## 2 Feasibility Analysis and Modeling of Energy Storage in Transmission Network Expansion Planning
### Modeling of the Energy Storage
The diagram of multi-stage coordinated expansion planning of the transmission network and energy storage is shown in Figure 2.  
The division of planning stages needs to be combined with the situation of load demand and the growth of new energy grid-connected capacity. Before planning the transmission network and energy storage system, according to the prediction of future load demand and new energy grid-connected level, the coordinated expansion planning of transmission network and energy storage is divided into \(N\) stages. As shown in Figure 2, the load demand and new energy grid-connected capacity in the to-be-built area increase in segmented steps [28]. As shown in Figure 2, the overall idea of multi-stage coordinated expansion planning of transmission network and energy storage is as follows: first, in the initial stage of stage \(S_{1}\) planning, expand the relevant transmission lines and configure the corresponding energy storage device \(E_{set1}\) to meet the maximum load and new energy consumption demand of stage \(S_{1}\) planning. Then, in the initial stage of stage \(S_{2}\) planning, on the basis of the power transmission lines expanded in the previous stage and the energy storage device \(E_{set1}\) configured, plan and configure the power transmission lines and energy storage device \(E_{set2}\) of this stage to meet the maximum load and new energy consumption demand of stage \(S_{2}\) planning. This process continues until the completion of the last planning stage \(S_{N}\), where power transmission lines are expanded and energy storage devices are configured. Finally, the configuration of transmission lines and energy storage devices in each planning stage and the corresponding optimization operation scheme for each stage are obtained. Traditional power grid planning aims to minimize the investment and operating costs of the grid, where operating costs can include the generation costs of generator units, load shedding penalty costs, and renewable energy curtailment penalty costs, etc. The constraints include the investment status constraints of candidate lines and constraints related to the operation of the power grid [29]. When the optimization of energy storage is considered in the planning process of the power grid, the output of the power grid expansion scheme at the power grid planning level, the energy storage optimization configuration layer determines the location and capacity of the energy storage based on the new power grid structure, and then returns the configuration strategy of the energy storage. At this time, the model needs to consider the constraints of the energy storage power station, including the investment status constraints of the energy storage power station and the operation constraints of the energy storage power station. At the same time, it is necessary to add the investment and operation costs of the energy storage power station to the objective function. time value for comparison [30]. Introducing the present value factor, when calculating various cost expenses during the planning period, the costs generated in different years should be discounted to the equivalent present value at the beginning of the planning period. The present value factor \(R_{Y}\) corresponding to the year \(Y\) when the planning cost occurs is. \[R_{Y}=(1+\lambda)^{-Y} \tag{8}\]  
where \(\lambda\) represents the annual discount rate. The objective function of the multi-stage coordinated expansion planning model for transmission network and energy storage is to minimize the sum of the transmission investment cost \(f_{line}\), energy storage investment cost \(f_{ess}\), wind curtailment penalty cost \(f_{wind}\), and solar curtailment penalty cost \(f_{solar}\) over the entire planning period. The objective function is as follows:  
\[\min(c_{P}P+c_{E}S)+c_{0}P \tag{1}\]0  
(1) Investment cost of transmission line:  
\[f_{line}=\sum_{Y\in N_{Y}}\sum_{ \begin{array}{c}(i,j)\in N_{P}\\ i\
eq j\end{array}