# A Resilience-Oriented Methodology for Transformation of the Distribution Networks into MicroGrid

Authors: Atbin Kia; Mehdi Farzinfar; Meysam Amirahmadi; Mahmoud Samieimoghaddam
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Transformation of the distribution network, integrated with Distributed Energy Resources (DER), into a MicroGrid (MG) is an attractive approach in improving the reliability and resilience of the network. In this paper, by introducing the important and necessary aspects of the MG formation problem, an effective methodology for transformation of a distribution network into the MG is proposed. In the presented methodology, optimal allocation of DERs within MG is obtained by optimization of power losses and voltage stabilization along feeders. Moreover, the short-circuit constraints are also taken into account simultaneously while allocating DERs. The reason for the latter is that the integration of DERs alters the amplitude and direction of the short circuit current, which can cause the overall fault current to exceed the designed fault-level capability of the circuit breakers. This issue may put CBs at risk of failure and degrading MG resilience. In this regard, resilience-oriented evaluation of the MG formation, from the perspective of considering short circuit level and coordination of OCRs, is also performed. Another advantage of short circuit studies is devising complete and economic overcurrent-based protection plan for MG in both operating modes (grid-connected and islanded). It should be pointed out that adopting an appropriate control routine is a key element in the MG formation. Hence, a control strategy, based on Energy Storage System (ESS) utilization, is suggested in this paper. This feature, which is another contribution of the paper, will guarantee seamless transition to island mode and stable operation of the MG. The proposed formulation of the MG formation is solved using a modified multi-objective PSO and the Pareto-optimal set is obtained. However, since the optimal solutions are nondominated to each other, a Fuzzy Satisfaction Method (FSM) is utilized to find the optimal solution among the Pareto-set. Utilization of the proposed methodology leads to the successful transformation of the distribution network into a MG, which not only considers the load flow constraints but also preserves the optimal coordination of the protective relays and resilience of the MG. In addition, seamless transition and stable operation of the MG in island mode is achieved.


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## Body

## 1. Introduction

The emergence of the MicroGrid (MG) concept after development of the Distributed Energy Resources (DER) is one of the most significant advances in modernizing power distribution networks. A MG generally operates while connected to the utility grid, but importantly, during grid outages it is able to get isolated and sustain its local loads (islanded mode) [1, 2]. The island feature of the MG, which is the clearest benefit in resilience increasing, along with other benefits, such as reduction in energy transfer costs and losses, improvement of voltage profile, and feeder loading [3–6], have created a high tendency to turn part of the distribution network into a MG among the Distribution System Owners (DSO).In this regard, and to take advantage of these benefits, there are several excellent researches devoted to the subject of DERs placement in traditional distribution networks [7–15]. In this perspective, the use of optimization methods in DER placement has gained many attentions as through them various objective functions (OFs) and constraints can be considered simultaneously. Besides, such OFs related to the allocation problem are commonly solved by utilizing metaheuristic algorithms, like Genetic Algorithm (GA) or Particle Swarm Optimization (PSO). In this respect, the optimal siting and sizing of DER is obtained [9, 11–13]. For brevity, the research performed in this field can be categorized as: finding optimal placement of DERs for predetermined capacities [16, 17], finding optimal DER capacities at specific locations, and simultaneous calculation of optimal locations and capacities of DERs [7, 10, 13, 18].Although the methods presented in these papers can lead to the appropriate allocation of DERs within the distribution networks, they do not take into account the operational capabilities of the MG, thus they are not a proper solution for the formation of a MG. In other words, by transforming part of an active distribution network into MG in this way, the technical criteria of the MG will not be met. In summary, DERs allocation without considering MG indices may lead to the following issues in the MG operation:(i)
The islanding operation of the MG may not be possible due to a power mismatch between loads and DERs [5, 19–21].(ii)
Impairing the integrity or the safety of the islanded MG due to the voltage/frequency instability.(iii)
Improper allocation of DERs may increase power losses and voltage deviation within the grid.(iv)
Integration of DERs causes two-way power flow and also increases the voltage at the point of coupling. This issue is more severe in the light load conditions [22].To avoid the problems raised, many of the existing projects and researches offer strategies for designing and planning a MG from scratch [1, 23–25], and needless to say, all of these researches are less challenging. However, due to the existence of distribution networks in operation, the main issue is the transformation of the distribution network or part of it into a MG (so-called MG formation), which is also very important and attractive. In this regard, successful MG formation, as the main concern of this research, requires responding to all existing challenges [26].In Ref. [5], a methodology for transforming a distribution network into a MG is proposed, where the optimal sites and corresponding sizes of DERs are determined beforehand. Then, to improve voltage profile of the MG, structural modifications are performed. In Ref. [27], it has been shown that the system resilience by the proactive MG formation is enhanced. Paper [28, 29] formulates a mixed-integer linear program for the transformation of a radial distribution network to multiple MGs, each energized by a DER. The formation is based on controlling the ON/OFF status of the automatic Circuit Breakers (CB) to maximize supplying the critical loads of the network. A restoration process of the distribution network is modeled in Ref. [22] where MG formation is performed with allocation of fixed and mobile DERs. Authors of Ref. [30] have presented a model for transformation of the distribution network into islanded MG in which only control aspects have been addressed. Furthermore, relying on the droop-controlled DERs cannot guarantee the MG stability following a severe disturbance.The salient shortcoming of the above papers is the lack of evaluation of the stability and security of the MG, and the presentation of a solution for the stable and smooth transition to the island mode. On the other hand, one of the salient criteria in the efficient MG formation, while allocating the DERs, is to consider the performance of the protection system and the coordination between the Over Current Relays (OCRs). In this perspective, changing the short circuit level of the network is another technical issue of DERs integration, which can disrupt the performance of the protection system. Notably, not paying attention to this issue, which is not addressed in the most reviewed papers, can reduce the reliability of the system. Although papers such as [31–34] have suggested methods based on changes of OCRs settings or using separate setting groups, the specific point that exists is that system operators are usually reluctant to change the protection system settings. This further highlights the importance of considering OCRs settings in the process of optimal allocation of the DERs.In the view of the above mentioned criteria/challenges, in this paper, a new methodology for transformation of the distribution network into a MG is proposed, which contributes in three main aspects, as follows:(1)
First, optimal allocation of DERs within MG, considering simultaneous reduction of power losses and voltage deviation in both operating mode of MG, is formulated. Meeting these objective functions ensures secure performance of the MG in both grid-connected and islanded modes of operation.(2)
As the second aspect of the methodology, in the process of DERs allocation, short circuit studies are also considered to cover the following issues:The contribution of DERs to the fault level may change the short circuit capacity and line current amplitude and direction within the MG. This may cause miscoordination among Over Current Relays (OCRs). Therefore, while solving the DERs allocation problem, the optimal results are modified according to the permissible short circuit level of equipment. Moreover, the coordination among the OCRs is optimally obtained while allocating the DERs. It should however be noted that the optimal coordination, in this case, is solely valid for the grid-connected mode of the MG, and during the islanded mode, due to the loss of contribution of the upstream network, new settings would be required.The contribution of the DERs can cause the overall fault current passing through the Circuit Breakers (CB) to exceed their designed fault-level capability. In this case, the pertinent CBs are exposed to increased stress, which puts them at risk of failure. This issue, which is categorized as a rare but high impact one, can significantly deteriorate the resilience of the MG. Hence, prediction of this condition that endangers MG resilience is important, and as per that, the optimal methodology for MG formation is devised to result in the least amount of Expected Energy Not Supplied (EENS). In this respect, the resilience-oriented evaluation of the MG formation is also performed. At last, it should be mentioned that other resilience features such as adaption and recovery after this disruptive event is out of scope of this paper.(3)
The final aspect of the proposed methodology is devising a control strategy to ensure seamless transition and stable operation of the MG in the islanded mode. This strategy is based on utilization of the ESS along with speed droop control of allocated DERs. Frequency control and transient stability aspect of the islanded MG are fully addressed through proposed control strategy.The optimal MG formation problem of the paper is solved via a modified Multi-Objective PSO (MOPSO), and the optimal Pareto-set is obtained. However, since the Pareto-optimal set consists of solutions that are nondominated to each other, a Fuzzy Satisfaction Method (FSM) is utilized to find the optimal solution among the Pareto-set. In the second part of the paper, the formulation of transforming the distribution network into a MG, including the contribution of the paper, is described.


## 2. Design Aspects of the MG Formation Problem

The principle of MG formation and its configuration varies depending on the objectives of the MG planning. In this respect, implementation of the MG projects in the world has been done based on specific objectives. Accordingly, in MG formation, various aspects should be considered in order to achieve effective performance in both modes of grid-connected/islanded, and particularly in transfer between two modes [6]. The most important of these technical aspects are as follows:(i)
Determination of the MG zone and PCC point(ii)
Allocation and control of DERs and Energy Storage Systems (ESS) within the MG(iii)
Analysis of load flow within the MG (and load forecasting) and necessity of utilization of load/generation shedding schemes(iv)
Short circuit analysis(v)
Adaptation of proper control and management scheme in the MG(vi)
MG stability and security assessments(vii)
Configuration of the MG protection schemeHowever, the process of designing a MG varies depending on the objectives and requirements set, which is well documented in IEEE2030.7, IEC TS 62898-1. The proposed methodology of this paper for transforming a part of the distribution network to a MG is presented considering the above aspects and on the basis of international standards.It should be mentioned that the load and generation level within the studied network is assumed equal, and hence, implementation of load shedding scheme for the island operation is not required.In the following, solutions for a successful MG formation are presented. However, due to the limited pages of the paper and also with the aim of highlighting contributions, some details, like those related to the adapted control technique or MG analysis in various scenarios have been avoided.


