This paper presents an analysis of the natural voltage balancing dynamics of a three phase flying capacitor converter when supplying an induction motor. The approach substitutes Double Fourier harmonic series for the PWM switching waveforms and the frequency response of the motor, to create a linear state space model of this type of load. The model requires the mid-frequency response (500 Hz - 20 kHz) of the induction motor impedance to be identified, and takes skin and proximity effects into account by adding parallel R-L networks to a standard motor model. Model parameters were measured by applying FFT analysis to variable frequency square waves injected into the motor terminals, and fitting parameter values to these measurements using a least squares minimisation method. From the analysis, it was found that the converter voltage balancing behavior degrades substantially at low motor speeds, and that a balance booster filter, as previously proposed, considerably improves the dynamic response. Experimental verification results using a scaled-down flying capacitor converter drive are included in the paper.