A lagrange relaxation-based alternating iterative algorithm for non-convex combined heat and power dispatch problem

This paper proposes a Lagrange relaxation-based alternating iterative (AI) algorithm for economic dispatch problem with non-convex operating characteristic of combined heat and power (CHP) units. In this algorithm, the non-convex operating area of each CHP unit is divided into multiple convex piecewise sub-areas. Then, a bigM based method is adopted to transform the piecewise constraints to continuous linear constraints. Then, an alternating iterative algorithm is proposed to decompose the non-concave bilinear term in the objective to linear term. And the original combinatorial optimization problem is converted into the conventional quadratic programming problem for each unit, which can be easily solved by comparing the symmetry axis and the upper and lower bounds. The proposed algorithm can reach the global optimum point with a high efficiency, which is suitable for online application. Numerical results proved the validity and efficiency of the proposed method.