## 1 Introduction  
The green and low-carbon transformation of the power system is crucial for achieving the \"dual carbon\" goals. According to relevant data, the power generation from coal-fired units in China currently accounts for over 70% [1, 2, 3]. However, as the proportion of installed capacity from coal-fired power units decreases and the proportion of installed capacity from renewable energy increases, system frequency security issues become more prominent [4, 5, 6]. If the system security and stability are not considered in the planning process, the anti-disturbance ability of the system may not be guaranteed. In severe cases, major power outages may occur, such as the 2019 blackout in the UK [7] and the power crisis in Texas in 2021 [8]. The issue of decommissioning coal-fired units currently encompasses three main approaches: setting a definitive retirement age for coal-fired units, treating the units to be decommissioned as uncertainty factors, and designating decommissioned units as decision variables. Research [9] mandates the forced decommissioning of coal-fired units upon reaching the specified retirement age, without considering early retirement or optimization of retrofitting. Research [10] treats power investment and the decommissioning of coal-fired units as uncertainty factors and employs robust methods to solve the planning model. Research [11] acknowledges that the decommissioning of large coal-fired units may lead to power supply or reserve shortages, thus treating the retirement of coal-fired units as a decision variable. It proposes a transitional model for the low-carbon transformation of the power system that comprehensively considers the decommissioning of coal-fired units, the planning of new energy units, and the planning of transmission networks. Similarly, research [12] suggests that during the retirement of coal-fired power units, the expansion of new energy units such as wind and solar should be considered. Therefore, coal-fired power unit retirement, renewable energy unit expansion, and energy storage system investment are treated as decision variables. A model is constructed with the objective of minimizing investment and operational costs, aiming to optimize the allocation of power sources and energy storage while ensuring power and energy balance. The aforementioned studies approach the decommissioning of coal-fired units from various angles, discussing in detail the quantification methods during the decommissioning process and the collaborative optimization of sources, networks, and storage. However, there is a lack of analysis regarding the frequency of security issues arising from the decommissioning of coal-fired units. References [13; 14; 15; 16] developed frequency response models and formulated linearized constraints, which were then embedded into the planning models. However, they lack discussion on coal-fired power unit retirement. References [17; 18] incorporate the evaluation of the minimum inertia of the system to improve the frequency security of the system in a new power system planning problem that considers the retirement of coal-fired power units. While existing studies have modeled the inertia levels of the system during the decommissioning of coal-fired units, they still lack analysis of the differentiated characteristics of inertia levels at various nodes. Unlike traditional synchronous machines, the active power of new energy units is decoupled from the system frequency. As a result, different new energy grid connection ratios will lead to uneven distribution of inertia in various regions of the system [19]. On the one hand, due to the uneven distribution of inertia in the system, the dispersion of the frequency response after perturbation is more significant, which reduces the accuracy of inertia estimation [20]. On the other hand, widely varying levels of regional inertia will constrain further increases in the overall new energy ratio [21].