As distributed power sources via grid-connected inverters equipped with functions to support system stabilization are being rapidly introduced, individual systems are becoming more complex, making the quantification and evaluation of the stabilizing functions difficult. Therefore, to introduce distributed power sources and achieve stable system operation, a system should be reduced to a necessary but sufficient size in order to enable the quantification of its behavior supported by transient theory. In this study, a system in which multiple distributed power supplies equipped with virtual synchronous generator control are connected is contracted to a two-machine system: a main power supply and all other power supplies. The mechanical torque of each power supply is mathematically decomposed into inertia, damping, synchronization torques, and the governor effect. The system frequency deviations determined by these elements are quantitatively indexed using MATLAB/Simulink. The quantification index displayed in three-dimensioned graphs illustrates the relationships between the various equipment constants of the main power supply, the control variables of the grid-connected inverter control, and the transient time series. Moreover, a stability analysis is performed in both the time and frequency domains.
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