Abstract
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.
Highlights
The system stability contribution function for the synchronization power of a smart inverter is an interference factor between power supplies, and it is difficult to perform mathematical analyses for complicated connection configurations. Functions such as the fault ride-through (FRT) in the grid code require fast responsiveness from the grid-connected inverters, which depends on the detailed data acquisition and accurate numerical analysis of these operations
By applying linear Koopman Operator (KO) to these observables, we could analyze the nonlinear dynamics of the power system
The simulation system included two virtual synchronous generator (VSG) inverters, which are classified as smart inverters, and one conventional synchronous generator as the main power source
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [5,6], the correlations among frequency fluctuation, time, and control parameters were quantified by presenting analyses of the transient response of a VSG inverter based on the generator mechanism. Williams et al [19] presented a data-driven method for approximating the leading KEs and KMs. Surana [20] demonstrated forecasting and anomaly detection using nonlinear dynamic generative modeling of a time series based on the KO. Described a method of applying the KO to the aerodynamic analysis of a wind power generation system to reproduce a low-dimensional linear state-space model accurately, thereby reducing the design cost of the controller. The transient responses and DFTs of the system frequencies and terminal voltages were calculated and compared with the results of KMD, thereby confirming the effect of cross-interference in the VSG control that appears only in KMD. It is useful to divert control library assets that are commonly applied to linear dynamics
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