The influence of water column elasticity on the stability limits of a hydro- turbine generating unit with long pen-stock operating on an isolated load is investigated. D-decomposition method is used for deriving the stability regions including the elastic water column. It has been shown that a modified water column compensator enhances the stability regions and dynamic performance considerably.

Analysis and Improvement of the Stability of a Hydro-Turbine Generating Unit With Long Penstock

Modern control theory is being used more and more in regulator design of synchronous generator automatic regulating equipment. Making use of the well-established linearized equations of the synchronous machine and its control equipment, the characteristic equation of the system is developed from which the eigenvalues of the system are found. The sensitivities of these eigenvalues to the various parameters of the control system are calculated. This approach can provide a basis for optimal design of the system. A detailed sensitivity analysis is made of a particular system under various operating conditions, and results are tabulated, making it possible to obtain a clear idea about the effect of any parameter on the system performance and dynamic stability limit.

Sensitivity Analysis of Power Systems

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.

Sensitivity Analysis in Power System Dynamic Stability Studies

This paper concerns itself with the time-optimal control of large oscillations in power systems by bang-bang excitation control. The determination of the instants at which the control is switched from one level to another and the application of such a piece-wise constant control to a tenth order nonlinear model which includes the effects due to field time lag and damper bars and the dynamics of exciter and govternor are the principal aspects of the paper. The results show that as compared to the normal proportional voltage regulator the bang-bang control effects more efficient damping of the system. Significant improvements are seen in the rate of response and the number and amplitudes of oscillations. The enhancement of the critical clearing time due to bang-bang network control is inidicated. It is hoped that the approach to the bang-bang control outlined in this paper would serve as a guide to future system studies on discontinuous control.

Bang-Bang Excitation Control

The method of D-decomposition technique is used for the analysis of steady state stability of a two-machine system with the distant station provided with a fast acting electronic excitation voltage regulator using proportional signals of voltage and current and the first and second derivative of current signals. Analytical results are obtained on a digital computer of the type CDC 6600 for a typical two-machine system. Analysis is given for determining the voltage regulator gains for maximum alternator stability which to a great extent would overcome the often encountered difficulty of setting the regulator gains at commission stage by trial and error, until a good step response under open circuit condition is achieved. The effect of several parameters as also the electro-mechanical transient process of the receiving-end system represented by an equivalent machine of finite capacity on steady state stability of the system is investigated, for properly designing the parameters of the voltage regulator.

Analysis of Steady State Stability of a Two Machine System by the D-Decomposition Technique

The paper presents a case for correlating transient response with transient-stability limit of power systems. An elementary power system provided with fast acting voltage regulators using various feedback signals is analysed in detail. The effect of varying regulator gains on transient response is investigated with the help of gain-locus diagrams on a gain plane. The Runge-Kutta method with fourth-order approximation is used to determine the transient-stability limit of the same system for various gains. The gains which give good transient response are compared with those which give high stability limit. Efforts have thus been made to see whether it is possible to correlate good transient response with high transient-stability limit.

M.V. Hariharan

Papers

Transient response and transient stability of power systems