Comprehensive analysis of steady-state and dynamic interactions between Kalman filter-based GFLI and Droop/VSM-based GFMI in conventional and fully Inverter-interfaced power systems

Journal article, 2026

The global energy transition toward renewable sources is driving a shift from conventional synchronous-machine-dominated grids to inverter-based power systems. This necessitates the integration of grid-following (GFL) and grid-forming (GFM) inverters, each with distinct characteristics. As future power systems are expected to include a high share of inverter-based resources, understanding the steady-state and dynamic interactions between GFL, GFM, and synchronous-machine-based grids is important for reliable operation. This research investigates steady-state and transient responses in several prospective scenarios of future power systems. For GFL inverters, a Kalman Filter-based Phase Locked Loop (PLL) is adopted to improve performance under weak-grid conditions, while GFM inverters are modeled using established droop and Virtual Synchronous Machine (VSM) controllers. The study employs inverter capacities from 2.5 MVA to 10 MVA and synchronous machines from 2.5 MVA to 200 MVA to represent different grid conditions. MATLAB/Simulink is used to investigate the interactions between grid-GFL, grid-GFM, and GFL-GFM systems under steady-state small disturbances and transient bolted symmetrical faults. The findings show that the Kalman Filter-based PLL improves the GFL inverter response against transient disturbances compared with a conventional PID-based PLL, particularly in terms of reduced short-circuit current and faster settling. The results also indicate that GFL-GFM interaction can operate stably within the studied 100% renewable-energy-based scenario. For GFMI-SM operation, the results show that stability is strongly affected by the network X/R ratio, and virtual impedance compensation can improve stability under low-X/R conditions within specific limits. In addition to the time-domain study, eigenvalue analysis of the state-space models of both GFM and GFL inverters is carried out to support the observed stability trends. The paper provides a comparative simulation-based assessment of inverter-grid interactions relevant to future renewable-rich power systems.