
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12453-X
10.1016/j.heliyon.2024.e36422
e36422
Research Article
Resiliency planning of distribution network using of active distribution network partitioning
Khanavandi Hamid Amini
Gandomkar Majid majid.gandomkar@iau.ac.ir
⁎
Nikoukar Javad
Department of Electrical Engineering, College of Engineering Technology, Saveh Branch, Islamic Azad University, Saveh, Iran
⁎ Corresponding author majid.gandomkar@iau.ac.ir
16 8 2024
30 8 2024
16 8 2024
10 16 e364226 6 2024
12 8 2024
15 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Today, micro-grids (MGs) include all kinds of energy storage systems (ESSs), wind turbines (WTs), photovoltaic (PV), combined heat and power (CHP), etc., also demand response are active on the demand side. In this paper, single-level robust methods for partitioning and planning the active distribution network (ADN) into several MGs are presented. According to the desired purpose, the objective function of the model is investment costs minimization for installing the capacity of distributed generations (DGs) and switches, the activity of responsive loads based on the forecast of the generation of non- DG, losses and the risk of the load points of the costumers. On the other hand, maximizing the income from the MGs energy sales to the upstream grid and the technical constraints include optimal power flow (OPF) equations. The mentioned problem is a complex nonlinear model, and therefore, the improved genetic algorithm (GA) is used. In order to validate the efficiency, the improved method has been used on a 25-bus ADN including five switches. The simulation results obtained from the case studies prove the fact that the use of the retrofitted model increases the investment costs of the MG, especially in the case of an island operation, in contrast to the active presence of responsive loads that significantly reduce costs.

Keywords

Resiliency
Partitioning
Planning
Micro-grids (MGs)
Distributed generation (DGs)
Demand response (DR)
Uncertainty
==== Body
pmc Abbreviations

MG	Micro-Grid	DG	Distributed Generation	
GA	Genetic Algorithm	OPF	Optimal Power Flow	
DERs	Distributed Energy Resources	DR	Demand Response	
ADN	Active Distribution Network	DN	Distribution Network	
PV	Photovoltaic	WT	Wind Turbine	
RES	Renewable Energy Sources	ESS	Energy Storage System	
CHP	Combined Heat and Power	SW	Switch	

1 Introduction

Nowadays, MGs have been used in distribution networks with various structures to achieve the benefits of improving stability, power quality and reducing greenhouse gas emissions [1], often in a state connected to and disconnected from the upstream national distribution network. Wind turbine (WT) and photovoltaic (PV) sources in MGs have variable and unpredictable nature of generation, and ESS and participation of demand responses are used to cover the uncertainties of their operation [2].

Determining the appropriate installation location and capacity of DGs and ESSs to meet local demand and subscriber reliability is the most important challenge in planning MGs [3,4]. In the operational mode connected to grid, the MG reliability subscribers is provided by the national network, and only the regulation of exchanges with the upstream national network is of great importance [5].

In the past, MGs were planned and operated based on certain criteria of reliability to face uncertainties, but in this method, the actual conditions of the system were not taken into account, and as a result, to improve the accuracy of calculations with the method Probabilities were replaced [6,7]. The main planning purpose is actually determine the state of connection of MGs to each other or to the national network, the location and capacity of installing distributed production sources and their energy storages according to the level of participation of responsive loads and the reliability of subscriber load points.

Resilience methods are used as one of the types of probabilistic methods for planning MGs to optimize system costs even under the worst scenarios of using WT and PV resources due to redundancy and or the lack of production is guaranteed. Due to the discussion importance, many works have been done in this study, for example, a retrofitted model for optimal planning of the capacity of MGs connected to the national grid during different production scenarios with the aim of increasing Productivity of production resources and minimization of operating costs and emission of greenhouse gases have been developed in Ref. [8]. In Ref. [9], a robust model was proposed for the operation of the MG under the current market conditions, considering the uncertainties of the production of PV and WT sources as well as the load.

In [10], a modified model of multi-period investment planning with regard to the growth of load demand and depreciation of equipment with time to support the decision of stakeholders in determining the optimal size and also the time of investment on resources. Dispersed generation of MGs separated from the national distribution network is discussed.

In [11], a robust method is introduced to minimize the energy generation costs of MGs equipped with variable production sources and sources of simultaneous production of electricity and heat, which takes into account the fluctuation of thermal load demand in addition to electrical give In Ref. [12], a two-stage reinforced planning model for dealing with the worst scenarios has been built based on the gray relation theory, which can decrease the uncertainty of the WT-PV-ESS hybrid system.

In [13], a method of planning offshore MGs with minimum cost is proposed, which consider the fluctuations of oceanic production resources through model retrofitting. In Ref. [14], a robust model for minimization of MG costs including storage resources and simultaneous production of electricity and heat according to operational uncertainties such as variable production of PV sources, variable consumption Heaters and coolers have been developed, which are solved through the port decomposition method. In Ref. [15], the economic exploitation of several MGs is formulated as a problem in the placement of units, and to solve it, a two-stage adaptive retrofit approach is used for residential MGs according to the worst PV scenarios.

Also, in Ref. [16] an [17], a model has been used to improve the renewable energy sources (RESs) performances and decrease their power fluctuations.

In [18], a multi-stage retrofitted energy management model for MGs connected to the national grid has been developed considering the renewable resource and demand uncertainty. In Ref. [19], a retrofitted MG segmentation program has been proposed for maximum load recovery when faced with a set of operational uncertainties, observing the radial constraint of the ADN structure. The summary of recent studies shows that the planning and operation of MGs still requires models due to the existence of operational uncertainties such as shortage-surplus production of PV and WT as well as load fluctuations.

