With the increase of inverter-based resources, the reduction in grid inertia has become an issue. To overcome this problem, various virtual inertia controls have been proposed. df/dt control is a candidate for practical application since it can be integrated into conventional current controlled inverters. However, df/dt control can make the system unstable under certain conditions. A common solution is to use a low-pass filter (LPF), but there is no clear answer to why df/dt control becomes unstable and the LPF can improve stability. As a result, there are no general design criteria of the LPF for various plants. This paper focuses on the stability of a current-controlled inverter with df/dt -type virtual inertia control. The authors analyze the dynamic characteristics of a synchronous generator and demonstrate the existence of a second-order delay between the frequency of the point of common coupling (PCC) voltage and the speed of the rotor. The result demonstrates an equivalence between this delay and LPF for stabilization in df/dt control. Then, this second-order delay is implemented in df/dt control as an LPF. The influence of this LPF for stability is analyzed by EMT simulations and Bode plot of the entire system. These results illustrate that the LPF is indispensable for df/dt control, and parameters corresponding to synchronous generators can be used as a design criterion of the LPF.
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