Analytical Approximations of Critical Clearing Time for Parametric Analysis of Power System Transient Stability

An analytic approximation for the critical clearing time (CCT) metric is derived from direct methods for power system stability. The formula has been designed to incorporate as many features of transient stability analysis as possible such as different fault locations and different post-fault network states. The purpose of this metric is to analyse trends in stability (in terms of CCT) of power systems under the variation of a system parameter. The performance of this metric to measure stability trends is demonstrated on an aggregated power network, the so-called two machine infinite bus network, by varying load parameters in the full bus admittance matrix using numerical continuation. The metric is compared to two other expressions for the CCT which incorporate additional non-linearities present in the model

Sensitivity of Transient Stability Critical Clearing Time

Once the critical clearing time of a fault leading to transient instability has been computed, it is desirable to quantify its dependence on system parameters. We derive for a general power system model a new and exact formula for the first order sensitivity of the critical clearing time with respect to any system parameter. The formula is evaluated by integrating variational equations forward in time along the base case faulton trajectory and integrating adjoint variational equations backward in time along the post-fault trajectory. The computation avoids recomputing the critical clearing time for each parameter change and gives insight into how parameters influence power system transient stability. The computation of the sensitivity of the critical clearing time with respect to load impedances and generator inertias is illustrated on a 39-bus system

Contingency filtering scheme for on-line dynamic security assessment

This research focused on developing an on-line contingency filtering scheme for dynamic security analysis.;Severity ranking and analysis of contingencies is thought of as a filtering process. The most severe cases are identified and ranked high on the contingency list while the non-severe cases are filtered out of the list. A cascade of progressively restrictive contingency filters is used. Three levels of filters are used. Each level of filter is divided into an inertial transient and post-inertial transient period. The first two levels of filters are very fast and approximate, but most conservative. The third level of filter uses exact analysis. The inertial transient filters capture cases which are potentially severe with respect to the inertial transient period. On the other hand, the post-inertial transient filters are designed to capture cases which are potentially severe with respect to the post-inertial transient period. These filters make use of the signatures left by the power system during the inertial transient period. The tool used in the analysis is a sparsity based direct method which is based on the exit point technique

Application of normal forms of vector fields to stressed power systems

Approximations to nonlinear system performance are useful in analysis of power-system dynamic response to small or large disturbances. Linear analysis provides a modal picture that describes the system\u27s natural response to a disturbance (small or large). Applications, such as modal analysis and energy methods, have taken advantage of linear system approximations. This work investigates the significance of including higher-order terms in the series expansion of the power system\u27s differential equations to the modal behavior of a large, stressed system\u27s transient response. Normal forms of vector fields are used to simplify the system dynamics and to derive an approximate solution to the second-order system in closed form. Interactions of the natural modes of oscillation within the system can be quantified in terms of the solutions for the original-system states. Second-order analysis indicates that many more frequencies of oscillation may have significant influence on the system response. These additional frequencies result from second-order interactions of the linear modes and can not be studied using linear analysis. A methodology based on the normal-form method is developed and utilized to describe the stressed, nonlinear system response by extending linear concepts such as modal dominance and mode-state participation. The relationship between system stress and nonlinearity of the system equations is investigated;The results show that second-order information may be essential to understanding the modal behavior in an interarea-type system separation, whereas linear information may be sufficient for disturbances affecting single plants. Data from the 50-generator IEEE test system is used in this investigation. The contribution of this work is that it includes second-order effects on system performance in a form similar to the linear concept of modal oscillations. In addition, this application of normal forms indicates that higher-order applications may yield additional useful information. Thus, in stressed system conditions where system behavior is not explained using linear analysis, the existing linear methods of control design and placement can be adapted to account for second-order effects. In this manner, the range of usefulness of the existing methods has been extended

Transient stability of power systems with non-linear load models using individual machine energy functions

Using the classical model of power system, Fouad and Vittal developed individual machine energy functions in order to identify the transient energy tending to separate a particular machine from the rest of the system(\u271);To improve the confidence in first swing transient stability assessment a more realistic model of the loads is used. In the proposed non-linear model, the loads are represented by any desired combination of constant impedance, constant current or constant-MVA models. The effect of the non-linear loads is reflected at the internal nodes of the generators as injected currents. The non-linear injected currents account for the sudden voltage changes immediately following the disturbance;Expressions for the individual machine energy functions, which represent the effects of the non-linear load models, are obtained. Using the criterion of stability suggested by Fouad and Vittal, first swing transient stability assessments are made for two multimachine test power networks. A number of cases, under a variety of load compositions, were tested. Analysis of the results obtained have demonstrated the effects of non-linear load representation on the energy absorbing capacity of the network, critical fault clearing time and the mode of instability. Comparisons have also been made between the critical fault clearing times obtained above and those;obtained using time solution such as Philadelphia Electric Co.\u27s transient stability program; (\u271)Vittal, V. Power System Transient Stability using the Critical Energy of Individual Machines. Ph.D. dissertation. Iowa State University, Ames, IA, 1982