In [20], network partitioning has been done considering the demand side response program. In Refs. [[21], [22], [23]], models for estimating the electrical equipment life have been examined.

Optimal load distribution has been checked by method 1 and by coding in MATLAB software in Ref. [24]. According to this reference, optimal load distribution has been checked as single objective optimization. Reference [25] also investigated the optimal load distribution by 2. Also, reference [26] has investigated the optimal load distribution by method 3 and using the fuzzy mechanism.

Also, wind turbine power output has been improved by using virtual wind speed forecasting in the grid in Ref. [27].

Forecasting the impact of disasters on the power grid using artificial intelligence has been investigated in Ref. [28]. Also, the use of recovery methods to increase the flexibility of power grids has also been stated according to Ref. [29] and its results have been analyzed. The use of hydrogen sources, which is widely used as a modern electricity generation technology, is also stated in Refs. [30,31].

In this paper, single-level retrofitted method for distribution network partitioning and planning in the form of several micro-grids with the aim of minimizing the costs of grid is presented, where the installation location and the capacity of distributed generations, the installation location of switches, the utilization capacity of DG, the participation of responsive loads, the level of exchanges of MGs with the upstream network, as well as the risk of subscriber load points are optimally determined based on the forecast of the production of non-DG.

The limitations of solving the problem in this paper are as follows.• Maximum installation capacity of DGs and energy storage systems,

• Reactive compensators,

• Participation of responsive loads and the maximum number of switches,

• optimal utilization capacity at each load level

• power balance constraints

• Charge and discharge level of SEEs

So, the contributions are as follows.• Proposed single-level method for planning and partitioning of ADN.

• Minimized the costs of several micro-grids in distribution network according to new indices and limitation.

• Proposed new resiliency approach for the planning and partitioning of AND.

• Proposed GA methodology for the planning and partitioning of AND.

So, in section 2, the proposed retrofitting approach is described and the risk formulation corresponding the WT and PV resources uncertainties is done. In section 3, the proposed method of the objective function and technical limitations are described. In part 4, coding of the reinforced model is done with the aim of planning and partitioning the ADN in the form of several MGs by genetic algorithm. In section 5, simulation studies are performed on 25-basin system to validate and confirm the effectiveness of this model, and in section 6, conceptual results are stated.

2 Resilience and risk of ADN including several MGS

To solve of the problem and related optimization, it is necessary to state proposed resiliency approach and uncertainty modeling and shortage-surplus risk of WT and PV. After achieving this initial plan, the problem can be solved. In this section, the proposed retrofitting approach is explained and the mathematical formulation of the risk corresponding to the operational uncertainties caused by the shortage and surplus of WT and PV resources is done.

2.1 Proposed resiliency approach

One of the most common ways to resiliency the optimization models against the occurrence of various possible and valid scenarios is the minimization of the mathematical hope of the desired objective function. Often, the objective function in such problems is defined based on economics, which is actually known as a stochastic model. In this article, in order to strengthen the proposed method for the partitioning and planning of the ADN in the form of several MGs under the occurrence of different scenarios of shortage and excess of WT and PV resources, equation (1) is used.(1) uE(OFi)=s.t.→Xi∑Sci=1ScnPriSci.OFiSciXi={IPMGs,DERsBuses,IPMGsESSsBuses,IQMGs,DRSsBuses,NSWsLines,PGMGs,DERsBuses,LLs,SCs,SoCMGs,ESSsBus,LLs,SCs,QGMGs,DRSBus,LLs,SCs,PMGs,DRsBus,LLs,SCs,PMGs,ExchangesBus,LLs,SCs,PMGs,ShedBus,LLs,SCs}DERs→{PVs,WTs,CHPs}LLs→{LL1,LL2,...,LLk},Buses→{Bus1,Bus2,....,Busm},Lines→{Line1,Line2,...,Lineh}OFiSCs=f(Xi,Sc1,Sc2,...,Scn)→{OFiSc1,OFiSc2...OFiScn}

If there is no guarantee for the occurrence of a specific scenario for the planning and segmentation of MGs of the ADN, then the process will be executed for a certain level on all the parameters space with uncertainty, and in addition, attention to the evaluations The surplus of technical and economic strengthening is necessary. Here, a unique type of economic retrofitting evaluation is considered according to the worst scenario with the highest cost according to equation (2). The final solution of the problem is strengthened based on the cost of the worst possible scenario and mathematical hope on all scenarios according to equation (3).(2) uWC(OF)=Max{OFiSci|Sci=Sc1,Sc2,..,Scn}

(3) OFRobust=MinXi(uE(OF),uWC(OF))

2.2 Uncertainty modeling and shortage-surplus risk of WT and PV

As mentioned, WT and PV resources assigned in each MG have variable production and it is not possible to accurately predict their production. In this section, the formulation of the risk corresponding to the uncertainty mentioned in the improved model of planning and segmentation of the ADN in the form of several MGs with regard to the activity of responsive loads, the presence of ESS and the possibility of disconnecting the load of subscribers to establish balance between total production and consumption is done according to equation (4).(4) RiskMMGsTot=∑MGi=1MGw(∑LLi=1LLk∑Sci=1Scn∑Busi=1BusmPrMGiSci×{PMGs,ShedBus,LLi,Sci×VollMGi,ShedBus})

