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Optimal distribution of power among generating units to meet a specificdemand subject to system constraints is an ongoing research topic in the powersystem community. The problem, even in a static setting, turns out to be hardto solve with conventional optimization methods owing to the consideration ofvalve-point effects which make the cost function nonsmooth and nonconvex. Thisdifficulty gave rise to the proliferation of population-based global heuristicsin order to address the multi-extremal and nonsmooth problem. In this paper, weaddress the economic load dispatch problem (ELDP) with valve-point effect inits classic formulation where the cost function for each generator is expressedas the sum of a quadratic term and a rectified sine term. We propose twomethods that resort to piecewise-quadratic surrogate cost functions, yieldingsurrogate problems that can be handled by mixed-integer quadratic programming(MIQP) solvers. The first method shows that the global solution of the ELDP canoften be found by using a fixed and very limited number of quadratic pieces inthe surrogate cost function. The second method adaptively buildspiecewise-quadratic surrogate under-estimations of the ELDP cost function,yielding a sequence of surrogate MIQP problems. It is shown that any limitpoint of the sequence of MIQP solutions is a global solution of the ELDP.Moreover, numerical experiments indicate that the proposed methods outclass thestate-of-the-art algorithms in terms of minimization value and computation timeon practical instances.

Mixed Integer Programming to Globally Minimize the Economic Load Dispatch Problem With Valve-Point Effect