A Multi-Objective Approach for the Optimal Placement of Protection and Control Devices in Distribution Networks with Microgrids

Protection and control systems represent an essential part of distribution networks by ensuring the physical integrity of components and by improving system reliability. Protection devices isolate a portion of the network affected by a fault, while control devices reduce the number of de-energized loads by transferring loads to neighboring feeders. The integration of distributed generation has the potential to enhance the continuity of energy services through islanding operation during outage conditions. In this context, this paper presents a multi-objective optimization approach for sizing and allocating protection and control devices in distribution networks with microgrids supplied by renewable energy sources. Reclosers, fuses, remote-controlled switches, and directional relays are considered in the formulation. The demand and generation uncertainties define the islanding operation and the load transfer possibilities. A non-dominated sorting genetic algorithm is applied in the solution of the allocation problem considering two conflicting objectives: cost of energy not supplied and equipment cost. The compromise programming is then performed to achieve the best solution from the Pareto front. Results show interesting setups for the protection system and viability of islanding operation.


I. INTRODUCTION
The traditional fault isolation and supply service restoration methods are essential for planning a distribution network to reach good reliability indices. Insolation methods include circuit breaker, reclosers and fuses action, while restoration methods comprise manual and automatic switches operation.
About 80% of faults occur in the distribution network, where approximately 75-90% are temporary in nature [1]. For this reason, reclosers play the important role of mitigating temporary failures in fast trip mode. If the fault becomes permanent, the recloser changes its operation mode, allowing fuses closer to the fault melt first, minimizing the impact on the system. Permanent faults, although less frequent, have a greater impact on the service interruption for customers, drastically increasing the amount of energy not supplied (ENS). During permanent faults, automatic switches (AS) available in the network could change their status by the system's operator and transfer part of the interrupted loads, into not faulted feeder sections, to neighbor feeders.
The integration of distributed generation (DG) brings several benefits and new challenges to distribution companies. A potential advantage is the islanding operation of DG units with part of the distribution network loads, operating as a microgrid [2]. However, the microgrid must have an adequate control system to guarantee the quality of energy supply to customers, in addition to safety when reconnecting with the distribution system. This strategy enables a substantial reduction in customer service interruptions during fault conditions. Therefore, the emergence of distribution systems with distributed generators and advanced autonomous systems offers a valuable opportunity to improve reliability through the islanding operation of microgrids [3], [4].
Several works consider the optimal allocation of protection and control devices without DG to improve the system reliability, [5]- [17]. In the last decade, the integration of DG units in distribution systems has grown exponentially, bringing several publications approaching the optimal allocation of protective devices in distribution networks with DG units [18]- [27]. However, just a few works consider the technical differences between dispatchable and renewable DG [24], [25], [27].
Some works consider the islanding operation [19]- [25], [27], while a few publications consider the demand and generation uncertainties to allow the operation of microgrids [27]. Most countries do not allow the DG islanding operation, despite the benefits that this technique can provide. The most common technical barriers comprise dual modes of operation, quality and control of energy, and problems of protection systems [2]. However, some papers in the literature have shown promising results in these topics [4], [21]- [25], [27]. Therefore, the islanding operation can be an attractive alternative to maximize the DG benefits and improve the distribution system's reliability.
A summary of the main features from specialized literature review is shown in Table I. Protection and control include devices such as circuit breakers, reclosers, fuses, ASs, and island interconnection devices (IID). DG units are categorized as dispatchable (D) and renewable (R), where the second one depends on the power output uncertainties. The reliability indices considered in the literature review includes the cost of energy not supplied (CENS), system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), momentary average interruption frequency index (MAIFI), and the average system interruption duration index (ASIDI).
This work proposes an optimal allocation method of protection and control devices in distribution networks, considering the islanding operation and load transference possibility in a multi-objective approach. Unlike [5]- [9], [11]- [16], [18]- [22], this work includes DG units from different technologies.
