Power balance, including active and reactive power, between the system supply and the demand from induction motor loads is a potentially necessary condition for system stable operation. Motion of system states depends on the balancing of active and reactive powers. Therefore, this paper proposes an induction machine model in electromechanical timescale from a power balancing viewpoint, in which the induction motor load is modeled as a voltage vector driven by power balancing between the system supply and the demand from induction motor load, so as to describe the dynamic characteristics of induction motor loads in a physical way for power system dynamic analysis. Then a voltage magnitude-phase dynamic analysis with the proposed induction machine model is constructed. Based on the voltage magnitude-phase dynamic analysis, the characteristics of grid-connected induction motor loads are explored, and the instability mechanisms of grid-connected induction motor loads induced by a large disturbance are discussed. It is shown that the dynamic behavior of grid-connected induction motor loads can be described as the dynamic process of the terminal voltage vector driven by coupled active and reactive power balancing in different timescales. In this way, the dynamic behavior of induction motor loads in terms of voltage magnitude-phase dynamics and its physical characteristics are clearly illustrated. Time-domain simulation results are presented to validate the above analyses.