Theoretical convergence guarantees versus numerical convergence behavior of the holomorphically embedded power flow method
Theoretical convergence guarantees versus numerical convergence behavior of the holomorphically embedded power flow method
复制标题
全纯嵌入潮流方法的理论收敛保证与数值收敛行为
DOI：
10.1016/j.ijepes.2017.08.018
复制
发表时间：
2018
影响因子：
5.2
通讯作者：
D. Tylavsky
中科院分区：
文献类型：
--
作者：
S. Rao;D. Tylavsky
全纯嵌入潮流法（HELM）是基于Trias博士提出的一种新的潮流计算方法而发展起来的。该方法的优点是，它带有收敛到高电压（可操作的）解决方案的理论保证，如果它存在的话，只要方程是适当的框架。虽然理论上的收敛性是由斯塔尔定理保证的，但数值收敛性不是;它取决于所选择的解析延拓算法。由于全纯嵌入方法（HEM）已经开始找到更广泛的应用（它已被应用于非线性结构保持网络的减少，弱节点识别和鞍结分叉点的确定），检查哪些算法提供最佳的数值收敛性能，哪些没有，为什么有些工作，而不是别人，以及可以做些什么来改善这些方法，已经变得很重要。HEM的数值阿喀琉斯之踵是Padé近似的计算，这需要提供理论收敛保证和加速数值收敛。在过去，只有两种方法获得Padé逼近适用于电力系统类型的问题所产生的幂级数进行了详细讨论：矩阵方法和Viskovatov方法。本文探讨了几种加速这些幂级数收敛和/或提供解析延拓的方法，并区分了那些由斯塔尔定理的理论收敛保证支持的方法（即，那些计算Pade逼近的），和那些不是。对于方法是一致的斯塔尔的理论收敛保证，我们确定哪些方法是计算成本较低，有更好的数值性能和补救措施存在时，这些方法无法收敛数值。
The holomorphic embedding load flow method (HELM) is an application for solving the power-flow problem based on a novel method developed by Dr. Trias. The advantage of the method is that it comes with a theoretical guarantee of convergence to the high-voltage (operable) solution, if it exists, provided the equations are suitably framed. While theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not; it depends on the analytic continuation algorithm chosen. Since the holomorphic embedding method (HEM) has begun to find a broader range of applications (it has been applied to nonlinear structure-preserving network reduction, weak node identification and saddle-node bifurcation point determination), examining which algorithms provide the best numerical convergence properties, which do not, why some work and not others, and what can be done to improve these methods, has become important. The numerical Achilles heel of HEM is the calculation of the Padé approximant, which is needed to provide both the theoretical convergence guarantee and accelerated numerical convergence. In the past, only two ways of obtaining Padé approximants applied to the power series resulting from power-system-type problems have been discussed in detail: the matrix method and the Viskovatov method. This paper explores several methods of accelerating the convergence of these power series and/or providing analytic continuation and distinguishes between those that are backed by the theoretical convergence guarantee of Stahl’s theorem (i.e., those computing Pade approximants), and those that are not. For methods that are consistent with Stahl’s theoretical convergence guarantee, we identify which methods are computationally less expensive, which have better numerical performance and what remedies exist when these methods fail to converge numerically.