Mixed Integer Programming for the Global Solution of the Economic Load Dispatch Problem With Valve-Point Effect∗

Optimal distribution of power among generating units to meet a specific demand subject to system constraints is an ongoing research topic in the power system community. The problem, even in a static setting, turns out to be hard to solve with conventional optimization methods owing to the consideration of valve-point effects, which make the cost function nonsmooth and nonconvex. This difficulty gave rise to the proliferation of population-based global heuristics in order to address the multi-extremal and nonsmooth problem. In this paper, we address the economic load dispatch problem (ELDP) with the valve-point effect in its classic formulation, wherein the cost function for each generator is expressed as the sum of a quadratic term and a rectified sine term. We propose an approach that adaptively builds piecewise-quadratic surrogate under-estimations of the ELDP cost function, and the resulting sequence of surrogate mixed-integer quadratic programming (MIQP) problems can therefore be handled by MIQP solvers. We show that any limit point of the sequence of MIQP solutions is a global solution of the ELDP.