STABILITY LIMITS OF HYDROELECTRIC POWER PLANTS By Oscar F. Jimenez 1 and M. Hanif Chaudhry, 2 M. ASCE ABSTRACT: It is well known that the inertia of the water in the penstock is the main unstabilizing factor for the stability of a hydropower plant. Most of the analytical studies on this subject use the lumped-system approach to include the water-hammer effects. However, the elasticity of the pipe walls and the compressibility of the water column could have in many cases significant det- rimental influence on the governing characteristics of a plant. An analytical cri- terion for the stability of a single, isolated hydro-unit is derived including the effects of elastic water hammer. It is concluded that for a system having Allievi parameter (p) less than one, the elastic effect of the conduit should be taken into consideration. INTRODUCTION A hydraulic turbogenerator feeding an isolated AC grid has to operate at constant rotational speed to generate electricity at constant frequency. Therefore, a governor is provided to control speed oscillations produced by load changes or due to other causes. System parameters such as pen- stock diameter, hydro-unit inertia, and governor settings are selected to minimize speed deviation and time required to settle down to the syn- chronous speed, following a load change or perturbation. One of the main unstabilizing factors is the inertia of the water in the penstock. This effect is twofold. First, when the governor acts to de- crease or increase the turbine output by closing or opening the wicket gates, the resulting water-hammer pressure produces an effect which is the opposite of what the governor tries to do. Second, as the water col- umn is not accelerated instantaneously, there is a time lag between the governor action and the resulting hydraulic torque. Most of the previous analytical works on the subject had used the rigid water-column theory to include the water-hammer effect. This ap- proach allows a representation of the system in terms of ordinary dif- ferential equations. Then, assuming small oscillations, so that the gov- erning equations may be linearized, the stability of the system can be readily obtained. Following this approach, Stein (1948), Paynter (1955), Hovey (1960), and Chaudhry (1970) investigated the stability of a dash- pot-type governor. Hagihara, et al. (1979), and Howe (1981) made sim- ilar analyses for a PID governor. Based on frequency response tests on the Apalachia Power Plant, Oldenburger and Donelson (1962) concluded that the lumped-parameter approach gives adequate results. However, this conclusion, obtained on a medium-head plant, cannot be general- ized to other types of plants.' 'Instituto Costarricense de Electricidad, San Jose, Costa Rica. 2 Assoc. Prof., Dept. of Civ. and Envir. Engrg., Washington State Univ., Pull- man, WA 99164. Note.—Discussion open until February 1, 1988. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on September 12, 1986. This paper is part of the Journal of Energy Engineering, Vol. 113, No. 2, September, 1987. ©ASCE, ISSN 0733-9402/87/0002-0050/$01.00. Pa- per No. 21801. 50 J. Energy Eng., 1987, 113(2): 50-60 Downloaded from ascelibrary.org by Oscar Jimenez on 10/30/15. Copyright ASCE. For personal use only; all rights reserved.