converters that have the ability of inertial, primary frequency and voltage regulation [5]. Compared to SGs, adjustable virtual inertia and damping are advantages of VSGs, and their optimization can improve the dynamic response and support of grid-configured energy storage systems [6]. However, the application of VSG technology also leads to some undesirable properties, which motivated our research. A significant issue is the emergence of low-frequency oscillations caused by the internal dynamic nature of the system, which is due to a periodic energy exchange between generators. These oscillations can lead to power and frequency instability, potentially resulting in disconnection or damage to the power converters. Moreover, power systems with VSGs often exhibit lower damping levels than conventional systems, further jeopardizing grid stability [7]. Another challenge of VSG-based power systems comes from the finding that high virtual inertia reduces RoCoF and the frequency nadir but worsens oscillation damping, while low inertia improves damping but reduces inertial response [8; 9]. These trade-offs highlight the importance of optimizing inertia constants and damping coefficients to achieve balanced system performance [10; 11]. Experts in this field are aware of this problem, and many studies have been conducted to solve it. Our previous research [12] suggested a possible optimal point of inertia for damping a specific mode and an optimal range of inertia that ensures the best controllability of interconnected VSGs. Furthermore, Ref. [13] proposes a VSG control strategy based on Transient Damping Compensation (TDC), which exhibits superior active response performance and transient oscillation suppression capabilities, effectively eliminating active steady-state deviations caused by frequency disturbances in the power grid. TDC primarily enhances transient stability and damping, requiring precise models with risks of over-damping if not properly implemented. Ref. [14] proposes an adaptive strategy of co-regulating the droop coefficient of active power versus speed characteristics, virtual inertia, and the damping coefficient for the VSG. This approach can solve the uncoordinated performance between the virtual inertia and damping using conventional adaptive control, in which the system may experience serious frequency fluctuations. However, its performance is highly dependent on accurate system measurements, and improper tuning or measurement errors may introduce instability risks. In ref. [15], the VSG control is applied for power sharing and inertia emulation to increase the dynamic response and improve system stability. Inertia emulation with coordinated power sharing improves frequency stability by boosting inertial response but may introduce undesirable oscillations. Ref. [16] focuses on the optimal damping design of VSGs to enhance transient stability through state-space trajectories. State-space optimal damping design targets suppression of oscillatory modes, but it needs accurate state estimation. Ref. [17] introduces an approach for optimizing renewable distributed generation (RDG) and VSG sizing and placement within distribution networks, utilizing the Multi-objective Salp Swarm Optimization Algorithm (MOSSA) to achieve an optimal solution. The objective function aims to minimize frequency deviation while maximizing total annual energy savings and reducing the operational costs of RDG and VSG units. Ref. [18] proposes an optimization method that adaptively adjusts the damping and inertia coefficients of VSGs using a fuzzy logic controller (FLC). The differential evolution (DE) algorithm is used to optimize the gains of the FLC, ensuring the effective tuning of the VSG parameters and allowing the damping and inertia coefficients to be continuously adjusted, providing optimal frequency stabilization. It handles nonlinearity, and no precise model is required, but it incurs high computational costs.