Exponential Synergistic Adaptive Control for PV–Storage Grid-Forming Inverters to Eliminate Overdamped Hysteresis in Weak Grids

Traditional virtual synchronous generator (VSG) control in photovoltaic–storage systems struggles with severe dynamic deterioration under high-impedance weak grid conditions. Through small-signal modeling, this paper analytically reveals that increased grid inductance forces the system’s dominant poles to migrate significantly toward the real axis, inducing a critical “overdamped hysteresis” that degrades transient tracking speed and oscillation attenuation. To break these physical constraints, an improved exponential synergistic adaptive control strategy is proposed. By establishing a synergistic optimization mechanism between the virtual inertia and damping coefficients via a square-root coupled exponential function, the proposed method achieves precise multi-parameter coordination. During the initial phase of disturbances, it triggers an explosive parameter surge to provide “stiff” transient support, strictly limiting frequency deviations and the rate of change of frequency (RoCoF). During the recovery phase, it drives a precipitous parameter decay to actively neutralize the overdamped coupling effect, forcibly pulling the migrated poles back to the ideal underdamped region. Rigorous switching-model simulations demonstrate that, compared to conventional fixed-parameter and power function-based adaptive methods, the proposed synergistic strategy significantly improves transient performance. Quantitatively, during load steps, it restricts the frequency nadir to 49.85 Hz (compared to 49.73 Hz for fixed parameters). During extreme grid stiffness transitions (SCR drops), it completely eliminates active power tracking hysteresis by reducing the settling time to just 0.26 s and aggressively clamps AC overcurrent peaks from 38 A down to 31 A. Supported by coordinated PV–storage energy management, the proposed method offers a highly robust grid-forming framework for renewable-dominated weak power grids. Supported by coordinated PV–storage energy management, the proposed method offers a highly robust grid-forming framework for renewable-dominated weak power grids.