A convex quadratic programming model for unit commitment global optimization

Abstract

This paper presents a convex quadratic programming (CQP) model of the thermal unit commitment (UC) problem based on the recent advancement in mathematics. The proposed model employs convex transformation techniques and is able to achieve the global optimal solution. In the CQP model, the startup cost is represented by using two kinds of binary variables (0-1); the nonconvex constraints, namely the minimum up and down times, are expressed as equivalent linear constraints via a set of linear inequalities; then the nonconvex UC problem is transformed into a convex problem with a quadratic objective function and linear constraints. Comparison studies are carried out based on the results obtained from 20 algorithms applied to 10-60 unit 24-h systems. The appendices give the details of these results. The CQP model shows unbeatable performance on global optimal searching and arrives at the overall global optimization solution constantly, and so, for the first time, is able to get the globally optimal solution of the UC problem. The proposed CQP formulation serves as a reliable standard reference for various optimization algorithms.

DLMPCS‐based improved yaw stability control strategy for DDEV

“… and it is the positive definite matrix; thus, the QP is a convex algorithm [28]. The objective function is considered as a convex function and satisfies the Karush–Kuhn–Tucker (KKT) condition [29].…”

Enhanced Lagrange relaxation for the optimal unit commitment of identical generating units

“…Although priority list constitutes the simplest and fastest method to UC, it possesses a weakness in concluding to a final solution which in many cases may stand out from the optimal [1]. Classified as linear [2], quadratic [3] or non-linear [4] programming, mixed-integer approaches are able to enhance the generation modelling accuracy though they require increased computational efforts to converge to the desired solution.…”