energies Article A Novel Agent-Based Power Management Scheme for Smart Multiple-Microgrid Distribution Systems Zagros Shahooei, Lane Martin, Hashem Nehrir * and Maryam Bahramipanah Electrical and Computer Engineering Department, Montana State University, Bozeman, MT 59717, USA; z.shahooei@gmail.com (Z.S.); lanemartin921@gmail.com (L.M.); maryam.bahramipanah@montana.edu (M.B.) * Correspondence: hnehrir@montana.edu Abstract: In this work, a novel agent-based day-ahead power management scheme is proposed for multiple-microgrid distribution systems with the intent of reducing operational costs and improving system resilience. The proposed power sharing algorithm executes within each microgrid (MG) locally, and the neighboring MGs cooperate via a multi-agent system cooperation scheme, established to model the communication among the agents. The power management for each agent is modeled as a multi-objective optimization problem (MOP) including two objectives: maximizing load coverage and minimizing the operating costs. The proposed MOP is solved using the Nondominated Sorting Genetic Algorithm (NSGA-II), where a set of Pareto optimal solutions is obtained for each agent through the NSGA-II. The final solution is obtained using an Analytical Hierarchical Process. The effectiveness of the proposed scheme is evaluated using a benchmark 4-MG distribution system. It is shown that the proposed power management scheme and the cooperation of agents lead to a higher overall system resilience and lower operation costs during extreme events.   Keywords: power management; multi-agent system; resilience; multiple-microgrid; multi-objective Citation: Shahooei, Z.; Martin, L.; optimization Nehrir, H.; Bahramipanah, M. A Novel Agent-Based Power Management Scheme for Smart Multiple-Microgrid Distribution 1. Introduction Systems. Energies 2022, 15, 1774. https://doi.org/10.3390/ With the frequent occurrence of extreme events and their severe impact on the existing en15051774 grid architecture, the need for improving the resilience of the grid has also grown. Power system resilience is defined as the ability to withstand the High Impact Low Probability Academic Editor: Abu-Siada (HILP) events, such as wildfires and hurricanes, and continue to energize at least the Ahmed critical loads and quickly recover from any interruptions caused by the extreme events [1]. Received: 13 December 2021 The HILP events can cause severe damages throughout the power grid and may lead to Accepted: 25 February 2022 cascading outages and blackouts [2]. Traditional power systems are more prone to failure Published: 28 February 2022 during extreme events due to their centralized and interconnected structure, and enormous Publisher’s Note: MDPI stays neutral size. As a result, failure of one component may lead to cascading failures and finally with regard to jurisdictional claims in wide-spread outage or blackout of the entire system [3]. Furthermore, maintaining grid published maps and institutional affil- reliability is challenging due to the load growth and integration of intermittent renewable iations. energies. One of the promising solutions to the above-mentioned challenges is to form autonomous multiple-microgrid-based distribution systems with peer-to-peer communica- tion and power sharing ability among the microgrids (MGs) [4]. During an extreme event, an MG can be islanded and operated independently using its own resources in order to Copyright: © 2022 by the authors. prevent the propagation of the impact of the extreme event through the whole network [5]. Licensee MDPI, Basel, Switzerland. Moreover, networked MGs can cooperate to ensure that all their critical loads are sup- This article is an open access article plied [6]. Such control schemes can reduce the total curtailed load, ensure uninterrupted distributed under the terms and supply of the critical loads, such as hospitals and data centers, and improve the overall conditions of the Creative Commons resilience of the system [7]. Attribution (CC BY) license (https:// The growing use of distributed energy resources (DERs) demonstrates the necessity of creativecommons.org/licenses/by/ distributed control in the MG-based architecture [3]. Indeed, distributed control algorithms 4.0/). Energies 2022, 15, 1774. https://doi.org/10.3390/en15051774 https://www.mdpi.com/journal/energies Energies 2022, 15, 1774 2 of 13 can overcome three major issues that can occur in a centralized control architecture: (1) there is a huge computational burden associated with centralized control algorithms and decision- making processes, specifically in larger systems; (2) failure of the central controller could result in losing the control of the entire network; (3) maintaining the data privacy and ownership regulations are prone to being violated since all the information has to be gathered in one single node. On the other hand, establishing a decentralized control scheme is a robust solution for tackling these issues. In our proposed scheme, each MG processes its own information locally and shares only the necessary data with its neighboring MGs. Moreover, during an extreme event, the MGs can communicate with each other on a plug- and-play basis in such a way that if an MG is severely affected by an extreme event, it can be islanded from the grid to avoid propagation of the fault(s). The agent-based MG power management problem has been explored and solved using a variety of optimization frameworks. In [3], a power management scheme is introduced by locating fair solutions on the Pareto frontier using the Nash Bargaining system. The objectives for each agent are formulated to maximize the efficiency, profit, and utility of power consumption. In [8], the energy trading between multiple MGs is formulated as a distributed optimization