Unit Commitment Using An Improved Lagrangian Relaxation Method

Unit commitment is an important research topic of economic operation and optimal dispatch in power system. Lagrangian relaxation method is a desirable method to solve the unit commitment, but because of its non-convexity of the objective function, certain measures are required to make the dual solution to be a feasible one of original problem. In addition, the algorithm is prone to oscillate on an iterative process. Furthermore, if considering the ramp constraints, the difficulty of its solution will significantly increase.To address the above problems, this paper proposes an improved Lagrangian relaxation approach for unit commitment. Adaptive adjustment of Lagrangian multiplier is brought to make the infeasible solution to approach a feasible one. After the gain of feasible solution, aggregative projection subgradient with the usage of historical information is applied for updating the multipliers. Simulation examples show that these two strategies used alternately can alleviate the oscillation. The improved Lagrangian relaxation approach can also be used to solve the ramp constrained unit commitment. It is solved by a directly relaxation of the ramp constraint via adding Lagrange multipliers corresponding to the ramp constraints. Numerical simulations demonstrate the feasibility of the proposed method.