This paper aims to study the hydropower system operation stability considering the coupling effect of water potential energy in surge tank and power grid. Firstly, the mathematical formulation for hydropower system with surge tank that connected to power grid is established. Then, the hydropower system operation stability is investigated. The coupling effect mechanism of surge tank and power grid on stability is revealed. Finally, the formula for critical stable sectional area (CSSA) of surge tank considering power grid is derived and analyzed. The results indicate that the free vibration equation for hydropower system with surge tank that connected to power grid under step load disturbance is a ninth order linear homogeneous differential equation. The domain at the bottom left corner of the critical line on the Proportional-Integral plane is the stable domain. The proposed novel analytic solution of stable domain has a high precision and is feasible for practical applications. The formula for CSSA of surge tank considering power grid realizes the unity of the coupling effect of water potential energy in surge tank and power grid. The CSSA contains four terms, i.e. headrace tunnel term, penstock term, governor term and power grid term. (C) 2018 Elsevier Ltd. All rights reserved.