Date of Award

Winter 1983

Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil & Environmental Engineering


Civil Engineering

Committee Director

Hanif Chaudhry

Committee Member

A. Osman Akan

Committee Member

John M. Kulman


The governing equations describing water level oscillations in a closed surge tank with compressed air at the top of the tank are a set of nonlinear ordinary differential equations if the hydraulic system is analyzed as a lumped system. These oscillations are stable or unstable depending on the parameters of the plant and the type and magnitude of the disturbance.

The present available stability criterion has been developed by linearizing the governing equations and is, therefore, valid only for small disturbances.

In the research reported herein, the governing equations are normalized to reduce the number of parameters from nine to four and the stability of oscillations is studied by using the phase plane method which allows inclusion of nonlinear terms in the analysis and, therefore, would be valid for small and large disturbances.

Four cases of turbine flow demand are investigated. These are: constant discharge, constant gate opening, constant power and constant power combined with constant gate opening. Singularities of the governing equations are determined and analyzed in each case and stability criteria are developed. For illustration purposes, Driva Hydroelectric Power Plant System in Norway is analyzed and phase portraits are presented.

These investigations show that the oscillations are always stable for the case of constant discharge and of constant gate opening. For the constant power case, oscillations are stable only if the system parameters satisfy certain criteria. For a combination of constant power and constant gate opening, it has been found that stability criteria for constant power are valid for heads greater than rated head and for constant gate opening for heads less than the rated head.


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