problem and solved using an iterative subgradient-based algorithm to minimize operation cost. Reference [9] proposes a multiple-MG-based power management scheme through a common interface to offer ancillary services, black start capability, and for improving stability of the system. The power management of a multiple- MG system is modeled as a bi-level optimization problem in [10]. Reference [11] proposes a two-layer optimization model to improve stability and security for multi-MG systems. Optimal solutions are found using a bilateral bidding and trading strategy. The scheduling method encourages the MGs to share power rather than importing power from the main utility. A robust power flow control strategy between multiple interconnected MGs is presented in [12] with a focus on frequency stabilization. A bi-level power management scheme is proposed in [13], where the energy trading (upper layer) is formed as a mixed integer quadratic programming and the MG energy production (lower layer) is formed as a robust optimization model. Reference [14] utilizes an agent-based platform to establish autonomy, proactivity, and social communication among the interconnected MGs. This work, however, focuses on a plug-and-play-based secondary regulation control system rather than the day-ahead component-wise scheduling. Reference [15] proposes a peer-to-peer voltage control strategy through dual decomposition and linearization. The voltage control problem is formulated as a decentralized constrained optimization and the voltage deviation is minimized with the help of a peer-to-peer communication protocol. A prosumer-based peer-to-peer energy trading platform is developed in [16]. In this platform, the individual users shift their tasks between a producer and a consumer, based on the situation. The overall objective is to establish an efficient utilization of local resources and minimize the transfer of energy with other areas. References [17,18] propose using the Java Agent Development Environment (JADE) to facilitate the power management of agent-based systems. Indeed, JADE is an application platform for developing agent-based communication protocol. Reference [18] used a decentralized power management approach to enhance the system self-healing. However, these references did not consider any energy storage systems (ESSs). JADE is a highly capable system that enables the formation of agents with easy plug-and-play operation that can lead to robust solutions. Reference [19] proposes a hybrid multi-agent system (MAS) using electric vehicles (EVs). The hybrid system combines centralized and distributed control to improve efficiency and system resilience. However, in this reference, the proposed MAS does not protect data privacy; all the information is distributed through the whole system. In [20], a resilient and extreme-event-aware planning framework was proposed for MGs to ensure maximum load coverage during a prolonged period of extreme event. Reference [21] developed a demand and congestion management strategy during extreme events and contingency focusing on home appliances and available electric vehicles. Energies 2022, 15, x FOR PEER REVIEW 3 of 14 Energies 2022, 15, 1774 management strategy during extreme events and contingency focusing on home a3popfl1i-3 ances and available electric vehicles. Different indices such as consumer convenience and demand rebound are considered in this study. DiffeIrne ntht iisn pdaicpeesrs, uwceh parsocpoonsseu am neorvceol ndvisetnriebnucteda npdowdemr manadnargeebmouendt sacrheecmoen sfiodre mreudltiin- pthleis-MstGud dyi.stribution systems in order to improve the overall system resiliency and reduce the opInerthatiisnpga cpoesrt,sw. Feoprr tohpios speuarpnovse,l adnis atrgiebnutt eisd apsoswigenremd aton aegaechm MenGt s’sc hceomnterofollrambleu lctoipmle-- pMoGnednitsst. rTibhuet rionle soyfs eteamchs aigneonrt dise rtot osoilmvep ritosv oewthne mouvletri-aolbl jseycstitveme prreosbillieemnc (yMaOnPd) raenddu ctoe cthome ompuenraictainteg wcoitshts i.tsF noerigthibsopriunrgp aogsee,ntasn toa gcerneat ties aa ssseitg onfe dopttoimeaalc hsoMluGtio’snsc otnhatrto llilea bolne tchoem Ppaorneteon tfsr.oTnht.e Eraoclhe oMfGea dchetaegrmenint iess tao sseotl voef oitpstoimwanl msoululttii-oonbsje tchtiavte imprporbolvemes (tMheO oPv)earnaldl stoysctoemm reusniliiceantecyw withhiiltes sniemiguhltbaonreinougsalgye mntisntiomcizreinatge oapseertaotifnogp tciomstasl. sIot lushtioounlsdt hbaet nlioeteodn tthhaetP sainrecteo tfhroe nPtV. E oauchtpMutG pdoweteerrm isi neessseansteiatlolyf ofrpeteim, iat liss oultuitliizoends twhahteinmevperro vaevsaitlhaebloev; eirt ailsl nsyost tienmcluredseidli einn ctyhew ohpitleimsiizmautilotann perooucselsys.m inimizing operating costs. It should be noted that sTinhcee mthaeinP cVonoturtipbuuttipoonws oerf tishiess sweonrtika lalryef arese f,oiltloiswust:i lized whenever available; it is not (i1n)c luFdoerdminultihzaetoiopnti omf iaz autinoinquper oMceOsPs. that encourages each agent to find an optimal solu- tTiohne mthaaitn wciolln rterisbuultt iionn lsoowfetrh oisvweroarlkl oapreeraastifnogll ocowsst:s. ((21)) EFsotrambluislhiziantgio an roefcaipurnoicqaule cMomOmPuthnaitcaetnicoonu arangde sneegacohtiaagtieonnt btoetfiwnedeann loopcatilm aaglesnotlsu atinodn ntheiagthwboilrlirnegs uMltGins.l ower overall operating costs. ((32)) PErsottaebcltiisnhgi ndgataar pecriipvarocyca alsc oemacmh uMnGic adtoioens annodt snheagroet iiatst ilooncable itnwfoeremn aloticoanl awgietnht sotahnedr MneGigs.h boring MGs. (3) Protecting data privacy as each MG does not share its local information with other MGs. The paper is structured as follows: Section 2 describes the proposed methodology and pTrhoeblpemap feorrims ustlrauticotnu.r Seedcatisonfo 3ll powress:enStesc tthioen b2endcehsmcrairbke smtuhletipprleo-pMosGe dtesmt esythsotedmo laongdy danesdcrpirboebsl ethme fsoorlmutuiolant iaopnp. rSoeacctiho.n T3hpe rpersoenptosstehde pboewncehrm maarnkamgeumltiepnlte -sMchGemtees tthsyrostuegmh atnhde mdeosdcerilbinegs tahneds soilmutuiolantiaopnp orfo aacnh a. gTehnet-pbraospedos medupltoipwlee-rMmGa nsyasgteemme tnhtastc ihse immeptahcrtoedu gbhy tahne emxotrdeemlien gevaenndt sisim purelasetinotnedo fina nSeacgteionnt- b4a. sFeidnamllyu,l tSipecleti-oMnG 5 scyosntcelmudtehsa tthise ipmappaecrt ewditbhy thane feixntarle mreemeavreknst oisn pthrees eandtveadnitnagSeesc taionnd 4th. Fe ianpaplllyi,cSaebcitliiotyn o5f ctohnec plurodpesosthede paappperrowacihth. the final remarks on the advantages and the applicability of the proposed approach. 