Switching Markov Gaussian Models for Dynamic Power System Inertia Estimation

Future power systems could benefit considerably from having a continuous real-time estimate of system inertia. If realized, this could provide reference inputs to proactive control and protection systems which could enhance not only system stability but also operational economics through, for example, more informed ancillary reserve planning using knowledge of prevailing system conditions and stability margins. Performing these predictions in real time is a significant challenge owing to the complex stochastic and temporal relationships between available measurements. This paper proposes a statistical model capable of estimating system inertia in real time through observed steady-state and relatively small frequency variations; it is trained to learn the features that inter-relate steady-state averaged frequency variations and system inertia, using historical system data demonstrated over two consecutive years. The proposed algorithm is formulated as a Gaussian Mixture Model with temporal dependence encoded as Markov chains. Applied to the U.K. power system, it produces an optimized mean squared error within 0.1 s 2 for 95% of the daily estimation if being calibrated on a half-hourly basis and maintains robustness through measurement interruptions of up to a period of two hours.