A Novel Passivity-Based Nonlinear Control Framework for Grid-Forming Inverters in Weak Grid Nigerian Power Systems

This research develops a novel passivity-based nonlinear control framework for grid-forming inverters connected to weak grid conditions representative of Nigerian rural and semi-urban distribution networks, making original theoretical contributions to the stability analysis and control design for the next generation of inverter-based generation systems. As solar PV penetration in Nigerian distribution networks increases, the transition from grid-following to grid-forming inverter architectures becomes necessary to maintain voltage and frequency regulation in weak grids where the short-circuit ratio at the point of interconnection falls below the threshold for reliable grid-following operation. Existing grid-forming control strategies, including droop control and virtual synchronous machine control, lack rigorous nonlinear stability guarantees for weak grid operation and exhibit performance degradation under the high harmonic distortion and large voltage fluctuations characteristic of Nigerian distribution networks. The proposed framework is grounded in port-Hamiltonian systems theory, which enables a systematic energy-based analysis of inverter-grid interaction dynamics and guarantees Lyapunov stability by construction through the passivity property of the interconnected system. Original contributions include the derivation of a port-Hamiltonian model for the grid-forming inverter-weak grid system that incorporates Nigerian grid impedance uncertainty characterised from field measurements at 20 representative rural connection points, and the development of an adaptive control law that online identifies the grid impedance and adjusts the control parameters to maintain the passivity margin above a guaranteed threshold. Hardware validation confirms stable operation under short-circuit ratios as low as 1.2. Keywords: grid-forming inverter, passivity-based control, weak grid, port-Hamiltonian, Nigeria.