Synchronous Operation Stability of Three‐Stage Hydropower Stations Based on Feedback Regulation of Regulating Reservoir Water Levels

ABSTRACT This paper focuses on the stability of synchronous operation (SSO) of three‐stage hydropower stations cascaded by regulating reservoirs (THSRRs). Firstly, the model of synchronous operation of THSRRs is established. According to the model, the Hopf bifurcation theory is utilized to analyze the SSO of THSRRs. Then, the critical stable sectional areas(CSSAs) of the first and second‐stage regulating reservoirs (FSRR and SSRR) are identified. The role of the regulating reservoir areas on the stable domain is explored. Finally, the coupling effects of the governor‐regulating reservoirs on the system are analyzed. The results show that the largest stable domain is found in the third‐stage hydropower station(TSHS). The smallest one is found in the second‐stage hydropower station(SSHS). The increase in area of regulating reservoir is beneficial to the upstream hydropower station but detrimental to the downstream hydropower station. Under the parameters of the hydropower stations, there are two positive solutions for the CSSAs of the adjacent regulating reservoirs and only one positive solution for the nonadjacent reservoir. The increase in integral gain is detrimental to the stable domain. As the proportional gain increases, the stable domain firstly increases and then decreases. This study provides technical support for the secure running of THSRRs.