## 1 Introduction  
To alleviate the growing shortage of fossil fuels and environmental pollution, clean energy in the form of photovoltaics (PV) and wind energy has received much attention. As renewable energy sources, photovoltaics and wind energy can be distributed widely and cause no pollution; these have been rapidly developed in recent years. PV power is an important type of renewable energy. Compared with wind power generation, PV power is not affected by geographical factors, and its working characteristics have certain regularity [1, 2, 3, 4]. The combined operation of PV and an energy storage system (ESS) can effectively alleviate the intermittency and instability in the PV output. Among the various energy storage components, lithium-ion batteries are widely used in PV-ESSs owing to their high energy density and fast response [5, 6, 7]. However, during their operation, because of frequent charging and discharging, along with the intermittent and unstable PV output, battery life degradation is accelerated, thus increasing the operating cost (OCT) of the system [8, 9]. As a new type of energy storage device, a supercapacitor (SC) has excellent power density, cycle life, and charge and discharge rates. Therefore, it can effectively alleviate the power fluctuation in lithium-ion batteries and prolong the battery life [10]. The OCT of PV-ESS can be effectively reduced by appropriately determining the size of the lithium-ion batteries and SC, making sizing configuration an important aspect of the design. In recent years, extensive studies have been conducted on the application of hybrid energy storage systems (HESSs) in the field of renewable energy. [PERSON] et al. highlightedthe importance of optimizing the size of ESSs to overcome the challenges in using them in distribution networks. A review was conducted on the optimal capacity allocation and control of ESS, and the advantages of different types of ESSs were discussed [11]. [PERSON] et al. proposed a sizing method for a user-shared ESS. The optimal size of the ESS was analyzed and a cost-benefit analysis was performed by randomly modeling the needs of each user. The results showed that a shared ESS can realize resource conservation [12]. [PERSON] et al. discussed the types of ESSs that can be applied to PV and wind energy systems. The simulation results showed that the type and size of the ESS significantly affect the economics of the system [13]. The above research demonstrated the advantages of jointly operating a renewable energy power generation system and an ESS in terms of the energy efficiency, cost-effectiveness, and system stability through different methods. Moreover, the importance of optimizing the size of the ESS was emphasized. [PERSON] et al. applied a hybrid ESS to PV power generation and calculated the discharge depth of a battery using the rainflow-counting method. A quantitative model of the battery life was established based on the equivalent cycle life curve. An optimal capacity sizing model was established by analyzing the cost structure of the ESS, taking the minimum annual OCT of the system as the objective function and considering the volatility and confidence as constraints. Particle swarm optimization was used to optimize the model, reduce the OCT of the optical storage system, and improve its economic feasibility [14]. [PERSON] and [PERSON] et al. proposed a method for planning the optimal size of a multi-source power system. The wind-solar power supply system of a HESS system was modeled. Considering the reliability of the system, an energy management strategy based on discrete Fourier transform was proposed, and the energy utilization rate and power cost were taken as the objective functions [15; 16]. [PERSON] et al. proposed a method for optimizing the sizes of a PV system, wind and electric vehicle charging stations, and ESSs. The time characteristics of loads, such as of electric vehicles, were considered, and the actual load data were simulated.