Analytical solutions for determining extreme water levels in surge tank of hydropower station under combined operating conditions

Combined operating condition usually refers to the control operating condition under which the highest and lowest water levels occur in a surge tank of hydropower station. In this paper, with the basic equations of surge analysis and nonlinear vibrational asymptotic method, analytical expressions of the worst superimposition time of surge waves in an upstream surge tank under four typical combined operating conditions (i.e. load-acceptance-then-rejection, successive load rejection, successive load acceptance and load-rejection-then-acceptance) are derived firstly. Then using these expressions, the analytical extreme water levels are determined. The analytical solutions are verified with numerical simulation results. Finally, the effect of the hydraulic resistance coefficient of surge tank on the control operating condition is investigated. The results indicate that: The analytical solutions for determining extreme water levels in surge tank under various combined operating conditions are accurate due to the good agreements between the analytical results and the numerical results. With the increase of the hydraulic resistance coefficient of surge tank, the control operating condition for the highest water level shifts from load-acceptance-then-rejection condition to successive load rejection condition, and the control operating condition for the lowest water level shifts from load-rejection-then-acceptance condition to successive load acceptance condition.