### 2.1. Specifying the Point of Common Coupling (PCC)

PCC is the point where the MG is coupled to the upstream network in the grid-connected mode [3]. This paper assumes the formation of a single MG, and the formation of nested MG is out of the scope of this paper. In addition, to evaluate the efficiency of the proposed methodology for large networks, it is assumed that the entire network under this study will become a MG. In Figure 1, the location of the PCC is depicted.Figure 1
Schematic diagram of the test system.


### 2.2. Analysis of Generation/Load of the MG

In order to determine the configuration of DERs in the MG, economic analysis, reliability, and environmental issues must be considered comprehensively. In addition, the requirement of generation and demand balance in all loading conditions of the MG is one of the basic and important requirements in the planning process [4, 5]. In this regard, the conditions of maximum/minimum loading of the MG, as well as periods of minimum/maximum generation of DERs (if they are intermittent energy sources) are considered in the analysis.In this research, the ratio of installed capacity of DERs to loads within the MG is adjusted in such a way that it can continuously provide the maximum demand required in island mode, and therefore the load shedding schemes are out of the scope of this paper. In addition, an effective control scheme is proposed to ensure the stability of the MG after transition to island mode.


### 2.3. Control Strategy for Seamless Transition and Stable Operation of the MG

A MG control system generally includes functions that enable the MG to manage itself and exchange power with the upstream network and operate adaptively in grid-connected and island modes. Depending on the variety of goals and configurations of the MGs, the requirements and functions of the control strategy can also be different. Various control strategies have been proposed in Refs. [35–37]. Furthermore, one of the vital features in the MG formation is that it should enable seamless transition between two modes. Hence, the developed methodology for transformation of the distribution network into MG should guarantee stable operation of the MG in grid-connected and island modes and smooth transition between two modes. Therefore, this matter is one of the main aspects and objective of the presented control strategy of the paper. It should be pointed out that objectives such as synchronization or energy management are not covered in this paper (although the effective control strategy of this paper can meet them as well). Traditionally, implementation of such control functions, through which frequency and transient stability of the MG is preserved, can be done by controlling the active and reactive power of the DERs. However, relying only on DERs to control MG has the following shortcomings and challenges:In general, the rate of response of synchronous based DERs, like gas turbines, is low (the time required to ramp-up to 100% load is about a few minutes). Therefore, the implementation of the primary frequency control loop, which is done automatically via the governor, is not as effective in restoring the frequency within the allowable range [38].(i)
On the other hand, due to the presence of the small scale DERs, islanded MG has a low inertia, which is one of the most important challenges in the operation and frequency control of the MG. It should be noted that with more penetration of renewable energy sources, the issue of inertia also increases.(ii)
Due to the low Critical Clearing Time (CCT) of the DERs, there is a possibility of angular instability of DERs when a severe disturbance occurs in the upstream network. This reduces the effectiveness of DERs in MG control and its smooth transition.(iii)
In this paper, to overcome the above-mentioned challenges, installation of an Energy Storage System (ESS) along with allocated DERs (according to the proposed formulation in section2.4) is recommended. Regarding the adopted control strategy of the paper, the following points should be emphasized:(iv)
In order to enable the black start capability in the MG, the ESS is installed in the vicinity of the largest DER (according to optimal allocation provided in the next section) to be able to provide black start conditions for the gas units of this DER.(v)
The ESS is used only to maintain an accurate balance between load and DERs in real-time (load tracking) as well as dynamic frequency control. This means that under normal operating conditions, the power output of the ESS will be zero. On the other hand, it should be noted that in the event of island conditions, the ESS must have the appropriate energy level for charging/discharging. Therefore, State of Charging (SOC) of the ESS must always be kept in the 50% range (i.e., between 45% and 55%).(vi)
According to the proposed control strategy, after implementing the primary frequency control, the DERs must participate in the secondary frequency control. Thus, in the first 30 seconds after a severe disturbance occurs or when the MG is islanded, ESS plays a vital role in controlling the frequency. However, up to 15 minutes, the DERs must participate in the secondary frequency control process and release the ESS capacity to prepare for the next disturbance while providing the required power to the MG.(vii)
In the conditions of continuous change of load in the MG, it is obvious that both ESS and DERs will participate in frequency control.(viii)
When the MG is connected to the upstream network, the DERs are set in the constant power factor mode (PQ), while once the MG gets islanded, the control mode of the DERs is changed to control voltage and frequency as per their droop characteristic. The droop setting is done based on dynamic analysis.In summary, the following are the advantages of utilization of the presented control strategy from two different aspects:


### 2.4. Frequency Control Aspect

As stated earlier, an MG with very low inertia has a high rate of change of frequency, and even a small imbalance between generation and demand can lead to deep frequency Nadir point within the MG. In such cases, the ESS, by dynamically injecting/absorbing power to/from the network can regulate MG frequency in a fast and effective manner.


### 2.5. Transient Stability Aspect

Unlike synchronous generators that have a delayed response to the control signal, the response of the ESS to regulate its power output is almost instantaneous [36, 38]. In this way, the ESS, by imitating the natural inertial response of synchronous based DERs, provides the so-called virtual inertia service and can enhance the transient stability of the MG.It is necessary to mention that the main emphasis of this research is on the seamless transition and stable operation of the MG, and the way of modeling the MG stability is not our concern.


### 2.6. Optimal Allocation of the DERs within the MG

As per the context of the paper, the transformation of the distribution network into a MG is possible only for networks that contain DERs, relying on which; the MG can be operated in the stand-alone mode [19]. Hence, addressing challenges like the siting/sizing of DERs and type of DERs are vital in solving the MG formation problem. On the other hand, DERs allocation should be done in such a way that satisfies the existing constraints and requirements, not only for the main grid-connected mode but also for the island mode.Today, due to the complexity and dimensions of such problems, it is efficient to use optimization methods that are able to meet different constraints. In the following, the formulation of the optimal DERs allocation within MG and related electrical constraint is explained. It should be noted, given that the MG design is based on available DERs, addressing economic goals is not formulated specifically. However, goal of improving power losses and voltage stability (equations (1) and (2)), goal of optimal OCRs setting and coordination (equation (5)), as well as not exceeding the thermal capacity of the CBs are actually recognized as economic benefits of the network operator.


#### 2.6.1. Power Losses and Voltage Stabilization OFs

Generally, in the DERs allocation problem and MG formation, reducing power losses and voltage stabilization are the main objective functions. In the present study, these functions, which are necessary from the point of view of economical operation of the network, are considered separately for both grid-connected and islanded modes [7, 9, 39–41]. Equations (1) and (2) state the total Ohmic losses in MG and total voltage deviation in MG terminals, respectively, and should be minimized after DERs allocation.(1)minPLoss_Total=∑ij=1NLRij×Iij_Grid2+∑ij=1NLRij×Iij_Island2,(2)minVoltDev=∑n=1NbusVref−Vbus−Grid+∑n=1NbusVref−Vbus−Island.In (1), the line resistance is shown. Iij_Grid and Iij_Island parameters stand for lines current, in the grid-connected and island mode, respectively. Nbus is the number of terminals within the MG. Vref is the reference voltage, and unlike many references, in this paper, this value is not fixed and is assumed to be a range of voltages, i.e., [0.975–1.025] p.u. In this regard, voltage deviation occurs out of this range, and this would result in lower capacity of allocated DERs.In addition, during optimization of some constraints, including power flow constraint, loading of the feeders, voltage range constraint, and DER power output should be met [42, 43].The minimum/maximum capacity of DER, with incremental steps of 0.5 MW, has been determined in equation (3). Furthermore, the maximum capacity of each considered feeder has been demonstrated by equation (4) to guarantee the apparent power through any feeder would stay less than its rating value after DERs allocation.(3)0.5MW≤DERCapacity≤5MW,(4)Sij≤Sijmax∀ij∈NL.


#### 2.6.2. OCRs Coordination OF

Due to the structural differences between the conventional distribution network and the MG, the proper protection scheme for them also has key differences with each other. Usually the protection of distribution networks (which are mainly operated radially) can be implemented by installing an OCR at the beginning of the feeder. However, such a simple scheme is not suitable for protection of the MG due to the presence of DERs within the network, which leads to a change in the level of short circuit and bilateral power flow, as well as the need to isolate the fault faster in order to preserve the stability of the MG.On the other hand, in the case of fault, the DERs contribute to the short circuit current and thus affect the performance of the OCRs of network and MG. In other words, DERs placement without considering their impact on the performance of the protection system can make the process of OCRs coordination difficult or even impossible. Therefore, in this paper, first, a complete and economic overcurrent-based protection plan is suggested that is able to protect the MG in both operating modes. The proposed location for the installation of OCRs is specified in Figure1.In the next step, DERs allocation is done, considering the performance of the protection system and with the aim of minimizing the operation time of OCRs and the amount of miscoordination between them. This topic, which is one of the outstanding features of this paper, also guarantees the successful formation of the MG from the perspective of the protection system.In this regard, the following formulation, for the purpose of minimization of the summation of trip time of OCRs (Tik), is considered while solving the optimal DER allocation.(5)Minα1∑inTik2+α2∑inΔTmb−β1ΔTmb−ΔTmb2.In this paper, it is assumed that the OCRs have standard Inverse Definite Minimum Time (IDMT) characteristics, for which the operation time is calculated as (6).(6)Tik=0.14×TSMiIsci/Ipi0.02−1,where Ipi and TSMi are the pickup current and Time Setting Multiplier of the ith relay, respectively, and Isci stands for the short circuit current.The coordination constraint in the protection philosophy has been formulated in the second term of equation (5), where ΔTmb states the coordination time among the main and backup relays. In fact, a minimum discrimination time between operation of the main OCR and its backup should be set. This can be formulated as follows:(7)Tj−back−upF1−Ti−primaryF1≤CTI.The Coordination Time Interval (CTI) depends upon type of relays, speed of the circuit breaker, and a safety margin which can be selected between 0.2 sec and 0.5 sec [44]. Ti−primaryF1, Tj−back−upF1 are the operating time of ith main OCR and jth backup OCR, respectively, for the near-end fault F1. Parameters α1, α2, β1 are the weighting factors.The limits on the OCRs parameters setting are other constraints that should be considered in the formulation:(8)TSMimin≤TSMi≤TSMimax,(9)maxIloadimax,Ipimin≤Ipi≤minIfaultimin,Ipimax.Equation (9) states that the minimum pickup current setting of the OCR is the maximum value between the minimum available current setting (Ipmin) and maximum load current (Iloadmax) passing through it. Similarly, the maximum pickup current setting is the chosen minimum value between (Ipmax) on the OCR and minimum fault current (Ifaultmin) which passes through it [44, 45]. At last, the operating time of each main relay must lie between 0.05 sec and 1 sec.(10)Timin≤Ti≤Timax.According to (5), determining the optimal TSM and Ip of OCRs, which leads to optimal coordination between them, is another goal in the MG formation problem of the present study.


