Coordination in Markets With Nonconvexities as a Mathematical Program With Equilibrium Constraints—Part I: A Solution Procedure

This paper is concerned with developing an algorithm for solving the coordination problem that arises in a new equilibrium model , which for the purpose of this presentation applies to a static (no-time coupling costs or constraints) electricity pool market with price inelastic demand and no network. The new equilibrium model has the following main properties: i) every scheduled generator satisfies its minimum surplus (or bid profit) condition; ii) the energy price is a system marginal cost (Lagrange multiplier associated with the power balance constraint in the related economic dispatch problem where all of the discrete variables are fixed to their optimal values); iii) the power balance and all the generators' technical constraints are satisfied. To solve the coordination problem, which is a subproblem of the new equilibrium model, it is mathematically convenient to cast the former as a three-level nested optimization problem. We substitute the ensuing lower-level subproblems with an equivalent set of explicit algebraic equalities and inequalities. Hence, we obtain a one-level problem, which is a discrete-continuous mathematical program with complementarity or equilibrium constraints (MPEC). Finally, we transform the one-level mathematical program into mixed-integer linear form by substitution of the complementarity terms and the remaining nonlinear terms.