abstract: In the recent past, due to regulatory hurdles and the inability to expand transmission systems, the bulk power system is increasingly being operated close to its limits. Among the various phenomenon encountered, static voltage stability has received increased attention among electric utilities. One approach to investigate static voltage stability is to run a set of power flow simulations and derive the voltage stability limit based on the analysis of power flow results. Power flow problems are formulated as a set of nonlinear algebraic equations usually solved by iterative methods. The most commonly used method is the Newton-Raphson method. However, at the static voltage stability limit, the Jacobian becomes singular. Hence, the power flow solution may fail to converge close to the true limit. To carefully examine the limitations of conventional power flow software packages in determining voltage stability limits, two lines of research are pursued in this study. The first line of the research is to investigate the capability of different power flow solution techniques, such as conventional power flow and non-iterative power flow techniques to obtain the voltage collapse point. The software packages used in this study include Newton-based methods contained in PSSE, PSLF, PSAT, PowerWorld, VSAT and a non-iterative technique known as the holomorphic embedding method (HEM). The second line is to investigate the impact of the available control options and solution parameter settings that can be utilized to obtain solutions closer to the voltage collapse point. Such as the starting point, generator reactive power limits, shunt device control modes, area interchange control, and other such parameters. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2017

abstract: 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. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2018

abstract: The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists. In this report, HEPF will be used for two power system analysis purposes: a. Estimating the saddle-node bifurcation point (SNBP) of a system b. Developing reduced-order network equivalents for distribution systems. Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP. Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes. Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested. The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017