### 2.7. Considering the Short Circuit Capability of CBs in Optimal Solution

One of the challenges of DERs placement for the purpose of MG formation is increasing the short circuit level of the network, due to fault current contribution of the DERs. This issue may put the Circuit Breaker (CB) under increased stress and thus more prone to failure in the time of operation [33, 45].In the proposed methodology of this paper and with the aim of addressing this issue (as per flowchart of Figure2), short circuit current assessment is also done as one of the important constraints in the optimal allocation program. In this respect, the maximum fault current (Isc) passing through the CBs, when a severe fault in front of CBs occurs, is compared with the maximum interrupting rating of CB (Ith).Figure 2
Flowchart of the proposed methodology for the MG formation.It should be noted that, as per the IEC60900 standard, the CBs are sized based on 80% of their maximum interrupting rating (Ith). Thereafter, based on the comparison result, if Isc is greater than Ith, the obtained results are not optimized from the point of view of short circuit studies. Therefore, the optimization routine is re-run in order to find new solutions.


## 2.1. Specifying the Point of Common Coupling (PCC)

PCC is the point where the MG is coupled to the upstream network in the grid-connected mode [3]. This paper assumes the formation of a single MG, and the formation of nested MG is out of the scope of this paper. In addition, to evaluate the efficiency of the proposed methodology for large networks, it is assumed that the entire network under this study will become a MG. In Figure 1, the location of the PCC is depicted.Figure 1
Schematic diagram of the test system.


## 2.2. Analysis of Generation/Load of the MG

In order to determine the configuration of DERs in the MG, economic analysis, reliability, and environmental issues must be considered comprehensively. In addition, the requirement of generation and demand balance in all loading conditions of the MG is one of the basic and important requirements in the planning process [4, 5]. In this regard, the conditions of maximum/minimum loading of the MG, as well as periods of minimum/maximum generation of DERs (if they are intermittent energy sources) are considered in the analysis.In this research, the ratio of installed capacity of DERs to loads within the MG is adjusted in such a way that it can continuously provide the maximum demand required in island mode, and therefore the load shedding schemes are out of the scope of this paper. In addition, an effective control scheme is proposed to ensure the stability of the MG after transition to island mode.


## 2.3. Control Strategy for Seamless Transition and Stable Operation of the MG

A MG control system generally includes functions that enable the MG to manage itself and exchange power with the upstream network and operate adaptively in grid-connected and island modes. Depending on the variety of goals and configurations of the MGs, the requirements and functions of the control strategy can also be different. Various control strategies have been proposed in Refs. [35–37]. Furthermore, one of the vital features in the MG formation is that it should enable seamless transition between two modes. Hence, the developed methodology for transformation of the distribution network into MG should guarantee stable operation of the MG in grid-connected and island modes and smooth transition between two modes. Therefore, this matter is one of the main aspects and objective of the presented control strategy of the paper. It should be pointed out that objectives such as synchronization or energy management are not covered in this paper (although the effective control strategy of this paper can meet them as well). Traditionally, implementation of such control functions, through which frequency and transient stability of the MG is preserved, can be done by controlling the active and reactive power of the DERs. However, relying only on DERs to control MG has the following shortcomings and challenges:In general, the rate of response of synchronous based DERs, like gas turbines, is low (the time required to ramp-up to 100% load is about a few minutes). Therefore, the implementation of the primary frequency control loop, which is done automatically via the governor, is not as effective in restoring the frequency within the allowable range [38].(i)
On the other hand, due to the presence of the small scale DERs, islanded MG has a low inertia, which is one of the most important challenges in the operation and frequency control of the MG. It should be noted that with more penetration of renewable energy sources, the issue of inertia also increases.(ii)
Due to the low Critical Clearing Time (CCT) of the DERs, there is a possibility of angular instability of DERs when a severe disturbance occurs in the upstream network. This reduces the effectiveness of DERs in MG control and its smooth transition.(iii)
In this paper, to overcome the above-mentioned challenges, installation of an Energy Storage System (ESS) along with allocated DERs (according to the proposed formulation in section2.4) is recommended. Regarding the adopted control strategy of the paper, the following points should be emphasized:(iv)
In order to enable the black start capability in the MG, the ESS is installed in the vicinity of the largest DER (according to optimal allocation provided in the next section) to be able to provide black start conditions for the gas units of this DER.(v)
The ESS is used only to maintain an accurate balance between load and DERs in real-time (load tracking) as well as dynamic frequency control. This means that under normal operating conditions, the power output of the ESS will be zero. On the other hand, it should be noted that in the event of island conditions, the ESS must have the appropriate energy level for charging/discharging. Therefore, State of Charging (SOC) of the ESS must always be kept in the 50% range (i.e., between 45% and 55%).(vi)
According to the proposed control strategy, after implementing the primary frequency control, the DERs must participate in the secondary frequency control. Thus, in the first 30 seconds after a severe disturbance occurs or when the MG is islanded, ESS plays a vital role in controlling the frequency. However, up to 15 minutes, the DERs must participate in the secondary frequency control process and release the ESS capacity to prepare for the next disturbance while providing the required power to the MG.(vii)
In the conditions of continuous change of load in the MG, it is obvious that both ESS and DERs will participate in frequency control.(viii)
When the MG is connected to the upstream network, the DERs are set in the constant power factor mode (PQ), while once the MG gets islanded, the control mode of the DERs is changed to control voltage and frequency as per their droop characteristic. The droop setting is done based on dynamic analysis.In summary, the following are the advantages of utilization of the presented control strategy from two different aspects:


## 2.4. Frequency Control Aspect

As stated earlier, an MG with very low inertia has a high rate of change of frequency, and even a small imbalance between generation and demand can lead to deep frequency Nadir point within the MG. In such cases, the ESS, by dynamically injecting/absorbing power to/from the network can regulate MG frequency in a fast and effective manner.


## 2.5. Transient Stability Aspect

Unlike synchronous generators that have a delayed response to the control signal, the response of the ESS to regulate its power output is almost instantaneous [36, 38]. In this way, the ESS, by imitating the natural inertial response of synchronous based DERs, provides the so-called virtual inertia service and can enhance the transient stability of the MG.It is necessary to mention that the main emphasis of this research is on the seamless transition and stable operation of the MG, and the way of modeling the MG stability is not our concern.


## 2.6. Optimal Allocation of the DERs within the MG

As per the context of the paper, the transformation of the distribution network into a MG is possible only for networks that contain DERs, relying on which; the MG can be operated in the stand-alone mode [19]. Hence, addressing challenges like the siting/sizing of DERs and type of DERs are vital in solving the MG formation problem. On the other hand, DERs allocation should be done in such a way that satisfies the existing constraints and requirements, not only for the main grid-connected mode but also for the island mode.Today, due to the complexity and dimensions of such problems, it is efficient to use optimization methods that are able to meet different constraints. In the following, the formulation of the optimal DERs allocation within MG and related electrical constraint is explained. It should be noted, given that the MG design is based on available DERs, addressing economic goals is not formulated specifically. However, goal of improving power losses and voltage stability (equations (1) and (2)), goal of optimal OCRs setting and coordination (equation (5)), as well as not exceeding the thermal capacity of the CBs are actually recognized as economic benefits of the network operator.


### 2.6.1. Power Losses and Voltage Stabilization OFs

Generally, in the DERs allocation problem and MG formation, reducing power losses and voltage stabilization are the main objective functions. In the present study, these functions, which are necessary from the point of view of economical operation of the network, are considered separately for both grid-connected and islanded modes [7, 9, 39–41]. Equations (1) and (2) state the total Ohmic losses in MG and total voltage deviation in MG terminals, respectively, and should be minimized after DERs allocation.(1)minPLoss_Total=∑ij=1NLRij×Iij_Grid2+∑ij=1NLRij×Iij_Island2,(2)minVoltDev=∑n=1NbusVref−Vbus−Grid+∑n=1NbusVref−Vbus−Island.In (1), the line resistance is shown. Iij_Grid and Iij_Island parameters stand for lines current, in the grid-connected and island mode, respectively. Nbus is the number of terminals within the MG. Vref is the reference voltage, and unlike many references, in this paper, this value is not fixed and is assumed to be a range of voltages, i.e., [0.975–1.025] p.u. In this regard, voltage deviation occurs out of this range, and this would result in lower capacity of allocated DERs.In addition, during optimization of some constraints, including power flow constraint, loading of the feeders, voltage range constraint, and DER power output should be met [42, 43].The minimum/maximum capacity of DER, with incremental steps of 0.5 MW, has been determined in equation (3). Furthermore, the maximum capacity of each considered feeder has been demonstrated by equation (4) to guarantee the apparent power through any feeder would stay less than its rating value after DERs allocation.(3)0.5MW≤DERCapacity≤5MW,(4)Sij≤Sijmax∀ij∈NL.


