In the field of microgrids (MGs), steady-state power imbalances and frequency/voltage fluctuations in the transient state have been gaining prominence owing to the advancing distributed energy resources (DERs) connected to MGs via grid-connected inverters. Because a stable, safe power supply and demand must be maintained, accurate analyses of power system dynamics are crucial. However, the natural frequency components present in the dynamics make analyses complex. The nonlinearity and confidentiality of grid-connected inverters also hinder controllability. The MG considered in this study consisted of a synchronous generator (the main power source) and multiple grid-connected inverters with storage batteries and virtual synchronous generator (VSG) control. Although smart inverter controls such as VSG contribute to system stabilization, they induce system nonlinearity. Therefore, Koopman mode decomposition (KMD) was utilized in this study for consideration as a future method of data-driven analysis of the measured frequencies and voltages, and a frequency response analysis of the power system dynamics was performed. The Koopman operator is a linear operator on an infinite dimensional space, whereas the original dynamics is a nonlinear map on a finite state space. In other words, the proposed method can precisely analyze all the dynamics of the power system, which involve the complex nonlinearities caused by VSGs.
On the Stochastic Filtering Theory of a Power System Dynamics
