Frequency Measurement Practices for Inertia Assessment in Inverter Based Resources Dominated Power Systems

Abstract

Transmission system operators and protective relays compute the rate of change of frequency (RoCoF) from frequency averaged over tens to hundreds of milliseconds, as standards and grid codes specify. Any response delivered inside that window lowers the measured RoCoF, so the inferred inertia depends on the window and the responses in service. This paper defines the windowed inertia estimate and derives an exact identity the system inertia divided by one minus the fraction of the disturbance energy delivered inside the window and a closed-form prediction that applies the same estimator to the trajectory of a linear response model. Eleven IEEE 9-bus RMS runs synchronous, grid-following and grid-forming configurations, disturbance sizes and parameter sweeps are reproduced by that model, and the identity closes on the measured response powers. Fast frequency response inflates the estimate most: at 500 ms a grid-following system with 20 % less synchronous inertia reports the same value as the all-synchronous system, the grid-forming system a higher one. On a reduced Greek transmission system the 500ms estimate exceeds the inertia by 17-26%, and a scenario with 10% less synchronous inertia reports more than the all-synchronous scenario's inertia. Operators can thus compute what their measurement reports.