### 2.6.2. OCRs Coordination OF

Due to the structural differences between the conventional distribution network and the MG, the proper protection scheme for them also has key differences with each other. Usually the protection of distribution networks (which are mainly operated radially) can be implemented by installing an OCR at the beginning of the feeder. However, such a simple scheme is not suitable for protection of the MG due to the presence of DERs within the network, which leads to a change in the level of short circuit and bilateral power flow, as well as the need to isolate the fault faster in order to preserve the stability of the MG.On the other hand, in the case of fault, the DERs contribute to the short circuit current and thus affect the performance of the OCRs of network and MG. In other words, DERs placement without considering their impact on the performance of the protection system can make the process of OCRs coordination difficult or even impossible. Therefore, in this paper, first, a complete and economic overcurrent-based protection plan is suggested that is able to protect the MG in both operating modes. The proposed location for the installation of OCRs is specified in Figure1.In the next step, DERs allocation is done, considering the performance of the protection system and with the aim of minimizing the operation time of OCRs and the amount of miscoordination between them. This topic, which is one of the outstanding features of this paper, also guarantees the successful formation of the MG from the perspective of the protection system.In this regard, the following formulation, for the purpose of minimization of the summation of trip time of OCRs (Tik), is considered while solving the optimal DER allocation.(5)Minα1∑inTik2+α2∑inΔTmb−β1ΔTmb−ΔTmb2.In this paper, it is assumed that the OCRs have standard Inverse Definite Minimum Time (IDMT) characteristics, for which the operation time is calculated as (6).(6)Tik=0.14×TSMiIsci/Ipi0.02−1,where Ipi and TSMi are the pickup current and Time Setting Multiplier of the ith relay, respectively, and Isci stands for the short circuit current.The coordination constraint in the protection philosophy has been formulated in the second term of equation (5), where ΔTmb states the coordination time among the main and backup relays. In fact, a minimum discrimination time between operation of the main OCR and its backup should be set. This can be formulated as follows:(7)Tj−back−upF1−Ti−primaryF1≤CTI.The Coordination Time Interval (CTI) depends upon type of relays, speed of the circuit breaker, and a safety margin which can be selected between 0.2 sec and 0.5 sec [44]. Ti−primaryF1, Tj−back−upF1 are the operating time of ith main OCR and jth backup OCR, respectively, for the near-end fault F1. Parameters α1, α2, β1 are the weighting factors.The limits on the OCRs parameters setting are other constraints that should be considered in the formulation:(8)TSMimin≤TSMi≤TSMimax,(9)maxIloadimax,Ipimin≤Ipi≤minIfaultimin,Ipimax.Equation (9) states that the minimum pickup current setting of the OCR is the maximum value between the minimum available current setting (Ipmin) and maximum load current (Iloadmax) passing through it. Similarly, the maximum pickup current setting is the chosen minimum value between (Ipmax) on the OCR and minimum fault current (Ifaultmin) which passes through it [44, 45]. At last, the operating time of each main relay must lie between 0.05 sec and 1 sec.(10)Timin≤Ti≤Timax.According to (5), determining the optimal TSM and Ip of OCRs, which leads to optimal coordination between them, is another goal in the MG formation problem of the present study.


## 2.6.1. Power Losses and Voltage Stabilization OFs

Generally, in the DERs allocation problem and MG formation, reducing power losses and voltage stabilization are the main objective functions. In the present study, these functions, which are necessary from the point of view of economical operation of the network, are considered separately for both grid-connected and islanded modes [7, 9, 39–41]. Equations (1) and (2) state the total Ohmic losses in MG and total voltage deviation in MG terminals, respectively, and should be minimized after DERs allocation.(1)minPLoss_Total=∑ij=1NLRij×Iij_Grid2+∑ij=1NLRij×Iij_Island2,(2)minVoltDev=∑n=1NbusVref−Vbus−Grid+∑n=1NbusVref−Vbus−Island.In (1), the line resistance is shown. Iij_Grid and Iij_Island parameters stand for lines current, in the grid-connected and island mode, respectively. Nbus is the number of terminals within the MG. Vref is the reference voltage, and unlike many references, in this paper, this value is not fixed and is assumed to be a range of voltages, i.e., [0.975–1.025] p.u. In this regard, voltage deviation occurs out of this range, and this would result in lower capacity of allocated DERs.In addition, during optimization of some constraints, including power flow constraint, loading of the feeders, voltage range constraint, and DER power output should be met [42, 43].The minimum/maximum capacity of DER, with incremental steps of 0.5 MW, has been determined in equation (3). Furthermore, the maximum capacity of each considered feeder has been demonstrated by equation (4) to guarantee the apparent power through any feeder would stay less than its rating value after DERs allocation.(3)0.5MW≤DERCapacity≤5MW,(4)Sij≤Sijmax∀ij∈NL.


## 2.6.2. OCRs Coordination OF

Due to the structural differences between the conventional distribution network and the MG, the proper protection scheme for them also has key differences with each other. Usually the protection of distribution networks (which are mainly operated radially) can be implemented by installing an OCR at the beginning of the feeder. However, such a simple scheme is not suitable for protection of the MG due to the presence of DERs within the network, which leads to a change in the level of short circuit and bilateral power flow, as well as the need to isolate the fault faster in order to preserve the stability of the MG.On the other hand, in the case of fault, the DERs contribute to the short circuit current and thus affect the performance of the OCRs of network and MG. In other words, DERs placement without considering their impact on the performance of the protection system can make the process of OCRs coordination difficult or even impossible. Therefore, in this paper, first, a complete and economic overcurrent-based protection plan is suggested that is able to protect the MG in both operating modes. The proposed location for the installation of OCRs is specified in Figure1.In the next step, DERs allocation is done, considering the performance of the protection system and with the aim of minimizing the operation time of OCRs and the amount of miscoordination between them. This topic, which is one of the outstanding features of this paper, also guarantees the successful formation of the MG from the perspective of the protection system.In this regard, the following formulation, for the purpose of minimization of the summation of trip time of OCRs (Tik), is considered while solving the optimal DER allocation.(5)Minα1∑inTik2+α2∑inΔTmb−β1ΔTmb−ΔTmb2.In this paper, it is assumed that the OCRs have standard Inverse Definite Minimum Time (IDMT) characteristics, for which the operation time is calculated as (6).(6)Tik=0.14×TSMiIsci/Ipi0.02−1,where Ipi and TSMi are the pickup current and Time Setting Multiplier of the ith relay, respectively, and Isci stands for the short circuit current.The coordination constraint in the protection philosophy has been formulated in the second term of equation (5), where ΔTmb states the coordination time among the main and backup relays. In fact, a minimum discrimination time between operation of the main OCR and its backup should be set. This can be formulated as follows:(7)Tj−back−upF1−Ti−primaryF1≤CTI.The Coordination Time Interval (CTI) depends upon type of relays, speed of the circuit breaker, and a safety margin which can be selected between 0.2 sec and 0.5 sec [44]. Ti−primaryF1, Tj−back−upF1 are the operating time of ith main OCR and jth backup OCR, respectively, for the near-end fault F1. Parameters α1, α2, β1 are the weighting factors.The limits on the OCRs parameters setting are other constraints that should be considered in the formulation:(8)TSMimin≤TSMi≤TSMimax,(9)maxIloadimax,Ipimin≤Ipi≤minIfaultimin,Ipimax.Equation (9) states that the minimum pickup current setting of the OCR is the maximum value between the minimum available current setting (Ipmin) and maximum load current (Iloadmax) passing through it. Similarly, the maximum pickup current setting is the chosen minimum value between (Ipmax) on the OCR and minimum fault current (Ifaultmin) which passes through it [44, 45]. At last, the operating time of each main relay must lie between 0.05 sec and 1 sec.(10)Timin≤Ti≤Timax.According to (5), determining the optimal TSM and Ip of OCRs, which leads to optimal coordination between them, is another goal in the MG formation problem of the present study.


## 2.7. Considering the Short Circuit Capability of CBs in Optimal Solution

One of the challenges of DERs placement for the purpose of MG formation is increasing the short circuit level of the network, due to fault current contribution of the DERs. This issue may put the Circuit Breaker (CB) under increased stress and thus more prone to failure in the time of operation [33, 45].In the proposed methodology of this paper and with the aim of addressing this issue (as per flowchart of Figure2), short circuit current assessment is also done as one of the important constraints in the optimal allocation program. In this respect, the maximum fault current (Isc) passing through the CBs, when a severe fault in front of CBs occurs, is compared with the maximum interrupting rating of CB (Ith).Figure 2
Flowchart of the proposed methodology for the MG formation.It should be noted that, as per the IEC60900 standard, the CBs are sized based on 80% of their maximum interrupting rating (Ith). Thereafter, based on the comparison result, if Isc is greater than Ith, the obtained results are not optimized from the point of view of short circuit studies. Therefore, the optimization routine is re-run in order to find new solutions.


