Dynamic Security Assessment Research Articles

Dynamic security assessment of power systems using structure-preserving energy functions

An application of direct methods to dynamic security assessment of power systems using structure-preserving energy functions (SPEF) is presented. The transient energy margin (TEM) is used as an index for checking the stability of the system as well as ranking the contigencies based on their severity. The computation of the TEM requires the evaluation of the critical energy and the energy at fault clearing. Usually this is done by simulating the faulted trajectory, which is time-consuming. In this paper, a new algorithm which eliminates the faulted trajectory estimation is presented to calculate the TEM. The system equations and the SPEF are developed using the centre-of-inertia (COI) formulation and the loads are modelled as arbitrary functions of the respective bus voltages. The critical energy is evaluated using the potential energy boundary surface (PEBS) method. The method is illustrated by considering two realistic power system examples.

The closest unstable equilibrium point method for power system dynamic security assessment

The closest unstable equilibrium point (u.e.p.) method is an important tool for problems associated with power system dynamic security assessment. A study is made of the closest u.e.p. method from both theoretical and computational points of view. Issues regarding the existence and uniqueness of the closest u.e.p. are investigated. A dynamical characterization of the closest u.e.p. is derived, and the problem of its robustness with respect to changes in different parameters of a power system is studied. This robustness property highlights the practical applicability of the closest u.e.p. method to power system dynamic security assessment. An improved closest u.e.p. method is then proposed on the basis of theoretical results which uses a reduced model approach and is shown to be optimal, in the sense that the estimated stability region characterized by the corresponding energy function is the largest one within the entire stability region. Examples are given to illustrate the robustness of the closest u.e.p. and improved closest u.e.p. methods. >

Dynamic security assessment practices in North America

The dynamic security assessment practices followed by some of the member utilities of the interconnected power network of North America are reviewed. Condensed versions are included of the presentations made by seven panelists at two National Meetings of the Power Engineering Society. A cross section of the industry practices is given, including the issues involved, the concerns and problems encountered, the various measures and approaches to deal with these problems (e.g., offline studies or by online schemes), and future plans, when applicable. >

Probabilistic steady-state and dynamic security assessment

A comprehensive framework for probabilistic steady-state and dynamic security assessment is presented. The time to insecurity is used as the measure of system security. Its probability distribution is obtained from the solution of a linear vector differential equation having coefficients that are expressed in terms of steady-state and dynamic security regions. An illustrative example for a simple system is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

External subsystem equivalent model for steady-state and dynamic security assessment

A method for external subsystem model reduction is proposed. The reduction process starts with the load node elimination, resulting in a Ward-PV equivalent which contains all boundary and generator nodes. The number of the generator nodes is significantly decreased by aggregation. This is done by the Zhukov method, which replaces each selected group of the generator nodes by one equivalent generator node. The obtained equivalent is called the reduced Ward-PV equivalent. All generating units attached to the aggregated generator nodes are also aggregated into equivalent generating units. The equivalent obtained by such a method may be used for both steady-state and dynamic security analysis. The reduced Ward-PV equivalent retains the static and dynamic properties of the original Ward-PV equivalent if the aggregated generator nodes are grouped for aggregation on the base of coherency. The Yugoslav electrical power system was used as the sample system for testing the proposed method. >

Dynamic Security Assessment Utilizing the Transient Energy Function Method

This paper presents applications of an efficient computerized technique for power system dynamic system security assessment using the transient energy function (TEF) method. The technique exploits the sensitivities of the unnormalized transient energy margin with respect to operating indices and critical interface flows in order to arrive at the stability limits for various system outage states and operating conditions, that would be required for on-line application. The paper describes the sensitivity technique and demonstrates a practical application to the dynamic security problem in one portion of the Ontario Hydro system including results of the validation and accuracy tests of the technique.

On-Line Stability and Dynamic Security Assessment of Electric Power Systems

Security functions designed for on-line use in modern control centers are first considered and steady-state functions are scanned. Missing dynamic functions are then identified and related methods recently proposed reported. Particular attention is focused on transient stability issues : practical direct criteria are reviewed, and stability indices for on-line analysis and control are assessed. Finally, a list of promising new theoretical approaches is tentatively given.