Affine Arithmetic Based Methods for Power Systems Analysis Considering Intermittent Sources of Power

Intermittent power sources such as wind and solar are increasingly penetrating electrical grids, mainly motivated by global warming concerns and government policies. These intermittent and non-dispatchable sources of power affect the operation and control of the power system because of the uncertainties associated with their output power. Depending on the penetration level of intermittent sources of power, the electric grid may experience considerable changes in power flows and synchronizing torques associated with system stability, because of the variability of the power injections, among several other factors. Thus, adequate and efficient techniques are required to properly analyze the system stability under such uncertainties. A variety of methods are available in the literature to perform power flow, transient, and voltage stability analyses considering uncertainties associated with electrical parameters. Some of these methods are computationally inefficient and require assumptions regarding the probability density functions (pdfs) of the uncertain variables that may be unrealistic in some cases. Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches for voltage and transient stability assessment of power systems, considering uncertainties associated with power injections due to intermittent sources of power. In the proposed AA-based methods, the estimation of the output power of the intermittent sources and their associated uncertainty are modeled as intervals, without any need for assumptions regarding pdfs. This is a more desirable characteristic when dealing with intermittent sources of power, since the pdfs of the output power depends on the planning horizon and prediction method, among several other factors. The proposed AA-based approaches take into account the correlations among variables, thus avoiding error explosions attributed to other self-validated techniques such as Interval Arithmetic (IA).4 month

Modeling and analysis of power processing systems: Feasibility investigation and formulation of a methodology

A review is given of future power processing systems planned for the next 20 years, and the state-of-the-art of power processing design modeling and analysis techniques used to optimize power processing systems. A methodology of modeling and analysis of power processing equipment and systems has been formulated to fulfill future tradeoff studies and optimization requirements. Computer techniques were applied to simulate power processor performance and to optimize the design of power processing equipment. A program plan to systematically develop and apply the tools for power processing systems modeling and analysis is presented so that meaningful results can be obtained each year to aid the power processing system engineer and power processing equipment circuit designers in their conceptual and detail design and analysis tasks

Assessing placement of controllers and nonlinear behavior of electrical power system using normal form information

In this dissertation, normal form (NF) theory is used to characterize and quantify nonlinear modal interaction near critical equilibria. The research focus is on the analysis of second-order modal interaction and the study of nonlinear aspects of system behavior of interest to the design and location of system controllers;A systematic approach to derive second-order NF representations in the neighborhood of equilibrium points is presented. Nonlinear interaction measures based on this model are then obtained to assess the extent and distribution of nonlinearity in the system. Finally, analytical criteria are developed to predict the existence of nonlinear modal interactions that significantly affect system dynamic performance;A nonlinear analysis framework based on normal form (NF) theory and center manifold reduction is proposed to most effectively select generating units which should be equipped with power system stabilizers (PSS). The effect of control action on nonlinear behavior is approximated via suitable modification of initial conditions in the nonlinear coordinate transformations that relate the physical system to the NF coordinates. Using this representation, nonlinear PSS sensitivity indices are then proposed to determine the optimum sites at which to locate PSS. The technique can predict aspects of a system\u27s nonlinear behavior not obtainable from linear approaches and can therefore result in improved placement of system controllers;Test cases developed on standard test systems are presented to demonstrate the effect of nonlinear interaction and to estimate the controllers\u27 effects on system dynamic performance. The efficacy and accuracy of the method is demonstrated through comparison with conventional analysis techniques

Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization

University of Minnesota Ph.D. dissertation. June 2017. Major: Electrical Engineering. Advisor: Sairaj Dhople. 1 computer file (PDF); viii, 85 pages.Rampant integration of renewable resources (e.g., photovoltaic and wind-energy conversion systems) and uncontrollable and elastic loads (e.g., plug-in hybrid electric vehicles) are rapidly transforming power systems. In this environment, an analytic method to quantify the impact of parametric and input uncertainty will be critical to ensure the reliable operation of next-generation power systems. This task is analytically and computationally challenging since power-system dynamics are nonlinear in nature. In this thesis, we present analytic methods to quantify the impact of parametric and input uncertainties for two important applications in power systems: i) uncertainty propagation in power-system differential-algebraic equation model and power flow, and ii) robust stability assessment of power-system dynamics. For the first topic, an optimization-based method is presented to estimate maximum and minimum bounds on state variables while acknowleding worst-case parametric and input uncertainties in the model. The approach leverages a second-order Taylor-series expansion of the states around a nominal (known) solution. Maximum and minimum bounds are then estimated from either Semidefinite relaxation of Quadratically-Constrained Quadratic-Programming or Alternating Direction Method of Multipliers. For the second topic, an analytical method to quantify power systems stability margins while acknowleding uncertainty is presented within the framework of Lyapunov's direct method. It focuses on the algorithmic construction of Lyapunov functions and the estimation of the robust Region-Of-Attraction with Sum-of-Squares optimization problems which can be translated into semidefinite problems. For both topics, numerical case studies are presented for different test systems to demonstrate and validate the proposed methods