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Analysis of waterhammer effect on speed change and governing stability of hydraulic turbines

University of British Columbia

A linearized mathematical model for the analysis of turbine speed governing problem is presented. This model includes the elasticity effects of both water and penstock walls, the effects of turbine characteristic slopes, and the linearized equation of a proportional-integral hydraulic governor. The procedure can be extended to a governor with a derivative term as well. Exact, travelling-wave solutions for the different possible cases are derived and presented in simple forms. Taylor's expansion formulas which offer a more efficient alternative for numerical evaluation of the speed are also derived. Solutions in both cases take into consideration penstock friction losses in a linearized form, as well as permanent speed droop (or speed regulation) and self-regulation coefficient. These travelling-wave solutions are then compared to numerical solution by the method of characteristics with close agreement in the results. This new analytical method is then used to study the influence of elasticity on maximum speed deviation and on the stability of oscillations and to define the limitation of a rigid-column analysis. For high-head plants, elasticity of the water and penstock walls increases maximum speed if governor settings are kept the same. The major influence of the elastic waves, however, is the reduction of the stability margin for the speed variation. Optimum governor settings will be, therefore, different from those obtained by neglecting elasticity of the water and penstock walls.

Text

2010-03-11

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http://hdl.handle.net/2429/21774

Civil Engineering

University of British Columbia

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