# Two-Stage Configuration of User-Side Hybrid Energy Storage Based on Fuzzy Optimization
## 1 Introduction  
Recently, due to the rapid development of the global economy, the power consumption on the user side has increased significantly [1], and the difference between peak and valley loads on the user side is increasing [2; 3]. Therefore, with the further expansion of peak-valley difference of users' electricity load, the government has established a two-part tariff system to encourage users to participate actively in load regulation [4]. The electricity charged by the two-part tariff in a charge cycle (CC) is as follows,  
\[p=P_{peak}\times a+E\times b \tag{1}\]  
where \(P_{peak}\) is the maximum load in the charge cycle, \(a\) is the demand price, \(E\) is the quantity of electricity consumed during the charge cycle, and \(b\) is the energy price. Due to the increasing depletion of fossil fuels, many high-load industrial users are building photovoltaic power (PV) generation devices on the user side [5; 6]. However, PV generation is greatly affected by light intensity and many other environmental factors [7; 8], and its output fluctuates obviously. If directly connected to the grid, PV generation will affect the power quality and stability of the grid. Therefore, it is necessary to install energy storage devices (ES) in photovoltaic power generation system to suppress output fluctuations [9]. The power density and energy density when configuring ES on the user side need to be fully considered [10]. This paper establishes a hybrid energy storage model to suppress photovoltaic fluctuations, as shown in Figure 1. The expression of the load after configuration \(P_{loadafter}\) is  
\[P_{loadafter}=P_{load}+P_{ES}+P_{PV} \tag{2}\]  
where \(P_{load}\) is the original user load, \(P_{ES}\) is the ES output (the discharge is negative, and the charge is positive), and \(P_{PV}\) is the PV output. In this paper, supercapacitors (SC) are selected as ES with high power density and lithium-ion batteries as ES with high energy density. This form of hybrid energy storage can reduce ES loss [11] and improve the power quality of the grid [12, 13]. In [14], ES on the user side were divided into two layers: scheduling and operating. These two layers were optimized separately. [PERSON] et al. [15] proposed three evaluation indicators for the optimal allocation of ES on the user side from an economic point of view. In [16], the probabilistic weighted Markov process was used to predict future loads and determine the charging and discharging strategy based on state trajectory and ES loss. The whole life-cycle cost and benefit of ES were comprehensively considered in [17, 18], but the model revenue part was too basic, and peak load reduction was not considered. [PERSON] et al. [19] analyzed the pricing strategy under a fixed investment return period on the basis of three different mechanisms, but they did not consider the actual charging and discharging strategy, and the evaluation of the overall value of ES was incomplete. To summarize, the existing optimal configuration schemes hardly consider prolonging the energy storage life from the point of reducing the number of charging and discharging cycles in each CC. There is seldom reference analyzing the impact of self-built distributed renewable energy generation on user-side ES configurations. Therefore, this paper establishes a two-stage multi-objective optimization model [20]. The optimization objective of the first stage is to suppress the fluctuation of PV output. The optimization objectives of the second stage are increasing the income of users' ES investment and reducing the number of ES actions in each CC. The constraint conditions of this model include the limitation of the number of charging and discharging cycles, the SOC of ES, and the caps on ES investment. Figure 1: Structural chart of user-side photovoltaic hybrid energy storage model. The remainder of this paper is arranged as follows. The SC optimization model (Stage 1) and the large capacity battery optimization model (Stage 2) are introduced in Section 2.