It is possible to determine the value of load shedding from each bus if it is not possible to establish a balance between production and consumption of active and reactive power in MG buses during various operating scenarios through exchange with upstream, participation of responsive loads and energy storage in each The MG was calculated according to the equations (5), (6).(5) {PGMGs,DERsBuses,LLs,SCs+PMGs,ESSs(DisCh)Bus,LLs,SCs+PMGs,Exchanges(Buy)Bus,LLs,SCs=PMGs,DemandBus,LLs,SCs+PMGs,Exchanges(sell)Bus,LLs,SCs+PMGs,ESSs(Ch)Bus,LLs,SCs−PMGs,DRs±Bus,LLs,SCs−PMGs,ShedBus,LLs,SCs

(6) {QGMGs,DERsBuses,LLs,SCs+QMGs,ESSs(DisCh)Bus,LLs,SCs+QMGs,DRSsBus,LLs,SCs+QMGs,Exchanges(Buy)Bus,LLs,SCs=QMGs,DemandBus,LLs,SCs+QMGs,Exchanges(sell)Bus,LLs,SCs+QMGs,ESSs(Ch)Bus,LLs,SCs−QMGs,DRs±Bus,LLs,SCs−QMGs,ShedBus,LLs,SCs

The above equations must be established for all network buses. It should be noted that buying and selling energy, charging and discharging the battery, increase and decrease in consumption of responsive loads do not happen simultaneously. However, extracting different WT resource utilization scenarios (n wind scenario) and PV (m radiation scenario) of each of the MGs by using the tree-probability tool through the probability distribution function according to equations (7), (8), (9), respectively.(7) {OSMGi,WTsSCs={(PGMGi,WTsBuses,LLs,Sc1,PrMGi,WTsBuses,LLs,Sc1),(PGMGi,WTsBuses,LLs,Sc2,PrMGi,WTsBuses,LLs,Sc2),....,(PGMGi,WTsBuses,LLs,Scn,PrMGi,WTsBuses,LLs,Scn)}PrMGi,WTsBuses,LLs,Sc1+PrMGi,WTsBuses,LLs,Sc2+........+PrMGi,WTsBuses,LLs,Scn=1

(8) {NMGiSCs=n(OSMGi,WTsSCs)×n(OSMGi,PVsSCs)PrMGiSCs=(PrMGi,WTsBuses,LLs,Sc1×...×PrMGi,WTsBuses,LLs,Scn)×(PrMGi,PVsBuses,LLs,Sc1×....×PrMGi,PVsBuses,LLs,Scm)

(9) {NMMGsSCs=NMG1SCs×NMG2SCs×.....×NMGwSCsPrMMGsSCs=PrMG1SCs×PrMG2SCs×.....×PrMGwSCs⇒∑Sci=1ScnPrMMGsSCi=1

3 Proposed methodology

The proposed method includes the objective function and technical constraints for planning and partitioning the active distribution network in the form of several MGs have been discussed in this section.

3.1 Objective function

Minimization of investment costs for the installation capacity of distributed generation sources and energy storages, as well as segmentation switches of active distribution grid MGs, maintenance and operation costs of distributed generation sources and energy storages, losses, the risk of subscriber load points, the participation of responsive loads, the purchase of energy from upstream network, and on the other hand, the energy sale by the MG is deducted from the overall costs. Therefore, the overall objective function includes two parts according to equations (10), (11), (12).(10) OFi(MMGs)SCs=OFi(MMGs)Planning+OFi(MMGs)Operation,SCs

(11) OFi(MMGs)Planning=∑MGs{∑i(DERs)(ICi(DERs)Tot+OMi(DERs)Tot)+∑i(ESSs)(ICi(ESSs)Tot+OMi(ESSs)Tot)+∑i(DRSs)(ICi(DRSs)Tot+OMi(DRSs)Tot)}+∑i(SWs)(ICi(SWs)Tot+OMi(SWs)Tot)

(12) OFi(MMGs)Operation,SCs=∑MGs{∑LLi=1LLk[(PMGs,Exchanges(Buy)Bus,LLi,SCs×EPMGs,ExchangesLLi)−(PMGs,Exchanges(Buy)Bus,LLi,SCs×EPMGs,ExchangesLLi)]}+∑MGs{∑LLi=1LLk(RiskMGsLLi,SCs+PLCMGsLLi,SCs)+∑i(DERs)∑LLi=1LLk(OCi(DERs)LLi,SCs+OCi(ESSs)LLi,SCs)}

In the above equations, the cost of using energy storages and compensators and WT and PV sources is considered zero. The exchange cost with the upstream grid is calculated based on energy price at corresponding load level. In addition, the risk of the subscriber's load points is calculated according to the value of load shedding during that operating scenario and the amount of the lost demand of the subscribers.

3.2 Technical limitations

In order to plan and optimally divide the active distribution network into several MGs, the maximum installation capacity of distributed generations and energy storage systems, reactive compensators, the participation of responsive loads and the maximum number of switches according to the equation block (13) should be entered in the modeling.(13) {IPi(DERs)MGi≤PDERsCap−max→(PVs,WTs,CHPs)∈DERsIPi(ESSs)MGi≤SoCESSsCap−maxIQi(DRSs)MGi≤QDRSsCap−maxIPi(DRs)MGi≤PDRsCap−maxNSWsMin≤Ni(SW)MGi≤NSWsMax

To determine the optimal utilization capacity at each load level, the technical limits of production of distributed generations, energy storage systems, reactive compensators and responsive loads in each MG should be taken into account according to the equation (14).(14) {PGMGs,DERsBuses,LLs,SCs≤IPi(DERs)MGiPMGs,ESSs(DisCh/Ch)Bus,LLs,SCs≤IPi(ESSs)MGiPMGs,DRs±Bus,LLs,SCs≤IPi(DRs)MGiQMGs,DRSsBus,LLs,SCs≤IQi(DRSs)MGi

