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The paper first proves the existence of a non-linear, feedback loop due to the effect of the APF on the grid voltage for a multifunctional electric vehicle charging station. A linear, open loop model is derived based on DQ theory in discrete time domain. Based on this model, a linear, closed loop model is further developed with DQ theory in discrete time domain. Triangle hold theory instead of zero order hold theory is employed in the model for better representation. The developed linear, closed loop model is finally generalized to generalized 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 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 discrete time domain.