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

Abstract

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. Surge chambers are typically installed in hydropower systems to effectively mitigate water hammer pressures. However, an inappropriate cross-sectional area of the surge chamber may lead to system instability when subjected to small oscillation. To ensure stable operation of the hydropower station, Svee ignored water inertia in the penstock and draft tube during the derivation process, obtaining the Svee stable area of the ACSC. This study assessed the applicability of the Svee formula by analyzing the stability of a hydropower system with an ACSC when the water inertia in the penstock and draft tube was considered. The research results indicate that the Svee formula is theoretically questionable. The stability of a hydropower system with an ACSC is primarily influenced by the WHRCs of the turbine, whereas the cross-sectional area of the ACSC exhibits a minimal influence on stability. Consequently, the constraints imposed by the Svee formula during the design of ACSCs should be lessened, which could reduce investment costs for hydropower stations and provide greater flexibility and freedom when designing ACSCs.