The generator speed is an important index in maintaining the stable connection between the hydraulic turbine and the electric power system. Historically, researches carried out are based on deterministic models. It is therefore a challenge to investigate the effects of random fluctuating speed on the dynamic evaluation of the hydraulic–mechanical–electric system as variable renewable generation sources link to the electric power system. Here, we proposed a probabilistic model and solved it by the Chebyshev polynomial approximation method. We also made a careful comparison implemented by the deterministic and the probabilistic models. Finally, we showed how the random excitations affect the dynamic evaluation of the system output.
- Chebyshev polynomial approximation
- elastic water hammer
- hydraulic–mechanical–electrical system
- randomly fluctuating generator speed
- vibration characteristics