Dispatchable DG units can easily operate in islanded mode, while renewable DG units, like photovoltaic (PV) and wind turbines (WT), depends on the associated uncertainties to provide the necessary power output to the load demand. In [27], the authors define the microgrid zone manually, considering a sum of total loads that can be easily supplied by the DG in island mode. In [24], the island operation using dispatchable or renewable DG units depends on the probability to generate power greater than or equal to a certain level. In [25], the island operation depends on the DG capacity and DG utilization, while [26] consider the DG capacity and voltage profile. However, evaluate the necessary energy during the island operation must be considered in renewable  DG units to ensure a safer island operation since the associated uncertainties could provide lower power than the microgrid's demand, directly affecting the quality of energy supply and the microgrid's stability. The inclusion of batteries increases reliability in such conditions. Therefore, in contrast to [24]- [27], proper islanding operation in microgrids powered by renewable DG units is ensured comparing the necessary energy during outage conditions and the available energy from all distributed energy sources within the microgrid, including battery energy storage systems (BESS). The uncertainties from demand and generation are carried out using historical data classified by the k-means method.
The main contributions of this work are the following: 1) The sizing and allocation of all traditional protective and control devices: reclosers, fuses, and sectionalizing switches. The recloser's protection zone is expanded during temporary faults, increasing the reliability indices. Furthermore, the proposal considers the fusesave scheme and load transference to neighbor feeders; 2) The use of dispatchable and renewable DG units, taking into account their power output uncertainties. For example, solar irradiation for PV units and wind speed for WT units; 3) The inclusion of IID to provide the possibility of islanded operation using DG units with part of distribution network loads as a microgrid. This strategy provides dual operation modes, allowing microgrids to change their status during temporary and permanent fault conditions. For microgrids supplied by intermittent generation, the islanded operation is strictly subject to the balance of energy available from distributed energy resources and microgrid's demand; 4) A fuzzy inference system (FIS) to estimate the batteries' state of charge (SoC) during the entire year. The fuzzy sets and fuzzy rules are adjusted using neural network tuning techniques. Associated uncertainties are used as input data, and the batteries' SoC from an optimal power flow model is considered output data. Also, a comparison is performed solving the allocation problem using batteries' SoC from both methods. 5) NSGA-II is implemented to solve the allocation problem of protective and control devices. The proposed method includes variable crossover and mutation rates and elitism strategy. NSGA-II generates efficient solutions while the compromise programming (CP) finds the best compromise solution among them, where the equipment cost and the CENS are the conflicting objectives.

II. METODOLOGY
In the problem for allocating protection and control devices, the best place to install each type of device is found by reducing outage impacts and equipment cost and by maximizing the reliability indices. Such devices have different behaviors and costs to mitigate faults.

A. PROTECTION DEVICES AND ISLAND OPERATION
Fuses are the most basic protective equipment in distribution networks. If a fault occurs downstream of a fuse, the high short-circuit current flowing through the circuit heats the fuse link and causes it to melt, de-energizing downstream loads [21]. This type of equipment is helpful during permanent faults mainly because its low acquisition cost. However, fuses can also melt during temporary outages, unnecessarily deenergizing downstream customers. Therefore, reclosers play an important role in distribution networks with fuses by the fuse-save scheme. On the other hand, fuse-blow scheme melts the fuse first than reclosers' trip. Such technique reduces the MAIFI, but at the cost of increasing the SAIDI. The fuse-blow scheme is used in regions with high short-circuit currents, where the coordination cannot be realized.
A recloser is an AS with instantaneous and temporary overcurrent relays, ANSI 50/51, and a reclosing relay, ANSI 79. Instantaneous recloser's characteristic includes a predefined number of operations. The recloser opens the circuit to reduce the fault propagation during permanent faults, and the circuit remains opened until the maintenance team fix the problem. During temporary faults, the recloser's protective zone is expanded overlapping the protection zone of downstream fuses [22]. This scheme protects the fuse from melting during temporary faults. Fig. 1 shows an example of a distribution system with a recloser installed in branch 1 or B1, ASs in B19 and B88, a fuse in B32, and an IID in B37. If a fault occurs downstream of the fuse, the recloser will trip before the fuse melts. After a predefined sequence of operations, the recloser blocks the instantaneous function and operates slowly than the fuse, allowing it to melt first.
