A Spectral Model of Grid Frequency for Assessing the Impact of Inertia Response on Wind Turbine Dynamics

Journal Paper published to energies (MDPI) The recent development in renewable energy has led to a higher proportion of converter-connected power generation sources in the grid. Operating a high renewable energy penetrated power system and ensuring the frequency stability could be challenging due to the reduced system inertia that is usually provided by the conventional synchronous generator. Wind turbines, as one major role of renewable generation sources, have the advantage to provide synthetic inertia response to the grid. This is achieved by controlling the kinetic energy extraction from the rotating parts by its converters. Previous studies have shown the potential of wind turbines to provide inertia response based on the measured rate of change of grid frequency. In this paper, we derive a spectral-based model of the grid frequency by analyzing historical measurements. The spectral model is then used to generate realistic, generic, and stochastic signals of the grid frequency for typical aero-elastic simulations of wind turbines. The spectral model enables the direct assessment of the additional impact of the inertia response control on wind turbines: the spectra of wind turbine output signals such as generator speed, tower base bending moment, and shaft torsional moment are calculated directly from the developed spectral model of the grid frequency and a commonly used spectral model of the turbulent wind with high accuracy. The calculation of output spectra is verified with non-linear time-domain simulation and spectral estimation. Based on this analysis, a notch filter is designed to alleviate significantly the negative impact on wind turbine structural loads due to inertia response with only small impacts on the grid support