Optimal operation of microgrids with demand-side management based on a combination of genetic algorithm and artificial bee colony

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. 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