Power system dynamic equivalence, which has been developed to overcome the computational issues, is faced with new challenges by emerging distributed energy resources (DERs). The switching characteristic between DERs operational modes beside non-dispatchable inherent, that is, generation uncertainties, should be take into account in power system dynamic equivalencing. This paper proposes a switching-based dynamic equivalence modeling for power system considering DERs. Prony analysis is employed to fit a reduced-order model to a high-order system in frequency domain. The developed modelling strategy consists of high and low frequency equivalences. When the external system reconnects to the main network through the breaker, high-frequency equivalence is replaced with external system. This period contains 4 cycles for communication delay beside 5 cycles governor time constant, which give rises to a six-order equivalence model. Afterwards, a four-order low-frequency equivalence model is fitted to the external system in the connected grid mode. Accuracy of the fitted dynamic equivalences is investigated by calculating the mean square error between the measured signal and the Prony approximated one. A synchronous-based DER, a doubly-fed induction generators and a fuel cell DER are added to the CIGRE benchmark in order to analyse the proposed dynamic equivalence modelling. Simulation results demonstrate that the proposed equivalence modelling could exhibit the same results as the real external system in the frequency domain. Simulation results also reveal that increasing penetration of DERs affect the dynamic equivalence in grid-connected mode by degrading the higher frequencies while it has no impact on transient period equivalence.
