Continuous real-time inertia estimation in power systems using ARMAX, ARX, and OE models

With the increasing integration of converter-interfaced generation (CIG), the continuous and real-time monitoring of inertia has become essential for maintaining the reliability and security of operation in power grids. However, despite different inertia estimation methods existing in the literature, the discernments about the online assessment of the alternatives in real-time, and suitability to provide continuous estimates, is in general very limited. Based on this, the practical effectiveness of three recursive system identification approaches, such as ARMAX (Auto-regressive Moving Average with eXogenous input), ARX (Auto-Regressive with eXogenous Input), and OE (Output Error), is investigated in this paper to continuously track physical and virtual inertia in a sample power system. The considered parametric model structures are implemented and evaluated using the real-time simulation environment ePHASORsim from OPAL-RT. Using ambient frequency and power measurements from the test grid, the numerical accuracy, computational efficiency, and robustness of these alternatives is validated under normal operating conditions and a set of system disturbances. By assessing the performance of the estimation algorithms in real time, the research validates measurement-based alternatives that move beyond offline studies, do not rely on disturbance events, and operate without detailed mathematical models. This offers valuable insights on the practical aspects and potential of the considered approaches for actual real-world applications. • Measurement based recursive polynomial estimators can continuously extract inertia values in real-time. • Virtual inertia from CIG with VSM control can be effectively tracked with polynomial models. • ARMAX based strategies can provide relatively accurate inertia estimates even during transient events. • Real-time simulation validates inertia estimation algorithms beyond offline studies. • Algorithms’ practical insights under realistic constraints are possible through real-time environments.