2026-05-23T21:21:48Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1541652024-12-20T18:25:12Zoai_pmh:alloai_pmh:repo_items154165
https://hdl.handle.net/2286/R.I.36427
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2015
xiv, 100 pages : illustrations (some color)
Masters Thesis
Academic theses
eng
Li, Yuting
Tylavsky, Daniel J
Undrill, John
Vittal, Vijay
Arizona State University
Partial requirement for: M.S., Arizona State University, 2015
Includes bibliographical references (pages 82-85)
Field of study: Electrical engineering
Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded.<br/><br/>This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.<br/><br/>By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.<br/><br/>With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.
Electrical Engineering
Condition number
Holomorphic Embedding
Numerical Performance
Power Flow Algorithm
POWER SYSTEM
Holomorphic functions
Convergence
Electric power systems--Reliability.
Electric power distribution--Costs.
Electric power distribution
Effect of various holomorphic embeddings on convergence rate and condition number as applied to the power flow problem