Here, it is assumed that according to the energy price, MGs can exchange power without restrictions, but for optimal network load distribution, power balance constraints (5) and (6) along with equations (15), (16) are used.(15) Pnet,MGsBusi,LLs,SCs=VMGsBusi,LLs,SCs∑Busj=1Busi≠BusjNBVMGsBusj,LLs,SCs(Gij.cos(δMGs(Busi,Busj),LLs,SCs)+Bij.sin(δMGs(Busi,Busj),LLs,SCs))

(16) Qnet,MGsBusi,LLs,SCs=VMGsBusi,LLs,SCs∑Busj=1Busi≠BusjNBVMGsBusj,LLs,SCs(Gij.sin(δMGs(Busi,Busj),LLs,SCs)−Bij.cos(δMGs(Busi,Busj),LLs,SCs))

The above equations show the relationship between active and pure reactive power injection with angle and magnitude of bus voltage. By using the optimal load part, the transmission power from the branches, the bus voltage and the losses of all MGs during operation are determined at the load levels, and the currents and voltages should be within the permissible limits according to equations (17), (18).(17) VMGsBusi,Min≤VMGsBusi,LLs,SCs≤VMGsBusi,Max

(18) IMGs(Busi,Busj),Min≤IMGs(Busi,Busj),LLs,SCs≤IMGs(Busi,Busj),Max

For all operating scenarios, optimal load distribution is carried out on MGs, and during the scenarios of insufficient production of wind turbine and photovoltaic resources, load shedding value is calculated. So, amount of the lost demand of the subscribers, the risk of the load points of the subscribers is determined, which is limited to the maximum value according to equation (19) for each MG.(19) RiskMGsTot≤RiskMGsMax

The operating cost of reactive compensators and scattered production sources of wind turbine is assumed to be zero, and the maintenance cost of wind and photovoltaic turbines is modeled according to equation (20). Meanwhile, the cost of exploiting scattered production resources is included in model only for simultaneous production of electricity and heat according to equation (21).(20) OMi(DERs)Tot=∑MGi[(λPViMGi×PMGi,PViBus,LLs)+(λWTiMGi×PMGi,WTiBus,LLs)]

(21) OCi(DERs)Tot=∑MGi∑LLs∑SCs[αi+Bi×(PMGi,CHPiBus,LLs,SCs)+γi×(PMGi,CHPiBus,LLs,SCs)2]

According to the power capacity, energy storages cover part of the uncertainty of wind turbine and photovoltaic sources production in each MG. When there is a shortage of production in the MG, they are discharged and when there is an excess of production, they are charged to prevent imbalance between production and consumption in the MG. This function of energy storages is included in the model by equations (22), (23).(22) bMGs,ESSs(DisCh)Bus,LLs,SCs+bMGs,ESSs(Ch)Bus,LLs,SCs≤1→bMGs,ESSs(DisCh)Bus,LLs,SCs,bMGs,ESSs(Ch)Bus,LLs,SCs∈{1,0}

(23) SOCbMGs,ESSs(Ch)Bus,LLs+1,SCs=SOCbMGs,ESSs(Ch)Bus,LLs,SCs+[(ηBattC×PMGs,ESSs(Ch)Bus,LLs,SCs×bMGs,ESSs(DisCh)Bus,LLs,SCs)−(PMGs,ESSs(DisCh)Bus,LLs,SCs×bMGs,ESSs(DisCh)Bus,LLs,SCsηBattdisc)]

In each of the MGs, the peak hour demand during the year is determined from the long-term forecast and the load levels from the short-term forecast, in addition, the radiation and wind conditions in the region are also predicted. As a result, the production amount of photovoltaic and wind turbine resources is almost certain. The main criterion for the owners of each of the MGs to sell and buy energy from or to the upstream network is economic issues according to equation (24). Therefore, its optimal value is determined through cost-benefit analysis in the objective function.(24) {if→PGMGs,DERsBuses,LLs,SCs+PMGs,ESSs(DisCh)Bus,LLs,SCs≤PMGs,DemandBus,LLs,SCs→PMGs,Exchanges(Buy)Bus,LLi,SCs=0,PMGs,Exchanges(sale)Bus,LLi,SCs>0if→PGMGs,DERsBuses,LLs,SCs+PMGs,ESSs(DisCh)Bus,LLs,SCs<PMGs,DemandBus,LLs,SCs→PMGs,Exchanges(Buy)Bus,LLi,SCs>0,PMGs,Exchanges(sale)Bus,LLi,SCs=0

In general, the surplus production of MGs is first consumed by the responsive loads with a higher priority, and if the balance is not established, the rest is stored in the energy storage, and if the generation and consumption balance is not established, so the rest sold to the upstream grid. However, if the production is less than the forecast, then the responsive loads will decrease their consumption with a higher priority, and then the energy storages will be in a discharge state. It is done and if the generation and consumption balance is not established in the MG, the load shedding tool is used to create balance.

4 Planning and partitioning optimization of ADN

Since the partitioning and planning of the ADN by means of load distribution equations is considered a complex nonlinear problem, therefore, genetic meta-heuristic methods are used in this section to solve the proposed model. Genetic algorithm is one of the methods of searching and solving mathematical optimization problems based on natural genetic mechanisms and selection of survival of the fittest, which is equivalent to the initial random solutions of the programming and partition problem from the production of the initial population of chromosomes. The classification of the MG includes the location, capacity of installation and operation of distributed generation sources including wind turbine sources, photovoltaics and CHP energy and heat generators, DRS reactive compensator, ESS, participation of DR responsive loads and SW tie switches from the location. Candidates are started according to all distribution network exploitation scenarios due to the presence of PV and WT according to Table (1).Table 1 Chromosome structure to solving the resilience problem of ADN planning and partitioning.

