## 1 Introduction
The mathematical model was transformed into a stochastic programming problem and solved. [PERSON] et al. optimized the sizes of the ESS and PV unit of the system to minimize the system cost. To reduce the computational complexity, the problem was transformed into a mixed-integer linear programming problem, and a two-stage Benders decomposition strategy was used to solve the optimization problem [17; 18]. [PERSON] et al. identified and clustered the characteristics of consumer groups based on online energy management tools and determined the working status of PV-ESS according to the established rules [19]. [PERSON] studied the residential load effect of the system under different pricing strategies, thus establishing the optimal power flow model, and confirmed the optimal battery size by analyzing the systems with different battery sizes [20]. [PERSON] et al. accurately modeled a PV-HESS system. The power output of each energy storage unit was controlled using frequency domain management and a hysteresis controller. They showed that configuring the SC can avoid the fast charging and discharging cycles of the battery and alleviate the battery life degradation [21]. [PERSON] et al. proposed a size optimization method for a microgrid ESS based on a cost-benefit analysis. The feedforward neural network algorithm was used to predict the wind speed and illumination. Differences in the optimal size of the ESS were found under grid and off-grid connections [22]. In the above studies, different methods were used to solve the sizing problem of the ESS in a renewable energy system. The overview of related research streams is shown in Table 1.  
By comparing and summarizing relevant studies, it should be noted that some research methods used, such as heuristic algorithms, cannot guarantee the optimal energy output between system components. In contrast, theoretically, the optimal capacity obtained by using globally optimal optimization algorithms is smaller because it can fully utilize the limited size of system components. However, some studies mostly focused on implementing new algorithms or modifying existing ones. The effects of energy management optimization and the combination of different components on the system were rarely studied. Meanwhile, relevant research rarely considers that the irregular charging and discharging of the ESS during system operation often leads to an accelerated degradation of its lifespan. Therefore, the output curve of the ESS should be controlled to reduce system costs and user anxiety. In addition, during the operation, because of the intermittent output of the PV system, the charge and discharge times and the charge and discharge rates of the battery vary irregularly, and it is difficult to quantify the battery degradation during operation. In most studies, the battery sharing cost was determined by calculating the battery purchase cost, and the battery degradation cost was determined using the equivalent model to find the equivalent life of the ESS. The former cannot optimize the battery cost by reflecting it in the objective function, and the battery life degradation due to the latter has a large error with respect to the actual situation. Moreover, in most studies, the effects of climate, seasons, and other factors on the overall system sizing were rarely considered. For a PV system, the amount of electricity generated in summer and winter and the amount of electricity generated on cloudy and sunny days are different. Therefore, it is often unreasonable to calculate the size based on only a few days of illumination. Hence, this paper proposes a PV-HESS system sizing method that considers the power difference and system economy. First, the power generated by PV panels of different sizes was obtained by determining the change in the light intensity in one year in Harbin, China. Second, considering the composition of the components in the system, four different scenarios were set, and their optimal capacity configurations were calculated separately.