The elastic property of water and penstock’s effect on the governor stability

Abstract

To gain stable operation of a hydro power plant, it is mostly a matter of having the right ratio between the time constant of the rotating masses, T_a, and the time constant for the water masses, T_w. If T_a/T_w> 6 (or at least >4), the stability is normally not a problem. However, for power plants with long penstocks, this criterion is not enough. The elastic property of the penstock becomes an issue. The solution of the wave equation includes a term, which mathematically is defined as tanh (tangents hyperbolicus). This function is notoriously unstable. It has a similarity to the tan-function, which goes from to ±∞ as it approaches ± 90°. The cross frequency defines the frequency up to which the governor will function. Above the cross frequency, any disturbance will go without any interference from the governor. Therefore, the issue is to make sure that the elastic frequency is well above the cross frequency. In this paper, the transfer functions are solved analytically and the pressure response calculation is partly verified by measurements. However, the quality of the measurements are not quite adequate and will be repeated this spring.