Table 1MG1 … MGw	
IPDERs,ESSs,DRSs,DRs(Bus1..Busm)	PDERs,ESSs,DRSs,DRs(Bus1..Busm)	SW1(Bus1,Bus2),...,.SWk(Busi,Busj)	

In the structure of the sample chromosome, the number of MGs covered by the studied ADN is w, and m is the number of candidate places equivalent to buses for installing and operating each of the sources of distributed generation, ESS, and reactive compensators. Of course, the arrangement of MGs is determined by choosing the optimal location for installing switches from h number of candidate branches. For the first iteration of the algorithm, the population is randomly generated and so the fitness score of population of chromosomes is calculated according to the objective function of the proposed model according to equations (10), (11), (12), (1), (1), (2), (3). Any violation of constraints (13)–(24) is calculated as a penalty according to equation (26) and appears in the fitness function according to equation (25).(25) fitnessi(MMGs)GA=OFi(MMGs)SCs+∑MGi=1MGw∑limit=1nlPenaltiesMGiLimitj

(26) PenaltiesMGiLimitj=|VarMGilimitj−VarMGitargetj|×10+6

Based on this, the chromosome with less fit is arranged in higher priority for the execution of the algorithm in the next iteration to be subjected to the crossover process according to Table (2). After applying the intersection operator, the jump operator is used according to Table (3).Table 2 Apply the intersection operator to the two parent chromosomes.

Table 2SW1(Bus1,Bus2),...,.SWk(Busi,Busj)	PDERs,ESSs,DRSs,DRs(Bus1..Busm)	IPDERs,ESSs,DRSs,DRs*(Bus1..Busm)	
SW1(Bus1,Bus2),...,.SWk(Busi,Busj)	PDERs,ESSs,DRSs,DRs*(Bus1..Busm)	IPDERs,ESSs,DRSs,DRs*(Bus1..Busm)	

Table 3 Apply mutations to two new child chromosomes.

Table 3SW1**(Bus1,Bus2),...,.SWk**(Busi,Busj)	PDERs,ESSs,DRSs,DRs(Bus1..Busm)	IPDERs,ESSs,DRSs,DRs*(Bus1..Busm)	
SW1(Bus1,Bus2),...,.SWk(Busi,Busj)	PDERs,ESSs,DRSs,DRs**(Bus1..Busm)	IPDERs,ESSs,DRSs,DRs*(Bus1..Busm)	

From the algorithm point of view, the intersection and mutation operators were considered as tool to apply changes in current evolving answers. Therefore, as mentioned, in the process of solving the improved problem of planning and partitioning the active distribution network, instead of working on the parameters or variables of the problem, the intelligent genetic algorithm works with their coded form called chromosome. The genetic solution flowchart of the proposed methodology is shown in Fig. (1). The conventional GA is mentioned in the appendix section.Fig. 1 Flowchart of proposed GA methodology for the purpose of planning and partitioning the ADN.

Fig. 1

5 Numerical and simulation results

In this section, simulation works for validating and confirming the effectiveness of the proposed improved method for partitioning and planning of several MGs on a 25-bus test distribution grid with 12 kV and a substation capacity of 10 MVA has been used. As can be seen in Fig. (2), in the ADN structure under study, three sub-feeders are considered as potential places for equipment installation and investment as a MG. Five switches SW1 to SW5 are intended to connect MGs to each other and to the DN. For MG1, the set of branches between node 4 and node 18 is considered. This network is connected to the infinite network and has the ability to function as an island.Fig. 2 Single line diagram of the 25-base active standard DN under study.

Fig. 2

CHP1 and 2, PV1 and PV2, Batt1 and Batt2, and WT1 and WT2 are considered for this set. According to this figure, three reactive power compensators DRS1, DRS2 and DRS3 have been considered for installation. The minimum and maximum allowed capacity of each of them is 10 and 20 kVAr, 15 and 30 kVAr, 20 and 35 kVAr, respectively.

For MG2, the set of branches between node 23 and node 25 is considered. For the MG2, a CHP4, Batt4, and a PV4 have been considered. For MG3, the set of branches between node 19 and node 22 is considered. For the MG3, one CHP3, Batt3, PV3 and WT3 are considered respectively. Three Wind Turbine 1 to Wind Turbine 3 have been installed on Bus 12, Bus 20, and Bus 22 of the study DN, respectively, and the installed capacity of two Wind Turbine 1, Wind Turbine 2 in Micro Grid 1 is equal to 5 and 12 kW. Also, the capacity of installing one Wind Turbine 3 in the Micro Grid 3 is equal to 15 kW.

The technical specifications, including the low and high cut-off speed, normal operation speed and predicted wind speed for each of the WTs, are shown in Table (4). The number of 4 PV sources are installed on buses 9, 15, 20 and 24. The amount of radiation under normal conditions is according to Table (5). The uncertainties of MG operation in the form of possible scenarios of WT generation and radiation on PV for 4 load levels during one-year time horizon are shown in Table 6, Table 7, respectively.Table 4 Technical specifications and wind speed forecasting for WT assigned in Micro Grid 1 to Micro Grid 3.

