Paper ID sheet UCL-INMA-2014.08

Title

Mixed integer programming to globally minimize the economic load dispatch problem with valve-point effect

Authors

Michael Azzam, S. Easter Selvan, Augustin Lefèvre, P.-A. Absil

Abstract

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 valve-point effect in its classic formulation where the cost function for each generator is expressed as the sum of a quadratic term and a rectified sine term. We propose two methods that resort to piecewise-quadratic surrogate cost functions, yielding surrogate problems that can be handled by mixed-integer quadratic programming (MIQP) solvers. The first method shows that the global solution of the ELDP can often be found by using a fixed and very limited number of quadratic pieces in the surrogate cost function. The second method adaptively builds piecewise-quadratic surrogate under-estimations of the ELDP cost function, yielding a sequence of surrogate MIQP problems. It is shown that any limit point of the sequence of MIQP solutions is a global solution of the ELDP. Moreover, numerical experiments indicate that the proposed methods outclass the state-of-the-art algorithms in terms of minimization value and computation time on practical instances.

Key words

economic load dispatch; global convergence; mixed integer quadratic programming; valve-point effect

Status

Technical report

Download

• Preprint

BibTeX entry

@misc{AzzSelLefAbs2014.08,
  author = "Michael Azzam and S. Easter Selvan and Augustin Lef\`evre and P.-A. Absil",
  title = "Mixed integer programming to globally minimize the economic load dispatch problem with valve-point effect",
  howpublished = "http://sites.uclouvain.be/absil/2014.08",
  month = "July",
  year = 2014,
}