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This paper presents two new induction machine models with a direct interface to an external power system, for EMTP-type simulations. The models' improved efficiency and their overall superiority over existing formulations are shown by numerical simulations involving different machines. It is shown that models that use currents as output variables possess a high degree of numerical accuracy at relatively large time steps making them competitive with a state-of-the-art model that uses the stator currents and rotor fluxes as output variables. The use of a single set of variables is shown to simplify considerably the models' representations, resulting in highly efficient formulations.