摘要
潮流计算在电力系统分析中有着基础和核心的地位,属于稳态分析的范畴,在电力系统的规划、运行、调度、安全可靠分析以及预案优化调整中均广泛应用。但伴随着现代电力系统发展的日益复杂化,病态系统显著增多,其往往表现出潮流计算无解,或应用常规的潮流算法时发散。为此,积极努力地研究病态潮流的收敛性问题就显得重要且很有实际意义。
潮流计算在数学上实质是求解一组多元非线性方程组的问题,其解法与迭代的过程密不可分,所以能否收敛成为衡量潮流算法性能的重要指标。在研究人员提出的大量算法中,牛顿法解非线性方程组是非常有效的,被广泛应用于电力系统潮流计算中。
小阻抗支路是现代电力网络中比较常见的病态条件之一,在进行牛顿法潮流计算时常常会表现出发散。在研究小阻抗支路牛顿潮流算法是否发散时,从分析牛顿算法的潮流计算机理出发,对小阻抗支路潮流算法发散原因进行研究。牛顿法潮流方程线性化的基础是泰勒展开式,因小阻抗支路所具有的特性,非线性的潮流计算方程在线性化过程中,泰勒展开式的高次项很大,不满足舍去条件,所得到牛顿法潮流计算的收敛性自然就无法得到保证,因而成为牛顿法潮流计算发散的主要原因。本文的主题就是改进牛顿法潮流计算来解决病态潮流发散的问题。
在对牛顿潮流算法的理论进行分析后,立足于牛顿法潮流方程,对直角坐标形式的牛顿潮流算法进行改进,得到的一种新算法可使小阻抗病态支路在进行潮流计算时得到收敛。方法就是通过变换,使潮流方程的泰勒展开式余项部分变小至忽略,剩余部分与原方程的求解部分构成新的潮流计算方程,求解并验证其收敛性。其实质就是从雅可比矩阵自身结构的缺陷出发,修正雅可比矩阵的元素,来达到改善直角坐标牛顿潮流算法收敛性能的目的。通过对含有小阻抗支路的病态系统进行理论分析,并结合算例结果,得出结论：改进的算法可以避免小阻抗支路潮流算法发散。
The Power flow is the core and foundation of the power system's analysis,It belongs to the steady-state analysis, and widely used in power system's operation, scheduling, planning, analysis of security and reliability, and plan for optimal adjustment. However, with the increasing complexity of the power system development in modern society, there are more and more ill-conditions in the power system, which often cause the power flow unsolved, or make the power flow divergent with the conventional methods. To this end, the positive study on the convergence of power flow is particularly important and very meaningful.
Flow in mathematics is actually solving the problem on a set of multivariate nonlinear equations to, its solution can not be separated from the iterative process, convergence is an important indicator to measure the trend of performance of the algorithm. Of this algorithms Researchers proposed, the Newton power flow for solving nonlinear equations is very effective and widely used in power flow.
Power systems with small impedance branches are a common ill-condition, which may lead to the divergence of the power flow. When analysising the convergence of Newton power flow with small impedance branch, standing at the point of mechanization of convergence is useful. Newton flow for linearization of power flow equations is based on the Taylor expansion. With the small impedance branch, in the process of non-linear flow equation to linear, Partial derivatives of Taylor expansions are great, resulting in more than able to ignore conditions, if still calculated in accordance with the traditional Newton, then the flow calculation convergence naturally can not be guaranteed, and thus become the trend of the Newton method to calculate the divergence of the main reasons. The theme of this paper is to improve the Newton power flow of the Newton method to solve the problem of ill condition which trend of divergence.
Based on the deeply analysis on Newton process and combined with the characteristics of the small impedance branch, an improved Newton power flow in rectangular form for systems is presented. Its purpose is by changing the remainder part to smaller, end to satisfy the ignorance, the remaining part and the original equation can be obtained, then get the solution and verify the convergence. Its essence is to proceed from the structural defects of Jacobian, fix the elements of the Jacobian to get the purpose of improving convergence performance. Small impedance branch system theoretical analysis and numerical results show that the improved flow can make a small impedance branch's flow convergence.
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