Equivalent virtual inertia modeling and time-constant analysis for multi-generator DC microgrids

In multi-generator DC microgrids employing diversified virtual inertia control strategies, the interactions among multiple DC-type virtual synchronous generators (VSGs) complicate the accurate evaluation of the equivalent virtual inertia. To overcome the evaluation difficulties caused by interactions among multiple DC-type VSGs, this paper proposes an equivalent modeling method that considers inertia interaction. An equivalent inertia model for a multi-generator DC microgrid under two typical virtual inertia control strategies is established. Based on this model, analytical expressions for the time-domain response of the DC bus voltage and an estimation formula for the inertia time constant are derived. The physical essence of inertia equivalence is interpreted by means of an equivalent RC circuit model. Moreover, a method for constructing an inertia time-constant mapping surface based on inertia equivalence is proposed. A three-dimensional mapping surface is constructed to quantitatively analyze the effects of cutoff frequency, virtual inertia coefficient, load power, and droop coefficient on the equivalent virtual inertia of the multi-generator DC microgrid. Finally, a multi-generator DC microgrid and its equivalent inertia model are established in the Piecewise Linear Electrical Circuit Simulation environment. The comparison between the analytically calculated DC bus voltage responses and the simulation results reveals that the relative deviations of the DC bus voltage responses are less than 3%, which verifies the accuracy of the proposed equivalent inertia model.