## 1 Introduction
The water cycle algorithm (WCA) was implemented in [3] for placement of the capacitor and DGs in the distribution system, to minimize power losses and voltage deviation in the network. Although the results are efficient and acceptable, this approach is prone to very slow convergence to the global optima and needs more computational time. A hybrid search-GA is utilized for placing optimally sized capacitors at ideal locations, aiming to minimize both active and reactive power losses [19]. However, increasing the size of the network required a longer computational time and slow convergence. [PERSON] et al. reported distribution system reconfiguration and an optimal capacitor placement based hybrid approach to enhance the voltage profile and minimize the losses [20]. Despite producing good results, this method yields continuous capacitor values instead of discrete values, which may not be available in the market. A new approach, called Ant Lion Algorithm (ALO), was introduced to place the capacitor optimally in the distribution system to increase the net annual saving [21]. However, consideration is also only given to fixed capacitors (continuous value), which may not be available in the market. Voltage, loss, and cost are formulated as multi-objective functions in [22], solved by (PSO) and the gravitational search algorithm (GSA)-based hybrid PSOGSA algorithm. The hybrid algorithm has produced significantly convincing results; however, the purchasing and installation costs are missing in the problem formulation. Annual capacitor cost and cost of power losses are minimized in [23] using PSOGSA, however, the voltage stability is ignored in this work. Particle swarm optimization (PSO) is a powerful technique with an additional benefit of easy implementation. [PERSON] et al. proposed the PSO algorithm to solve the optimization problem [24]. This method has gained popularity for addressing complex optimization problems and is widely utilized in power system optimization. For example, PSO is utilized for optimal sizing and allocation of DGs in the radial distribution network (RDN) [25], while PSO is utilized for stability analysis of the power system by [PERSON] and [PERSON] [26]. The optimal dispatch problem, i.e., optimal power generation sizing, is done by PSO [27]. Meanwhile, PSO is used for optimal control of the smart nano grid [28]. Researchers have also utilized PSO for the optimal design of the grid-connected solar system in [29]. The authors in Reference [30] presented a brief survey of the methods used for loss reduction in low voltage networks. The optimal capacitor placement for reducing the active power losses and system annual costs is done using PSO [31], ant colony optimization (ACO) [32], plant growth simulation algorithm (PGSA) [33], direct search algorithm (DSA) [34], genetic algorithm (GA) [35], and bacteria foraging algorithm (BFA) [36]. IEEE 33 and 48 node RDNs are also considered for implementation and validation [31]. It is worth noting that even though a reactive power injection impacts the reactive power flow and losses directly, it is not considered in these works. Moreover, contrary to practical scenarios, these methods considered static load only. Additionally, the methods need to be tested for larger networks. The prime contribution of this paper are: (i) the reduction of active and reactive power losses; (ii) minimization of total annual cost; and (iii) voltage profile improvement in RDNs. To assess the efficacy and usefulness to the fullest, the proposed method is tested for both static and seasonal load profiles. Moreover, two use cases of capacitor sizes, i.e., the discrete capacitor sizes, according to their market availability and continuous sizes as calculated by the algorithm, are considered. Loss sensitivity indices (LSIs) are used to rank the buses according to their sensitivity for capacitor placement [37]. The sizes of the capacitors are found using PSO. To make the proposed system more suitable for larger networks, the simulation is performed for IEEE 34 and 85 node RDNs.