Theoretical convergence guarantees versus numerical convergence behavior of the holomorphically embedded power flow method
•Theoretical convergence guarantee doesn’t confer numerical convergence guarantee.•Numerical convergence depends on the analytic-continuation algorithm used.•Eight acceleration schemes for obtaining converged HEPF voltage series compared.•Eta method is shown to be 5 times more efficient and as robus...
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| Published in: | International journal of electrical power & energy systems Vol. 95; pp. 166 - 176 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01.02.2018
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| ISSN: | 0142-0615, 1879-3517 |
| Online Access: | Get full text |
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| Summary: | •Theoretical convergence guarantee doesn’t confer numerical convergence guarantee.•Numerical convergence depends on the analytic-continuation algorithm used.•Eight acceleration schemes for obtaining converged HEPF voltage series compared.•Eta method is shown to be 5 times more efficient and as robust as matrix method.•Despite theoretical convergence guarantee, Viskovatov method has poor performance.•Integral and algebraic Hermite-Padé approximants explored to assess suitability.
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. |
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| ISSN: | 0142-0615 1879-3517 |
| DOI: | 10.1016/j.ijepes.2017.08.018 |