The general electric propulsion orbit-raising maneuver of a spacecraft must contend with four main limiting factors: the longer time of ight, multiple eclipses prohibiting continuous thrusting, long exposure to radiation from the Van Allen belt and high power requirement of the electric engines. In order to optimize a low-thrust transfer with respect to these challenges, the choice of coordinates and corresponding equations of motion used to describe the kinematical and dynamical behavior of the satellite is of critical importance. This choice can potentially afiect the numerical optimization process as well as limit the set of mission scenarios that can be investigated. To increase the ability to determine the feasible set of mission scenarios able to address the challenges of an all-electric orbit-raising, a set of equations free of any singularities is required to consider a completely arbitrary injection orbit. For this purpose we developed a new quaternion-based formulation of a spacecraft translational dynamics that is globally nonsingular. In this paper we consider the minimum-time low-thrust transfer of a GEO satellite and include the new set of equations of motion inside a direct optimization scheme implemented using an AMPL model and LOQO as NLP solver. Our goal here is to investigate the applicability of the new quaternion-based formulation to the low-thrust orbit-raising problem and compare the new methodology to previous approaches.