Table 4Technical Specification	Vci	Vco	VN	LL = 1	LL = 2	LL = 3	LL = 4	
Micro-Grid 1 (Wind Turbine 1)	5	25	15	5	11	19	12	
Micro-Grid 1 (Wind Turbine 2)	4	23	10	6	12	20	14	
Micro-Grid 3 (Wind Turbine 3)	10	30	18	10	17	25	15	

Table 5 Irradiance for PV assigned in Micro Grid 1 to Micro Grid 3.

Table 5Radiation (KW)	LL = 1	LL = 2	LL = 3	LL = 4	
Micro-Grid 1 (Photovoltaic 1)	1	25.3	7.8	5.35	
Micro-Grid 1 (Photovoltaic 2)	1	22.3	12.8	7.35	
Micro-Grid 2 (Photovoltaic 3)	1	26.3	10.8	6.35	
Micro-Grid 3 (Photovoltaic 4)	1	28.3	8.8	3.35	

Table 6 Possible scenarios for WT generation installed in Micro Grid 1 and Micro Grid 3.

Table 6Micro Grids (WT)	Scenarios	ρWindS	AFWindS	
Micro-Grid 1 (Wind Turbine 1)	SC 1	0.50	AF (L1:L4) = 1.035	
SC 2	0.15	AF (L1:L2) = 0.99	AF (L3:L4) = 0.98	
SC 3	0.15	AF (L1:L3) = 1.01	AF (L4) = 1.02	
SC 4	0.10	AF (L1) = 0.975	AF (L2:L4) = 0.95	
SC 5	0.10	AF (L1:L2) = 1.025	AF (L3:L4) = 1.05	
Micro-Grid 1 (Wind Turbine 2)	SC 1	0.30	AF (L1:L4) = 1.015	
SC 2	0.25	AF (L1:L2) = 0.96	AF (L3:L4) = 0.97	
SC 3	0.15	AF (L1:L3) = 1.02	AF (L4) = 1.03	
SC 4	0.15	AF (L1) = 0.965	AF (L2:L4) = 0.945	
SC 5	0.15	AF (L1:L2) = 1.015	AF (L3:L4) = 1.025	
Micro-Grid 3 (Wind Turbine 3)	SC 1	0.30	AF (L1:L4) = 1.025	
SC 2	0.25	AF (L1:L2) = 0.98	AF (L3:L4) = 0.99	
SC 3	0.15	AF (L1:L3) = 1.025	AF (L4) = 1.015	
SC 4	0.10	AF (L1) = 0.945	AF (L2:L4) = 0.925	
SC 5	0.20	AF (L1:L2) = 1.045	AF (L3:L4) = 1.015	

Table 7 Uncertainty modeling of radiation scenarios PV1 to PV4.

Table 7Scenarios	ρPVS	AFPVS	
Micro-Grid 1 (Photovoltaic 1)	SC 1	0.6	AF (L1:L4) = 1	
SC 2	0.2	AF(L1:L2) = 0.99	AF(L3:L4) = 0.98	
SC 3	0.2	AF(L1:L3) = 1.03	AF(L4) = 1.05	
Micro-Grid 1 (Photovoltaic 2)	SC 1	0.5	AF (L1:L4) = 1.03	
SC 2	0.3	AF(L1:L2) = 0.95	AF(L3:L4) = 0.96	
SC 3	0.2	AF(L1:L3) = 1.25	AF(L4) = 1.15	
Micro-Grid 2 (Photovoltaic 3)	SC 1	0.4	AF (L1:L4) = 1.015	
SC 2	0.3	AF (L1:L2) = 0.92	AF(L3:L4) = 0.97	
SC 3	0.3	AF (L1:L3) = 1.13	AF(L4) = 1.11	
Micro-Grid 3 (Photovoltaic 4)	SC 1	0.45	AF (L1:L4) = 1.023	
SC 2	0.3	0.91	0.985	
SC 3	0.25	1.14	1.16	

According to the available budget, the operator of the DN is only allowed to install 3 of the 5 candidate locations for installing tie switches according to Fig. (2). In addition, studies are carried out during the time horizon of 1 year for 4 load levels with coefficients of 0.8, 0.85, 0.90 and 0.95. The candidate locations for the installation of the tie switch provide the conditions for connecting the end buses of the MG1 to the MG2, as well as the MG2 to the MG3. For example, if these switches are open and the tie switches on the input branch to each MG are opened, the isolation function is provided for each of the MG1, MG2 and MG3. This is despite the fact that the types of switch installation situations in candidate locations and their open or closed conditions affect the structure of the radial DN, the losses and the level of reliability of the subscribers of each of the MGs and the entire system.

The information related to the demand of active and reactive loads of the subscribers and the studied DN branches impedance are shown in Table 8, Table 9, respectively. Uncertainty in the partitioning and planning of several MGs covered by the distribution network in the variable production of active power by WT as well as PV installed in MG1, MG2 and MG3 will lead to uncertainty in predicting the electricity market price. The number of four CHP sources is considered to be placed in the MGs covered by the studied network. These sources are.• CHP1, CHP2 sources with the same capacity of up to 10 kwatt for installation in Micro Grid 1,

• CHP3 source with a maximum authorized capacity of 15 kwatt to be installed in the Micro Grid 3,

• CHP4 source with a maximum authorized capacity of 20 kwatt for installation in the Micro Grid 2.

Table 8 Active and reactive demand information of the DN of 25 studied buses.

