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This paper presents the distribution locational marginal pricing (DLMP) method through quadratic programming (QP) designed to alleviate the congestion that might occur in a distribution network with high penetration of flexible demands. In the DLMP method, the distribution system operator (DSO) calculates dynamic tariffs and publishes them to the aggregators, who make the optimal energy plans for the flexible demands. The DLMP through QP instead of linear programing as studied in previous literatures solves the multiple solution issue of the aggregator optimization which may cause the decentralized congestion management by DLMP to fail. It is proven in this paper, using convex optimization theory, the aggregator's optimization problem through QP is strictly convex and has a unique solution. The Karush-Kuhn-Tucker (KKT) conditions and the unique solution of the aggregator optimization ensure that the centralized DSO optimization and the decentralized aggregator optimization converge. Case studies using a distribution network with high penetration of electric vehicles (EVs) and heat pumps (HPs) validate the equivalence of the two optimization setups, and the efficacy of the proposed DLMP through QP for congestion management.
Huang et al. (Tue,) studied this question.