Characterizing Temporal-Coupled Feasible Region of Active Distribution Networks

With an increasing penetration of distributed energy resources (DERs), it has become a public interest regarding how to efficiently manage large-scale DERs into wholesale markets. The existing literature has focused on various coordination methods including iteration-based (e.g., Lagrangian relaxation) and projection-based (e.g., vertex enumeration) ones, which may not work for the cases with complicated constraints due to curse of dimensionality. In this article, we propose an efficient projection-based method that adapts to characterizing the feasible region of active distribution networks with temporal-coupled constraints. The problem of finding the temporal-coupled feasible region is formulated as a max–min optimization program, aiming to determine the largest set allowing zero-valued slack variables. Based on Duality Principle, the max–min model is transformed into a solvable mixed-integer linear programming that can be efficiently optimized by off-the-shelf solvers. In contrast to the existing methods searching for a vertex from interior points, we develop an outer progressive approximation algorithm that generates feasibility cuts for each iteration. Case studies based on a modified IEEE 33-bus feeder and Caracas 141-bus system demonstrate the effectiveness and efficiency of our proposed method in characterizing the feasible region with large-scale temporal-coupled constraints.