AS is used by the system's operator to isolate a fault or transfer loads to neighbor feeders. After the recloser's trip during a permanent fault within its protective zone, the system's operator can open the AS in B19 and close the AS in B88, transferring the loads to feeder 2 and reducing the number of disconnected customers.
IID is a bidirectional automatic recloser with reclosing function subjected to the synchronization verification [22]. This equipment is responsible to identify upstream faults and perform the microgrid's island operation. Dispatchable DG units can operate in island mode with voltage and frequency levels within limits set by regulatory agencies. Renewable DG units have their power output depending on the generation 17  uncertainties. For instance, a PV unit with an adequate capacity could supply a microgrid if the solar irradiation provides sufficient power to the microgrid's loads. However, the associated uncertainties could provide lower power than the microgrid's demand, directly affecting the quality of energy supply and the microgrid's stability. Therefore, renewable DG units are not allowed to operate in islanded mode, except in cases of renewable DG with BESS, where its operation mode depends on the batteries' SoC.

B. UNCERTAINTY MODELLING
The growth of demand in distribution networks and its behavior during the year are uncertain. Renewable DG units also present uncertainties in their power output. Thus, based on [28], a set of scenarios for load demand, solar irradiation, wind speed, and SoC are generated from annual historical data of stochastic parameters to predict the hourly behavior throughout a year (8760 hours).
The estimation of batteries' SoC is based on the scenarios of demand, energy price, in addition to irradiation and wind speed due to PV and WT units, respectively. A fuzzy decisionmaking approach is proposed to achieve the SoC in each scenario. The fuzzy inference system (FIS) is shown in Fig. 2. Each input variable is represented by three triangular membership functions (MF).
The SoC from an entire year, obtained from the optimal power flow (OPF) model in [29], [30], is also used for tunning the FIS parameters using a neuro-fuzzy designer tool in MATLAB® environment [31]. Thus, 81 rules are created for the model structure considering the four inputs mentioned above. Besides, the output MF type is linear. Three days of each month are considered to train the FIS to reduce the computational response during the tuning process. Finally, the annual hourly SoC can be estimated and applied to the kmeans method joint with the other parameters. Fig. 3 shows the proposed structure process. Initially, all stochastic parameters are normalized, dividing each one by the maximum value. The annual historical data is divided into two seasons (time blocks), summer and winter, corresponding to the months April-September and October-March, in that order. Each time block presents two sub-blocks, day and night.
The user must define the number of clusters. Each cluster represent a part of the stochastic parameters during the year. Thus, the k-means method is applied to each sub-block to reduce the stochastic parameters to the predetermined number of clusters [31]. As a result, the k-means method presents the centroids of each cluster. Finally, these centroids generate the set of scenarios.

C. OBJECTIVE FUNCTION AND CONSTRAINTS
The mathematical model comprises two conflicting objective functions (OFs), the CENS and costs of all protective and control devices (1). The equipment cost includes the acquisition, installation, and maintenance of each protective device.
The CENS in (2) is based on [22]. This OF evaluates the CENS considering for each year of the set of years userdefined planning horizon, where is the cost of ENS for each type of consumer : residential , commercial , and industrial . and are the ENS during temporary and permanent faults, respectively, while is the internal rate of return.
and can be estimated in (3) and (4), in that order, where and are the failure rates of temporary and permanent faults per km year of the branch ℎ, respectively. The set comprises each scenario . The set contains just the reclosers' protective zone, while the set includes the protection zone of reclosers and fuses. is the set of branches within the protection zone of the i-th protective device.
