Abstract：With the proposal of the“dual carbon”goals and the development of new power systems，the

proportion of renewable energy sources such as wind and solar power continues to increase，and the load volume

grows with enhanced volatility，posing higher demands on the expansion of transmission lines due to uncertainties

on both the supply and demand sides. Meanwhile，the increase in transmission volume makes line losses a critical

factor affecting the economic efficiency of transmission line planning schemes. To address this，a robust planning

method for AC transmission line extension considering both line losses and supply-demand uncertainties was

proposed. Firstly，an AC power flow model considering line losses was established to improve modeling accuracy

and ensure the economic efficiency of the planning scheme. Secondly，typical scenario sets were used to replace

traditional extreme scenario sets to reduce decision conservatism，and an N-1 contingency constraint set based on

typical scenarios was constructed to ensure system safety. The proposed model was a mixed-integer second-order

cone programming problem with large-scale integer variables，which has high computational complexity. To

improve solving efficiency，the constraint-and-column generation（C&CG）algorithm was employed to decompose

the model into a master problem and multiple typical scenario subproblems，achieving efficient computation

through iterative solving. Finally，simulation calculations based on the modified IEEE-24 node system and the

IEEE-118 node system verify the effectiveness of the proposed model and method.

      Key words：line losses；AC current model；robust optimization；constraint-and-column generation（C&CG ）

algorithm；line expansion planning