Fully Distributed Second-Order Cone Programming Model for Expansion in Transmission and Distribution Networks

As the penetration level of distributed energy resources (DERs) is increasing at distribution level, the stakeholders at the distribution level are no longer pure consumers and they play a more active role. DERs can be used for transmission needs, and the technical impacts of them may propagate to the transmission level. To unlock the full benefits of the transmission-distribution coordination, this article proposes a second-order cone programming (SOCP) based expansion model for coordinated transmission and distribution networks by decomposition and parallelization. First, we formulate an SOCP-based subnetwork expansion problem related to voltage phase angle variables which is valid for both transmission and distribution networks. Then, a fully distributed decision-making framework is presented to solve the coordinated transmission-distribution expansion problem iteratively. Taking the total power output of each subnetwork as the interacting variable, we deploy the operation optimization of substations as the master problem and the expansion optimization of subnetworks as the subproblems in the modified iteration algorithm. The feasibility and optimality of the iteration are proved and numerically verified. Simulation results indicate the advantages of the coordinated transmission-distribution expansion which can prevent line congestion, decrease boundary power mismatches and accommodate more DERs.