1. Introduction
All techniques used in the creation of microgrids fall into two main groups. The first group includes a range of issues related to the creation of microgrids by analyzing the existing distribution network so as to select the type of current for the entire microgrid or its individual parts, the optimal connection points of microgrids, and the mix and capacity of DERs. At this stage, the use of optimal power flow and scheduling makes it possible to evaluate the technological performance of the decisions made to ensure microgrid resilience. The second group covers the issues of choosing the optimal configuration of microgrids, microgrid ACS, protection system, and ICT, with an assessment of the technological and economic effects of their implementation ^{[1]}^{[2]}.
Oftentimes, when solving optimization problems in microgrids (optimal power flow, scheduling, and planning) various metaheuristic methods are applied. Their application yields good results when solving multicriteria problems peculiar to microgrids with a predominance of intermittent renewable electricity generation as well as variable and uncertain electricity consumption ^{[3]}.
Key metaheuristic methods include ^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}^{[10]}^{[11]}:

Evolutionary computation: modeling the evolution of a population of different individuals; genetic algorithms (GAs) and differential evolution (DE);

Swarm intelligence: the use of properties of selforganizing groups of biological organisms with “smart” global behavior;

Artificial immune systems: the modeling of the immune system’s response to external threats;

Local search: timeconstrained search for a local optimum (simulated annealing; tabu search; greedy randomized adaptive search procedure (GRASP); variable neighborhood search (VNS)).
Metaheuristic methods have a strategy (search model and abstraction), a goal (efficient exploration of the solution search space), algorithms (from simple local description procedures to trainable systems), and the (un)availability of trap avoidance in a limited search space. Metaheuristic algorithms are nondeterministic, so the scope of their operations is limited to certain categories: initialization, neighborhood, neighborhood selection criteria, candidate selection, acceptance criteria (determination of the objective function and penalties for constraint violations), and stopping criteria (computation time; number of iterations; speed of solution improvement).
The choice of the specific metaheuristic method for solving optimization problems in microgrids is based on the available time and required accuracy of decision making ^{[8]}. Various types of metaheuristic strategies can lower the computational cost. For example, GAs can be applied to any microgrid, whereas DE ensures faster convergence. The performance of GAs and DE is largely determined by their parameter settings, which need to be adapted to different combinations of network topologies and load flows. The use of GAs imposes fewer limitations than DE because less coding time is required. In this case, methods that do not require coding, such as swarm intelligence ^{[9]}, should be used. The particle swarm method is simpler because it does not require coding, so its application is feasible when computational resources are limited ^{[10]}. Further reduction of computational costs is possible through the use of distributed metaheuristic algorithms, such as artificial immune systems that use only local information but have low accuracy compared to GAs and DE ^{[11]}.
The applicability of specific metaheuristic methods is determined based on the available computing power of the controller and the number of function convergence estimates ^{[5]}. For example, evolutionary computations based on genetic algorithms ^{[6]} are applicable to any configuration of microgrids, allow for the use of hybrid approaches, are easily scalable, and do not impose restrictions on the functions they perform. However, the performance of the algorithm is determined by the quality of the coding of the optimization problem, as well as by its sensitivity to parameter settings. At the same time, the differential evolution method, which has a higher rate of function convergence than the genetic algorithm, is a simple and reliable method applied to optimization problems with constraints that require a relatively small number of control variables. However, this algorithm strongly depends on parameter settings, which determines the convergence rate ^{[7]}^{[8]}.
Swarm intelligence methods do not require special coding for their application. For example, the particle swarm optimization method is quite simple to implement and, given its efficiency, is the optimal solution in the case of the limited computing power of the controller ^{[9]}^{[10]}. Artificial immune systems are formed on the basis of a distributed control model, when there is no single control center, and they require only local information. These methods require a minimal amount of computational resources, unlike populationbased methods. However, these methods require calibration to solve optimization problems, unlike evolutionary computation and swarm intelligence methods ^{[11]}.
Nonpopulationbased metaheuristic methods have the lowest computational power requirements of all the methods, but also the lowest accuracy, which is not suitable for solving a number of problems in microgrids ^{[12]}.
To evaluate microgrid performance, one should use economic criteria and apply methods based on artificial intelligence. In the absence of convergence, it proves efficient to use combinations of two or more algorithms that form a hybrid optimization algorithm ^{[13]}^{[14]}.
2. Optimal Power Flow and Scheduling Methods
Ref. ^{[15]} discussed the application of economic dispatch in microgrids that minimized fuel costs for fuel DERs that were either dispatchable or nondispatchable under different operational constraints. The optimization problem was solved using four methods: direct search method, particle swarm optimization, lambda iteration method, and iterationfree method based on lambda logic.
Ref. ^{[16]} proposed to perform an economic and technological feasibility analysis of microgrids based on the cost of electricity when operating in the gridconnected and islanded modes. At the same time, a comprehensive analysis should be made of the available capacity of dispatchable and nondispatchable DERs, taking into account the annual growth of electricity consumption by 12%.
