Dynamic evolution of a hydraulic-mechanical-electric system with randomly fluctuating speed based on Chebyshev polynomial approximation method

Abstract

The research proposed in this paper focuses on the dynamic evolution of a hydraulic-mechanical-electric system under the effect of randomly fluctuating speed. The rapid growth of installed wind power capacity may potentially affect the stability of power grids, causing larger fluctuations of the generator speed to hydropower stations. In this work, a probabilistic component is associated to the generator speed of a deterministic hydraulic-mechanical-electric system providing a novel random model. This latter is analyzed to investigate the dynamic evolution of the system adopting the Chebyshev polynomial approximation method. A careful comparison of the numerical application results obtained by the deterministic and the probabilistic approaches is carried out. In addition, the influence of the fluctuation intensity (D) on the differential gain (kd) of the PID is investigated, proposing a law for kd as function of D. Finally, the operating ranges of the grid water hammer and of the elastic water hammer models are compared in order to validate the consistence of the law. The results of the study provide robust bases for the stable and safe operation of hydropower stations.