Paper ID sheet UCL-INMA-2016.11


MIQP-based algorithm for the global solution of economic dispatch problems with valve-point effects

P.-A. Absil, Benoît Sluysmans, Nicolas Stevens
The economic load dispatch problem (ELDP), namely the cost-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. Even in a static setting, the ELDP 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 gave rise to the proliferation of population-based heuristics that can cope with these difficulties but without offering global optimality guarantees. In this paper, we propose a deterministic iterative method that adaptively builds piecewise-quadratic under-estimations of the ELDP cost function, yielding mixed-integer quadratic programming (MIQP) surrogate problems that can be addressed by state-of-the-art solvers. At each iteration, the proposed method produces an interval in which the ELDP optimal value is guaranteed to lie. The interval length can be made arbitrarily small by taking sufficiently many iterates and ensuring that the sequence of gap tolerances assigned to the MIQP solver goes to zero. The method is illustrated on two widely investigated ELDP instances.
Key words
economic dispatch; global optimization; mixed-integer programming; piecewise linearization; valve-point effect
Technical report, 2016