Two-phase Optimization Approach To Unit Commitment Problems

Unit Commitment (UC) is a high-dimensional, non-convex, multi-constraint mixed integer programming problem. The optimization could be decoupled by Lagrangian Relaxation algorithm(LR) which simples the model, but can hardly ensure the convergence of the duality gap because the single search direction of sub-gradient and non-convex of the target, while security constraints will also increase the complexity. To solve these problems, this paper presents a two-phase optimization method(LR-DE). First the problem is calculated by LR with sub-gradient to derive the dual solution; second, the space of updating Lagrange multipliers is determined by the optimal dual solution, and searched by Differential Evolution algorithm (DE), the unit commitment is changed through communication of the population, and then Lagrangian dual solution is amended, the duality gap is narrowed, and finally the ultimate solution of the original problem is obtained. Analysis of examples shows that the search is more overallly, the precision of convergence has been improvd, the solution is feasible because of the combination of the two method. This algorithm can also be adopted to solve the security constrained unit commitment. It is solved by changing the constraint of branch into generator, simulation demonstrates the applicability of the proposed method.