Description
Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models.
In light of the advantages and disadvantages of the HEM, this report focuses on three topics:
1. Exploring the effect of double and extended precision on the performance of HEM,
2. Investigating the performance of different embedding formulations of HEM, and
3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements.
The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance.
A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems.
The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.
In light of the advantages and disadvantages of the HEM, this report focuses on three topics:
1. Exploring the effect of double and extended precision on the performance of HEM,
2. Investigating the performance of different embedding formulations of HEM, and
3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements.
The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance.
A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems.
The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.
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Details
Title
- Numerical performance of the holomorphic embedding method
Contributors
- Li, Qirui (Author)
- Tylavsky, Daniel (Thesis advisor)
- Lei, Qin (Committee member)
- Weng, Yang (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2018
Subjects
- Education, Elementary
- Holomorphic Embedding Method
- Numerical Performance
- Saddle node bifurcation point
- Voltage stability analysis
- Electric power systems--Mathematical models.
- Embedding theorems--Mathematical models.
- Embedding theorems
- Numerical analysis--Acceleration of convergence--Mathematical models.
- Numerical Analysis
- Bifurcation theory--Mathematical models.
- Bifurcation theory
- Voltage regulators--Mathematical models.
- Voltage regulators
Resource Type
Collections this item is in
Note
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thesisPartial requirement for: M.S., Arizona State University, 2018
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bibliographyIncludes bibliographical references (pages 147-151)
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Field of study: Electrical engineering
Citation and reuse
Statement of Responsibility
by Qirui Li