22.. MMeetthhooddoollooggyy TThhee ggeenneerraall ffrraammeewwoorrkk ffoorr tthhee mmuullttiippllee--MMGG aaccttiivvee ddiissttrriibbuuttiioonn ssyysstteemm iiss sshhoowwnn iinn FFiigguurree 11,, wwhheerree aa ddiissttrriibbuuttiioonn ggrriidd iiss ddiivviiddeedd iinnttoo sseevveerraall MMGGss.. EEaacchh MMGG hhaass iittss oowwnn rreessoouurrcceess,, aanndd uunnddeerr nnoorrmmaall ccoonnddiittiioonnss ssuuppppllyy––ddeemmaanndd bbaallaannccee iiss mmaaiinnttaaiinneedd wwiitthhiinn tthhee MGG.. DDuurriinngg aann eexxttrreemee eevveenntt,, eeaacchh MGG iissoollaatteess ffrroom tthhee rreesstt ooff tthhee ggrriidd aanndd ooppeerraatteess iinn iissllaanndd mooddee.. FFuurrtthheerrmoorree,, tthhee maaiinn pprriioorriittyy wiitthhiinn eeaacchh MGG iiss ttoo ssuuppppllyy tthhee ccrriittiiccaall llooaaddss wiitthhiinn tthhee MGG..I nIno oththererw worodrsd,sM, MGsGhsa hvaevthe ethaeb ialibtyilittoyc toon tcroonl ttrhoeli rthoewirn ocwomn pcoonmepnotsn,esnutcsh, sauscDhi astsr iDbiustteridbuGteende Graetnioenra(tDioGn) (uDnGit)s u, EnSitSss, ,EaSnSds,c aonndtr coollnatbrloelllaobaldes lofaacdisli tfaatceilditbatyedD ebmy aDned- mReasnpdo nRseesp(DonRs)e. (DR). FFiigguurree 11.. MMuullttiippllee--MMGG DDiissttrriibbuuttiioonn NNeettwwoorrkk.. The general framework of the proposed agent-based active power management ap- proach is shown in Figure 2. The scheme is visualized in three different layers: (1) The physical layer, which includes the actual components of the MG (loads, DGs, ESSs, etc.). (2) The multi-agent layer, where the local agents are located. One agent is assigned to each Energies 2022, 15, x FOR PEER REVIEW 4 of 14 E nergies 2022, 15, x FOR PEER REVIEW 4 of 14 The general framework of the proposed agent-based active power management ap- Energies 2022, 15, 1774 proacThh eis g sehnoewranl firna mFiegwuroer k2 .o Tf hthee s pchroepmoes eisd vaigseunatl-ibzaedse din a tchtirveee pdoifwfeerre nmt alnayaegresm: (e1n4)t o Tfah1p3e- pprhoyascihca ils l asyheorw, wn hinic hF iignucrlue d2e. sT thhee sacchtuemal ec oism vpisounaelniztse do fi nth teh MreGe d(lioffaedres,n Dt lGays,e ErsS: S(s1,) e Ttch.)e. p(2h)y Tshicea ml luayltei-ra, gwehnitc lha yienrc,l uwdheesr eth teh ea clotucaall acgoemnptso anreen ltosc oaft etdh.e O MnGe a(gloeandt sis, DasGsisg, nEeSdS tso, eetacc.)h. c(co2on)n Tttrrhooelll lmaabbullelet icc-oaomgeppnoot nnlaeeynnettr o,o fwf tthhheeer Me tGhe,, ili.o.eec..,a, tlth ahegee DDnGts aaagrgeee nlnott,c,a EEtSeSSdS. a aOggenenent ta,,g aaennnddt DiDsR aRsa sagiggeennnett.d. ( (t33o)) e TTahchehe cccooomntmrouullnnaibicclaaett iicooonnm llpaayoyenerre,,n wwt hohefe rtrehe etth hMee GM, GGi.e c.ca, antnh ceco oDmmGmm auugnneiniccata,t teEe SwwSi itathhg eoontthth,e earrn Md GDGsRs.. TaTgooe mnto.o d(d3ee)ll Ttthhheee pcpeoeemerr-m-ttoou--pnpeieceearrtc icooonmm mlmayuuennri,ci cawatithoioenrn,e,a atc hcoeom mMmmGuu ncniacicnaa tticoioonmna maggeuennntitc( (CaCtOeO MwMiMth)) i osista hasessrsi igMgnneGedds.t toToe oea acmchhoM deGGl ,t, ahases spshheooewrw-ntno i-inpne FFeiigrg ucuorreme 3m3.. TuThnheiecssaeeti CCoOnO,M Ma McMom aaggmeenuntntssi caaallltloioowwn tathhgeee MnMtG G(CssO ttooM ccMoomm) mims uausnnsiiiccgaantteeed ww tioitth hea eecaahcch hM ooGtthh, eaersr isinnh oorwrddnee rirn tto oFf ifagacuciilrlieitt a3at.te eTa ahp eposoeww CeeOrrs MshhaMarri niangges nsccthshe eammlleoe.w. TT hthheee a aMnnaGallysyt ttiiocca acllo ffmoorrmmuunllaiacttiaiootnen wooffit tthh eeea ddciihfff feoertrehenentrt aiangge eonnrtdtsse aarn ntdod tfthahecei plpirtroaobtbel leaemm pf ofoworrmemru uslhlaatatiroioinnga a rsrecehp perremesseen. ntTetheddeb abeneloalowlyw.ti. cal formulation of the different agents and the problem formulation are presented below. FFiigguurree2 2.. Geenneerraall ffrraameewoorrkk oofft thheep prrooppoosseedda aggeenntt--bbaasseedda accttiviveep poowweerrm maannaaggeemmeenntts scchheemmee. . Figure 2. General framework of the proposed agent-based active power management scheme. Figure 3. Communication agent structure (COMM). FFiigguurree 33.. Communiiccaattiioon aaggeenntt ssttrruuccttuurree ((CCOMM)).. 22.1. E2..11.. EES SSS SS A Ag Agge ent enntt AAnna aggeenntti sisa asssisgignnededto toth teheE SESS(Ss()sw) withitihniena echacMh GM,Gw,h wichhicishu isse udsaesd aabs aac bkaucpksuopu rscoeufrocre efor An age me ergmeenrcgyesn ncty isitua sti atussiona itgs iao nnesd atnod th cea nE SbSe( sc)h warigthedin a enadc hb eM pGre, pwahriecdh iifs auns eedxt ares ma eb aecvkeunpt isso fuorrcee- fcoars teemd.e Trgheen ocbyj escittuivaeti o nnds caannd bceanch baer gcehdaragnedd baenpdr bepe aprreedpiafraend eixf tarnem exeterevmenet eisvefonrte icsa fsoterde-. Tchaseteodb.j eTctive of the ES oSf tahgee EnStSd eapgeenntd dseopnenthdes sotnat tehoef stthaeteM ofG t.hDe uMriGn.g Daunrienxgtr aenm eexetrveemnte wevent wh heer eo tbhjeec MtivGe iosf d tihsec oEnSnSe acgteedn tf rdoemp etnhde sm oanin t hger isdta, tthe eo Ef tShSe a MgeGn.t Dcrueraitnegs aa nd iesxcthraermgee ehscvhe enret wthhe Meme toe rme G ath is xeim dMisGco ins ndeicsted from thize load