【作者】 葛晓琳；

【导师】 张粒子；

【作者基本信息】 华北电力大学（北京） ， 电力系统及其自动化， 2010， 硕士

【摘要】 机组组合问题(UC)是高维、非凸、多约束的混合整数规划问题。拉格朗日松弛算法(LR)可将UC问题进行解耦,使模型简化,但由于目标函数的非凸性,以及梯度搜索方向的单一性,难以保证对偶间隙的可靠收敛,同时安全约束的引入会进一步增加求解的难度。针对这些问题,提出了一种两阶段优化方法(LR-DE),第1阶段利用次梯度优化的LR对UC问题进行计算,快速获得对偶解；第2阶段根据对偶解信息设定全时段拉格朗日乘子更新空间,并利用DE算法进行搜索,通过种群信息的传递改变机组启停,进而修正对偶解,缩小对偶间隙,求出机组组合问题的近似最优解。不同规模的算例分析表明,次梯度与DE算法的配合,搜索更为全面,保证了解的可行性,提高了收敛的精度。同时对于考虑网络安全约束的机组组合问题,将支路约束转换为发电机功率约束进行求解,通过算例验证了算法的适用性。更多还原

【Abstract】 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.更多还原