## 3. Solving the Proposed Optimal Formulation

MG formation problem with three main objective functions is called the Multi-Objective Problem (MOP). The essence of such complicated problems is the incompatibility or conflicting of optimal solutions with each other, which makes it impossible to find a single global optimum solution; instead a set of optimal solutions, Pareto-optimal set, is calculated. Generally, the optimal solution among the Pareto-set can be selected by a trade-off, or an analysis done by experts.On the other hand, utilizing mathematical or linear programming methods for solving the MOP of the present work is difficult. Hence, metaheuristic algorithms, like PSO, are used to solve the MOP. PSO algorithm is a population-based optimization technique inspired by social behavior of fish schooling or bird flocking. For multi-objective problems, the positions of the particles, as nondominated vectors, based on the historical record of particles, are restored in the repository [46].In this paper, for finding the optimal solution in the MG formation problem, a modified version of classical PSO (MOPSO) has been employed which is able to perform better global exploration and local exploitation of the search space and to synchronously search for multiple Pareto-optimal solutions. Detail of this algorithm can be found in paper [13]. Furthermore, in the utilized MOPSO, the related parameters are set based on the values obtained in Ref. [47].


### 3.1. Selection of the Optimum Solution Based on Fuzzy Satisfaction Method (FSM)

Generally, in solving multi objective problems, like the MG formation problem of the present study, Pareto-optimal set, which are nondominated to each other but are superior to the rest of solutions in the search space, are obtained. In some cases, the optimal solution among the Pareto-set is determined by expert analysis and trade-off. However, when the number of objective functions, which are sometimes not compatible with each other increases, finding the optimal solution is not easy. To address this issue, in this paper, the Fuzzy Satisfaction Method (FSM) is used to find the optimal solution among Pareto-set.In the applied FSM technique, fuzzy sets, with membership level of 0 to 1, are defined for all the objective functions. The membership value “1” means full compatibility with the set, while the value “0” represents full incompatibility. The membership function is defined in equation (11).(11)μXi=0,Xi≤Ximin,Ximax−XiXimax−Ximin,Ximin≤Xi≤Ximax,1,Xi≥Ximax.Where Ximin and Ximax are the minimum and maximum values of ith objective function in which the solution is expected.The value of the membership functions (μX) indicates how well the solution satisfies the objective function. On the other hand, the minimum membership value for the studied objective functions indicates the optimal state. Therefore, in the MG formation problem with combination of three OFs, among minimum value of the membership functions, the maximum (larger) one is more favorable, since it can lead to more objective functions with individual optimum values.Hence, for multi-objective MG formation problem of the present study, which have three objective functions, the FSM index (ϕ) is calculated for every Pareto solution in repository as follows:(12)ϕ=MaxMinμXi,∀i=1:3.According to equation (12), the optimal solution in the obtained Pareto-set would be the optimal solution for which ϕ is maximum.


### 3.2. Resilience Oriented Evaluation of the MG Formation

As described in the previous two sections, in the process of MG formation, location of the DERs affects the amount of fault current passing through the CBs, as well as the coordination among the OCRs, which is the reason for including these aspects in the proposed methodology.In fact, with an increase in the amplitude and duration of the fault current, the probability of hidden CB failure might also be increased. Therefore, considering the effect of DERs allocation at the level of short circuit and coordination among OCRs, the study of probable exposing of hidden CB failure and subsequent assessment of MG resilience is a good indicator in evaluating the efficiency of the proposed methodology. It should be remembered that types of events, their assessment, and the impact timing distinguish two concepts of reliability and resilience. Reliability is about keeping the power on and focusing on high probability events, while resiliency focuses on high-impact events that are usually rare due to network design. Hence, in the present work, exposing hidden failure of the CBs in the MG formation, which is not a common occurrence but can cause a lot of damage, is a phenomenon where its MG resilience has been calculated and its behavior investigated. It should be remembered that the failure rate of a CB is normally calculated in networks based on long-term planning studies, and exposing hidden failure due to DERs integration would increase the failure rate in the short term; therefore, it falls into the resilience category. On the other hand, the presented methodology refers to the prediction feature of the MG resilience, which is one of the most important aspects of resilience.In this paper, the effect of the above issues and also verification of the efficiency of the proposed methodology in the MG formation is evaluated via an Markov Chain Monte Carlo (MCMC) algorithm, which has been modified based on the proposed method in Ref. [45]. In other words, in this way, implementation of the proposed methodology from the resilience point of view is evaluated.In the MCMC algorithm, firstly, Markov chain of each component is separately built where the failure and repair rate of the studied components are described. Then, by implementation of MC simulation, the dynamic behavior of the network and OCRs is simulated in a random process and the resiliency of the network is calculated. The distinguishing feature of the MCMC algorithm used in this paper is the calculation of CB failure rate according to the amount of short circuit current and its continuity.In this regard, failure rate of each CB (λCB) is considered variable, and is formulated as follows:(13)λCB=∑titclearIscit−ICB−ratedΔt+∑tktclearIscit−IintΔt∑t=02IShortTimeiΔt.WhereICB−rated and Isci are the rated current and the short circuit current passing through each CB. It is clear that Iscit depends upon location and size of the DERs. In this relation, Iint stands for interrupting current of each CB and is considered 6 times of the rated current of CB [33]. Parameters and tk is the time in the process of simulation when the fault current exceeds andIint, respectively. The fault duration is also specified by tclear, which actually is the tripping time of related OCR.In the utilized MCMC technique, to determine behavior of the lines and CBs, the MC simulation is run hourly but for a long period of 1,000 years. To make the analysis more convenient, the failure rates of all lines is assumed as 0.8 failure/year. Furthermore, the repair time of all components is considered to be 3 hours/failure. Then, based on the modeling, the Expected Energy Not Supplied (EENS) index is calculated at the end of a year to assess the resiliency of the MG. It should be noted that given that network behavior is modeled according to the resilience conditions, here EENS is applied as resilience index. Moreover, it is proved that exposing hidden failure of CB, as a rare event, may cause outages that reliability studies do not consider them in solutions for EENS reduction because they have a low amount of probability to inception [48].


## 3.1. Selection of the Optimum Solution Based on Fuzzy Satisfaction Method (FSM)

Generally, in solving multi objective problems, like the MG formation problem of the present study, Pareto-optimal set, which are nondominated to each other but are superior to the rest of solutions in the search space, are obtained. In some cases, the optimal solution among the Pareto-set is determined by expert analysis and trade-off. However, when the number of objective functions, which are sometimes not compatible with each other increases, finding the optimal solution is not easy. To address this issue, in this paper, the Fuzzy Satisfaction Method (FSM) is used to find the optimal solution among Pareto-set.In the applied FSM technique, fuzzy sets, with membership level of 0 to 1, are defined for all the objective functions. The membership value “1” means full compatibility with the set, while the value “0” represents full incompatibility. The membership function is defined in equation (11).(11)μXi=0,Xi≤Ximin,Ximax−XiXimax−Ximin,Ximin≤Xi≤Ximax,1,Xi≥Ximax.Where Ximin and Ximax are the minimum and maximum values of ith objective function in which the solution is expected.The value of the membership functions (μX) indicates how well the solution satisfies the objective function. On the other hand, the minimum membership value for the studied objective functions indicates the optimal state. Therefore, in the MG formation problem with combination of three OFs, among minimum value of the membership functions, the maximum (larger) one is more favorable, since it can lead to more objective functions with individual optimum values.Hence, for multi-objective MG formation problem of the present study, which have three objective functions, the FSM index (ϕ) is calculated for every Pareto solution in repository as follows:(12)ϕ=MaxMinμXi,∀i=1:3.According to equation (12), the optimal solution in the obtained Pareto-set would be the optimal solution for which ϕ is maximum.


## 3.2. Resilience Oriented Evaluation of the MG Formation

As described in the previous two sections, in the process of MG formation, location of the DERs affects the amount of fault current passing through the CBs, as well as the coordination among the OCRs, which is the reason for including these aspects in the proposed methodology.In fact, with an increase in the amplitude and duration of the fault current, the probability of hidden CB failure might also be increased. Therefore, considering the effect of DERs allocation at the level of short circuit and coordination among OCRs, the study of probable exposing of hidden CB failure and subsequent assessment of MG resilience is a good indicator in evaluating the efficiency of the proposed methodology. It should be remembered that types of events, their assessment, and the impact timing distinguish two concepts of reliability and resilience. Reliability is about keeping the power on and focusing on high probability events, while resiliency focuses on high-impact events that are usually rare due to network design. Hence, in the present work, exposing hidden failure of the CBs in the MG formation, which is not a common occurrence but can cause a lot of damage, is a phenomenon where its MG resilience has been calculated and its behavior investigated. It should be remembered that the failure rate of a CB is normally calculated in networks based on long-term planning studies, and exposing hidden failure due to DERs integration would increase the failure rate in the short term; therefore, it falls into the resilience category. On the other hand, the presented methodology refers to the prediction feature of the MG resilience, which is one of the most important aspects of resilience.In this paper, the effect of the above issues and also verification of the efficiency of the proposed methodology in the MG formation is evaluated via an Markov Chain Monte Carlo (MCMC) algorithm, which has been modified based on the proposed method in Ref. [45]. In other words, in this way, implementation of the proposed methodology from the resilience point of view is evaluated.In the MCMC algorithm, firstly, Markov chain of each component is separately built where the failure and repair rate of the studied components are described. Then, by implementation of MC simulation, the dynamic behavior of the network and OCRs is simulated in a random process and the resiliency of the network is calculated. The distinguishing feature of the MCMC algorithm used in this paper is the calculation of CB failure rate according to the amount of short circuit current and its continuity.In this regard, failure rate of each CB (λCB) is considered variable, and is formulated as follows:(13)λCB=∑titclearIscit−ICB−ratedΔt+∑tktclearIscit−IintΔt∑t=02IShortTimeiΔt.WhereICB−rated and Isci are the rated current and the short circuit current passing through each CB. It is clear that Iscit depends upon location and size of the DERs. In this relation, Iint stands for interrupting current of each CB and is considered 6 times of the rated current of CB [33]. Parameters and tk is the time in the process of simulation when the fault current exceeds andIint, respectively. The fault duration is also specified by tclear, which actually is the tripping time of related OCR.In the utilized MCMC technique, to determine behavior of the lines and CBs, the MC simulation is run hourly but for a long period of 1,000 years. To make the analysis more convenient, the failure rates of all lines is assumed as 0.8 failure/year. Furthermore, the repair time of all components is considered to be 3 hours/failure. Then, based on the modeling, the Expected Energy Not Supplied (EENS) index is calculated at the end of a year to assess the resiliency of the MG. It should be noted that given that network behavior is modeled according to the resilience conditions, here EENS is applied as resilience index. Moreover, it is proved that exposing hidden failure of CB, as a rare event, may cause outages that reliability studies do not consider them in solutions for EENS reduction because they have a low amount of probability to inception [48].


