Research on Critical Stable Sectional Area of Surge Chamber Considering the Fluid Inertia in the Penstock and Characteristics of Governor

According to the fact that the existing critical stable sectional area of surge chamber does not consider the effect of the fluid inertia in the penstock and characteristics of governor, mathematical model of hydraulic and governor system considering those two factors is established. Critical stable sectional area criterion is equivalent to that the first derivative term of homogeneous differential equation is greater than zero, and the analytical formula of critical stable sectional area is deduced. The analytical formula is composed of diversion tunnel term, penstock term and governor term, diversion tunnel term is Thoma’s formula, penstock term is positive and governor term is negative. Finally, the mathematics essence of the governor parameters’ effect on critical stable sectional area is revealed: the effect of temporary droop b_t and damping device time constant T_d exist critical values, but the critical value is only meaningful in mathematics and would not appear in actual engineering. Critical stable sectional area is a monotone decreasing function of b_t and T_d.