True Inertia Constant of Synchronous Grid-Forming Control Strategies

Synchronous Grid-Forming (SGFM) algorithm. There are two prominent SGFM Virtual

Synchronous Machine (VSM) implementations commonly discussed in the literature: the PLLbased solution and the PLL-free solution. Although both methods have a similar control structure, incorporating an “inertia constant” and a “damping coefficient,” this paper demonstrates that they are fundamentally different. Even when configured with the same control parameters, they do not provide the same level of inertia to the system. The core distinction, which has been theoretically proven in this paper, lies in the dependency present in the PLL-free solution between the “inertia constant” and the “damping factor”. This dependency when not considered prevents the converter from delivering the effective inertia constant, which is usually calculated as the ratio of power variation to the Rate of Change of Frequency (RoCoF). Based on the proposed method for evaluating inertia, the paper also aims to provide guidance on how to set effective inertia for any type of Synchronous Grid-Forming

(SGFM) control.