ion wi h
ABC algo i hm.
•
In es iga ing he e ec o uni ypes on cos educ ion including PV, WT, MT, FC, MT,
BAT and CHP.
•
Compa ison o GA-ABC algo i hm wi h me a-heu is ic algo i hms such as PSO, DEHS,
AHP and IQPSO.
•
Analysis and e iew o he esul s o he p oposed me hod du ing di e en scena ios
wi h he bes pe o mance educ ion o 57.01%.
Au ho Con ibu ions:
Concep ualiza ion, M.D. and A.F.; me hodology, M.D.; so wa e, M.D.; alida-
ion, S.M.S.H.; o mal analysis, M.D.; in es iga ion, H.K.; esou ces, S.M.S.H.; da a cu a ion, S.M.S.H.
and E.J.; w i ing—o iginal d a p epa a ion, M.D. and M.D.; w i ing— e iew and edi ing, M.J.,
E.J. and A.F.; isualiza ion, A.F.; supe ision, H.K., M.J., R.G. and Z.L.; p ojec adminis a ion, M.J.;
unding acquisi ion, H.K., R.G. and Z.L. All au ho s ha e ead and ag eed o he published e sion o
he manusc ip .
Funding:
This esea ch is unde he SGS G an om VSB— he Technical Uni e si y o Os a a unde
g an numbe SP2022/21.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Nomencla u e
DSM demand-side managemen
ABC a i icial bee colony
OPF op imal powe low
DG dis ibu ed gene a ion
PSO Pa icle swa m op imiza ion algo i hm
DSM Demand-side managemen
GA Gene ic algo i hm
CHP Combined hea and powe
Re e ences
1.
Hosseinimoghadam, S.M.S.; Dash da , M.; Dash da , M. Imp o ing he Sha ing o Reac i e Powe in an Islanded Mic og id
Based on Adap i e D oop Con ol wi h Vi ual Impedance. Au om. Con ol Compu . Sci. 2021,55, 155–166. [C ossRe ]
2.
Dash da , M.; Nazi , M.S.; Hosseinimoghadam, S.M.S.; Bajaj, M. Imp o ing he Sha ing o Ac i e and Reac i e Powe o he
Islanded Mic og id Based on Load Vol age Con ol. Sma Sci. 2021,10, 142–157. [C ossRe ]
3.
Aghdam, F.H.; Sina, G.; Na id, T.K. E alua ion o loss minimiza ion on he ene gy managemen o mul i-mic og id based sma
dis ibu ion ne wo k in he p esence o emission cons ain s and clean p oduc- ions. J. Clean. P od.
2018
,196, 185–201. [C ossRe ]
4.
Dash da , M.; Naja i, M.; Esmaeilbeig, M. P obabilis ic planning o pa icipa ion o i ual powe plan s in he p esence o he
he mal powe plan s in ene gy and ese e ma ke s. S¯
adhan¯
a2020,45, 1–9. [C ossRe ]
5.
Dash da , M.; Bajaj, M.; Hosseinimoghadam, S.M.S. Design o Op imal Ene gy Managemen Sys em in a Residen ial Mic og id
Based on Sma Con ol. Sma Sci. 2021,10, 25–39. [C ossRe ]
6.
Bazmohammadi, N.; Tahsi i, A.; An a i-Moghaddam, A.; Gue e o, J. A hie a chical ene gy managemen s a egy o in e con-
nec ed mic og ids conside ing unce ain y. In . J. Elec . Powe Ene gy Sys . 2019,109, 597–608. [C ossRe ]
7.
Kak an, S.; Chanana, S. Sma ope a ions o sma g ids in eg a ed wi h dis ibu ed gene a ion: A e iew. Renew. Sus ain. Ene gy
Re . 2018,81, 524–535. [C ossRe ]
8.
Ja a i, M.; Zah a, M.; Jianguo, Z. A magne ically coupled mul i-po , mul i-ope a ion-mode mi-c o-g id wi h a p edic i e dynamic
p og amming-based ene gy managemen o esiden ial applica ions. In . J. Elec . Powe Ene gy Sys .
2019
,104, 784–796.
[C ossRe ]
Sus ainabili y 2022,14, 6759 25 o 26
9.
