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Virtual inertia controllers (VICs) for wind turbine generators (WTGs) have been recently developed to compensate the reduction of inertia in power systems. However, VICs can induce drivetrain torsional oscillations of WTGs. This paper addresses this issue and develops a novel nonlinear VIC based on objective holographic feedback theory and the definition of a completely controllable system of Brunovsky type. Simulation results under various scenarios demonstrate that the proposed technique outperforms existing VICs in terms of enhancement of system frequency nadir, suppression of WTG drivetrain torsional oscillations, fast and smooth recovery of WTG rotor speed to the original maximum power point (MPP) before the disturbance as well as preventing secondary frequency dip caused by traditional VIC. The proposed technique is also able to adaptively coordinate multiple WTGs to enhance the frequency support and the dynamic performance of each WTG. [ABSTRACT FROM AUTHOR]

• A comprehensive review of inertia estimation techniques is provided for SGs, including the model-based and measurement-based approaches. • This is the first attempt to propose new potential algorithms for the estimation of the inertia from different VIE-based CIGs according to their various control characteristics. • New insights for future work on quantifying power system inertia considering CIGs and their potential applications are extensively discussed. Understanding and quantifying the inertia of power systems with the integration of converter-interfaced generation (CIG) plays an essential role in the safe transition to a future low-inertia scenario. This paper provides a comprehensive summary of inertia definitions for both synchronous generators and CIGs as well as their corresponding estimation methods. In particular, the estimation methods are categorized as model-based and measurement-based approaches considering both small and large disturbances. The advantages and disadvantages of different methods are carefully discussed. This paper also offers for the first time a framework to quantify the virtual inertia of CIGs at the component and aggregation levels, an open problem in the literature. Finally, future directions for inertia estimation are identified and discussed. This significantly benefits the design of appropriate control and protection schemes in achieving a more reliable, secure, and resilient power system. [ABSTRACT FROM AUTHOR]