In this paper, we present an analysis of an electrostatic vibration harvester operating in the constant-charge mode. The goal of the study is to bound regions of control parameters where the system displays steady-state harmonic oscillations as required for practical use. We show how the system can be presented as a nonlinear oscillator and analysed employing the multiple scales method, Floquet theory and Lyapunov exponents. We determine the conditions for the onset of steady-state oscillations, the period doubling bifurcation and transition to chaos. This allows us to bound regions of control parameters where the system displays desired regular oscillations and, therefore, to identify maximal harvestable power for a particular architecture.