Research on the Critical Stable Area of Air Cushion Surge Chambers in Hydropower Stations

The Svee formula plays a crucial role in assessing the stability of hydropower systems with an air cushion surge chamber (ACSC). This formula is derived from the Thoma formula, a stability criterion for the common open-surge chamber (COSC), which overlooks the water inertia in the penstock and draft tube. Therefore, the validity of this approach demands further exploration. In this paper, based on the rigid water column (RWC) assumption, the second- and third-order mathematical models of a hydropower system with an ACSC were established. The Svee formula for the RWC models of different orders was analyzed. The stability criterion considering the real-life elasticity of the water column was also proposed to assess the plausibility of the Svee formula. The results indicate that both based on the RWC assumption and for the elastic water column (EWC), a hydropower system with an ACSC consistently fails to maintain stability under the equal output regulation (EOR) mode. The Svee formula opens to question in theory. Under the RWC assumption and the EOR mode, the derivation processes of Thoma and Svee formulas both neglected the water inertia in the penstock and draft tube, a crucial factor affecting system stability. As long as the preceding water inertia is considered, the system is unstable. Furthermore, the paper reveals that the water hammer reflection coefficients (WHRCs) of the hydropower system and the head loss coefficient significantly impact system stability, whereas the cross-sectional area of the ACSC has a comparatively minor influence.