Advanced Nonlinear Control of Grid Forming Battery Energy Storage Inverters for Enhanced Transient and Voltage Stability: Application to the Nigeria 330 kV Transmission Network

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.