Abstract
The 330 kV national transmission network of Nigeria is a 34-bus, 38-line and 14-generator system. The network
suffers endemic voltage instability and transient fragility due to the increasing replacement of synchronous generation by
inverter-based resources (IBRs). Power flow studies performed in the Power System Analysis Toolbox (PSAT) show
undervoltage violations at Gombe (0.9068 p.u.) and Jos (0.9489 p.u.) busses, a negative reduced Jacobian eigenvalue (0.464)
indicating small signal instability, a maximum loadability parameter of λ_critical = 1.7337, and unbounded rotor angle
divergence for three phase short circuit contingencies. We develop a hierarchical nonlinear control methodology for grid
forming (GFM) inverters with battery energy storage systems (BESS), comprising (i) a Lyapunov stable adaptive virtual
synchronous machine (VSM) with a dynamically modulated virtual inertia J and damping D, (ii) a finite horizon model
predictive control (MPC) voltage loop co-optimizing voltage tracking, dq axis current limiting, and state of charge (SoC)
preservation, and (iii) a washout filtered transient damping injection channel.