应用Levenberg-Marquardt方法提高电力系统大规模潮流计算收敛性研究

发布时间：2018-07-01 18:37

本文选题：大规模潮流计算 + 最优乘子法　；参考：《上海交通大学》2014年硕士论文

【摘要】：电力系统是人类所建立的最复杂的工业系统之一，是一个实现能量转换、传输、分配复杂、大型、强非线性、高维数、分层分布的动态大系统。同时，电力系统也是现代社会中极为重要的工程系统，提供人类生产生活中所需要的绝大部分能量，，同时也消耗大量煤、石油等不可再生的一次能源。随着电力工业的迅猛发展，其大系统、大电网、超高压、重负荷、大区域联网、交直流联合输电和高度自动控制等特点日益鲜明。电力系统分析是进行电力系统研究、规划设计、运行调度与控制的重要基础和手段，随着研究工作的深入和计算机的普及，已形成了潮流计算、短路计算和稳定分析计算这三大计算模块。其中潮流计算是电力系统运行控制中最基本的工具，其结果可以帮助运行调度人员了解电网的实际运行状况，也可以为后续分析计算如稳定分析做准备。随着实际电力系统规模的日益扩大，运行工况多样化，当调度员在做日常或长期规划时，经常在得到满足实际要求的潮流分布前，碰到大量常规的牛顿法难以收敛的工况。此时调度员或方式规划人员难以获得有效信息对潮流进行调整，凭借人工经验进行调整，效率较低工作量大而且难以获得贴近现实的实际工况。所以研究在多种工况下提高潮流计算收敛性的算法具有重要的理论价值和实际意义。本文首先介绍了提高大规模潮流计算收敛性算法的历史发展，在理论上介绍了至今提高潮流收敛性应用最广泛的最优乘子法及新兴张量法，总结了两种算法的优点及有待发展的参考方向。其次，本文还详细介绍了提高潮流计算收敛性的优化算法及其特点。然后基于潮流方程的最小二乘模型，介绍了Levenberg-Marquardt(LM)方法的历史及发展，并结合最新自适应LM方法的数学成果，将其引入潮流计算。研究并总结了自适应LM方法具有一定能力绕开迭代过程中雅克比矩阵近似奇异区，从而提高潮流计算收敛性的机理，发现自适应LM方法也是一种永不发散的潮流计算方法，且依据相关数学定理，该方法具有以局部二阶收敛阶数收敛到非线性方程组最小二乘解的能力。在深入研究自适应LM方法提高潮流收敛性原理的基础上，提出了将自适应LM方法应用于大规模潮流计算的迭代步稀疏实现方法，简化了程序同原有常规牛顿法的接口，增强了算法的工程实用性。通过国内大规模实际电网算例验证，采用稀疏技术实现的自适应LM方法的大规模电力系统潮流计算具有很好的工程应用前景。最后，将自适应LM方法同传统提高潮流收敛性的最优乘子法及新兴张量法在计算量、不同工况下的收敛性等方面做比较，说明了LM方法是一种通用的提高大规模潮流计算收敛性的算法。在本文最后，将自适应LM方法应用至中小规模的交直流混联系统，说明自适应LM方法具有提高大规模交直流互联系统潮流计算收敛性的潜力。
[Abstract]:Power system is one of the most complex industrial systems established by human beings. It is a large dynamic system which realizes energy conversion, transmission, distribution, large scale, strong nonlinearity, high dimension and hierarchical distribution. At the same time, the power system is also an extremely important engineering system in modern society. It provides most of the energy needed by human beings in production and life, and also consumes a large number of non-renewable primary energy sources such as coal, oil and so on. With the rapid development of power industry, the characteristics of large power system, large power grid, ultra-high voltage, heavy load, large area interconnection, AC / DC combined transmission and height automatic control are becoming more and more distinct. Power system analysis is an important basis and means for power system research, planning and design, operation dispatching and control. With the deepening of research work and the popularization of computers, power flow calculation has been formed. Short circuit calculation and stability analysis calculation are the three major calculation modules. Power flow calculation is the most basic tool in the operation control of power system. The results can help the dispatcher to understand the actual operation state of the power network and prepare for the subsequent analysis calculation such as stability analysis. With the expansion of actual power system scale and diversification of operation conditions, when dispatchers make daily or long-term planning, they often encounter a large number of conventional Newtonian methods that are difficult to converge before they get the power flow distribution to meet the actual requirements. It is difficult for dispatcher or mode planner to get effective information to adjust the current and adjust it with artificial experience. The efficiency is low and the actual working condition close to reality is difficult to obtain. Therefore, it is of great theoretical and practical significance to study the algorithm to improve the convergence of power flow calculation under various working conditions. In this paper, the historical development of convergence algorithms for large-scale power flow computation is introduced. The optimal multiplier method and the emerging Zhang Liang method, which are widely used to improve the convergence of power flow, are introduced in theory. The advantages of the two algorithms and the reference directions to be developed are summarized. Secondly, the optimization algorithm to improve the convergence of power flow calculation and its characteristics are introduced in detail. Then the history and development of Levenberg-Marquardt (LM) method are introduced based on the least square model of power flow equation. Combined with the mathematical results of the latest adaptive LM method, the Levenberg-Marquardt (LM) method is introduced into power flow calculation. This paper studies and summarizes the mechanism of adaptive LM method which can bypass the approximate singular region of Jacobian matrix in the iterative process and improve the convergence of power flow calculation. It is also found that the adaptive LM method is a non-divergent power flow calculation method. According to the relevant mathematical theorems, the method has the ability to converge to the least square solution of nonlinear equations by order of local second order convergence. On the basis of deeply studying the principle of adaptive LM method to improve the convergence of power flow, an iterative sparse implementation method of adaptive LM method for large-scale power flow calculation is proposed, which simplifies the interface between the program and the original conventional Newton method. The engineering practicability of the algorithm is enhanced. Based on the examples of large scale power system in China, it is proved that the adaptive LM method with sparse technique has a good prospect of engineering application. Finally, the adaptive LM method is compared with the traditional optimal multiplier method to improve the convergence of power flow and the emerging Zhang Liang method in terms of computational complexity and convergence under different working conditions. It is shown that LM method is a universal algorithm to improve the convergence of large-scale power flow computation. Finally, the adaptive LM method is applied to small and medium scale AC / DC hybrid systems. It is shown that the adaptive LM method has the potential to improve the convergence of power flow calculation for large-scale AC / DC interconnected systems.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TM744

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