## 1 Introduction
Lithium-ion batteries have advantages such as portability, high energy density, and fast response time, as well as disadvantages such as capacity degradation over time and high cost [19]. [PERSON] et al. (2013), a hybrid multi-objective particle swarm optimization (HMOPSO) approach was developed to minimize power system costs and improve voltage profiles by investigating the sizing of storage units in wind turbines, considering the uncertainties in energy generation [20]. However, in the study, only the power system cost is considered, without considering the effect of battery energy storage systems' (BESS') integration on network power losses. [PERSON] et al. (2018), a multi-stage hybrid energy storage (ESS) system is proposed without analyzing the effect of the ESS on network power losses and voltage fluctuations and considering only the market profit and stabilizing effect of the ESS without considering the SOC model of the ESS [21]. [PERSON] et al. (2020), a hierarchical optimization algorithm is proposed to simultaneously optimize the capacity of the equipment in a distributed power generation (DG) plant consisting of a wind turbine, PV system, and an ESS [22]. A golden section Fibonacci tree optimization (GSFTO) is used to increase efficiency and solution accuracy in the model, which aims to maximize the generation of DGs. [PERSON] et al. (2020), the energy management and control methods of a large-scale ESS were analyzed [23]. The operating cost model of the ESS was developed by considering its life-cycle operating characteristics. [PERSON] at al. (2009), an approach using ESSs is proposed to make wind power generation systems more reliable, both in terms of energy and capacity [24]. In the study, no optimization method was used to configure the ESS. [PERSON] et al. (2024), which analyses the relationship between ESS allocation capacity and load fluctuations mitigation, an optimal capacity allocation method is proposed to minimize the overhead regulation problem of large-scale ESSs [25]. However, SOC for ESSs was not considered in this study. [PERSON] et al. (2018), the energy performance of a lithium-ion battery system was determined during the process of storing surplus energy in a photovoltaic power plant [26]. [PERSON] et al. (2018), proposed an optimal control and bidding policy for battery participation in frequency regulation markets, considering the cost of battery aging in operating strategies to increase market profits [27]. [PERSON] et al. (2024), a multi-scale linear programming formulation is proposed to evaluate storage system degradation for both energy and ancillary services in the day-ahead and real-time market [28]. Since the energy efficiency of a PV plant with an ESS is directly related to the income earned, the operating period of the plant needs to be optimized. This optimization will both increase the economic gain and positively affect the lifetime of the battery because the lifetime of batteries is determined by the number of charges and discharges. However, apart from these, the lifetime of the battery also depends on the ambient temperature, depth of charge, duration of shifting cycles, and power level [29]. For this reason, it should be ensured that batteries are not deeply charged. The economic analysis results of a power plant are affected by material costs, labor costs, maintenance costs, the load profile of the power plant, electricity price tariffs, loan interest, inflation, and local support policies. Therefore, there are different economic results for PV + ESS in the literature. In addition, since PV and battery prices generally tend to decrease, projects that were not attractive in previous years may become attractive today. For example, in studies conducted in England and Australia in 2017, it was stated that PV + ESS systems were not attractive [30; 31].