A General Method Approximating the Convex Hull for Single-Unit Commitment Problems

With the increasing penetration of renewable energy resources, it becomes time-consuming to optimize the unit commitment of power systems incorporating massive heterogeneous resources. A typical acceleration approach concentrates on formulating the convex hulls of single-unit commitment (1UC) problems. However, existing researches on acquiring the convex hull are limited to specific units, and the derivation of the convex hull is complex. In this paper, a general method is proposed to approximate the convex hulls of all types of resources with the cutting planes around the optimal solution. After solving the 1UC problem, cutting planes are obtained to form the approximated convex hull and then accelerate the following solving processes on the 1UC problem. Simulation results show that the proposed method can accelerate the solution of the 1UC problem and the Larangian-relaxation-based decomposing algorithm for unit commitment. The generality and efficiency of the proposed method facilitate its application in industrial practice.