Power System Stability Problems Research Articles

Stability analysis of power systems using Lie series and pattern-recognition techniques

This paper concerns the estimation of stability domains for transient stability problems in power systems. Lieseries methods are used for generating a solution to Zubov's partial differential equation and pattern recognition algorithms are applied to obtain the boundary defining a region of stability. Critical clearing times for representative problems are obtained using the analytical expression for the stability boundary, and these values are verified by observing the nature of the swing curves obtained by numerical integration.

A partial stability approach to the problem of transient power system stability

In this paper it is shown that a number of ambiguous points arising in transient stability analysis of power systems can be clarified if partial or output stability concepts are used instead of stato stability. This solves the question of the number of state variables and the validity of using positive semi-definite Lyapunov functions. It is further discussed how a very general Lur'e-type Lyapunov function can be derived for the power system stability problem, which unifies and generalizes numerous Lyapunov functions available in the technical literature.

Sensitivity Analysis in Power System Dynamic Stability Studies

In this paper, the second method of Liapunov is used to investigate the dynamic stability problem of power systems using the perturbed system dynamics in state variable form. Defining stability measure in terms of Liapunov functions and their time derivatives, the paper formulates a method for the calculation of the sensitivity of the dynamic stability measure to variations in various machine and control system parameters. The method provides a basis for optimal dynamic stability design of power systems, the criterion of optimality being that the sensitivity of the dynamic stability measure to parameter variations be zero. For simplicity, the case of a synchronous machine connected to an infinite bus is considered. The effect of various voltage regulator parameters on the sensitivity of the dynamic stability measure is investigated. A numerical example is used to demonstrate the superiority of the time response resulting from the choice of parameter settings corresponding to zero sensitivity of the dynamic stability measure. The method is readily generalized to the case of multi- machine power systems.

Direct method for transient stability studies in power system analysis

This paper deals with recent advances in developing direct methods for studying the transient stability problem of single-machine and multimachine power systems. The paper starts out with the construction of the mathematical model that is usually employed in the analyis of power system transient stability. Computer simulation methods are then briefly discussed, and it is indicated why accurate direct methods for transient stability investigations would be most welcome. It is shown that the classical direct methods, which are based on energy considerations, can be derived and generalized by means of Lyapunov's second method. The main purpose of the paper is to give an exposition of the interesting results that have been obtained by applying Lyapunov's second method to the transient stability problem of single-machine and multimachine power systems. In the final portion of the paper some areas for further research are discussed.

Transient Stability of Multimachine Power Systems via the Direct Method of Lyapunov

The direct method of Lyapunov applied to the problem of transient power system stability is developed to permit the practical study of n-machine systems. A simple physical interpretation and a proof are given for two Lyapunov functions. A new and better Lyapunov function is defined, and several possibilities for its evaluation are studied. Through an analysis of the singular points of the system the causes of the conservativeness of the results are established, and a further improvement on the Lyapunov function is made. A general structure for a computer program is proposed, and results of an example with a 10-machine system solved by the conventional and the new methods are presented; the computing time by the Lyapunov method was about 40-percent shorter. Finally, several ideas for a further generalization and optimization of the method and a possibility for the design and control of power systems are proposed.

Improved Lyapunov function for transient power-system stability

A Lyapunov function is determined for the problem of transient power-system stability; only the stability of a synchronous machine connected to an infinite bus is considered. It is shown that the obtained Lyapunov function includes governor action, pole saliency and damping torques, and is hence an extension of earlier results.

Direct Method of Liapunov Applied to Transient Power System Stability

The direct method of Liapunov is applied to the problem of power system stability. The method is first compared with the phase plane technique and equal-area criterion, with all three approaches giving identical results for the equivalent 1-machine system. A Liapunov function for the 3-machine system is developed, and conservative prediction of stability is possible if the machine velocities and angles are known at the time of final system disturbance. The method is easily extended to multimachine systems. Further work is needed in the area of easier determination of better Liapunov functions and the inclusion of such items as resistance, regulator action, governor action, and damping torques.

Transient Stability Solution by an Impedance Matrix Method

The authors' purpose is to develop matrix computational methods for solving power system stability problems with the inclusion of transient saliency, variable impedance type loads, voltage regulator effect, and governor response. A computer program was developed and is described, as well as the convergence characteristics of the major computational loops of the algorithm employed.

Graphical method for solving transient stability problems

A graphical method for solving transient power-system stability problems is presented. This method is especially simple and feasible for handling transient-stability problems of multimachines when damping is considered. Practical examples are presented to illustrate the applications of this method; tedious numerical computations are entirely eliminated, thus minimising arithmetical errors. The accuracy of this method is comparable to that of the analytical method. The allowable maximum input and effects of opening and reclosing a faulted line are considered in detail.

The Solution of Power System Stability Problems by Means or Digital Computers [includes discussion

The Solution of Power System Stability Problems by Means or Digital Computers [includes discussion

A simple mechanical analogue for solving certain power-system stability problems

This simple device, useful in solving many system stability problems, gives a clear physical picture of the performance of a synchronous machine under steady-state or transient conditions. The model permits the derivation of predetermined swing curves similar to those of Summers and McClure and offers a quick method of finding critical switching and reclosing times. Probably damping forces like effects of governors and regulators can be simulated.