## 4. Test System and Simulation Results

### 4.1. Description of the Test System

The proposed methodology has been derived in such a way that it can be implemented on any distribution network. However, to verify the effectiveness of the proposed methodology in transformation of a distribution network into MG, a test case (on the basis of the standard IEEE 34-buses distribution network) has been chosen (Figure1). The main advantage of using such a vast and large test system is that if the proposed algorithm gives a suitable optimal solution for such a case study, it will definitely be able to calculate the optimal solution for smaller networks.As can be seen in Figure1, there are some Disconnector Switch (DS) where the feeders are connected to each other for meshed operation of the MG. Examining this capability during the implementation of the algorithm confirms the efficiency of the proposed methodology for converting the distribution network to both types of radial and meshed MGs. However, this methodology can also be implemented in any other test systems. In the present study, modeling of the network, the simulation routine, and different analyses are fulfilled accurately in the DIgSILENT environment.To assess the effectiveness of the proposed methodology in MG formation, the results and findings are given in four parts. First, the optimal allocation of four DERs within the MG along with the Pareto-optimal set is found. Afterwards, the optimal setting of protection system and coordination among relays within the configured MG is reported. These results are calculated by implementing the proposed formulation, as formulated in section2, and depicted in flowchart of Figure 2. Then, by specifying the MG configuration, the ability of the control strategy for smooth and stable transition to the island mode is depicted. At last, in order to verify the obtained solutions, the resiliency-oriented study, presented in section 3.2, is performed.


### 4.2. Optimal DERs Allocation and Discussion

In solving the MG formation problem, first, the optimal solutions for siting and sizing of four DERs within the MG (i.e., the optimal capacity and location of DERs) are calculated. In the present study, the repository consists of 10 Pareto-optimal solutions, which has been reported in Tables1 and 2. The optimal placement and capacity of DERs related to each solution is reported in Table 1. From the perspective of the defined objective functions, i.e., power losses, voltage deviation, and protection coordination, the transformation of the distribution network into a MG can be done successfully by using the optimal allocation obtained in all these solutions. However, the values of the OFs in these solutions are different. The values of different OFs, including the total value of power losses, minimum and maximum voltage of buses, amount of improvement in the voltage deviation, and losses of the feeders in the presence of the allocated DERs, are separately reported in Table 2 for two grid-connected and islanded modes of the MG.Table 1
Optimal solutions for DERs allocation within the MG.
Solution no.DER 1DER 2DER 3DER 4Size (MW)Site (bus)Size (MW)Site (bus)Size (MW)Site (bus)Size (MW)Site (bus)11.5692131.528210422.51050.56526129931.5701.5581.5282.510142.51030.5526429951.5692150.5262.510561652.51081.55829972681.555126210781.5731621.5282.5105911051.5711.5262.5106102.51031962.563152Table 2
The Pareto-optimal set obtained by solving the proposed formulation.
Solution noGrid-connected modeIslanded modeOFs valueLoss (KW)V-deviation (p.u.)Min voltage (p.u.)Max voltage (p.u.)Loss (KW)V-deviation (p.u.)Min voltage (p.u.)Max voltage (p.u.)Total losses (KW)Total V-deviation (p.u.)Total relay times (Sec)Base case808.99582.244310.8667550.999921———0.999921808.99582.24431—1225.066900.9673871.01185241.09340.2353140.9336951.01185466.16030.23531415.561185241.392600.952941.003841259.32780.753040.9175361.003841500.72040.7530417.982337245.725300.9671820.999953263.96530.2701150.9323170.999953509.69050.17011513.149443253.168500.9606631.02406271.21470.192260.92661.02406524.38310.1922614.00529258.04300.9738271.013703271.23090.2419380.9391911.013703523.90320.24193814.741274267.4200.9737771.009282286.46830.1534990.9401561.009282553.88830.15349914.855842269.611600.9739281.012339288.68340.0951790.9403441.012339558.2950.09517918.760518268.654600.9739281.020798288.3750.1953530.939261.020798557.02970.19535316.2989210276.161300.9739571.025749295.63760.1246810.9403571.025749571.79890.12468113.989256289.800100.9737261.02135310.20910.0988540.9400491.02135600.00920.09885414.72705As can be seen, demonstration of the results in Table2 is based on their effectiveness in reducing power losses. To compare, the results for the base case of the network, when no DERs are allocated, are also presented. It is evident that all the reported solutions improve MG performance, in terms of voltage profile improvement and power loss reduction, compared to the base case. For example, the total power losses of the MG in the base case is 808.9958 kW, while in the first solution it is considerably reduced to 466.1603 kW. Similar findings are also comparable simply.In addition, in Table2, the results of the minimum and maximum voltage of the MG terminals prove that the voltage of all terminals is controlled within the permissible range, compared to the base case. Further, with the DERs allocation and the formation of the MG, the value of voltage deviation has been reduced from 2.244 p.u to 0.235314 p.u. It should be, however, noted that the total voltage deviation calculated in the solution 7 is the lowest (0.095179 p.u). This shows that none of the reported solutions are dominated, and this is due to the inconsistent behavior of the objective functions towards each other. For example, the best coordination time is obtained in solution 7 (13.14944 sec), while in this solution the values of power losses (509.6905 kW) and voltage deviation (0.2701 p.u) are not the best. In addition, plots of Figure 3 depict the behavior of three OFs value for each solution (among the Paretoset). The best solution found (solution No.7) is marked in the figure. It can be clearly seen in Figure 3 that in the best solution, not all objective functions (OFs) are necessarily optimized.Figure 3
Behavior of three OFs value for each solution (among the Pareto-set).According to the discussion above, it can be concluded that the solutions among Pareto-optimal set are nondominated to each other but are superior to the rest of the solutions in the search space. Aiming to determine the best solution among the reported Pareto-set, the FSM method, as described in section3.1, has been employed. The related results and index ϕ are given in Table 3.Table 3
The μX values for different of and FSM index for pareto solutions.
Solution no.μXMinimum valuePower lossesVoltage deviationRelay coordination10.593150.764680.688770.5931520.622110.90480.624780.6221130.669880.80770.719890.6698840.628320.84650.702880.628350.703210.246950.640350.2469560.563360.901140.705450.563367∗0.690570.72980.737010.6905780.623900.80460.674020.6239090.670550.758060.705170.67055100.603100.875310.720210.60310[100,1000][0,1][5,50]ϕ0.69057From the results of Table4, it can be concluded that solution 7 satisfies equations (11) and (12), and it is the best solution among the Pareto-set. The value of ϕ in this case is 0.69057. Moreover, in the last row of this table, the values of Ximin andXimax, related to each OF, have been specified. It should be noted that in this solution, the values of the OFs of losses, voltage deviation, and total OCRs trip times are 509.6905 kW, 0.170115 p.u., and 13.14944 sec, respectively, which are not their best values compared to other solutions. However, based on the FSM algorithm, the best solution for the MG formation would be solution 7. In fact, a reasonable compromise between different OFs is found in this solution.Table 4
Optimal setting of OCRs (obtained in solution 7).
Relay no.IpTMSDirectionRelay no.IpTMSDirection172.026940.40498Forward1856.256910.10568Forward28.4216570.149615Forward1938.055110.283627Forward334.105760.112237Forward2028.151990.05Forward4139.49850.189306Forward2133.84290.088465Forward574.127660.360521Forward2231.071980.161277Forward632.00290.240193Forward2319.65160.166711Forward722.136230.05028Forward2443.579680.050787Forward818.066450.301667Forward2514.592250.293759Forward983.413430.316163Forward261.9680630.507757Forward1069.00670.175124Forward2717.052880.71547Forward1197.874360.255932Forward2841.706710.539614Backward128.8629710.293306Forward2934.503350.34718Backward137.2081720.232125Forward3024.502930.543967Backward1429.440360.66205Forward319.504780.426613Backward1536.135140.069731Forward3223.775690.454979Backward1633.329610.277128Forward3316.278720.320204Backward1730.290950.187547Forward341.4940930.594948Backward


### 4.3. Optimal OCRs Coordination

As per the flowchart shown in Figure2, in the process of MG formation, to ensure the performance of protection system of the MG during fault condition, the DERs allocation is conducted simultaneously with calculation of the optimal setting of OCRs and coordination among them. In this respect, a complete protection scheme for the MG (when connected to the network) is achieved, which is effective even in the case of DERs disconnection. In Table 4, optimal parameters setting of OCRs (related to the selected solution No. 7) are reported. Note that all OCRs used in the protection strategy are directional and their direction has also been demonstrated in Table 4. It is also interesting to note that applying the obtained optimal OCRs settings reduces the total operating time of the OCRs, which is a very important factor for preserving the MG stability. In the last column of Table 2, the total relay time, as the studied objective function, is given.Furthermore, Table4 shows the optimal settings of the OCRs corresponding to the first solution, and based on that, the MG is protected against all faults in a reliable and coordinated manner.