, , and , , are the sum of loads within the protection zone of the i-th protective device in the scenario for temporary and permanent faults, respectively. In the same scenario, , , represents the microgrids' loads inside the protective zone , while , , represents the sum of transferred loads downstream the ASs installed in the same protective zone. Parameters and represent the time of power outage during temporary and permanent faults, in that order. is the time of power outage until the system's operator restoring the loads by using ASs. The sum of loads , , , , , , , , , and , , are previously multiplied by the demand factor in the scenario .
The total equipment cost is calculated as given in (5). and are the acquisition and installation costs of the sets of devices ω and ω , respectively. Finally, is the annual maintenance cost of all devices installed in the distribution network, Λ.
Every solution must have a recloser in the first branch. Besides, fuses cannot be installed in the main feeder nor upstream reclosers and IIDs. Therefore, there is no bidirectional flow through these devices.
The proposed formulation is based on the following operation strategies: 1) IIDs are configured to act and isolate the microgrids first than reclosers during faults in the distribution network. This strategy guarantees the continuous supply of energy to the microgrid loads; 2) During faults inside the microgrid, the local protection sensibilizes first than other protection devices, disconnecting the DG units and sending a signal to open the switch at the PCC. This strategy improves system reliability by reducing the de-energized area; 3) Microgrids supplied by renewable DG can operate in islanded mode if the energy necessary in the i-th scenario plus the power losses are less than the energy available from distributed energy resources within the microgrid; 4) All pairs of protection devices are coordinated and have selectivity between them. Therefore, the fuse-blow scheme is an uninteresting solution, and it is not considered in this work; 5) The amount of each protective device is limited by the user.

D. COMPROMISE PROGRAMMING
The evaluation of both proposed OFs is achieved using the CP method, which is applied to solve simultaneously two objectives into a single OF [28]. Thus, the NSGA-II is proposed to achieve efficient non-dominated solutions.
The CP identifies the closest-to-ideal solutions through some distance measurement. These closest non-dominated solutions are called compromise solutions and form the compromise set, , provided by NSGA-II method. Thus, the solution with the smallest length is presented to the decisionmaker. Therefore, the CP seeks the compromise solution among the objectives of a multi-criteria decision-making problem.
The proposed OF in (1) must be normalized, as in (6), weighting the objectives according to their importance, where is the distance metric.
Here, is the number of objectives and is the weighting factor for objective , while , and , are the best and worst values of the j-th objective. The parameter reflects the importance of the maximum deviation, while the parameter reflects the relative importance of the j-th objective.

E. NSGA-II
The process of natural selection and evolution of species in nature is a consequence of a stochastic optimization process in a given environment and in real-time. GA is inspired by the natural selection process, where a chromosome represents a solution to the optimal allocation problem and its alleles represent the allocating of the protective devices on each branch of the distribution network [14]. Thus, the strongest individuals survive during the optimization process by transmitting to their descendants the best genes through genetic operators such as selection, crossover, and mutation.
The selection stage consists of randomly choosing two pairs of individuals from a population and comparing their quality (OF value). The best individual from each pair goes through the crossover process. In this stage, genetic material is exchanged between selected individuals. Genes are randomly mixed, creating a new pair of individuals that compose the new population. The crossover process is variable, randomly modifying the individual genes. The crossover rate, , can vary according to (7). Such an approach prevents exploration restricted only to local solutions.
In (7), the number of similar solutions is represented by in the i-th generation, i.e., similar solutions concerning other population individuals, . The adjustment factor defines a minimum crossover rate to the GA process, while is a maximum rate. Thus, the crossover process starts at high rates and decreases as the population loses its diversity. Before including the crossover individuals in the new population, the mutation process begins. The population mutation rate in (8) can also vary according to the same concept given in (7), where the superscript is employed to represent the mutation parameters. Unlike the crossover process, the mutation rate increases as similar individuals in the population increase.
The elitism technique allows a more efficient exchange of genetic material between population individuals and is frequently applied in the specialized literature [14]. In the proposed methodology, elite solutions represent 1% of the current population. Such settings are updated every generation. GA runs until it reaches the stop criteria. Thus, the best solution is presented.