Direct Methods of Stability Analysis in Dynamic Security Assessment

Direct methods of stability analysis have been intensely investigated over the past two decades and are now found practicable in obtaining accurate critical breaker clearing times for a given fault. Obtaining this information on-line is only an indirect way of ascertaining robustness of the system. In this paper we propose to convert this information into more realistic criteria such as simultaneous interchange capability (SIC) or maximum load capability (LSC) of the system subject to the system surviving thp contingencies in a transiently stable manner. A fast transient stability algorithm combined with sensitivity of the energy margin to the LSC or SIC is proposed. Verification of the methodology on a 1O-machine system lends confidence in this technique as a tool for dynamic security assessment.

A dynamic state estimator for power system dynamic security assessment

A global modularized dynamic state estimator is formulated to provide the data which will be required for future dynamic security assessment and dynamic security enhancement applications. The dynamic state estimator is global because it is capable of estimating small and large dynamic fluctuations in voltage angle and frequency for an entire area. The dynamic state estimator is composed of the sum of the static state estimate, obtained by using present hardware and algorithms and a modularized dynamic state estimate based on a linearized classical transient stability model with a stochastic load model. This dynamic state estimate component is modularized to (1) eliminate the need to measure or model external system generation and (2) to permit a reduction in computation requirements for (a) updating the linearized power system dynamic model and (b) for computing the state estimate. The modularization, which is accomplished by decoupling the linearized dynamic model for each subregion by measuring the power injections on lines connecting the subregion to the rest of the power system, causes the dynamic state estimate to be locally referenced. A global referencing procedure is proposed and discussed. A linearized stochastic model for the Michigan Electric Coordinated System is developed to illustrate the procedures proposed for developing the stochastic load model and determining the constant gain approximation for the governor turbine energy system dynamics. A summary of results on the performance of the Kalman state estimator is presented.

Derivation of equivalents for dynamic security assessment

A method is described by which the order of interconnected power systems is reduced. When the system under study is composed of a main system and several subsystems connected to the main system, the method gives an equivalent model to each subsystem with far fewer generators, even when each subsystem is connected to the main system at more than one point. The paper also discusses the data that needs to be sent from each subsystem when it is expressed by a reduced-order equivalent model. A numerical example of a 250-bus and 61-machine system shows that the method is effective and causes no loss of accuracy. Although the proposed method provides an accurate reduced-order model, it is rather time-consuming, because it is based on the linearized dynamic equations of the system, and their eigenvectors are needed. This problem must be solved before practical use of the method can proceed.

Probabilistic dynamic security assessment of power systems-I: Basic model

A comprehensive framework for power system security assessment which incorporates probabilistic aspects of disturbances and system dynamic responses to disturbances is presented. Standard mathematical models for power system (steady-state) power flow analysis and transient stability (dynamic) analysis are used. A linear vector differential equation is derived whose solution gives the probability distribution of the time to insecurity. The coefficients of the differential equation contain the transition rates of system structural changes and a set of transition probabilities defined in terms of the steady-state and the dynamic security regions. These regions are defined in the space of power injections. Upper and lower bounds on the time to insecurity distribution are obtained.

A Dynamic State Estimator for Dynamic Security Assessment

A global modularized dynamic state estimator is formulated to provide the data which will be required For future dynamic security assessment and dynamic security enhancement applications. The dynamic state estimator is global because it is capable of estimating small and large dynamic fluctuations in voltage angle and frequency for an entire area.

Dynamic stability assessment model of a parallel AC-DC power system

A small displacement or linearized model of a parallel ac-dc power system is developed and verified by comparison with a detailed hybrid computer representation of the system. An eigenvalue analysis of this linearized model of the system illustrates the dynamic interaction between the controls associated with the machine (excitation system and power system stabilizer) and those of the dc system (current regulator with dc modulation). The techniques set forth in this paper may be directly incorporated into digital program for dynamic stability or security assessment studies of multimachine ac-dc power system.