内点法有功优化调度的降阶方法及应用研究

【作者】 武鹏；

【导师】 韩学山；

【作者基本信息】 山东大学 ， 电力系统及其自动化， 2006， 硕士

【摘要】 有功调度是电力系统运行管理工作中最核心的工作，随着系统规模扩大和自动化水平的提高，有功调度决策在时间和规模上的要求越来越苛刻，本文正是在这一背景下选择此课题，意义是明显的。 对有功优化调度问题，本文参阅了大量文献，在前人研究成果的基础上，突出了以下几个核心问题的研究：一是在网络约束中采用基于直流潮流的网络流模型使支路潮流得到显式表达；二是对KCL和KVL以及它们的结合和转换进行了深入的刨析；三是对二次规划内点法进行了综合分析并针对所研究问题的做了有效处理。本文突出的工作主要体现如下： (1) 使用内点算法求解基于直流潮流模型的有功调度问题时，将面对一个大型稀疏线性方程组的反复求解，算法的计算速度及处理问题的规模主要取决于此方程组。针对这一问题，本文充分利用了问题本身的电网络物理规律，将迭代过程中所要求解的大型稀疏线性方程组充分降阶。通过处理，使需要求解的最初形成的线性系统维数降至系统的节点数。根据对迭代过程中数值变化规律的分析，进一步利用Sherman-Morrison-Woodbury公式，使每次迭代中需要因子分解的矩阵的维数降至预参与调度机组数减一，从而减少了每次迭代求解的计算量。由此，在有功调度的解算速度和求解规模上有良好的适应性。 (2) 二次规划内点算法求解基于网络流模型的有功问题的解算速度同网络基本回路矩阵的稀疏度有一定的关系，本文基于拓扑理论，提出了一种基于最短路搜索技术的最小树决策方法，以提高回路阻抗矩阵的稀疏度。 (3) 在对支路变量的处理上，分别使用基于单边约束的网络流模型和基于双边约束的网络流模型对有功调度问题进行研究，并对两种模型处理下的优缺点和计算时间进行比较和总结。 实践表明，本文结合电力系统实际，以数学手段和物理规律融合为思路，研究应用的有功优化调度模型和算法在解决实际问题的规模和速度上有一定进展。更多还原

【Abstract】 With the enlargement of the system’s dimension and the enhancement of the automation’s level, It is rigorous both in the time and scale for the decision-making of the optimal power dispatch. It is obviously meaningful for this thesis to choose this topic.Based on the work of the predecessor and after reading a lot of documents about the optimal power dispatch problem, this thesis lays emphasis on the following several important problems: Firstly, the network flow model that is based on the dc power flow is used to make the power in the branch obviously expressed. Secondly, the KCL and KVL laws and their combination are deeply digged. Thirdly, the interior method especially for the quadratic programming is deeply analyzed and coped well to apply to the research problem. The main work in this thesis is listed as follows:(1) A large sparse linear system must be solved during its iteration when using interior point method to solve the optimal active power dispatch problem. The speed of the algorithm and the scale of the problem just depend on this linear system. This thesis reduces the dimension of the linear system by using the electric network law. The original linear system dimension can be reduced to the number of buses after primary derivation. Moreover, by the analysis of the variable matrix element formed, the Sherman-Morrison- Woodbury equation is used to reduce more linear system dimension to the number of units participated. So, the speed of calculations is quick obviously. Therefore, the method proposed in this thesis has a good adaptation for the solution of speed and size to the optimal active power dispatch problem.(2) The speed of the interior method that is especially used to solve the quadratic programming has certain relationship with the sparsity of the basic network loop reactance matrix. Based on the theory of the topology, this thesis puts forwards a method to get the relatively sparser loop reactance matrix.(3) For the variant of the branch, this thesis uses two network models based on the更多还原