Lagrangian Relaxation Method for Long-term Unit Commitment

Abstract

This paper presents a new method for large-scale long-term unit commitment problem composed of three types of generating units. In the proposed unit commitment algorithm, the transmission loss is expressed as a quadratic function of generator outputs. In the demand increasing period in the morning, the planning period (one hour) should be divided into shorter periods such as half an hour or fifteen minutes, and the ramping rate constraints should be imposed on generator outputs. Since the unit commitment problem (primal problem) is formulated as a large-scale mixed-integer programming problem, the Lagrangian relaxation method is employed to solve the problem efficiently. In the Lagrangian relaxation method, the metric matrix (an approximate Hessian inverse) may become too large. So the metric matrix is approximated by a block diagonal matrix. Since the primal problem is not a convex programming problem, the solution to the dual problem is not always a feasible one to the primal problem. Therefore, after solving the dual problem, a new device for finding a feasible solution must be developed. Moreover, a heuristic commitment modification procedure is proposed and it is combined with the commitment modification using the least square problem.