Pricing energy and ancillary services in integrated market systems by an optimal power flow

A detailed AC OPF-based formulation for procuring, pricing, and settling energy and ancillary service in simultaneous auctions by integrated market systems is presented. The paper provides clear definitions of locational marginal prices for energy and ancillary service marginal prices in terms of Lagrange multipliers. The characteristics of the prices are analyzed especially when economic substitution among ancillary services is required. The paper also evaluates the conditions under which opportunity costs are incurred to units that provide ancillary services. It is particularly shown that the intuitive belief that the provision of regulation down service does not incur opportunity cost to the provider, in general, is not true.