Abstract: Abstract: Whether the load regulation transition process of the hydropower unit can be stably carried out will have an important impact on the safe operation of the power grid and the coordination of the source network as it is the backbone power supply for peak and frequency modulation in the power system,. During the load regulation transition process, the governor power mode automatically completes the power closed-loop regulation by the governor, and quickly responds to the load adjustment command issued by the AGC, which responses fast and realizes the coordinated control of the primary frequency modulation and the AGC. Due to the combination of water hammer effect, the nonlinearity of the turbine and the time-varying parameters, the stability characteristics of load regulation transition process of hydropower units become more complicated than imagined. At present, the research on governor power mode mostly focuses on control logic, experimental simulation and control parameters optimization and rarely involves the stability problem of load regulation. Yet there are actually more than one hydropower plants that have experienced instability during operation. The problem of instability in the power mode leads to power oscillation, endangering the security of the grid and the coordination of the source network. In this paper, the method of theoretical analysis and numerical simulation is used to deeply analyze the stability of the transition process of load regulation under the governor power mode of hydraulic turbine, therefore the stability region of unit operation with the governor parameters as variables is obtained and the discriminant for the stability of load regulation transition process in the power mode of governor is deduced. Through this discriminant, the stable condition of load regulation transition process can be obtained quickly, and the parameter setting of governor in power mode can be effectively guided to ensure the stable operation of hydropower unit. The influence of water flow inertia Tw , servo response characteristic Ty and turbine characteristics on the stability domain are analyzed. The results show that the value of Tw has a great influence on the stability region. As the value of Tw increases, the area of the stable region decreases, which is not conducive to the stability of the system. With the increase of Ty's value, the area of the stability region increases, which is conducive to the stability of the system. When Ty's value decreases, the governor parameter Kp should be reduced in order to ensure the stability of the power regulation process. The study also indicates that the operating condition of water turbine has a great impact on the system's stability region. The size of the stability region is closely related to the product value of the comprehensive characteristic coefficient of water turbine e and the transfer coefficient of water turbine ey. The larger the product value, the smaller the system's stability region. Based on the research results of this paper, a detailed analysis of a case of hydropower unit is carried out. According to the comprehensive characteristic curve of the turbine, the most unfavorable working condition of power regulation stability can be accurately found. The research results of this paper can effectively guide the safe operation of hydropower units, which is of great significance to the safety of the power grid and the coordination of the source network.