Comprehensive stability analysis of complex hydropower system under flexible operating conditions based on a fast stability domain solving method

This paper aims to study the comprehensive stability of the multi-unit hydropower systems (MUHS) with complex hydraulic coupling under flexible operating conditions and to reduce the time consumption of batch conversions in the stability domain of high-order hydropower systems (HOHSs). Firstly, the models for an actual hydropower system with three-turbine sharing a long tailrace are established considering three typical operating scenarios. Subsequently, a trajectory search algorithm is proposed to improve the speed and flexibility of stable domain solving in HOHSs. On this basis, the stability variation law of the MUHS with the variation of water head and guide vane opening is studied, and the minimum stability domain index is introduced to evaluate the comprehensive stability of systems under full hydroturbine operating conditions. Finally, the comprehensive stability of the MUHS under flexible combination operating conditions is analyzed. Notably, the stability of the MUHS is poor when the hydroturbine is operated at a water head of 215-225 m and a guide vane opening within 55-70%. In addition, the reduction of operating units will significantly deteriorate the comprehensive stability of MUHS. This paper provides a powerful tool for the stability analysis of HOHSs and potentially supports the optimal operation of the MUHS.