  We analyze pricing mechanisms in electricity markets with AC power flow
equations that define a nonconvex feasible set for the economic dispatch
problem. Specifically, we consider two possible pricing schemes. The first
among these prices are derived from Lagrange multipliers that satisfy
Karush-Kuhn-Tucker conditions for local optimality of the nonconvex market
clearing problem. The second is derived from optimal dual multipliers of the
convex semidefinite programming (SDP) based relaxation of the market clearing
problem. Relationships between these prices, their revenue adequacy and market
equilibrium properties are derived and compared. The SDP prices are shown to
equal distribution locational marginal prices derived with second-order conic
relaxations of power flow equations over radial distribution networks. We
illustrate our theoretical findings through numerical experiments.
