With the growth in the share of variable renewable energy sources, fluctuations in the power generation caused by these types of power plants can diminish the stability and flexibility of the grid. These two can be enhanced by applying frequency containment using hydropower plants as an operational reserve. The frequency containment in hydropower plants is automatically controlled by speed governors within seconds. Disturbances such as fluctuations in the net head and aging may diminish the performance of the controllers of the speed governors. In this study, model reference adaptive control approaches based on the Massachusetts Institute of Technology (MIT) rule and Lyapunov method were exploited in order to improve the performance of the speed governor for frequency containment control. The active power control with frequency control was enhanced by the aforementioned adaptive control methods. A mathematical model of a hydropower plant with a surge tank and medium penstock was constructed and validated through site measurements of a plant. It was shown that, as they are applicable in real life, both methods perform significantly better compared to conventional proportional-integrator control. Even in first five deviations, the performance of the conventional controller improved by 58.8% using the MIT rule and by 65.9% using the Lyapunov method. When the two adaptive control approaches were compared with each other, the MIT rule outputted better results than the Lyapunov method when the disturbance frequency was higher; however, the latter was more functional for rare disturbances.