Interfacing of ac electrical machine models in power system transient simulation programs is receiving increasing attention in the literature. Models based on the voltage-behind-reactance (VBR) formulation have been recently proposed to achieve a direct interface with external power networks. However, the rotor-position-dependent interfacing inductances due to dynamic saliency in synchronous machine models increase the computational cost of the overall system solution and limit the application of most VBR formulations. This paper presents new methods for elimination of dynamic saliency using continuous-and discrete-time approximation techniques to achieve explicit formulations. The proposed models have simple interfacing circuit consisting of decoupled constant-parameter RL branches. The new models are implemented in MATLAB/Simulink and the PLECS toolbox, and are shown to offer simple and easy-to-use interface, high accuracy, and numerical efficiency as compared to the existing models. The proposed models can find wide application in common state-variable-based transient simulation programs.