Voltage Stability Indices Based on Active Power Transfer Using Synchronized Phasor Measurements

In recent years and in the foreseeable future, power demands generally around the world and particularly in North America will experience rapid increases due to the increase of customers\u27 requirements, while the development of transmission systems in North America is rather slow. Voltage stability assessment becomes one of the highest priorities to power utilities in North America. Voltage stability index is a feature for solving voltage stability problems. It is generated from the basic power flow equations and/or energy functions. The mathematical expression of a VSI is often written as a polynomial containing the systems real-time measurements such as voltage magnitudes, phase angles, bus injected power and branch power flow values, etc. In this thesis, the principle and derivation process of two voltage stability indices are presented. Relevant simulations are analyzed to demonstrate the VSIs\u27 functions as illustrating the system\u27s stability condition, estimating the systems operating states, determining system sensitive buses; and generator-sensitive buses and to help system apply voltage stability protection strategy. The thesis also discussed the application of VSIs with synchronized phasor measurement units, a precise system phasor measuring device using global positioning signal to obtain wide-area system measurements simultaneously. The effect of measurements errors on the computation of the VSI is studied and examined. Finally, a discussion of the future development of synchrophasors and VSI methods is given

Exploration of a Scalable Holomorphic Embedding Method Formulation for Power System Analysis Applications

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/ThesisDoctoral Dissertation Electrical Engineering 201

Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment

This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft

Multiparameter actuation of a neutrally-stable shell: a flexible gear-less motor

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multiparameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disk, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, owning a continuous manifold of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fiber-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully non-linear inextensible uniform-curvature shell model. We report on the fabrication, identification, and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a "gear-less motor", which is, in reality, a precession of the axis of principal curvature.Comment: 20 pages, 9 figure

Measurements, Models, Systems and Design

531 s.

Stroboscopic wave packet description of time-dependent currents through ring-shaped nanostructures

We present an implementation of a new method for explicit simulations of time-dependent electric currents through nanojunctions. The method is based on unitary propagation of stroboscopic wave packet states and is designed to treat open systems with fluctuating number of electrons while preserving full quantum coherence throughout the whole infinite system. We demonstrate the performance of the method on a model system consisting of a ring-shaped nanojunction with two semi-infinite tight-binding leads. Time-dependent electron current responses to abrupt bias turn-on or gate potential switching are computed for several ring configurations and ring-leads coupling parameters. The found current-carrying stationary states agree well with the predictions of the Landauer formula. As examples of genuinely time-dependent process we explore the presence of circulating currents in the rings in transient regimes and the effect of a time-dependent gate potential.Comment: corrections of typos compared to the previous versio