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The paper first proves the existence of a nonlinear, feedback loop due to the effect of an active power filter (APF) on the grid voltage for a multifunctional electric vehicle charging station. A linear, open-loop model is derived based on direct quadrature (DQ)-theory in discrete time (DT). Based on this model, a linear, closed-loop model is further developed with DQ-theory in DT. A triangle-hold equivalent instead of a zero-order-hold equivalent is employed in the model for better representation. The developed linear, closed-loop model is finally generalized to general power systems. Simulations are carried out to verify the developed models under transient conditions. The short-time (1–2 ms), transient stability of the grid with an APF is determined with the developed model. In contrast to existing stability analyses in the phasor domain, using DQ-theory can linearize the loop and simplify the loop model in DT domain. [ABSTRACT FROM AUTHOR]