Convex Relaxation Based Locational Marginal Prices.

We propose and analyze semidefinite relaxation based locational marginal prices (RLMPs) for real and reactive power in electricity markets. Our analysis reveals that when the non-convex economic dispatch problem has zero duality gap, the RLMPs exhibit properties similar to locational marginal prices with linearized power flow equations. Otherwise, they behave similar to convex hull prices. Restricted to radial distribution networks, RLMPs reduce to second-order cone relaxation based distribution locational marginal prices. We illustrate our theoretical results on numerical examples.