Ref. ^{[17]} reported information on the design of an optimal microgrid structure that provided maximum stability as well as the possibility of partial or complete recovery. To solve the nonlinear problem, the authors proposed to apply a heuristic method made available by them in two versions. The first version was the stationary heuristic methods that used static worstcase scenarios to solve the problem. The second version was a timedependent heuristic that searched for the optimal solution in a discrete representation of the time domain.
Ref. ^{[18]} presented an optimization model for minimizing operating costs in microgrids using a genetic algorithm. Considerable attention was paid there to the price aspect as it related to the response to the growth of electricity consumption. Furthermore, the article presented the results of a sensitivity analysis of changes in the factors affecting the value of microgrid operating costs.
Ref. ^{[19]} proposed to use mixed integer linear programming for the optimal design of microgrids with discrete catalogbased component selection. In addition, the authors established an explicit dependency of annuitized investment costs of the operation of fuelfired DERs and ESSs on the selected configuration of the microgrid.
Ref. ^{[20]} proposed to apply a stochastic method for optimal power flow in microgrid operation under high uncertainty of generation and electricity consumption. For this purpose, the Benders decomposition method was used, which decoupled the optimal power flow problem into a master problem, related to the distribution network, and a subproblem, solved iteratively with Benders cuts. This approach made it possible to ensure the reliable operation of microgrids after switching operations on tielines connecting microgrids to the distribution network.
Ref. ^{[21]} discussed the application of a dayahead electricity consumption scheduling method, taking into account network constraints, which requires minimum computing power of the controller. The method was based on the use of a secondorder cone program algorithm—the convex relaxation of power flow equations.
Ref. ^{[22]} contributed an alternative approach to the implementation of hierarchical control, in which only the primary and tertiary layers of control, as discussed above, were implemented. The optimal power flow was defined as the power flow that minimized the losses in the microgrids and was determined by applying an iterative algorithm.
Ref. ^{[23]} proposed an approach to arriving at the optimal microgrid configuration based on DER classification aimed at selecting the optimal DER mix and capacity. For this purpose, the authors used the method of preference based on similarity with the ideal solution and specified the optimization criteria (maximization of energy efficiency, minimization of CO_{2} emissions, labor costs, energy costs, and fuel costs). Next, using machinelearning algorithms (random forest and lightgradientboosting machine), an optimal DER mix was determined.
3. Methods for Microgrid Expansion Planning
Microgrid expansion planning techniques are based on uncertainty modeling ^{[24]}. For this purpose, a probabilistic power flow calculated using the Monte Carlo method is determined, which requires considerable computational power ^{[25]}. An alternative to the above method is approximated and improved iterative algorithms ^{[26]}^{[27]} that have good accuracy in estimating variables and probabilistic parameters, while requiring much less computational resources.
Ref. ^{[25]} presented a mathematical model that allowed the optimal microgrid design and operation to be realized. The proposed approach presupposed taking into account technological constraints (the value of power flow from the distribution network, the power consumption in microgrids, and the charge/discharge of the ESS), as well as economic constraints on the application of various DER technologies.
Ref. ^{[28]} discussed an approach to optimizing the microgrid structure when it is created on the basis of the existing distribution network in line with the Brownfield principle, which implies the purchase or lease of existing power grid infrastructure. Multicriteria optimization is used for this purpose.
Ref. ^{[29]} contributed a methodology for optimizing the structure of AC–DC microgrids, which served the electricity consumption profile without power flow from the distribution network. This minimized the cost of producing electricity in microgrids.
Ref. ^{[30]} examined optimal microgrid sizing in terms of the chosen optimization goals (minimization of the cost of electricity, maximization of the life cycle of DERs, increasing the reliability of power supply to microgrid consumers, etc.). A hybrid method of particle swarm and differential evolution with an appended fuzzy attainment module was chosen as the optimization method.
Ref. ^{[31]} reported a model for the longterm strategic planning of investment in the creation of microgrids, which allowed for improving the economic performance and controllability of the distribution network. The model took into account both existing microgrids and new ones, which made it possible to ensure the stable operation of the distribution network and optimal power flow when microgrids were operated in both gridconnected and islanded modes.
The decisions made to determine the optimal mix of the DERs in a particular microgrid connected to a single distribution network do not allow their replication in other distribution networks. The process of finding similar solutions is quite timeconsuming and inefficient. Ref. ^{[32]} examined an approach to the creation of microgrids that eliminated the need to determine the optimal connection point to the distribution network. It was based on tracking information about primary energy resources (fuel price; insolation level; average annual wind speed), which can be extrapolated to all microgrids that are built in an area. For this purpose, a unified index was introduced in order to determine the feasibility of including a certain type of DER in the microgrid generation mix. Next, the weighted average cost of electricity for each type of DER was determined. The resulting index was the sum of the three indices factored in the availability of primary energy resources in a given area. The resultant index omitted ESSs and FCs since their operating conditions do not depend on their location.