Polanco Vasquez, L.O.; Ca eño Meneses, C.A.; Pizano Ma ínez, A.; López Redondo, J.; Pé ez Ga cía, M.; Ál a ez He ás, J.D.
Op imal ene gy managemen wi hin a mic og id: A compa a i e s udy. Ene gies 2018,11, 2167. [C ossRe ]
10.
U ka sh, K.; S ini asan, D.; T i edi, A.; Zhang, W.; Reindl, T. Dis ibu ed model-p edic i e e-al- ime op imal ope a ion o a
ne wo k o sma mic og ids. IEEE T ans. Sma G id 2018,10, 2833–2845. [C ossRe ]
11.
Aghajani, G.R.; Shayan a , H.A.; Shayeghi, H. Demand-side managemen in a sma mic o-g id in he p esence o enewable
gene a ion and demand esponse. Ene gy 2017,126, 622–637. [C ossRe ]
12.
Dey, B.; Raj, S.; Mahapa a, S.; Má quez, F.P.G. Op imal scheduling o dis ibu ed ene gy esou ces in mic og id sys ems based on
elec ici y ma ke p icing s a egies by a no el hyb id op imiza ion echnique. In . J. Elec . Powe Ene gy Sys .
2021
,134, 107419.
[C ossRe ]
13.
Xie, S.; Zhai, R.; Liu, X.; Li, B.; Long, K.; Ai, Q. Sel -adap i e gene ic algo i hm and Fuzzy decision-based mul i-objec i e
op imiza ion in mic og id wi h DGs. Open Elec . Elec on. Eng. J. 2016,10, 46–57. [C ossRe ]
14.
Moghaddam, A.A.; Sei i, A.; Niknam, T.; Pahla ani, M.R.A. Mul i-objec i e ope a ion managemen o a enewable MG (mic o-
g id) wi h back-up mic o- u bine/ uel cell/ba e y hyb id powe sou ce. Ene gy 2011,36, 6490–6507. [C ossRe ]
15.
Dash da , M.; Flah, A.; Hosseinimoghadam, S.M.S.; Fa d, M.Z.; Dash da , M. Op imiza ion o mic og id ope a ion based on
wo-le el p obabilis ic scheduling wi h bende s decomposi ion. Elec . Eng. 2022, 1–15. [C ossRe ]
16.
Eseye, A.T.; Zheng, D.; Zhang, J.; Wei, D. Op imal ene gy managemen s a egy o an isola ed indus ial mic og id using a
Modi ied Pa icle Swa m Op imiza ion. In P oceedings o he 2016 IEEE In e na ional Con e ence on Powe and Renewable
Ene gy (ICPRE), Shanghai, China, 21–23 Oc obe 2016; pp. 494–498.
17.
Kuma , R.S.; Ragha , L.P.; Raju, D.K.; Singh, A.R. Impac o mul iple demand side managemen p og ams on he op imal
ope a ion o g id-connec ed mic og ids. Appl. Ene gy 2021,301, 117466. [C ossRe ]
18.
Ndwali, P.K.; Nji i, J.G.; Wanji u, E.M. Op imal Ope a ion Con ol o Mic og id Connec ed Pho o ol aic-Diesel Gene a o Backup
Sys em Unde Time o Use Ta i . J. Con ol. Au om. Elec . Sys . 2020,31, 1001–1014. [C ossRe ]
19.
Yang, X.; Zhang, Y.; He, H.; Ren, S.; Weng, G. Real-Time Demand Side Managemen o a Mic og id Conside ing Unce ain ies.
IEEE T ans. Sma G id 2018,10, 3401–3414. [C ossRe ]
20.
Kuma , R.S.; Ragha , L.P.; Raju, D.K.; Singh, A.R. In elligen demand side managemen o op imal ene gy scheduling o g id
connec ed mic og ids. Appl. Ene gy 2021,285, 116435. [C ossRe ]
21.
Ma zband, M.; Foulad a , M.H.; Ako ede, M.; Ligh body, G.; Pou esmaeil, E. F amewo k o sma ansac i e ene gy in
home-mic og ids conside ing coali ion o ma ion and demand side managemen . Sus ain. Ci ies Soc.
2018
,40, 136–154. [C ossRe ]
22.
