Extreme water level of surge chamber in hydropower plant under combined operating conditions

The design height of surge chambers is determined by the lowest and highest water levels under combined operating conditions. We considered four typical combined operating conditions: successive-load-rejection operating condition (SLROC), successive-load-acceptance operating condition (SLAOC), load-acceptance-then -rejection operating condition (LATROC), and load-rejection-then-acceptance operating condition (LRTAOC). A theoretical formula was derived to determine the worst superposition moment of extreme water levels using the implicit function theorem. An actual hydropower plant was used to analyse extreme water levels. The results showed that the tangential point for the headrace tunnel discharge-water level relationship curve of initial and superposed operating conditions was the worst superposition moment. The highest water level at the worst superposition moment was higher than that at the superposition moment of maximum flow into the surge chamber; similarly, the lowest water level at the worst superposition moment was lower than that at the su-perposition moment of maximum flow out of the surge chamber. When the cross-sectional area of impedance hole was small, the highest and lowest water levels occurred in SLROC and SLAOC, respectively. Conversely, when the cross-sectional area was large, the highest and lowest water levels occurred in LATROC and LRTAOC, respectively. The proposed formula avoids repeated trial calculations to determine extreme water levels, providing important theoretical significance and engineering application value.