# Surge wave characteristics for hydropower station with upstream series double surge tanks in load rejection transient

## Highlights

Mathematical model of hydropower station with upstream series double surge tanks is established..

Analytical formulas for water level oscillations in two surge tanks are derived.

Oscillation characteristics and superposition mechanism of water levels are analyzed.

Effects of damping on water level oscillations in two surge tanks are studied.

Guiding suggestions to design of upstream series double surge tanks are proposed..

## Abstract

In order to reveal the surge wave characteristics and provide design guidances for the hydropower station with upstream series double surge tanks in load rejection transient, this paper studies the water level oscillations in the surge tanks. Firstly, the mathematical model that describes the unsteady flow for pipelines system is established. Then, for undamped upstream series double surge tanks system, the water level oscillations in two surge tanks are studied by deriving the analytical formulas with a novel method and analyzing the oscillation characteristics and superposition mechanism of water levels. The effects of damping on water level oscillations are analyzed. Finally, the application guidances of the results for the design of surge tanks and headrace tunnels are proposed. It is demonstrated that: Under the assumption of step discharge change in penstock, the proposed method for the derivation of analytical formulas for water level oscillations is effective, and the obtained analytical formulas are reasonable and have good accuracy. For the water level oscillations in two surge tanks, there are two kinds of frequency for the subwaves (i.e. subwave 1 and subwave 2). Subwave 1 and subwave 2 are the fundamental wave and the harmonic wave, respectively. The amplitude of subwave 1 determines the basic range of the water level oscillation. The damping mainly affects the attenuation of the water level oscillations. The analysis results for surge wave characteristics can be applied to the design of real projects.

## Keywords

• Hydropower station;
• Upstream series double surge tanks;
• Water level oscillation;
• Wave superposition;
• Damping;