ccoovnenreacgteed th f ermo ain grid, the ESat mis bthiaes meda itno wgraird S, tahgeds me n oE tScSrre e a ea xg teensta crdeiasctehsa rag deisscchheamrgee tsochmeamxeim toiz me aload c pensive hours of gener- ation. A weigxhitminigz oev leoraadg ecothvaetraisgebiased towards more system is formu thlaatte dis bbaiasseedd o tno wthaer d esx mpeonrsei veexpheonusrisveo fhgoeunres roaft igoenn.eAr- wateiiognh. tAin gwseyigshtetmingis formulated based on the total cost tfootrala cnoMst Gforto asnu MppGly toa lslulopapdlys aaltl elaocahdsh oatu er.acThh ehoEuSrS. sTyhstee mES iSs afogremntu plalateyds baa kseeyd roonl et he total cost for anagent plays a key role in minimiinzi nmginthime iozvinegra tlhl eo MovGer atoll souppeprlayti nalgl lcooasdtss bayt reeadch ho perating costs by reducing theuocpinerg u a rt.th T ioe hoep eESS n of sryantico ange onft splayshronouynchr oa nkoeuys rgoelne eirna tmorins i(mSGizsi)n dgu trhien go vtheera mll oospt eerxaptienng- csoivsets h boyu rrse.d Tuhcein cgo tsht eo fo opperearatitoinng o tfh sey n scghernoenroautosr sge(SnGersa)tdorusr i(nSgGtsh) edmuroinstge txhpee mnsoivste ehxopuerns-. Tshiveec hoost of o SGs at ea urs. Tpheer actoinstg otfh oepSeGrastaint ge atchhe hSoGusr afto erain chd ehpoeunrd feonr tinMdGepseisndcaelnctu MlatGeds ibsy ca(1lc)u. lated by (1). ch hour for independent MGs is calculated by (1). C 2SG(t) = α ∗ PSG (t) + β ∗ PSG(t) + γ (1) where α, β, and γ are constant cost coefficients and PSG(t) is the SG’s power generation at time t. In this paper, they are considered as 0.008, 6.3, and 180, respectively. Energies 2022, 15, 1774 5 of 13 Before an extreme event, ESS is fully charged, and during the extreme event, it is discharged in order to minimize the power deficiency within the MG. When the healthy MGs reconnect, the ESS in each MG supplies its available power during the most expensive hours to minimize power import from its neighboring MGs, therefore minimizing the MG’s operation costs. The cost at each hour is determined by solving an economic dispatch problem formulated by (2). minCtotal(t) = ∑ Ci(Pi(t))s.t. PL(t) = ∑ PSG(t)PSG(t) ≤ Pi,available(t) (2) where Ci is the MG’s hourly cost and Pi(t) is the imported power from the neighboring MGs at each hour. PL(t) is the local MG’s total load and Pi,available(t) is the neighboring MG’s available power at time t. Solving the optimization problem, it will determine the required power from each neighboring MG with the objective to minimize the hourly costs. A cost weighting function is defined for the generation cost at each hour, as shown in (3). C w(t) = min (3) C(t) where Cmin and C(t) are the minimum hourly generation cost and generation cost at each hour, respectively. At each hour, the weighting function (w0) can range from 0 to 1; where w0 = 0 corresponds to the most expensive hour and w0 = 1 corresponds to the least expensive hour. Depending on the available resources within an MG during an extreme event, two objectives are considered. Generally, the ESS reserves its charge for emergency cases, and it only supplies critical loads. Therefore, the first objective function is given for ESS as follows. t2 ( ) ObjESS,1 = ∑ P 2Lcrit(t)− PESS(t) × w(t) (4) t=t1 where t1 and t2 are the forecasted times when the extreme event starts and ends. PESS(t) is the charge/discharge power of ESS, and PLcrit(t) is the amount of critical load in the MG at the time step t. If the MG does not have adequate power supply to cover all its loads during the extreme event, the ESS agent creates a discharge scheme that tries to supply critical loads at all hours of the extreme event. The objective function for this case is formulated by (5). t2 ObjESS,2 = ∑ (SE(t)− PESS(t)− SE(t + 1))2 (5) t=t1 where SE(t) is the stored energy in the ESS at time t. The following constraints, (6)–(9), are considered for the ESS agent to ensure it operates within its power limits and energy capacity. PminESS ≤ PESS(t) ≤ PmaxESS (6) SEmin maxESS ≤ SEESS(t) ≤ SEESS (7) |SE(t)− SE(t +(1)| ≤ P max ESS × ∆)t (8)t3 ∑ PESS(t) ≤ SEmax − SEmin (9) t=t2 2.2. DR Agent A DR agent is assigned to the controllable loads within each MG. This agent is respon- sible for managing load curtailments to find a balance between customer discomfort costs associated with curtailing of noncritical loads, generation costs associated with importing power from the neighboring MGs, and load coverage. In the case of an extreme event, Energies 2022, 15, 1774 6 of 13 the DR agent determines the level of curtailment of the price-sensitive controllable loads. Three objective functions are considered for the DR agent, as shown in (10)–(12). The first objective, (10), is to minimize the customer discomfort cost, expressed as a quadratic nonlinear function of the curtailed power, to show the exponential increase in the customers discomfort with increasing load curtailment. The second objective is to minimize the power import (and therefore its cost), and the third objective is to minimize the load curtailment. ObjDR,1 = m× Pc(t)2 + c× Pc(t) (10) N { } ObjDR,2 = ∑ α ∗ Pimport(t)2 + β ∗ Pimport(t) + γ (11) t=1 ObjDR,3 = (PL(t)− Pimport(t))2 (12) where Pc(t) is the amount of curtailed power, PL(t) is the local load power, and Pimport(t) is the power imported from the grid at hour t. m and c are constant cost coefficients associated with customer discomfort costs and α, β, and γ are constant cost coefficients associated with importing power from the (grid.The curtailed power is bound by the)constraints in (13), which do not let an MG curtail loads below a critical threshold PLcrit(t) . Pc(t) ≤ PL(t)− PLcrit(t) (13) 2.3. DG Agent The DG agent represents the synchronous generators in the MGs and sets their output power as per the local electricity demand and the requested power from the neighboring areas. For