Coordination in Markets With Nonconvexities as a Mathematical Program With Equilibrium Constraints—Part II: Case Studies

This paper is the second of a two-paper series. It is concerned with the numerical study of the solution procedure derived in to solve 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 (a 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 of the generators' technical constraints are satisfied. We present some numerical results based on three test systems: a simple three-generating unit system that can be solved by hand, a 32-generating unit system that consists of piecewise linear offer curves, and a large system of 768 generating units with monotone and nonmonotone, piecewise linear offer curves, some of which are set as must-run units. The results demonstrate that the proposed procedure is more efficient than a heuristic approach, both in terms of solution quality and computational efficiency.