Distribution System Restructuring: Distribution LMP via Unbalanced ACOPF

The emerging distribution system with a proliferation of distributed energy resources and flexible demand assets is expected to experience a restructuring process, just as what has been happening in the transmission system. This paper introduces the distribution locational marginal price (DLMP) as an effectively economic signal to quantify marginal cost for supplying next incremental loads at different phases of individual nodes. DLMP is calculated by solving the unbalanced ac optimal power flow (ACOPF) problem of distribution systems, with the objective of minimizing system operation cost. Indeed, in order to derive effective DLMPs, global optimal solution to the non-convex unbalanced ACOPF problem with a zero duality gap needs to be obtained. This paper solves the unbalanced ACOPF problem via the moment relaxation-based semidefinite programming (SDP) model. System sparsity is explored to accelerate the computational performance. In addition, a hierarchical approach is proposed to recover a good enough feasible solution to the original ACOPF, when the sparse moment relaxation-based SDP model is inexact. Numerical case studies on a modified IEEE 34-bus system evaluate the effectiveness and validity of the proposed approach. DLMP-based revenue adequacy of the distribution system is also analyzed.