Table 8Active and reactive demand of subscribers (kW and kVAr)	
P + iQ	Bus Number	
2	3	4	5	6	7	8	9	
100 + 60i	110 + 50i	120 + 80i	120 + 50i	140 + 70i	200 + 90i	200 + 90i	100 + 60i	
Bus Number	
10	11	12	13	14	15	16	17	
100 + 60i	145 + 60i	90 + 55i	90 + 55i	120 + 80i	160 + 60i	160 + 70i	160 + 70i	
Bus Number	
18	19	20	21	22	23	24	25	
95 + 50i	95 + 50i	95 + 50i	95 + 50i	95 + 60i	95 + 70i	120 + 85i	120 + 85i	

Table 9 Impedance information of the DN of 25 studied buses.

Table 9Branch impedance (ohm)	
R + iX	Bus Number	
2	3	4	5	6	7	8	9	
0.092 + 0.047i	0.49 + 0.251i	0.366 + 0.186i	0.381 + 0.194i	0.819 + 0.707i	0.187 + 0.618i	0.711 + 0.235i	1.03 + 0.74i	
Bus Number	
10	11	12	13	14	15	16	17	
1.044 + 0.74i	0.196 + 0.065i	0.374 + 0.123i	1.468 + 1.15i	0.541 + 0.712i	0.591 + 0.526i	0.746 + 0.545i	1.289 + 1.721i	
Bus Number	
18	19	20	21	22	23	24	25	
0.732 + 0.574i	0.164 + 0.156i	1.504 + 1.355i	0.495 + 0.478i	0.708 + 0.937i	0.4512 + 0.308i	0.898 + 0.709i	0.896 + 0.701i	

The coefficients of cost function of simultaneous energy and heat generation resources are displayed in Table (10).Table 10 Coefficients of cost function of four sources of CHP1 to CHP4.

Table 10Radiation (kW)	α	β	γ	
Micro Grid 1 (CHP1)	3	0.63	0.0003	
Micro Grid 1 (CHP2)	2.5	0.44	0.00025	
Micro Grid 2 (CHP3)	2	0.25	0.00035	
Micro Grid 3 (CHP4)	1.5	0.16	0.00045	

The number of four ESS units is also considered to be placed similarly to the CHP sources, which are considered in the following situations.• Batt1 and Batt2 with minimum allowed capacities of 1.5 kW and 2 kW, maximum allowed 8 kW and 10 kW with charging efficiencies of 0.97 and 0.92 and discharge of 0.99 and 0.97 for installation in Micro Grid 1, respectively;

• Batt3 source with the minimum allowed capacity of 3.5 kW and the maximum allowed capacity of 10 kwatt, with a charge efficiency of 0.90 and a discharge of 0.98 for installation in the Micro Grid 3; and

• Batt4 source with a minimum capacity of 2.5 kwatt and a maximum of 12 kwatt with a charge efficiency of 0.94 and a discharge of 0.98 for installation in the Micro Grid 2.

Probability scenario is used to the uncertainties model of distributed renewable generation system of MGs and price of energy in electricity market. The losses cost per kWh of electric energy is equivalent to 0.4 $.

GA is used to improve the model of partitioning and planning of the studied ADN. The number of the initial chromosomes population is 500, the probability of crossing between chromosome pairs is 0.7, the mutation probability is equal to 0.3, and the repetitions number of the algorithm is 1000 repetitions. The proposed modeling is implemented in MATLAB assigned to a computer with a 2.4 GHz 7-core processor, 8 GB of external memory, and then the obtained numerical results are evaluated and compared.

According to this test network, both modes connected to the infinite network and island mode are considered. In these two cases, several MGs are connected to it and different scenarios are seen. With these scenarios, this network will be closer to the real network and will represent the real state. This paper shows the general procedure of the study. Therefore, similar results can be achieved by expanding these relationships on the real network.

5.1 Case study 1: optimal planning of ADN in several MGS

Before running the program and solving the retrofitted model by GA, switches SW1, SW2 and SW5 are assumed to be closed and switches SW3 and SW4 are assumed to be open. The results of the optimal placement of DG, ESS and reactive compensators are shown in Fig. (3).Fig. 3 The results of optimal placement of DG, ESS and reactive compensators on the studied AND.

Fig. 3

In the MG1, bus8 and bus14 have been selected for the installation of CHP1 and CHP2 with a capacity of 8 kwatt and 7 kwatt, respectively, for the MG2, bus23 have been selected for the installation of CHP4 with a capacity of 18 kwatt, and for the Micro Grid 3, bus19 buses have been selected for the installation of CHP3 with a capacity of 14 kwatt. Also, Batt1 and Batt2 in Micro Grid 1 are selected for installation along with PV on bus9 and bus15 with capacities of 5.2 kW and 5.8 kwatt. Batt3 in the Micro Grid 3 on bus20 with a capacity of 6.7 kwatt and Batt4 in the Micro Grid 2 on bus23 with a capacity of 9.6 kwatt are selected for installation next to PV. While the utilization capacities of these CHP for four load levels during a one-year time horizon are shown in Fig. (4).Fig. 4 Optimal ESS results and CHP in MG1 to MG3.

Fig. 4

After the implementation of the program, the installation location of reactive power compensators DRS1, DRS2 and DRS3 in Micro Grid 1 on bus5, bus7 and bus13 with installation capacities of 17, 28 and 31 kVAr, respectively is optimally selected. Fig. (5) shows the operating conditions of reactive power compensators for four load levels during a one-year time horizon. From the simulation, the numerical value of proposed model objective function, which is the total cost of installing and operating equipment in MG, losses, reliability cost, is optimally determined to be equal to 203710 $. According to these results, the cost of installing and operating the equipment is equal to 174390 $, the losses cost is 1495.2 $, and the reliability cost is 27822 $.Fig. 5 Operating conditions of DRS1 to DRS3 reactive compensators for four load levels during a one-year time horizon.

