Random Model of Water Hammer Pressure and Probability Analysis in Waterpower Station

Considering such factors as the original load of turbine, closure time of wicket gate, and water level of reservoir are changeable in the practical operation of waterpower station, they should be regarded as random variables in water hammer analysis. Accordingly, random model of water hammer with random boundary conditions and random initial states is introduced in this paper. And the probability distribution law of each of random variables is concluded. Concerning a single hydraulic system, firstly, random computational formulas for increasing pressures and maximum pressures of water hammer with random variables are deduced. Then theoretical formulas for sensitivity analysis are provided and, with these formulas, sensitivity analysis for water hammer is made. Besides, probability density formulas for increasing pressures and maximum pressures of water hammer are given. And the method of distribution type fitting is introduced to determine the distribution of water hammer pressures. Thereby conclusions are drawn that the distribution of increasing pressures of water hammer in single systems of waterpower station is log-normal type and that of maximum pressures is normal type. Finally, all the methods involved are verified through computational examples.