Novel frequency-domain inertia mapping and estimation in power systems using wavelet analysis

In recent power systems, accurately estimating system inertia is crucial for stability, especially with the increased integration of renewable energy sources. This paper proposes a novel wavelet-based method for estimating the inertia of synchronous machines and the dynamic inertia of converterinterfaced generators (CIG). The proposed method estimates the inertia constant in the frequency domain, contrasting traditional time domain methods. The proposed method capitalises on the unique capability of wavelet transform coefficients to analyse rapid changes in active power and frequency signals. The magnitude of these coefficients is then utilised to measure the strength of the transit periods on those signals, which serves as an indicator of the power system's inertia constant. This paper also derives a novel mathematical relationship between frequencydomain inertia estimates and their time-domain equivalents. The proposed method is scalable, demonstrating efficiency across both small and large power systems. Control hardware-in-the-loop (CHiL) simulations are employed using a real-time, high-speed piecewise linear electrical circuit simulator (PLECS) alongside a digital signal processor (DSP) to validate the proposed method. The results reveal that the proposed method offers superior stability and demonstrates resilience against system noise, as well as potential numerical issues common in traditional methods