## 2 Feasibility Analysis and Modeling of Energy Storage in Transmission Network Expansion Planning
### Modeling of the Energy Storage  
In this section, we establish an optimal configuration model of energy storage embedded in a typical daily operation simulation. The decision variables are the power capacity and energy capacity of the energy storage system. The objective function minimizes the sum of the optimization configuration cost and the operation and maintenance cost of the energy storage system. The constraints include capacity constraints, as well as constraints  
Figure 1: Schematic diagram of energy storage delaying transmission line upgrades. on charging and discharging power and state of charge. The energy storage optimization configuration model is formulated as follows:  
\[\min(c_{P}P+c_{E}S)+c_{0}P \tag{1}\]  
\[e_{t}=e_{t-1}\cdot(1-\sigma)+\eta_{c}\cdot P_{c,t}\cdot\Delta t-\frac{P_{d,t}}{ \eta_{d}}\cdot\Delta t \tag{2}\]  
\[0\leq P_{c,t}\cdot\eta_{c}\leq P\cdot v_{c,t} \tag{3}\]  
\[0\leq P_{d,t}/\eta_{d}\leq P\cdot v_{d,t} \tag{4}\]  
\[SOC_{\min}\cdot S\leq e_{t}\leq SOC_{\max}\cdot S \tag{5}\]  
\[e_{0}=e_{T} \tag{6}\]  
\[v_{c,t}+v_{d,t}\leq 1 \tag{7}\]  
where \(c_{P}\), \(c_{E}\) and \(c_{0}\) denote the unit power capacity cost, unit energy capacity cost, and unit operation and maintenance cost of the energy storage, respectively; \(P\) and \(S\) represent the rated charge/discharge power and rated capacity of the energy storage, respectively; \(e_{t}\) denotes the remaining energy during the time (\(t\)) in the energy storage station; \(\sigma\) represents the self-discharge rate of the energy storage station; \(P_{c,t}\) and \(P_{d,t}\) represent the charging and discharging of power during the time (\(t\)) in the energy storage station, respectively; \(\eta_{c}\) and \(\eta_{d}\) denote the charging and discharging efficiency of the energy storage station, respectively; \(\Delta t\) represents the dispatch time interval, 1 h; \(v_{c,t}\) and \(v_{d,t}\) denote the charging and discharging states of the energy storage station, respectively, as binary variables. When the energy storage station is in a charging state, \(v_{c,t}=1\) and \(v_{d,t}=0\); when it is in a discharging state, \(v_{c,t}=0\) and \(v_{d,t}=1\); when both are 0, it indicates that the energy storage station is idle. \(SOC_{min}\) and \(SOC_{max}\) represent the lower and upper percentage limits of the state of charge of the energy storage station, respectively; \(T\) is the dispatch period, 24 h.  
In the aforementioned energy storage optimization configuration model, Equation (1) represents the objective function for optimizing energy storage configuration, aiming to minimize the sum of investment and operation and maintenance costs. Equation (2) addresses the energy constraint of the storage system. Equations (3) and (4) impose constraints on the charging and discharging power of the storage system, respectively. Equation (5) sets the capacity constraint, limiting the state of charge within the permissible range. Equation (6) ensures the daily clearance constraint, guaranteeing the operational continuity of the storage station. Equation (7) stipulates the charging and discharging state constraint to ensure that the storage station exhibits only one state at any given time period. Multi-Stage Expansion Planning Model for Transmission Network and Energy Storage Considering New Energy Acceptance Capacity  
Framework of Multi-Stage Coordinated Expansion Planning Model for Transmission Network and Energy Storage  
The multi-stage coordinated expansion planning model for transmission network and energy storage established in this paper considers the growth of wind power grid-connected capacity and load demand within the planning cycle, and according to the growth of wind power grid-connected capacity and load demand, divides the entire planning cycle into multiple planning stages.