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. Wong et al. highlighted the 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]. Bayram 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]. Al-Ghussain 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.
Han 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]. Abbassi and Wang 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]. Erdinc 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. The mathematical model was transformed into a stochastic programming problem and solved. Alhaider 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]. Korjani 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]. Koko 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]. Abbassi 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]. Chen 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 re-search 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. Among them, considering the effects of irregular charging and discharging on the life of the energy storage battery during the operation of PV-ESS, a semi-empirical model based on the Arrhenius model was developed to quantify the battery life degradation. A dynamic programming algorithm was used to solve the optimal charging and discharging problem of the ESS with different sizing configurations in each scenario and obtain the minimum OCT. Finally, the minimum operating costs (MOCTs) of different sizing configurations were compared, and the effects of the various components were analyzed to obtain an optimal capacity configuration for the system. In summary, the main contributions of this study are as follows:
− By modeling the components contained in the system and performing differential deformation on the Arrhenius model, the dynamic degradation of lithium-ion batteries was quantified.
− Based on the related research, three typical algorithms were designed, their performance was compared, and a system size optimization framework was proposed.
− The feasibility of applying various system components was analyzed based on the four proposed system configurations and system operating cost models.
The paper is organized as follows.
Section 2 introduces the system configuration and working principles and models the system components. And in
Section 3, a capacity size optimization framework is developed for planning the PV-ESS system.
Section 4 designs and selects three algorithms. Finally,
Section 5 introduces the data used in this article and provides simulation results and discussion, and this paper is concluded with
Section 6.