this purpose, cost coefficients α, β, and γ are generated for each DG to provide the cost of exported power to the neighboring MGs that suffer from lack of energy. The first objective is the Mean Squared Error (MSE) between the generation and the amount of power to be supplied (i.e., the summation of the output power of the DR agent and the power exported to the other MGs), and the second objective is to minimize the generation cost. The two objectives are given( in (14)–(15). ) Obj 2DG,1 = ∑ PDG(t)− (PL(t)− Pc(t)) + Pexp(t) (14) t ObjDG,2 = α ∗ P 2DG(t) + β ∗ PDG(t) + γ (15) PDG(t) is the DG power output, and Pexp(t) is the amount of power that an MG pro- vides to the neighbor MG, which is proportional to the power requested by the affected MG. The control variable of the DG agents is their output power, which is limited by the maximum and minimum generating limits of each DG, i.e., PminDG and P max DG , as given in (16). PminDG ≤ P (t) ≤ PmaxDG DG (16) PDG(t), must be within its ramping limit. This constraint is given in (17). |PDG(t)− PDG(t− 1)| ≤ ρ× ∆t (17) where ρ is the generation rate constant representing the ramp-up and ramp-down limits between two consecutive time steps, ∆t. It should be noted that the operation cost of the DGs is a function of their power output and duration of operation. Batteries do not directly change the operating cost of the DGs. However, batteries, and specifically the power management scheme, can affect the total operational cost of the MGs by scheduling appropriate amount of power import from the neighboring MGs and charging/discharging cycles of the ESSs. Energies 2022, 15, 1774 7 of 13 2.4. COMM Agent Each MG has a communication agent (COMM), which maintains peer-to-peer com- munication with its neighboring MGs to facilitate energy exchange and create a power sharing scheme. However, the COMM agents do not share their internal information with each other to ensure privacy of data. The only data shared among the MGs are the maximum available power that can be exported/imported as well as the information on common boundary buses, such as bus voltage and power limits. The COMM agent collects information from the other agents in the MG, such as their available power and generation costs and the information from the DR agent. 2.5. Problem Formulation The proposed power management algorithm is expressed as a multi-objective con- strained optimization problem. The Nondominated Sorting Genetic Algorithm (NSGA-II) is used to find a set of global minima for multiple, nonlinear objective functions. NSGA-II is one type of multi-objective evolutionary algorithm, which finds a set of solutions to the multi-objective problems with an elitist nondominating sort-based approach, ensuring population diversity preservation [22]. The sets of solutions obtained by NSGA-II are Pareto optimal, meaning they have a ‘fair’ balance between the different objectives. In this approach, a parent population is defined among each generation based on the fitness of each individual. A child population is created from the parent population using binary tournament selection, crossover, and mutation. The parent–children combined population is sorted as per their rank of nondomination, whereas each member of the population is evaluated using the objective functions and the crowding distances. More detail about this approach is given in [22]. In this algorithm, the usage of crowding distance as a measure of fitness ensures preservation of diversity. Meanwhile, the inclusion of the fittest chromosomes from the previous generation in the next generation reassures higher fitness properties (elitism). While the overall objectives include maximizing the load coverage and minimizing the operating cost, these objectives may be contradictory of each other and therefore a set of fair tradeoff solutions is obtained. The extent and weightage of the tradeoff for each objective can be defined by the MG operator to reach either lower operational costs or minimum load curtailments. 3. Test System and the Solution Approach 3.1. Test System The effectiveness of the proposed algorithm is evaluated using a modified 4-MG benchmark system [23], shown in Figure 4. A normally closed switch exists on the tie-lines between the MGs, giving the MGs the ability to import and export power. Hourly load data were taken from [23] considering a monsoon weekday. Only solar PV was considered in the modified benchmark, and the hourly PV profile was also generated from [23] considering a cloudy day during week 23–24. The total MVA capacity of the onsite SG and MWh capacity of the ESS units for each MG are given in Table 1. Table 1. MG Generation and storage power capacity. MG SG ESS(MVA) (MWh) 1 15 10 2 6 12 3 6 12.4 4 4 12 Energies 2022, 15, x FOR PEER REVIEW 8 of 14 3. Test System and the Solution Approach 3.1. Test System The effectiveness of the proposed algorithm is evaluated using a modified 4-MG benchmark system [23], shown in Figure 4. A normally closed switch exists on the tie-lines between the MGs, giving the MGs the ability to import and export power. Hourly load data were taken from [23] considering a monsoon weekday. Only solar PV was considered in the modified benchmark, and the hourly PV profile was also generated from [23] con- Energies 2022, 15, 1774 sidering a cloudy day during week 23–24. The total MVA capacity of the onsite SG 8aonfd1 3 MWh capacity of the ESS units for each MG are given in Table 1. Figure 4. Single line diagram of the modified benchmark 4-MG test system [23]. Figure 4. Single line diagram of the modified benchmark 4-MG test system [23]. A 24-h power management simulation is performed on each MG using parallel pro- Tcaebslsei n1.g MwGit Gheanetirmateiosnt eapndo sft1orhag. e power capacity. Energies 2022, 15, x FOR PEER REVIEW The set of solutions found lie on a threSeG-d imensional Pareto front asEshSoSw n in Fig9 uorfe 154. The set of PMarGet o optimal solutions is (hMigVhlAig) hted in blue, while th(eMsWetho)f all feasible solutions is sh1o wn in black. 