Xu, F.; Wu, W.; Zhao, F.; Zhou, Y.; Wang, Y.; Wu, R.; Zhang, T.; Wen, Y.; Fan, Y.; Jiang, S. A mic o-ma ke module design o
uni e si y demand-side managemen using sel -c osso e gene ic algo i hms. Appl. Ene gy 2019,252, 113456. [C ossRe ]
23.
Sedhom, B.E.; El-Saadawi, M.M.; El Mou si, M.S.; Hassan, M.A.; Eladl, A.A. IoT-based op imal demand-side managemen and
con ol scheme o sma mic og id. In . J. Elec . Powe Ene gy Sys . 2021,127, 106674. [C ossRe ]
24.
Eid, C.; Koliou, E.; Valles, M.; Reneses, J.; Hak oo , R. Time-based p icing and elec ici y demand esponse: Exis ing ba ie s and
nex s eps. U il. Policy 2016,40, 15–25. [C ossRe ]
25.
Mohsin, M.; Hani , I.; Taghizadeh-Hesa y, F.; Abbas, Q.; Iqbal, W. Nexus be ween ene gy e iciency and elec ici y e o ms: A
DEA-Based way o wa d o clean powe de elopmen . Ene gy Policy 2021,149, 112052. [C ossRe ]
26. Hu, Z.; Han, X.; Wen, Q. In eg a ed Resou ce S a egic Planning and Powe Demand-Side Managemen ; Sp inge : Be lin/Heidelbe g,
Ge many, 2013; pp. 63–133.
27. Keyhani, A.; Mohammad, A. Sma Powe G ids 2011; Sp inge Science & Business Media: Be lin, Ge many, 2012.
28.
Feue iegel, S.; Di k, N. In eg a ion scena ios o Demand Response in o elec ici y ma ke s: Load shi ing, inancial sa ings and
policy implica ions. Ene gy Policy 2016,96, 231–240. [C ossRe ]
29.
Kong, J.; Skjelb ed, H.I.; Fosso, O.B. An o e iew on o mula ions and op imiza ion me hods o he uni -based sho - e m hyd o
scheduling p oblem. Elec . Powe Sys . Res. 2020,178, 106027. [C ossRe ]
30.
Roldán-Blay, C.; Mi anda, V.; Ca alho, L.; Roldán-Po a, C. Op imal Gene a ion Scheduling wi h Dynamic P o iles o he
Sus ainable De elopmen o Elec ici y G ids. Sus ainabili y 2019,11, 7111. [C ossRe ]
31.
Liaqua , S.; Zia, M.F.; Benbouzid, M. Modeling and o mula ion o op imiza ion p oblems o op imal scheduling o mul- i-
gene a ion and hyb id ene gy sys ems: Re iew and ecommenda ions. Elec onics 2021,10, 1688. [C ossRe ]
32.
Jayade , V.; Swa up, K.S. Op imiza ion o mic og id wi h demand-side managemen using Gene ic Algo i hm. In P oceedings o
he IET Con e ence on Powe in Uni y: A Whole Sys em App oach, London, UK, 16–17 Oc obe 2013; pp. 1–12.
33.
Moghaddam, A.A.; Sei i, A.; Niknam, T. Mul i-ope a ion managemen o a ypical mic o-g ids using Pa icle Swa m Op imiza ion:
A compa a i e s udy. Renew. Sus ain. Ene gy Re . 2012,16, 1268–1281. [C ossRe ]
34.
Aska zadeh, A. A memo y-based gene ic algo i hm o op imiza ion o powe gene a ion in a mic og id. IEEE T ans. Sus ain.
Ene gy 2017,9, 1081–1089. [C ossRe ]
35.
Gao, R.; Juebo, W.; Wen, H.; Yun, Z. An imp o ed ABC algo i hm o ene gy managemen o mic og id. In . J. Compu . Commun.
Con ol. 2018,13, 477–491. [C ossRe ]
36.
Reddy, S.S.; Pa k, J.Y.; Jung, C.M. Op imal ope a ion o mic og id using hyb id di e en ial e olu ion and ha mony sea ch
algo i hm. F on . Ene gy 2016,10, 355–362. [C ossRe ]