With the continuous improvement of the p enetration level of renewable energy in the power transmission network，the negative resistance effect of the unit side caused by the grid connection of new energy is significantly enhanced，which brings severe challenges to the power angle stability of the power system and then restricts the ability of new energy consumption.In this study，the power angle stability characteristics of multi-node power transmission networks are systematically analyzed by establishing a ternary single-port coupling equivalent model including traditional generator sets，new energy access nodes，and equivalent load networks.Different from the traditional stand-alone system analysis method，a static power angle stability margin quantification index suitable for complex power grid structures is innovatively proposed，which can effectively characterize the system operation boundary，tackling the bottleneck posed by the marked nonlinearity of existing static voltage stability indexes and their inadequacy for grid planning optimization.Then，a marginal index linearization strategy based on the improved McCormick envelope method is proposed.By integrating ε constraint theory and the multi-objective mixed integer programming method，a power transmission network expansion planning model with both economy and stability is constructed.In particular，the Pareto optimal solution set screening mechanism is used to realize multi-objective collaborative optimization to ensure the optimal comprehensive performance of the planning scheme.The HRP- 38 high-proportion new energy grid planning case is verified，which fully proves the effectiveness and engineering applicability of the model.