Day-Ahead Distribution Market Analysis Via Convex Bilevel Programming

The proliferation of renewables in the distribution system has called for new constructs to manage the dispersed distributed energy resources (DERs). An effective approach is to employ a market-based dispatch in which private owners of DERs are financially motivated to participate in serving the local system. This paper conducts a day-ahead economic dispatch of a distribution system market where nodal prices are quantified using distribution locational marginal pricing (DLMP) to account for the system's spatial and temporal variations. This is formulated as a bilevel problem such that the upper level considers the on/off statuses of DERs, whereas the lower level is the second-order conic optimal power flow (SOCP-OPF) with an objective of minimizing the total generation cost of the active and reactive powers from DERs and the substation. Utilizing the SOCP duality, the overall problem is then recasted as a single-equivalent primal-dual mixed-integer SOCP (MISOCP) problem. A detailed presentation of the dual variables is provided. The effectiveness of the proposed formulation is validated on the 69-bus feeder, where DLMPs of both active and reactive powers are provided and analyzed.