Pricing Economic Dispatch With AC Power Flow Via Local Multipliers and Conic Relaxation

We analyze two locational marginal pricing schemes in electricity markets derived from an economic dispatch (ED) problem with AC power flow equations that define a non-convex feasible set. The first among these prices, termed AC-LMPs, are Lagrange multipliers satisfy Karush-Kuhn-Tucker conditions for stationarity/local optimality of the ED problem. second, called SDP-LMPs, optimal dual semidefinite programming (SDP)-based convex relaxation establish AC-LMPs and SDP-LMPs dual-equivalent problems. Hence, they coincide under zero duality gap, but may not be equal when gap is non-zero or associated stationary/locally optimal, globally dispatch. share interesting parallels hull prices (CHPs), being Lagrangian However, there important differences. For example, epigraphs SDP latter, parameterized by nodal demands, enjoy relationship CHPs derive their name from. Also, while minimize form side-payments, not. prove (and gap) guarantee revenue adequacy condition sufficient, necessary. Finally, shown to SOCP-DLMPs, distribution second-order cone programming-based relaxations over radial networks. illustrate our theoretical findings through numerical experiments.