15 10 2 6 12 3 6 12.4 4 4 12 A 24-h power management simulation is performed on each MG using parallel pro- cessing with a time step of 1 h. The set of solutions found lie on a three-dimensional Pareto front as shown in Figure 5. The set of Pareto optimal solutions is highlighted in blue, while the set of all feasible solutions is shown in black. Fiigurre 5.. Allll ffeeassiibllee ssolluttiionss and tthee opttiimall ssolluttiionss on tthee Parreetto ffrronttiieerr.. 3.2. Extreme Event 3.2. Extreme Event An extreme event is forecasted at hour 2, which prompts the ESS to begin charging in ordAenr etoxtbreempree epvaerendt ifso rfotrheecaesxtterdem aet hevouenr t2t,h wathoicchcu prrsoamt phtosu trh8e aEnSdS ltaos tbseugninti lchhoarugrin20g, idnu orirndgerw thoi bche ptirmeepathreedu ftoilrit tyhge reidxtirsempreo jeevcteendt ttohabtl aocckcuorust .atA hsoaurre 8s ualntdo flathstes euxntrteilm heouevr e2n0t,, dthueriwngh owlehniceht wtiomrke itshed iusctiolintyn egcrteidd ifsr opmrotjehcetegdri dto, abnladckea ochutM. AGs ias orepseurlatt ionfg thine ieslxatnredmede event, the whole network is disconnected from the grid, and each MG is operating in is- landed mode. At the same time, the generator in MG3 is considered out of service, causing a shortage of available power in that MG. Therefore, the MG3’s only available resources are its ESS and solar PV power production. 3.3. The Agent-Based Solution Process In the case of an extreme event, the solution process initiates with each DG agent determining its available generation and the generation costs, based on the local data. The ESS agent in each MG creates an optimal solution based on the output of the DG agent and the required power to supply the critical loads. The DG agent will then respond to the solution of the ESS agent by reassessing its available generation. If the DG agent is down, for example, in MG3, the solution process initiates with the ESS agent. After the ESS agent has reached an optimal solution, the DR agent will create a set of optimal solutions. It is up to the operator to select a solution set from the DR agent based on the weight of importance assigned to customer discomfort and the cost of power import. Finally, the solutions are sent to the neighboring MGs to reconnect and effectively create an optimal power sharing scheme. The flow chart for the power management process is shown in Figure 6. Energies 2022, 15, 1774 9 of 13 mode. At the same time, the generator in MG3 is considered out of service, causing a shortage of available power in that MG. Therefore, the MG3’s only available resources are its ESS and solar PV power production. 3.3. The Agent-Based Solution Process In the case of an extreme event, the solution process initiates with each DG agent determining its available generation and the generation costs, based on the local data. The ESS agent in each MG creates an optimal solution based on the output of the DG agent and the required power to supply the critical loads. The DG agent will then respond to the solution of the ESS agent by reassessing its available generation. If the DG agent is down, for example, in MG3, the solution process initiates with the ESS agent. After the ESS agent has reached an optimal solution, the DR agent will create a set of optimal solutions. It is up to the operator to select a solution set from the DR agent based on the weight of importance assigned to customer discomfort and the cost of power import. Finally, the solutions are sent to the neighboring MGs to Energies 2022, 15, x FOR PEER REVIEWre connect and effectively create an optimal power sharing scheme. The flow char 1t0f oorf t1h4e power management process is shown in Figure 6. FFigiguurere 66. .AAggenent-tb-basaesded mmicircoroggrirdid ppoowweer rmmaannaaggeemmeennt tpprorocceessss. . 44. .SSimimuulalatitoionn RReesusultlst s Figure 7 shows the simulation results for the sharFiniggu.rAe n7 sehxotrwems tehee vsiemntuilsatfioorne craessuteldts afot rh tohuer fo fouur rininte2, to sttaerrc r to connnneectceted MGat hourd8 .MFGrosm swwitihthoouhourut t power 2p, aolwl tehre shMaGrisnsgt.a Artnim exptorretmineg epvoewnet risf rfoomrecthaestgerdi datt ohcohuarr 2g,e ttoh esitrarEtS aSt ihnopurre p8.a rFartoiomn hfoorutrh 2e, eaxltlr tehmee MevGesn st.taOrtn icme pthoerteinxtgr epmowe eevr efnrot moc cthuers gartidh otou rc8h,atrhgee itnhteeirrc oEnSnSe icnt epdreMpGarsadtiiosnc ofnonr etchtef reoxm- trtehme me eavinengtr.i dOnanced tohpee erxattreeimn es teavnednatl ooncecumrso adte h. Touhre 8im, tphaec itnotefrtchoenenxetcretemde MevGesn dt iisscmoninniemcat l froonmth tehhe emalathiny gMriGds a1n,d2 ,oapnedra4t,ea isnt hsetayncdaanlosunep pmlyodthee. iTr hoew inmdpeamcta nodf .thHeo ewxetrveemr,eb eecvaeunste ios f mthineicmoainl coind etnhtea hl leoaslsthoyf cMonGvse 1n,t i2o, naanldg e4n, aersa tthioeny icnanM sGu3p,pitlyfo trhceeisr tohwe nD Rdeamgeanntdt.o Hdorawsetivcaerll,y bceucratuasilel oofa dthse. Tcohiennciodnecnrittailc alolslos aodf scoonf vMeGnt3ioanrealc guertnaeirleadtioann dini tMs aGv3a,i liat bfolercreesso tuhrec DesRa aregeanblte to drastically curtail loads. The noncritical loads of MG3 are curtailed and its available resources are able to supply all its critical loads except for the last two hours of the extreme event. During the last hour of the extreme event, all loads are curtailed in MG3, causing a complete blackout. Therefore, the overall system resiliency is compromised. Energies 2022, 15, 1774 10 of 13 Energies 2022, 15, x FOR PEER REVIEW 11 of 14 to supply all its critical loads except for the last two hours of