Distributed adaptive expansion approach for transmission and distribution networks incorporating source-contingency-load uncertainties

•Robust transmission and stochastic distribution grids are distributionally planned.•With source-load uncertainties, transmission contingency uncertainty is considered.•The convergence and optimality of the proposed iteration methods are guaranteed.•The benefits of dynamic TSO-DSO interaction are unlocked in a hierarchical manner.•A transmission-distribution network is designed to validate the proposed approach. The plurality of active distribution networks (DNs) has made it ready to connect the transmission network (TN) for the dynamic power interaction. Coordinated expansion of transmission and distribution networks is the key to the economic and reliable operation of the integrated system in the future uncertain environment. This paper proposes a distributed decision-making framework to determine the robust TN expansion solution and stochastic DN expansion solutions. Uncertainty sets are deployed to model the uncertainties in TN while the scenario-based technique is implemented to tackle the uncertainties in DNs. To guarantee the consistency of transmission-distribution interaction, the deviation penalties of the interactive power are introduced into the objective function of each level. The iteration solution algorithm is used to transform the robust min–max-min problem for transmission expansion into a two-stage mixed-integer linear programming problem, and coordinate transmission and distribution expansion problems in a parallel manner. Case studies validate the effectiveness and high performance of the proposed distributed expansion method and the solution procedure.