Online Inertia Estimation for Supply-Side Nodes Using ARX-IG-UKF

Conventional unscented Kalman filter (UKF)-based inertia estimators are constrained by slow convergence within the limited inertial response window and a fixed measurement noise variance that cannot capture time-varying uncertainty during disturbances. This paper proposes ARX-IG-UKF, an online nodal inertia estimation method combining autoregressive modeling with exogenous inputs (ARX) for initialization and inverse-gamma (IG) noise adaptation. First, an ARX model fitted to early post-disturbance power frequency data provides an initial nodal inertia estimate. This estimate initializes a state-space model describing the inertial responses of synchronous generators and renewable generation units, reducing the convergence time required for short-window estimation. An IG distribution is then used to update the measurement noise covariance online in response to deviations associated with primary frequency regulation. The adaptive covariance is incorporated into the UKF to reduce the influence of non-inertial dynamics and recursively estimate nodal inertia. Simulation studies demonstrate consistent convergence and stable estimates under a range of operating conditions, supporting the applicability of the method to online nodal inertia identification in complex operating scenarios.