Alternating Optimization Method for Virtual Inertia and Virtual Damping within Hybrid Systems

High-penetration renewables reduce system damping/inertia. While grid-forming (GFM) converters provide inertia and damping support, strong nonlinear coupling complicates multi-converter parameter configuration. This paper proposes a cooperative virtual inertia/damping optimization method integrating matrix perturbation theory and alternating optimization. A non-smooth optimization model with small-signal stability/frequency security constraints is formulated and decomposed into inertia/damping subproblems via alternating updates. Matrix perturbation-based eigenvalue sensitivity transforms subproblems into solvable linear sequences, while an adaptive trust-region strategy using second-order sensitivity accelerates convergence. Case studies confirms that the proposed method demonstrate enhanced small-signal synchronization stability, outperforming conventional methods in effectiveness and efficiency.