全局最小化带阀点效应的经济负荷分配问题的混合整数规划
Mixed Integer Programming to Globally Minimize the Economic Load Dispatch Problem With Valve-Point Effect
摘要：
在系统约束条件下，满足特定需求的发电机组间的功率优化分配是电力系统界正在进行的研究课题。由于考虑了阀点效应，使得费用函数非光滑和非凸，即使在静态设置下，该问题也很难用传统的最优化方法解决。这一困难导致了基于种群的全局规划的扩散，以解决多极值和非光滑问题。在本文中，我们解决的经济负荷分配问题（ELDP）的阀点效应在其经典的配方中，每个发电机的费用函数表示为一个二次项和整流正弦项的总和。我们提出了两种方法，采取分段二次代理费用函数，产生的代理问题，可以处理的混合整数二次规划（MIQP）求解器。第一种方法表明，ELDP的整体解决方案，往往可以找到通过使用一个固定的和非常有限的数量的二次件的代理费用函数。第二种方法自适应地建立分段二次代理欠估计的ELDP费用函数，产生一系列的代理MIQP问题。证明了MIQP解序列的任何极限点都是ELDP的整体解。此外，数值实验表明，所提出的方法优于国家的最小值和计算时间方面的最新算法的实际情况。
英文摘要：
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.
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