###### Abstract
It develops a mixed-integer linear programming model based on price-responsive demand schemes. In reference [14,15], a multistage robust optimization model is proposed to achieve the optimal expansion planning of transmission networks under the influence of uncertainty of wind power and load, and the robustness of the results is ensured by adjusting the uncertainty budget. Although the above methods consider the increased uncertainty of future power systems, single transmission grid planning methods ignore the synergistic effects between multiple types of resources. In particular, the potential of widely configured energy storage resources to delay line construction is not considered. This deficiency may lead to low utilization rates of transmission lines and overinvestment, hindering the effective economic sustainability of future power systems. Energy storage can serve as a non-wires alternative to traditional transmission line expansion schemes. Therefore the synergistic planning of transmission grid and energy storage has been widely studied in recent years. Reference [16] analyses the necessity and principles of energy storage coordination in energy internet development. Through constructing the energy storage coordination model with the aim of economic efficiency and energy utilization efficiency, respectively, the study concludes that economic efficiency plays the more important role in the energy storage coordination process. With the goal of minimizing the difference between total system cost and flexibility benefit, Reference [17] combined energy storage systems, wind farm power generation expansion planning, and bookstore expansion planning models to improve network flexibility. Reference [18] integrates system optimization with the Markov decision process to determine the least-cost grid line upgrade strategy under demand growth uncertainty, using this multi-stage decision process to assess the value of energy storage as a non-line alternative. Reference [19] proposes a method to quantify the delay in new grid line capacity construction using distributed generation, including energy storage. Reference [20] proposes a collaborative planning model for transmission networks and compressed air energy storage. The study uses an online solution method to conclude that energy storage can delay the construction of new transmission lines. In reference [21], a stochastic optimization model for the coordinated planning of transmission networks and energy storage is proposed, which considers both long-term and short-term uncertainties. Case study analysis demonstrates that energy storage can effectively reduce transmission network investments and increase wind power integration. Considering the intrinsic correlation between load demand and wind power production, reference [22] establishes a collaborative planning model for transmission networks and energy storage. This model uses polyhedral uncertainty sets to model the uncertainties in load demand and wind power generation. Reference [23] proposes a method for energy storage siting and sizing to delay grid upgrades, quantifying the benefits of energy storage in postponing grid upgrades and incorporating them into the upper-level objective function. The proposed bi-level model is solved using an improved differential evolution algorithm. However, most existing studies on the coordinated planning of energy storage and transmission lines are based on static planning. They implement a one-time planning process from the current state to the target year, failing to consider the gradual growth of load demand and renewable energy capacity. This approach does not align with the actual investment and construction needs of various resources. Sequentially conducting static planning calculations for each year is time-consuming and highly sensitive to previous plans, making it less effective compared to multi-stage dynamic planning.