Generally, GA improves one or several objective functions using a function weighting system. In the second case, GA must run several times to find a set of efficient solutions [32]. Different from GA, NSGA-II can find a set of non-dominated solutions running once through a non-dominated sorting procedure for fitness assignments [33]. Crossover and mutation operators are the same in NSGA-II, while the selection operator presents additional procedures based on the non-dominance level and crowd distance between other solutions [34]. Fig. 4 shows the flowchart of the proposed methodology.
NSGA-II starts generating and evaluating a random population , =0. Every evaluation process compares and stores the best fitness for each OF. Then, the offspring population is generated, evaluated, and combined with into a single double-size population, . The next step evaluates the dominance level of using a counter, . A non-dominated solution is not worse than others in all objectives and is better than others in at least one objective [33], presenting =0. All solutions not dominated by any other individuals are assigned to the best rank, front number 1, while other individuals are transferred to other frontiers according to their dominance level. Fig. 5 shows the nondominated sorting procedure and the crowding distance sorting.
The population to the next generation is selected from according to the frontier level, in ascending order. Since is 2 , the last frontier to be included may not fit into the new population. Then, individuals from such front are selected using the crowded-comparison operator in descending order, as shown in Fig. 5.
The crowd distance is the Euclidian distance between neighbors in the same frontier, calculated as in (9), where + 1 and − 1 are the neighbors from solution . The OF belongs to the OFs' set . The crowded-comparison operator provides a good spread between solutions from the Pareto Front, promoting better options to the decision-maker.
Finally, the next iteration starts with the new population, and the process repeats until the algorithm reaches the stop criteria. In Fig. 4, contains all individuals from the -1 best frontiers, and contains the best solutions from the frontier based on the crowded-comparison operator. The best fitness of each OF and the non-dominated solutions from the last population represent a compromise solution of the userdefined set . Thus, the CP method evaluates this set and presents the best compromise solution to the decision-maker.

III. NUMERICAL RESULTS
A 135-bus unbalanced distribution system has been employed to evaluate the proposed methodology, as shown in Fig. 6. This adapted network has 13.8 kV and 8.028 MVA. The planning horizon was established 20 years. Also, the demand increase is 2% per year, and the IRR is 5%. The recloser time is 0.01 hours for two reclosing shots in temporary faults ( ). Thereafter, the instantaneous function is blocked. If necessary, the recloser trips again and takes 4 hours of average repair during permanent faults ( ). The restoration  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  [36].
Scenarios from solar irradiation and wind speed are taken from [37]. The set for load demand is taken from [38], and the energy price is taken from [39]. Protective devices are limited to 6 reclosers (R), 15 fuses (F), 4 AS, and 5 IID. The equipment cost of each device depends on its nominal current.
The proposed method is implemented in C++ general programming language due to its speed and computational efficiency.

A. CONVERGENCE CAPABILITY, TUNING PARAMETERS, AND RESULTS OVERVIEW
The convergence capability and tuning parameters of the proposed methodology are evaluated using the hypervolume metric [40]. The hypervolume indicator, HV, is a well-known method for assessing multi-objective optimizers. Such a method calculates the region enclosed by the Pareto Front solutions and a reference point. Usually, the reference point is the anti-ideal solution, i.e., the worst value from each objective function [41]. Posteriorly, HV is calculated by dividing the region above Pareto Front solutions and the entire area, computed using the ideal solution and the reference point. Fig. 7 shows the Pareto Front for different runs, each of them considering a different number of generations (G) and population size (P). The similarity between most Pareto Front solutions and the HV indicators highlights the proposed methodology's capability. Tests performed highlight that the number of generations and population size equal to or higher than 50 and 100, respectively, can achieve a HV higher than 0.85. The increase in the number of generational cycles and population size raises the HV. This value begins to stabilize for G and P greater than or equal to 200 and 1000. The main differences between HVs are related to solver finding individuals with the lowest cost in one objective in contrast to other. For example, Run 6 presents a better HV regarding Run 5 because some solutions have lower equipment costs (see red circle). Thus, despite solutions in the middle of Pareto Front being better in Run 5, Run 6 presents slightly better HV using a lower population size.