Fig. 5

According to the numerical results, operation and installation cost of equipment includes approximately 86.50 %, losses 0.050 % and reliability 13.450 % of the total costs.

5.2 Case study 2: optimal partitioning and planning of the ADN in several MGS

After the second execution, the program is optimally selected by the GA of SW1 and SW5 in the closed state and SW2, SW3, SW4 in the open state. The results of the optimal placement of DG, ESS and reactive compensators with the existence of a MG with island function are as shown in Fig. (6).Fig.6 The results of optimal placement of DG, ESS and reactive compensators for the studied ADN with the presence of a MG with islanding function.

Fig.6

The following items have been selected for this study.• In Micro Grid 1, CHP1 and CHP2 are installed on bus8 and bus14, with 8 kW and 9 kW capacity, respectively;

• in Micro Grid 2 CHP4 is installed on bus23 with 7 kW capacity,

• MG3, Micro Grid 3 is installed on bus19 with 15 kW capacity,

• Batt1 and Batt2 are installed on bus9 and bus15 with 7.75 kW and 8.6 kW capacity, respectively;

• In Micro Grid 1, Batt3 is installed on bus20,

• in Micro Grid 3, Batt4 are installed on bus25 with 8.25 kW capacity; and

• In Micro Grid 2, PV is installed with 7 kW capacity.

The utilization capacities of these DG sources for four load levels during a one-year time horizon are shown in Fig. (7).Fig. 7 The optimal second implementation results of the model for the utilization capacity of DG in MG1 to MG3.

Fig. 7

Considering the selection of the island operation status for all three MG, it is expected that the amount of installation and exploitation capacity of DG and the corresponding costs for the three MGs covered by the studied DN will increase. From the simulation results, this cost is estimated to be 181,990 $, which shows an increase of 7,600 $ compared to the study of the first implementation of the algorithm, which was 174,390 $. After the second execution of the program, the DRS1, DRS2 and DRS3 reactive power compensators in the MG1 with island function on the 6th, 8th and 14th busbars of the three installation locations with the installed capacities of 17, 28 and 34 kVAr are selected, respectively.

According to the simulation results, due to the lack of connection of MG1 to the finite grid, the need to provide reactive power increases compared to the previous study. Also, by increasing the installation capacity, more compensation sources, especially DRS3, have been provided. The operating conditions of reactive power compensators are optimally displayed for four load levels during a one-year time horizon in Fig. (8).Fig. 8 The optimal results of the second implementation of the model for the utilization capacity of the reactive power compensating resources assigned in the MG1.

Fig. 8

For the second implementation of the simulation results, the numerical amount of the proposed model objective function, which is the total equipment cost of operation and installation in Micro Grids, losses, reliability cost, is optimally determined equal to 204,650 $. Of this amount, 940 $ shows an increase compared to previous work. The installation and operation cost of the equipment is equal to 181990 $, the losses cost is 1397.7 $ and the reliability cost is 21256 $.

According to the numerical results, it can be said that.• By using the proposed reinforced model under new structure by more investment on reactive power sources, the losses cost has been decrease by nearly 0.1 % annually.

• The cost of reliability of MGs has been significantly reduced by 0.75 % by using MG1, MG2 and MG3.

6 Conclusion

According to this study, new resilience modeling is proposed for partitioning and planning of ADN with regard to operational uncertainties by using intelligent GA. The objective function of reducing total investment costs on DG and ESS as well as tie switches for rearranging the structure of MGs in order to improve losses and reliability of DN subscribers has been defined. The limitations of the mentioned problem include the technical limitations of the problem such as the optimal demand distribution equations and the economic limitations of the electricity market. To confirm the efficiency and validation of methodology, simulation works have been used for two different implementations of the program on 25-bus DN including three Micro Grids. The obtained numerical results show that DN partitioning has a direct impact on investment costs and reliability and losses. If the MGs are connected to the infinite grid, compared to the situation of the MGs island operation, the costs of installing reactive power compensators and DGs show a decrease, while the cost of losses and reliability have higher values. According to the expansion of MGs in the power grid, using the above method will lead to reducing network costs and improving network limitations. It should be noted that in this paper, the MG has been investigated both as an infinite network and in island mode. However, it can be considered with other renewable sources.

Statement of data availability

All data and information are available on request.

CRediT authorship contribution statement

Hamid Amini Khanavandi: Writing – original draft, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Majid Gandomkar: Writing – review & editing, Validation, Supervision, Project administration. Javad Nikoukar: Writing – review & editing, Visualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix GA is adaptive heuristic search algorithms that belong to larger part of evolutionary algorithms. GAs are based on the idea of natural selection and genetic. These are random intelligent exploitation searches provided with historical data to direct the search into the region of better performance in solution space. Fig. (A1) provides the flowchart of the conventional GA.

Once the initial population is created, the algorithm evolves using following operators.• Selection Operator: This operator idea is to give preference to the individuals with good fitness scores and allow them to pass their genes to successive generations.

• Crossover Operator: This operator represents mating between individuals. Two individuals are selected using selection operator and crossover sites are chosen randomly. Then the genes at these crossover sites are exchanged thus creating a completely new individual (offspring).

• Mutation Operator: The key ideas are to insert random genes in offspring to maintain the diversity in the population to avoid premature convergence.

Fig. A.1 Conventional GA flowchart.

Fig. A.1
==== Refs
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