Decision-dependent distributionally robust integrated generation, transmission, and storage expansion planning: An enhanced Benders decomposition approach

Integrated generation, transmission, and storage expansion planning (IGT & SP) is the cornerstone to realize low-carbon transition considering security constraints in the long run. A novel IGT & SP planning scheme is proposed to balance the planning cost, i.e. renewable energy sources (RESs) and energy storage systems, based on the distributionally ambiguity sets. A novel decision-dependent ambiguity set is proposed to capture the relation between the uncertainties of RES output and long-term planning. A two-stage risk-averse distributionally robust optimization is formulated, where the RESs, energy storage systems, and transmission line expansion are optimized in the first stage and a unit commitment problem is proposed in the second-stage optimization to assess the performance of the expanded system. This problem is reformulated into a two-stage optimization problem with complete mixed-integer recourse, where the state variable is binary. A novel enhanced Benders decomposition algorithm is proposed to solve the IGT & SEP efficiently, where the cutting planes are generated by a primal-dual relaxation of the recourse problem. Simulations are conducted on the modified IEEE-30 test system and modified IEEE-118 test system. Compared with adjustable robust optimization and L1-norm Wasserstein distance-based distributionally robust optimization, numerical results verify the effectiveness of the proposed IGT & SP, together with the solution algorithm. A decision-dependent ambiguity set is proposed to quantify the uncertainty of renewable energy sources, enabling the optimization of uncertainties. The generation and transmission expansion planning problem is further reformulated into a two-stage optimization with a complete mixed recourse problem, which is solved by an enhanced Benders decomposition algorithm. The simulation is conducted on a modified IEEE-30 test system. The numerical results indicate the proposed ambiguity set can realize the optimization of renewable energy output uncertainty, reducing the renewable energy curtailment and investment cost. In comparison with the widely adopted branch and cut algorithm in the off-the-shelf commercial solvers, the merits of the proposed algorithm have been verified regarding computational time and scalability.image