Calculating negative LMPs from SOCP-OPF

Recent research shows that non-convex OPF problem can be recast as a convex Semidefinite Programming (SDP) problem or Second Order Cone Programming (SOCP) problem. However, in the most SOCP OPF problems, there are some cases that conic relaxation results in a miscalculation of negative Local Marginal Prices (LMPs). This paper reviews the SOCP formulation of the optimal power flow problem proposed in [1] and then proposes one way of generating negative Locational Marginal Prices, LMPs, using this SOCP formulation. The proposed model is coded in GAMS and its built MOSEK solver and tested on a modified version of IEEE-30 test system.