## 1 Introduction  
An increasing number of renewable energy sources (RESs) represented by wind and photovoltaic power are connected to the power grid. They are gradually replacing synchronous generators (SGs) and emerging as the predominant power sources in the renewable energy power system [1, 2]. RESs are connected to the power system through power electronic devices and are unable to provide inherent inertia [3, 4]. Moreover, the power output of RESs can be influenced by various factors, such as weather conditions, geographical locations, and control strategies [5]. Consequently, in the context of power disturbance events, the issues of fluctuations and uncertainties within the power system become more conspicuous, thereby affecting the frequency regulation capabilities of RESs, which are characterized by variations over time and across different locations [6]. Due to the low inertia and uncertainties of the power system, the frequency response of the power system deteriorates, the frequency regulation ability of RES exhibits distribution characteristics [7], and the increased rate of change of frequency (RoCoF) at some nodes poses a challenge to the secure operation of the grid. Compared with SGs, power electronic devices can achieve power control within a smaller time scale [8]. They have broad application prospects in RESs. At the same time, with the features of bidirectional transmission and rapid response [9], an energy storage system (ESS) is likely to exert a significant influence in the renewable energy power system. Therefore, ESSs can serve as an effective means to improve the stable operation of the power grid. The control methods used in ESSs can be categorized into grid-following (GFL) control and grid-forming (GFM) control [10; 11; 12]. Regarding the improvement of the secure operation capacity of the power system, techniques of applying GFM technology within low-inertia power systems have garnered substantial research attention. Many efforts have already been made by scholars in researching the evaluation methods of the inertia distribution characteristics of power systems. The authors of [13] propose a method to quantify estimation frequency characteristics to reflect the differences in the inertia support capability of various nodes. The frequency responses of each node in the power system under various inertia distribution characteristics were analyzed via simulation in [14]. In large-scale power systems, a variety of inertia distribution indexes are proposed to describe the impact of inertia on the frequency stability of the power systems [15; 16]. Quantitative assessment of power system inertia allocation can be made through trajectory analysis of electromechanical disturbance propagation [17]. In recent years, with the continuous development of GFM control strategies, extensive research has been conducted on the application of grid-forming control energy storage systems (GFM-ESSs) to enhance the secure and stable operation of renewable energy power systems. GFM control can effectively enhance the stability of the power system and is expected to solve the problem that the replacement of SGs by RESs leads to a significant decline in the inertia of the power system [18; 19]. An RES production forecasting method using artificial neural networks was proposed in [20]. This method exhibits a lower mean average prediction error and provides more accurate evaluation results. Regarding the configuration method of GFM-ESSs, the authors in [21] establish a frequency response model of the wind-energy storage system and achieve the allocation of virtual inertia between wind power and ESSs according to the inertia requirements of the system. A site selection and capacity optimization method was designed from the perspective of reactive-voltage sensitivity calculation in [22]. Based on multiple time scales, a plant siting and capacity optimization method for GFM-ESSs that can enhance the inertia of the power system and the cycle life of ESSs was proposed in [23].