The test with better hypervolume, Run 1, is chosen to detail in this section. Therefore, the number of generations and population is defined as 300 and 1500, respectively. Maximum and minimum mutation and recombination rates are defined before using the same technique, and their values are 0.9, 0.5, 0.1, and 0.025, in that order.
All solutions found by NSGA-II are shown in Fig. 8. Solutions highlighted in dark blue represent the set Ω or Pareto Front between both objectives CENS and equipment cost. Such a set includes 300 non-dominated solutions. Colors green, yellow, red, and orange represent the studied cases I, II, III, and IV, in that order, also belonging to the Pareto Front. Other individuals, highlighted in light blue, were evaluated during the resolution process.
Solutions with similar equipment costs can reach a CENS difference of around $299,000, while solutions with similar CENS can reach an equipment cost difference of $455,000, as shown in Fig. 8.
Maximum and minimum values from CENS and equipment cost are $564,684, $111,483, $428,057, and $37,085. The individual with the highest CENS is also a non-dominated solution. Such individual has merely the substation protection, R1. On the other hand, the individual with the highest equipment cost is dominated by other solutions. The cost of each control or protective device depends on the nominal current. Therefore, solutions with higher equipment costs include the maximum number of devices allowed and are installed in branches with higher current flow. Fig. 9 shows a comparison of Pareto Front solutions based on the number of protection and control devices. The first individual has the highest CENS value from left to right, while the last one has the lower value. All solutions have a reclosing relay in the substation due to restrictions imposed on such equipment. 61% includes more than one recloser. Solutions with at least one fuse represent 99.67% of Pareto Front individuals, while 13% include the maximum allowed number. ASs are present in 80.33% of solutions, with 26,67% including the maximum permitted limit. IIDs have minor participation in the entire set, with 44% of solutions with at least one device installed. Only 4% of solutions include four IID. The same behavior is observed in reclosers, where only 6.33% of Pareto Front solutions consider four or more of such devices. Reclosers can reduce large amounts of ENS, but its costs have low attractiveness from the equipment cost point of view.
Individuals with two reclosers represent 46.33% of Pareto Front solutions, while cases with three reclosers represent 8.33%. Companies usually recommend up to 3 devices in series due to the difficulties imposed when defining how to coordinate such equipment. Therefore, the associated high cost naturally avoids solutions with many reclosers in series.
Fuses and ASs are the most attractive options for the proposed methodology. Many IIDs can be allocated when ENS reduction is more relevant than the costs involved.  The CP emphasizing the CENS, =0.7 and =0.3; III) OFs with the same weighting factor, =0.5, ∀ ; IV) The CP focusing on the equipment cost, =0.2 and =0.8. Table III shows the cost of all protective and control devices installed in each case study. Also, Fig. 10 shows the compact test system with all protection devices allocated for each case.
The low cost of fuses encourages their installation in large quantities in most solutions of Pareto Front. Fuses allocation by the method occurred even on lines with low load, such as branches 3-4 and 39-40. These allocations are strategic because a fault in such lines can compromise a significant portion of the distribution network.
Transferring loads to neighboring feeders using AS is an attractive strategy, with cases I, II, and III including such devices. In cases I and II, due to emphasis on CENS, all ASs allowed are installed. Feeders 2 and 4 are the preferred choice in most solutions from Pareto Front because of their higher capacity. In Case III, only feeders with higher capacity are allocated. In some solutions, line segments downstream ASs includes fuses to reduce the fault propagation, such as AS1 in cases I and II. IID in microgrids supplied by renewable DG units represents 8% of Pareto Front solutions. However, this strategy has low attractiveness from the equipment cost point of view, including the compromise solutions in cases II, III, and IV. Thus, most solutions have no microgrids supplied by renewable DG.
