Matching Items (4)
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- All Subjects: Analytic continuation
- All Subjects: Convergence
- Creators: Tylavsky, Daniel J
- Creators: Johnson, Kory Alfred
- Member of: Theses and Dissertations
Description
With the power system being increasingly operated near its limits, there is an increasing need for a power-flow (PF) solution devoid of convergence issues. Traditional iterative methods are extremely initial-estimate dependent and not guaranteed to converge to the required solution. Holomorphic Embedding (HE) is a novel non-iterative procedure for solving the PF problem. While the theory behind a restricted version of the method is well rooted in complex analysis, holomorphic functions and algebraic curves, the practical implementation of the method requires going beyond the published details and involves numerical issues related to Taylor's series expansion, Padé approximants, convolution and solving linear matrix equations.
The HE power flow was developed by a non-electrical engineer with language that is foreign to most engineers. One purpose of this document to describe the approach using electric-power engineering parlance and provide an understanding rooted in electric power concepts. This understanding of the methodology is gained by applying the approach to a two-bus dc PF problem and then gradually from moving from this simple two-bus dc PF problem to the general ac PF case.
Software to implement the HE method was developed using MATLAB and numerical tests were carried out on small and medium sized systems to validate the approach. Implementation of different analytic continuation techniques is included and their relevance in applications such as evaluating the voltage solution and estimating the bifurcation point (BP) is discussed. The ability of the HE method to trace the PV curve of the system is identified.
The HE power flow was developed by a non-electrical engineer with language that is foreign to most engineers. One purpose of this document to describe the approach using electric-power engineering parlance and provide an understanding rooted in electric power concepts. This understanding of the methodology is gained by applying the approach to a two-bus dc PF problem and then gradually from moving from this simple two-bus dc PF problem to the general ac PF case.
Software to implement the HE method was developed using MATLAB and numerical tests were carried out on small and medium sized systems to validate the approach. Implementation of different analytic continuation techniques is included and their relevance in applications such as evaluating the voltage solution and estimating the bifurcation point (BP) is discussed. The ability of the HE method to trace the PV curve of the system is identified.
ContributorsSubramanian, Muthu Kumar (Author) / Tylavsky, Daniel J (Thesis advisor) / Undrill, John M (Committee member) / Heydt, Gerald T (Committee member) / Arizona State University (Publisher)
Created2014
Description
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.
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.
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.
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.
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.
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.
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.
ContributorsLi, Yuting (Author) / Tylavsky, Daniel J (Thesis advisor) / Undrill, John (Committee member) / Vittal, Vijay (Committee member) / Arizona State University (Publisher)
Created2015
Description
Much research has been devoted to identifying trends in either convergence upon a neoliberal model or divergence among welfare states in connection to globalization, but most research has focused on advanced industrialized countries. This has limited our understanding of the current state of convergence or divergence, especially among welfare states in developing regions. To address this research gap and contribute to the broader convergence vs. divergence debate, this research explores welfare state variation found within Latin America, in terms of the health policy domain, through the use of cross-national data from 18 countries collected between the period of 1995 to 2010 and the application of a series of descriptive and regression analysis techniques. Analyses revealed divergence within Latin America in the form of three distinct welfare states, and that among these welfare states income inequality, trust in traditional public institutions, and democratization, are significantly related to welfare state type and health performance.
ContributorsJohnson, Kory Alfred (Author) / Martin, Nathan (Thesis director) / Gonzales, Vanna (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / School of Politics and Global Studies (Contributor)
Created2014-05
Description
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.
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.
ContributorsRao, Shruti Dwarkanath (Author) / Tylavsky, Daniel J (Thesis advisor) / Undrill, John (Committee member) / Vittal, Vijay (Committee member) / Pal, Anamitra (Committee member) / Arizona State University (Publisher)
Created2017