Multi-timescale energy-aware grid-forming control with self-tuning virtual inductance for battery lifetime...

With the increasing penetration of converter-interfaced renewable energy, modern power systems are increasingly exposed to weak-grid conditions, where reduced short-circuit strength and low inertia significantly challenge the stability of grid-forming inverters. To address these issues, this paper proposes a multi-timescale energy-aware grid-forming (GFM) control strategy for PV-battery energy storage systems (PV-BES). The fast layer provides immediate stabilization by shaping the inverter output impedance and injecting virtual damping. The medium layer adaptively tunes the virtual inertia and damping gains according to the estimated DC-link energy and the online-evaluated grid strength, enabling the inverter to autonomously regulate its dynamic behavior under varying operating conditions. A slow layer regulates long-term energy trajectories to reduce battery cycling stress. In addition, a dedicated mode coordinator is introduced to ensure smooth transitions among MPPT, charging/discharging, and GFM operation, preventing discontinuities in DC-link energy and adaptive control gains. Numerical simulations demonstrate that the proposed strategy effectively enhances transient stability, suppresses oscillatory responses under weak-grid disturbances, and significantly mitigates battery degradation by reducing DC-link energy fluctuations. These results highlight the potential of incorporating energy-awareness into GFM control design for achieving both improved dynamic performance and extended battery lifetime.