**1. Introduction**

Distribution Network Operators take into account the implementation of smart solutions to improve both the voltage level in the subordinate networks and the power factor, with the aim to maintain the balance between power generation and consumption while meeting the quality of supply standards and regulations.

In this context, the use of capacitor banks is an easy solution to be implemented with technical and economic benefits to the smart grid, maximizing the long-term return on investment as the network develops. An intelligent control of capacitor banks leads to improved energy efficiency and voltage level in the buses of distribution networks, resulting in an increase in the percentage of energy delivered to consumers [1].

The advantages of integrating capacitor banks in the flexible smart grid communication and control infrastructure are the increase of network energy efficiency and power quality improvement [2]. Thus, the technologies and modern techniques enable today the large-scale integration of capacitor banks managed with smart control algorithms.

In the literature, many methods have been proposed to solve the Optimal Capacitor Banks Allocation (OCBA) in distribution networks as a combinatorial optimization problem. These techniques can be grouped in four main categories: numerical [3]; analytical [4]; heuristic [5–7]; and artificial intelligence, population based (Artificial Neural Networks, metaheuristics) [8,9]. An overview about the metaheuristics used for the problem of capacitor banks allocation is made in the following, highlighting their specific purpose. The OCBA solution for power losses or cost minimization is obtained using a genetic algorithm in [10,11], a fuzzy technique in [12] and an artificial neural network in [9]. Regarding the metaheuristics, a significant number of papers consider the joule loss minimization, voltage bus improvement, and total cost minimization. Thus, in [13–15] a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is proposed. For active power loss reduction using load flow computation, the branch and bound method is generally preferred, for its reduced computation time. For example, for the minimization of the total annual costs, the Crow Search Algorithm (CSA) is used in [16,17], the Particle Swarm Optimization (PSO) and hybrid PSO algorithm are adapted in [18–21], the Flower Pollination Algorithm (FPA) is preferred in [22,23], and an Improved Harmony Algorithm is chosen in [24]. On the other hand, the OCBA problem based on active power minimization was approached in [25,26] using the Bacterial Foraging Optimization Algorithm, the Intersect Mutation Differential Evolution (IMDE) Algorithm in [27], the Artificial Bee Colony (ABC) in [5,28] and the Ant Lion Optimization Algorithm in [29]. The improvement of the voltage profile carried out using the Symbiotic Organisms Search Algorithm (SOSA) in [30]. Another paper proposes the JAYA optimization algorithm [31] for power factor correction. For voltage profile improvement, the Oppositional Cuckoo Optimization Algorithm (OCOA) was used in [32]. It must be mentioned that the authors' previous approaches regarding the OCBA problem used several metaheuristic algorithms, such as PSO, BOA, Fireworks Algorithm (FWA), and WOA [33].

A brief description of the papers that use metaheuristics in the CBA problem considering both objective functions (OF) and constraints (C) is presented in Table 1. The considered objective functions are: OF1, active power losses minimization; OF2, voltage profile improvement; OF3, voltage deviation minimization; OF4, cost minimization; OF5—net savings maximization; OF6, voltage stability improvement. The main constraints for the OCBA problem are a combination of the following: C1, bus voltage allowable limits; C2, current flow limits on the branches; C3, bus reactive allowable limits; C4, maximum stock of capacitors; C5, bus apparent power balance; C6, maximum number of transformer tap changer steps; C7, the total reactive power injected should not exceed the total reactive power demand; C8, power flow limits on the branches; and C9, bus power factor limits.

This paper is focused on a comparative study of several metaheuristic algorithms adapted for solving the OCBA problem with the objective of energy loss minimization in MV distribution networks. During the analysis, the well-known GA and PSO are tested against two newer metaheuristics that have seen previous uses in power engineering applications, the BOA and WOA, and another recent but much less used method, the SWA. The latter is shown to outperform all its predecessors, when tested on two MV distribution networks with different characteristics: the smaller IEEE 33—bus test network [5,13,25] and a larger 215—bus 20/0.4 kV distribution network from Romania. During the case study, the algorithms use the same initial population and fitness function. Results are shown regarding active power and energy losses and bus voltage levels, for which the best results are obtained with the SWA. **Table 1.** Literature review regarding the capacitor allocation problem based on artificial intelligence.