the extreme event. During the Energies 2022, 15, x FOR PEER REVlIaE sWt hour of the extreme event, all loads are curtailed in MG3, causing a complete11b loafc k14o ut. Therefore, the overall system resiliency is compromised. FFiFiggiugurureere 77 .7. I.I nInntteteerrcrccooonnnneecctteedd MMGGss iiinn ooofffff---gggrrriididd mm mooodddee eaa nannddd ww witihitthohououtu tptp opwoowewre esrrhs ashhraianrrignin. gg.. DDuueee t too tthhee ppoooorrr rrreeesssiililiileeiennccece e oofof t fthhtehe s esyyssstyetsemtme, mt, ht,he tenh eneeedne edfoe fdro arf oparo pwaoewpr oeswrh aserhriansrghi nsagcrh isnecmgheesm cihse ee mivsi -evisi- edvdeiendnte.t n.T Tth.heTe hr reessruuellsttsus lootfsf ttohhfeet MheGGM ppGoowpeoerrw s shehararsirhningag rsi onsolgulutsiotoilnou,n tbi, oabsnae,sdbe daosn oe mnd imonniimnmiimzininiizgmi ntihgze itn hogev etohrvaeellor oavplel- roapll- oeperareatritanitnging c gcoocssottss t osoffo MMf MGGG33,,3 aa,rraeer eddedeppeipicctitceetdde di nini nF FiFgigiuguruer re8e .8 8B. .ByB yiym iipmopprotoirnrttiginn pggo pwoewr efrro fmro imts intse ingehibgohrbinogrri ing MMGGsss d duurririningg t ththeee eeexxxtttrrreeemmeee eeevvveeennttt,,, ttthheee c ccuuurrtrtataaiilielleded l olloaadd in iin M MGG3 3i3s i isssi sgsinigginfniicififaicncatalnnytt lrlyed rreuedcdeuudcc eefdro fmfrro om 88282.2.99.797%7% oo offf tt hthheee t totoottataalll l lloooaaaddd,,, tttooo 333111...555777%%;; ;t tthhhuuusss,, ,tt hthhee ess ysyysststetemem rer reseislsiilieilneiencnycc yhyah hsa aismsi mipmrpoprvroeovdve.e dd. . Figure 8. Interconnected MGs in off-grid mode and with power sharing. FFiigguurreeF 88u.. rIIntnhtteerrcmcoononnrnee,cc tbteeydd c MoMnGGdssu iincnt ioonfffgf-- gtghrrieidd Mm mOoodPde eaa nannddd tw hweiit tphhrp opopowowesererds sh hpaaorriwningeg.r. sharing scheme, MG3 is able to find optimal solutions that reduce its operating costs during the extreme event. The Ffiunratlh seorlmutoioren, ibsy s ecloenctdeudc ttoin rged thuece M thOeP o avnerda ltlh oep perroaptinosge cdo sptos.w er sharing scheme, MG3 is able to find optimal solutions that reduce its operating costs during the extreme event. The final solution is selected to reduce the overall operating costs. Energies 2022, 15, 1774 11 of 13 Energies 2022, 15, x FOR PEER REVIEW 12 of 14 Furthermore, by conducting the MOP and the proposed power sharing scheme, MG3 is able to find optimal solutions that reduce its operating costs during the extreme event. The final solution is selected to reduce the overall operating costs. TTaabbllee 22 sshhoowws sthteh eopoepreartaintign cgocsot,s ctu, sctuosmtoemr deriscdoismcofomrtf ocortstc, ogsetn, egreantieorna tcioosnt,c aonsdt, paenrd- cpeenrtc elonatdlo caudrtcauilrmtaeilnmt efonrt dfoifrfedrieffnetr ewnetigwheti gfahcttofarcst (oGrsc (aGncda Dncd).D Dcc). iDs tchies wtheeigwheti gfahcttofarc atos-r saoscsioactieadte wdiwthi tthheth leoaloda dcucrutartilamilmenetn atnadn dcucsutsotmomere rddisicsocmomfofrotr,t a, anndd GGcc isis ththee wweeiigghhtt ffaaccttoorr aassssoocciiaatteedd wiitthh tthee ttottall opeerrattiionaall ccosstt.. Thhee weeiigghhtt vaallueess fforr tthee miiniimum opeerrattiing ccosstt ooff MG33 aarree hhiigghhlliigghtteed.. Hooweevveerr,, tthe oopeerrattorr off MG33 ccoouulld sseelleecctt aa ddeessiirreedd ttrraaddeeooffff ssolluttiioonn,, ffoorr eexxaamppllee,, aa sseett ooff weeiigghhtt vvaalluueess tthhaatt maayy rreessuulltt iinn rreedduucceedd llooaadd ccuurrttaaiillmeenntt, , butt wiith an increase iin tthee ooppeerraattiinnggc coosst.t.A Alllw weeigighhtetedds osolulutitoinosnsfo froMr MGG3 3a raerpe rpersesnetnedteidn iFni gFuigruer9e. 9. Table 2. Weighted Power Request Options (MG3). Total Genera Total Customer WWeeigighhtsts Load Currttaiilled Total Gene torar tor Total CustomerDiDscioscmCosCt ost o fmofrot rt Operrattiing Costt (G(Gcc, ,D Dcc) ) ((%)) (US(UDS) D) Co Csot st (USD) (U(SUDS)D ) 11.0.0, ,0 0.0.0 6600..0000 511551 15 111,111,141 4 1166,,222299 00.6.6, ,0 0.4.4 47..81 724732 43 7473423 2 14,675 00.5.5, ,0 0.5.5 31..58 10,31502,3 52 353656 5 13,917 00.4.4, ,0 0.6.6 2200..3377 12,61128,6 18 1619649 4 1144,,331122 00.3.3, ,0 0.7.7 1111..7744 14,41644,4 64 71711 1 1155,,117755 00.2.2, ,0 0.8.8 44..9966 15,91258,9 28 21241 4 1166,,114422 00.1.1, ,0 0.9.9 00..0044 16,91963,9 93 1 1 1166,,999944 0.0, 1.0 0 17,006 0 17,006 0.0, 1.0 0 17,006 0 17,006 FFiiggurree 99.. Weiightted power request options (MG3). 55.. CCoonncclluussiioonnss IInn tthhiiss ppaappeerr,, aa rreessiilliieenntt aaggeenntt--bbaasseedd ppoowweerr mmaannaaggeemmeenntt sscchheemmee iinnvvoollvviinngg aaccttiivvee ppoowweerr sshhaarriinngg aanndd ccooooppeerraattiioonnb beetwtweeeennm muultlitpipleleM MGGs sin ina nanM MG-Gb-absaesdeddi sdtirsitbruibtiuotniosny sstyesm- theas been propThme hnaesi gbheebno rp orsoepdowseidth wthe iing MGs coimthm t nhteen int tteonitm top riomvpersystem resiliency and reduce opeunicate with eacohveo sthyestreomn raespileieenr-ctyo -apnede rrecdoumce r aotpinegractoinsts.municatiogn costs. The neighboring MGs communicate with each other on a peer-to-peer communica- tion basis through their communication agents while protecting their privacy of owner- ship by limiting the shared information only to the requested power and total generation Energies 2022, 15, 1774 12 of 13 basis through their communication agents while protecting their privacy of ownership by limiting the shared information only to the requested power and total generation capacities. It is shown that the overall system prepares for an upcoming extreme event in a fully decentralized and agent-based approach. The optimal solutions of these agents exist in the solution space containing an infinite number of possible solutions for the 24-h simulation horizon. To find those solutions, an evolutionary multi-objective solver