### 4.4. Seamless Transition and Stable Operation of the Islanded MG

As per description of the control strategy given in section2.3, DERs would participate in frequency control (especially in secondary frequency control) based on their droop setting. By conducting dynamic studies, droops of allocated DERs are set to 0.04 to meet the control requirements stated in section 2.3. The results of studies indicate that adjusting droop less than this value increases the frequency fluctuations and more than this amount reduces the effective participation of DERs in frequency control. Figure 4 shows frequency deviation of the MG under different droop setting in the transition mode. As can be seen, due to the poor response rate of DERs (and the absence of ESS), the amplitude of frequency deviation is large.Figure 4
Frequency deviation of the MG under different droop setting.Furthermore, in order to evaluate the performance of the proposed control strategy in the transition to the islanded mode, dynamic studies have been conducted. In these studies, the proposed control strategy is simulated in such a way that the MG, after detecting a 3-phase fault in the upstream network, separates from the PCC and switches to island mode. In such a condition, the control system must ensure the smooth transition and stable operation of the MG. The main purpose of these studies is MG stability assessment and CCT parameter–which is one of the most important criteria for assessing the transient stability of a network–as desire target is calculated. For the sake of comparison, the following scenarios are defined:Scenario 1: Voltage/frequency control strategy is adopted for all allocated DERs; however, droop value (R) is set higher than 0.04. In this scenario, ESS is not employed.Scenario 2: Voltage/frequency control strategy is adopted for all allocated DERs and calculated droop (R = 0.04) is set for DERs controller. In this scenario, ESS is not employed as well.Scenario 3: Apply the conditions mentioned in scenario 2, plus installation of the ESS in the MG.Scenario 4: MG intentional islanding is studied in this scenario.Rotor angle variation of the DER1 (as per the optimal results of Table1) for the various scenarios is depicted in Figure 5. This figure also reports the calculated CCT value in each scenario.Figure 5
Rotor Angle variation of DER1 in four studied scenarios and calculated CCT.By comparing rotor angle of DER 1 in two scenarios 1 and 2 (where ESS has not been utilized), it is observed that the value of CCT in scenario 2, where the calculated droop (R = 0.04) is set, is increased and therefore the stability of the MG is improved. However, the security margin is still low in this situation. Moreover, it is clear that the time interval for rotor angle variation is long when EES has not yet been added to the system. This is because the MG is only controlled by the performance of the DERs, which have a low response speed.As explained earlier, with installation of the ESS, which is able to quickly participate in MG control after separation from the upstream network, the MG stability is significantly improved. Looking at Figure5 and rotor angle variation of DER in scenario 3 proves this fact. Furthermore, in this scenario, the value of CCT has increased to 125 msec which indicates the positive effect of the proposed strategy in maintaining the MG stability.In this figure, the rotor angle variation of DER during planned islanding (scenario 4) is also illustrated, which, of course, due to the absence of disturbance, has low deviation from initial state and so a reasonable stability is obtained.


### 4.5. Resilience-Oriented Verification of the Proposed Methodology

To verify the calculated settings and efficiency of the proposed algorithm in the MG formation, network resilience estimation studies, which are described in section3.2, have been conducted here. To do so, the MCMC algorithm is implemented for the following two scenarios and the MG resilience by calculating EENS is evaluated. It has already mentioned that EENS is used for reliability and resilience study, while modeling the system behavior that leads to the calculation of EENS is different for the two concepts of reliability and resilience.In the first and base scenario, the allocation of the DERs is done without considering the allowable level of short circuit and optimal coordination among OCRs. In fact, in this scenario, the OCRs are set separately after installing DERs. To this end, although an attempt has been made to achieve the optimal level of coordination using the PSO algorithm, due to the impossibility of changing the location and capacity of the DERs, the quality of coordination is not desirable.In the second scenario, the MG formation is done according to the proposed algorithm and by applying the obtained solution No. 7 (see Tables1 and 2) to the MG.By implementation of the MCMC algorithm in the resulting MG in the scenarios 1 and 2, the values of the EENS are calculated as 59803.4 kWh/yr and 50247.7 kWh/yr, respectively. It can be concluded that MG resiliency in scenario 1 notably declined because of violation of the short circuit current and protection miscoordination, with both issues dramatically affecting system resiliency, as discussed in section3.2. In other words, comparison of these results shows that by applying the proposed methodology, the resiliency level of the MG increases, which is due to the possibility of controlling the level of short circuit current in proportion to the designed fault-level capability of the CBs and proper OCRs coordination in the process of MG formation.


## 4.1. Description of the Test System

The proposed methodology has been derived in such a way that it can be implemented on any distribution network. However, to verify the effectiveness of the proposed methodology in transformation of a distribution network into MG, a test case (on the basis of the standard IEEE 34-buses distribution network) has been chosen (Figure1). The main advantage of using such a vast and large test system is that if the proposed algorithm gives a suitable optimal solution for such a case study, it will definitely be able to calculate the optimal solution for smaller networks.As can be seen in Figure1, there are some Disconnector Switch (DS) where the feeders are connected to each other for meshed operation of the MG. Examining this capability during the implementation of the algorithm confirms the efficiency of the proposed methodology for converting the distribution network to both types of radial and meshed MGs. However, this methodology can also be implemented in any other test systems. In the present study, modeling of the network, the simulation routine, and different analyses are fulfilled accurately in the DIgSILENT environment.To assess the effectiveness of the proposed methodology in MG formation, the results and findings are given in four parts. First, the optimal allocation of four DERs within the MG along with the Pareto-optimal set is found. Afterwards, the optimal setting of protection system and coordination among relays within the configured MG is reported. These results are calculated by implementing the proposed formulation, as formulated in section2, and depicted in flowchart of Figure 2. Then, by specifying the MG configuration, the ability of the control strategy for smooth and stable transition to the island mode is depicted. At last, in order to verify the obtained solutions, the resiliency-oriented study, presented in section 3.2, is performed.


## 4.2. Optimal DERs Allocation and Discussion

In solving the MG formation problem, first, the optimal solutions for siting and sizing of four DERs within the MG (i.e., the optimal capacity and location of DERs) are calculated. In the present study, the repository consists of 10 Pareto-optimal solutions, which has been reported in Tables1 and 2. The optimal placement and capacity of DERs related to each solution is reported in Table 1. From the perspective of the defined objective functions, i.e., power losses, voltage deviation, and protection coordination, the transformation of the distribution network into a MG can be done successfully by using the optimal allocation obtained in all these solutions. However, the values of the OFs in these solutions are different. The values of different OFs, including the total value of power losses, minimum and maximum voltage of buses, amount of improvement in the voltage deviation, and losses of the feeders in the presence of the allocated DERs, are separately reported in Table 2 for two grid-connected and islanded modes of the MG.Table 1
Optimal solutions for DERs allocation within the MG.
Solution no.DER 1DER 2DER 3DER 4Size (MW)Site (bus)Size (MW)Site (bus)Size (MW)Site (bus)Size (MW)Site (bus)11.5692131.528210422.51050.56526129931.5701.5581.5282.510142.51030.5526429951.5692150.5262.510561652.51081.55829972681.555126210781.5731621.5282.5105911051.5711.5262.5106102.51031962.563152Table 2
The Pareto-optimal set obtained by solving the proposed formulation.
Solution noGrid-connected modeIslanded modeOFs valueLoss (KW)V-deviation (p.u.)Min voltage (p.u.)Max voltage (p.u.)Loss (KW)V-deviation (p.u.)Min voltage (p.u.)Max voltage (p.u.)Total losses (KW)Total V-deviation (p.u.)Total relay times (Sec)Base case808.99582.244310.8667550.999921———0.999921808.99582.24431—1225.066900.9673871.01185241.09340.2353140.9336951.01185466.16030.23531415.561185241.392600.952941.003841259.32780.753040.9175361.003841500.72040.7530417.982337245.725300.9671820.999953263.96530.2701150.9323170.999953509.69050.17011513.149443253.168500.9606631.02406271.21470.192260.92661.02406524.38310.1922614.00529258.04300.9738271.013703271.23090.2419380.9391911.013703523.90320.24193814.741274267.4200.9737771.009282286.46830.1534990.9401561.009282553.88830.15349914.855842269.611600.9739281.012339288.68340.0951790.9403441.012339558.2950.09517918.760518268.654600.9739281.020798288.3750.1953530.939261.020798557.02970.19535316.2989210276.161300.9739571.025749295.63760.1246810.9403571.025749571.79890.12468113.989256289.800100.9737261.02135310.20910.0988540.9400491.02135600.00920.09885414.72705As can be seen, demonstration of the results in Table2 is based on their effectiveness in reducing power losses. To compare, the results for the base case of the network, when no DERs are allocated, are also presented. It is evident that all the reported solutions improve MG performance, in terms of voltage profile improvement and power loss reduction, compared to the base case. For example, the total power losses of the MG in the base case is 808.9958 kW, while in the first solution it is considerably reduced to 466.1603 kW. Similar findings are also comparable simply.In addition, in Table2, the results of the minimum and maximum voltage of the MG terminals prove that the voltage of all terminals is controlled within the permissible range, compared to the base case. Further, with the DERs allocation and the formation of the MG, the value of voltage deviation has been reduced from 2.244 p.u to 0.235314 p.u. It should be, however, noted that the total voltage deviation calculated in the solution 7 is the lowest (0.095179 p.u). This shows that none of the reported solutions are dominated, and this is due to the inconsistent behavior of the objective functions towards each other. For example, the best coordination time is obtained in solution 7 (13.14944 sec), while in this solution the values of power losses (509.6905 kW) and voltage deviation (0.2701 p.u) are not the best. In addition, plots of Figure 3 depict the behavior of three OFs value for each solution (among the Paretoset). The best solution found (solution No.7) is marked in the figure. It can be clearly seen in Figure 3 that in the best solution, not all objective functions (OFs) are necessarily optimized.Figure 3
Behavior of three OFs value for each solution (among the Pareto-set).According to the discussion above, it can be concluded that the solutions among Pareto-optimal set are nondominated to each other but are superior to the rest of the solutions in the search space. Aiming to determine the best solution among the reported Pareto-set, the FSM method, as described in section3.1, has been employed. The related results and index ϕ are given in Table 3.Table 3
The μX values for different of and FSM index for pareto solutions.
Solution no.μXMinimum valuePower lossesVoltage deviationRelay coordination10.593150.764680.688770.5931520.622110.90480.624780.6221130.669880.80770.719890.6698840.628320.84650.702880.628350.703210.246950.640350.2469560.563360.901140.705450.563367∗0.690570.72980.737010.6905780.623900.80460.674020.6239090.670550.758060.705170.67055100.603100.875310.720210.60310[100,1000][0,1][5,50]ϕ0.69057From the results of Table4, it can be concluded that solution 7 satisfies equations (11) and (12), and it is the best solution among the Pareto-set. The value of ϕ in this case is 0.69057. Moreover, in the last row of this table, the values of Ximin andXimax, related to each OF, have been specified. It should be noted that in this solution, the values of the OFs of losses, voltage deviation, and total OCRs trip times are 509.6905 kW, 0.170115 p.u., and 13.14944 sec, respectively, which are not their best values compared to other solutions. However, based on the FSM algorithm, the best solution for the MG formation would be solution 7. In fact, a reasonable compromise between different OFs is found in this solution.Table 4
Optimal setting of OCRs (obtained in solution 7).
Relay no.IpTMSDirectionRelay no.IpTMSDirection172.026940.40498Forward1856.256910.10568Forward28.4216570.149615Forward1938.055110.283627Forward334.105760.112237Forward2028.151990.05Forward4139.49850.189306Forward2133.84290.088465Forward574.127660.360521Forward2231.071980.161277Forward632.00290.240193Forward2319.65160.166711Forward722.136230.05028Forward2443.579680.050787Forward818.066450.301667Forward2514.592250.293759Forward983.413430.316163Forward261.9680630.507757Forward1069.00670.175124Forward2717.052880.71547Forward1197.874360.255932Forward2841.706710.539614Backward128.8629710.293306Forward2934.503350.34718Backward137.2081720.232125Forward3024.502930.543967Backward1429.440360.66205Forward319.504780.426613Backward1536.135140.069731Forward3223.775690.454979Backward1633.329610.277128Forward3316.278720.320204Backward1730.290950.187547Forward341.4940930.594948Backward


