Matching Items (4)
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
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.
ContributorsLi, Qirui (Author) / Tylavsky, Daniel (Thesis advisor) / Lei, Qin (Committee member) / Weng, Yang (Committee member) / Arizona State University (Publisher)
Created2018
Description
Biological systems have long been known to utilize two processes for energy conservation: substrate-level phosphorylation and electron transport phosphorylation. Recently, a new bioenergetic process was discovered that increases ATP yields: flavin-based electron bifurcation (FBEB). This process couples an energetically favorable reaction with an energetically unfavorable one to conserve energy in the organism. Currently, the mechanisms of enzymes that perform FBEB are unknown. In this work, NADH-dependent reduced ferredoxin:NADP+ oxidoreductase (Nfn), a FBEB enzyme, is used as a model system to study this phenomenon. Nfn is a heterodimeric enzyme that reversibly couples the exergonic reduction of NADP+ by reduced ferredoxin with the endergonic reduction of NADP+ by NADH. Protein film electrochemistry (PFE) has been utilized to characterize the catalytic properties of three ferredoxins, possible substrates for Nfn enzymes, from organisms that perform FBEB: Pyrococcus furiosus (PfFd), Thermotoga maritima (TmFd), and Caldicellulosiruptor bescii (CbFd). Additionally, PFE is utilized to characterize three Nfn enzymes from two different archaea in the family Thermococcaceae: two from P. furiosus (PfNfnI and PfXfn), and one from Thermococcus sibiricus (TsNfnABC). Key results are as follows. The reduction potentials of the [4Fe4S]2+/1+ couple for all three ferredoxins are pH independent and modestly temperature dependent, and the Marcus reorganization energies of PfFd and TmFd are relatively small, suggesting optimized electron transfer. Electrocatalytic experiments show that PfNfnI is tuned for NADP+ reduction by both fast rates and a low binding constant for NADP+. A PfNfnI variant engineered to have only cysteines as coordinating ligands for its [FeS] clusters has significantly altered rates of electrocatalysis, substrate binding, and FBEB activity. This suggests that the heteroligands in the primary coordination sphere of the [FeS] clusters play a role in controlling catalysis by Nfn. Furthermore, a variant of PfNfnI lacking its small subunit, designed to probe allosteric effects at the bifurcating site, has altered substrate binding at the NADP(H) binding site, i.e. the bifurcation site. PfXfn and TsNfnABC, representing different types of Nfn enzymes, have different electrocatalytic properties than PfNfnI, including slower rates of FBEB. This suggests that Nfn enzymes vary significantly over phylogenetically similar organisms despite relatively high primary sequence homology.
ContributorsJennings, David Peter (Author) / Jones, Anne K (Thesis advisor) / Redding, Kevin E (Committee member) / Torres, César I (Committee member) / Arizona State University (Publisher)
Created2018
Description
One explanation for membrane accommodation in response to a slowly rising current, and the phenomenon underlying the dynamics of elliptic bursting in nerves, is the mathematical problem of dynamic Hopf bifurcation. This problem has been studied extensively for linear (deterministic and stochastic) current ramps, nonlinear ramps, and elliptic bursting. These studies primarily investigated dynamic Hopf bifurcation in space-clamped excitable cells. In this study we introduce a new phenomenon associated with dynamic Hopf bifurcation. We show that for excitable spiny cables injected at one end with a slow current ramp, the generation of oscillations may occur an order one distance away from the current injection site. The phenomenon is significant since in the model the geometric and electrical parameters, as well as the ion channels, are uniformly distributed. In addition to demonstrating the phenomenon computationally, we analyze the problem using a singular perturbation method that provides a way to predict when and where the onset will occur in response to the input stimulus. We do not see this phenomenon for excitable cables in which the ion channels are embedded in the cable membrane itself, suggesting that it is essential for the channels to be isolated in the spines.
ContributorsBilinsky, Lydia M (Author) / Baer, Steven M. (Thesis advisor) / Crook, Sharon M (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gardner, Carl L (Committee member) / Jung, Ranu (Committee member) / Arizona State University (Publisher)
Created2012