algorithm, NSGA-II, is used to find the Pareto front, and the final solution is selected from the Pareto front. A benchmark power system model consisting of four MGs is used to evaluate the effectiveness of the proposed method. Simulation results show that using the proposed approach during the occurrence of an extreme event, even with the grid blackout and pos- sible unit failure in the system, the MGs can survive by helping each other when necessary. It is shown that by using the proposed method the system resiliency is improved and the operating costs are reduced, thus reinforcing the proposed power management scheme. Author Contributions: Writing—original draft preparation, conceptualization, validation, and in- vestigation, Z.S. and L.M.; writing—review and editing, formal analysis, and supervision, H.N. and M.B.; writing—review and editing, and funding acquisition, H.N. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the US National Science Foundation under Award 1806184 and by Montana State University. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. The US National Academies of Sciences, Engineering, and Medicine Report: Enhancing the Resilience of the Nation’s Electricity System. 2017. Available online: http://www.nap.edu/24836 (accessed on 10 November 2021). 2. Dehghanpour, K.; Colson, C.; Nehrir, H. A survey on smart agent-based microgrids for resilient/self-healing grids. Energies 2017, 10, 620. [CrossRef] 3. Dehghanpour, K.; Nehrir, H. An agent-based hierarchical bargaining framework for power management of multiple cooperative microgrids. IEEE Trans. Smart Grid 2019, 10, 514–522. [CrossRef] 4. Chen, C.; Wang, J.; Ton, D. Modernizing distribution system restoration to achieve grid resiliency against weather events: An integrated solution. IEEE Proceeding 2017, 105, 1267–1288. [CrossRef] 5. Lasseter, R.H. Microgrids. In Proceedings of the IEEE Power Engineering Society Winter Meeting, New York, NY, USA, 27–31 January 2002; Volume 1, pp. 305–308. 6. Dehghanpour, K.; Nehrir, H. A market-based resilient power management technique for distribution systems with multiple microgrids using a multi-agent system approach. Elec. Power Comp. Syst. 2018, 46, 1744–1755. [CrossRef] 7. Khodaei, A. Resiliency-oriented microgrid optimal scheduling. IEEE Trans. Smart Grid 2014, 5, 1584–1591. [CrossRef] 8. Gregoratti, D.; Matamoros, J. Distributed energy trading: The multiple-microgrid case. IEEE Trans. Indust. Electron. 2015, 62, 2551–2559. [CrossRef] 9. Deng, N.; Zhang, X. A novel management scheme of multiple microgrids via a common interface. In Proceedings of the 11th IET International Conference on AC and DC Power Transaction, Birmingham, UK, 10–12 February 2015; pp. 1–6. 10. Zhao, B.; Wang, X.; Lin, D.; Calvin, M.M.; Morgan, J.C.; Qin, R.; Wang, C. Energy management of multiple microgrids based on a system of systems architecture. IEEE Trans. Power Syst. 2018, 33, 6410–6421. [CrossRef] 11. He, L.; Wei, Z.; Yan, H.; Xv, K.-Y.; Zhao, M.-Y.; Cheng, S. A day-ahead scheduling optimization model of multi-microgrid considering interactive power control. In Proceedings of the 4th International Conference on Intelligent Green Building and Smart Grid (IGBSG), Yichang, China, 6–9 September 2019; pp. 666–669. 12. Herrera, M.L.; Subramanyam, S.A.; Zhang, X. Robust control and optimal operation of multiple microgrids with configurable interconnections. In Proceedings of the IEEE Green Technologies Conference, Lafayette, LA, USA, 3–6 April 2019; pp. 1–4. 13. Wang, L.; Li, Q.; Zong, X. Distributed optimization for energy transactions and production of multiple microgrids under uncertainty. In Proceedings of the Chinese Automation Congress (CAC), Hangzhou, China, 22–24 November 2019; pp. 1334–1338. 14. Oyarzabal, J.; Jimeno, J.; Ruela, J.; Engler, A.; Hardt, C. Agent based micro grid management system. In Proceedings of the International Conference on Future Power Systems, Amsterdam, The Netherlands, 18 November 2005; pp. 1–6. 15. Bahramipanah, M.; Cherkaoui, R.; Paolone, M. Decentralized voltage control of clustered active distribution network by means of energy storage systems. Electr. Power Syst. Res. 2016, 136, 370–382. [CrossRef] Energies 2022, 15, 1774 13 of 13 16. Zhang, C.; Wu, J.; Zhou, Y.; Cheng, M.; Long, C. Peer-to-peer energy trading in a microgrid. Appl. Energy 2018, 220, 1–12. [CrossRef] 17. Balakrishnan, H.; Tomar, K.K.S.; Singh, S.N. An agent-based approach for efficient energy management of microgrids. In Proceedings of the 2017 IEEE Region 10 Symposium (TENSYMP), Cochin, India, 14–16 July 2017; pp. 1–5. 18. Colson, C.; Nehrir, M.; Gunderson, R.W. Distributed multi-agent microgrids: A decentralized approach to resilient power system self-healing. In Proceedings of the 2011 4th International Symposium on Resilient Control Systems, Boise, ID, USA, 9–11 August 2011; pp. 83–88. 19. Hintz, A.S.; Prasanna, U.R.; Rajashekara, K. Hybrid multi-agent based resilient control for EV connected micro grid system. In Proceedings of the 2014 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, USA, 15–18 June 2014; pp. 1–6. 20. Shimim, F.N.; Baharamipanah, M.; Nehrir, H. Resilient and extreme event-aware microgrid using energy storage and load curtailment. In Proceedings of the North American Power Symposium, Wichita, KS, USA, 13–15 October 2019; pp. 1–6. 21. Haider, Z.M.; Mehmood, K.K.; Khan, S.U.; Khan, M.O.; Wadood, A.; Rhee, S.-B. Optimal management of a distribution feeder during contingency and overload conditions by harnessing the flexibility of smart loads. IEEE Access 2021, 9, 40124–40139. [CrossRef] 22. Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002, 6, 182–197. [CrossRef] 23. Alam, M.N.; Chakrabarti, S.; Liang, X. A benchmark test system for networked microgrids. IEEE Trans. Ind. Inform. 2020, 16, 6217–6230. [CrossRef]