The section with WT unit is the preferred choice in case I than the section with only PV units and BESS due to their higher total capacity and the possibility to operate in islanded mode in more scenarios. WT units present a better power output during the day concerning PV units, which can't produce energy at night. Besides, microgrid MG3 has a long line length and more loads than the section with only PV units and BESS. Such details can also provide more advantages in allocating an IID in WT unit region.
The proposal in case III comprises a good relation between both OF, being an interesting option for the decision-maker. The solution of cases I and II can be an interesting alternative  depending on the period the company seeks the return on investment (ROI). The allocated devices last longer than the planning period established in the tests performed. Therefore, the equipment cost can be better spread over a more extended period. Moreover, the proposed method presents other solutions, allowing the decision-maker to choose the best solution based on the company's interest.

B. RESULTS CONSIDERING FIS
Estimating batteries' SoC using the OPF model provides a more realistic scenario regarding the island operation of microgrids supplied by renewable DG units and BESS. However, such a technique combined with the proposed method increases the computational response, leading a higher time to plan the protection system. Therefore, a FIS is also proposed to estimate the batteries' SoC. Fig. 11 compares batteries' SoC between the OPF model and the FIS during seven days in January. The correlation coefficient is calculated to analyze the affinity between data provided by OPF model and FIS during the entire year. The higher the correlation coefficient, the greater the affinity between the data.
The FIS model uses the input parameters of demand, irradiation, wind speed, and energy price to predict the SoC. As shown in Fig. 11, such a technique provides similar results with a slight deviation. In some cases, the difference is higher because the input parameters present uncommon behavior regarding other days (see Sunday). However, the overall results are similar, presenting a strong affinity, with a correlation coefficient of 0.6826 [42].
Tests are performed again, changing batteries' SoC from OPF model to FIS. A comparison of Pareto Frontier from both methods is shown in Fig. 12. The k-means method reduces the scenarios using all data at the same time. Thus, the replacement of SoC data promotes a slight difference in time blocks and input parameters used in each technique, leading to changes in the CENS and equipment cost. Fig. 13 shows a comparison between devices considered in Pareto Front solutions from both methods. Solutions with more than one recloser represent 54,33% of Pareto Front solutions against 61% using the OPF model. Solutions with at least one fuse also represent 99,67% of Pareto Front, while cases with the maximum number allowed are 14%, i.e., higher chances of allocating more fuses considering the FIS.
ASs are present in 77,67% of solutions compared to 80,33% using the OPF model. However, cases with the maximum number allowed are higher considering the FIS, with 28,33%. 43,66% of Pareto Front include IID, 0,44% less than using the OPF model. Cases with IID in microgrids supplied by renewable DG represent 4,33% of Pareto Front solutions compared to 4% using the OPF model. Thus, the FIS provides close conditions of islanded operation. Consequently, the solver finds similar solutions concerning the tests using the OPF model. The hypervolume using the FIS is 0.8721. Therefore, even with the difference in the input data, the results are similar, indicating that solving the optimal allocation problem using FIS also provides realistic results.

IV. CONCLUSIONS
This work proposes a method to solve the allocation problem of protection and control devices in distribution networks with microgrids. The NSGA-II solves the problem in a multi-objective approach, considering the CENS and equipment costs. The method includes the possibility of load transference and microgrids' island operation considering  dispatchable and renewable DG and BESS. Besides, the proposal considers uncertainties parameters to provide more realistic results. A set of solutions is presented, highlighting the best compromise solution between OFs. These results allow the decision-maker to choose the best solution based on their interests.
Using a FIS to estimate de batteries' SoC also provides good results solving the optimal allocation problem of protection and control devices. Thus, such technique is an attractive option depending on how fast the decision-maker needs the results for planning the protection system. This proposal determines the size and location of control and protection devices. It is assumed that coordination is possible in all solutions found. However, this is a feature that should be checked in future work.
Microgrids supplied by renewable DG units present low attractiveness from the equipment cost point of view. This strategy may be more interesting, for example, if the reduction of CO2 and NO2 emissions have been considered as an environmental restriction. Therefore, further studies must be carried out to evaluate the islanding operation of renewable DG units.