## 4.3. Optimal OCRs Coordination

As per the flowchart shown in Figure2, in the process of MG formation, to ensure the performance of protection system of the MG during fault condition, the DERs allocation is conducted simultaneously with calculation of the optimal setting of OCRs and coordination among them. In this respect, a complete protection scheme for the MG (when connected to the network) is achieved, which is effective even in the case of DERs disconnection. In Table 4, optimal parameters setting of OCRs (related to the selected solution No. 7) are reported. Note that all OCRs used in the protection strategy are directional and their direction has also been demonstrated in Table 4. It is also interesting to note that applying the obtained optimal OCRs settings reduces the total operating time of the OCRs, which is a very important factor for preserving the MG stability. In the last column of Table 2, the total relay time, as the studied objective function, is given.Furthermore, Table4 shows the optimal settings of the OCRs corresponding to the first solution, and based on that, the MG is protected against all faults in a reliable and coordinated manner.


## 4.4. Seamless Transition and Stable Operation of the Islanded MG

As per description of the control strategy given in section2.3, DERs would participate in frequency control (especially in secondary frequency control) based on their droop setting. By conducting dynamic studies, droops of allocated DERs are set to 0.04 to meet the control requirements stated in section 2.3. The results of studies indicate that adjusting droop less than this value increases the frequency fluctuations and more than this amount reduces the effective participation of DERs in frequency control. Figure 4 shows frequency deviation of the MG under different droop setting in the transition mode. As can be seen, due to the poor response rate of DERs (and the absence of ESS), the amplitude of frequency deviation is large.Figure 4
Frequency deviation of the MG under different droop setting.Furthermore, in order to evaluate the performance of the proposed control strategy in the transition to the islanded mode, dynamic studies have been conducted. In these studies, the proposed control strategy is simulated in such a way that the MG, after detecting a 3-phase fault in the upstream network, separates from the PCC and switches to island mode. In such a condition, the control system must ensure the smooth transition and stable operation of the MG. The main purpose of these studies is MG stability assessment and CCT parameter–which is one of the most important criteria for assessing the transient stability of a network–as desire target is calculated. For the sake of comparison, the following scenarios are defined:Scenario 1: Voltage/frequency control strategy is adopted for all allocated DERs; however, droop value (R) is set higher than 0.04. In this scenario, ESS is not employed.Scenario 2: Voltage/frequency control strategy is adopted for all allocated DERs and calculated droop (R = 0.04) is set for DERs controller. In this scenario, ESS is not employed as well.Scenario 3: Apply the conditions mentioned in scenario 2, plus installation of the ESS in the MG.Scenario 4: MG intentional islanding is studied in this scenario.Rotor angle variation of the DER1 (as per the optimal results of Table1) for the various scenarios is depicted in Figure 5. This figure also reports the calculated CCT value in each scenario.Figure 5
Rotor Angle variation of DER1 in four studied scenarios and calculated CCT.By comparing rotor angle of DER 1 in two scenarios 1 and 2 (where ESS has not been utilized), it is observed that the value of CCT in scenario 2, where the calculated droop (R = 0.04) is set, is increased and therefore the stability of the MG is improved. However, the security margin is still low in this situation. Moreover, it is clear that the time interval for rotor angle variation is long when EES has not yet been added to the system. This is because the MG is only controlled by the performance of the DERs, which have a low response speed.As explained earlier, with installation of the ESS, which is able to quickly participate in MG control after separation from the upstream network, the MG stability is significantly improved. Looking at Figure5 and rotor angle variation of DER in scenario 3 proves this fact. Furthermore, in this scenario, the value of CCT has increased to 125 msec which indicates the positive effect of the proposed strategy in maintaining the MG stability.In this figure, the rotor angle variation of DER during planned islanding (scenario 4) is also illustrated, which, of course, due to the absence of disturbance, has low deviation from initial state and so a reasonable stability is obtained.


## 4.5. Resilience-Oriented Verification of the Proposed Methodology

To verify the calculated settings and efficiency of the proposed algorithm in the MG formation, network resilience estimation studies, which are described in section3.2, have been conducted here. To do so, the MCMC algorithm is implemented for the following two scenarios and the MG resilience by calculating EENS is evaluated. It has already mentioned that EENS is used for reliability and resilience study, while modeling the system behavior that leads to the calculation of EENS is different for the two concepts of reliability and resilience.In the first and base scenario, the allocation of the DERs is done without considering the allowable level of short circuit and optimal coordination among OCRs. In fact, in this scenario, the OCRs are set separately after installing DERs. To this end, although an attempt has been made to achieve the optimal level of coordination using the PSO algorithm, due to the impossibility of changing the location and capacity of the DERs, the quality of coordination is not desirable.In the second scenario, the MG formation is done according to the proposed algorithm and by applying the obtained solution No. 7 (see Tables1 and 2) to the MG.By implementation of the MCMC algorithm in the resulting MG in the scenarios 1 and 2, the values of the EENS are calculated as 59803.4 kWh/yr and 50247.7 kWh/yr, respectively. It can be concluded that MG resiliency in scenario 1 notably declined because of violation of the short circuit current and protection miscoordination, with both issues dramatically affecting system resiliency, as discussed in section3.2. In other words, comparison of these results shows that by applying the proposed methodology, the resiliency level of the MG increases, which is due to the possibility of controlling the level of short circuit current in proportion to the designed fault-level capability of the CBs and proper OCRs coordination in the process of MG formation.


## 5. Conclusion

Today, with the development of smart grids, many distribution companies are planning to transform part of the network into an MG. The best feature of the MG is its ability to operate autonomously, which is possible based on the DERs integration within the MG. In this paper, a new methodology for DERs allocation with the aim of the MG formation is proposed in which a multi-objective programming (with goals of minimizing power losses, voltage deviation, and level of the OCRs miscoordination) has been developed. The paper showed that in the MG formation process, considering the coordination of OCRs via short circuit studies is of particular importance because changing of the amplitude of short circuit current after the integration of DERs can lead to miscoordination in the operation of OCRs, also expose hidden CB failure. Hence, resiliency-oriented evaluation of the MG formation by the MCMC algorithm is also performed. The results showed that resiliency is significantly reduced if short circuit studies and performance of the protection system are not considered in the process of MG formation.Finally, in the proposed methodology, in order to achieve seamless transition and stable operation of the MG in island mode, an efficient control strategy, based on utilization of the ESS along with speed droop control of allocated DERs, is also presented.The proposed method has been solved by a modified multi-objective PSO algorithm for a large network and the pertinent Pareto-set are obtained. However, due to nondominated optimal solutions, a Fuzzy Satisfaction Method (FSM) is utilized to find the optimal solution among the Pareto-set. The results show that the best optimal solution is not the best in all objective functions, but the FSM method by compromising between them finds the best solution.



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*Source: 6459044-2022-07-21.xml*