Interfacing machine models in either nodal analysis-based (EMTP-like) or state variable-based transient simulation programs play an important role in numerical accuracy and computational performance of the overall simulation. As an advantageous alternative to the traditional qd models, a number of advanced phase-domain (PD) and voltage-behind-reactance machine models have been recently introduced. However, the rotor-position-dependent conductance matrix in the machine-network interface complicates the use of such models in EMTP. This paper focuses on achieving constant and efficient interfacing circuit for the PD synchronous machine model. It is shown that the machine conductance matrix can be formulated into a constant submatrix plus a time-variant submatrix. Eliminating numerical saliency from the second term results in a constant conductance matrix of the proposed PD model, which is a very desirable property for the EMTP solution since the refactorization of the network conductance matrix at every time step is avoided. Case studies demonstrate that the proposed PD model represents a significant improvement over other established models used in EMTP while preserving the accuracy of the original/classical PD model.