# Parameterized Modeling and Planning of Distributed Energy Storage in Active Distribution Networks
## 1 Introduction  
With the integration of distributed generators (DGs) and flexible loads, traditional distribution systems are evolving into active distribution networks (ADNs) [1]. The integration of renewable DGs contributes to power loss reduction, power supply reliability enhancement, reduction of pollution gases emission, etc. [2; 3], while bringing new challenges to the planning and operation of distribution system like voltage violation [4], bi-direction power flow [5], power flow fluctuations [6]. In recent years, distributed energy storage (DES) as an important measure to alleviate the above problems has developed rapidly in both economic and technical aspects [7; 8]. Compared with large-scale centralized energy storage plants, DES has fewer restrictions on the geographical conditions of installation location and performs an increasingly important part in various application scenarios of ADNs [9]. By the criterion of discharge duration, the DES technologies can be divided into two categories, energy-type storage and power-type storage. The energy-type storage technologies, including pumped hydraulic storage (PHS), compressed air energy storage (CAES), and large-scale battery storage, are applied to provide long-term electricity support such as arbitrage [10], loss reduction [11], congestion alleviation [12], and long time-scale voltage control [13]. The latter type of energy storage, known as power-type storage, is suitable for distributed energy resources smoothing [14], power quality management [15], frequency regulation [16] and short time-scale voltage control [17]. Supercapacitoror ultracapacitor energy storage (SCES), flywheel energy storage (FES), superconducting magnetic energy storage (SMES) and small-scale battery storage belong to this category. However, the high costs of DES, especially high investment costs, are the major obstacles limiting further development. Although some new technologies such as lead-carbon battery and LiFePO\({}_{4}\) (LFP) battery have largely mitigated the economic problem [18], DES is not as widely used as other traditional electricity equipment. As a result, it is of great significance to optimize the sizing and allocation of DES to maximize the economic benefits in different scenarios. Many works in the literature have studied on the sizing and allocation of DES in ADNs. A combined genetic algorithm and sequential quadratic programming method is proposed in [19], and further testify the potential economic benefits of energy storage systems. Considering the voltage deviation, congestion, network losses and load shifting, a multi-objective planning model is proposed in [20]. A bi-level programming method is proposed in [21], and optimal planning and operation of energy storage system are solved by upper and lower programming respectively. Considering the influence of soft open point (SOP) and network configuration, a second-order cone programming (SOCP) method to determine the optimal siting and sizing DES is established in [22]. In [23], a relaxed convex optimal power flow (OPF) model is proposed, and solved by benders decomposition method. The optimal methods of resources allocation in the fields of information communication and industrial manufactory also provide ideas for DES planning. For instance, a resource service sharing model of cloud manufactory (CMfg) based on the Gale-Shapley algorithm is proposed in [24], indicating great advantages in promoting the resource-sharing utilization rate. In [25], to support the capacity sharing issue among independent firms, an advanced framework based on game theory and fuzzy logic is proposed. The type selection of energy storage is a critical issue in DES planning [26]. The characteristics of different DES types vary in economics and technology. Owing to the close correlation between the characteristics and the application scenarios, the DES modeling needs to be parameterized separately for various application demands.