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This paper presents the dynamic modeling of a ZETA converter in discontinuous conduction mode (DCM) applied to low power renewable sources using the generalized switch averaging technique. The whole system consists of a ZETA converter associated with a full bridge inverter operating at low frequency. Thus, the system works as a sinusoidal low power source. The ZETA converter plays the main role in this arrangement, producing a rectified sinusoidal current waveform synchronized with the power grid. Initially it is presented a brief analysis of the system, as well as the characteristics that make possible the dynamic analysis in DCM. The generalized switch averaging technique are discussed, and also the small-signal analysis of the ZETA converter. In order to validate the current study experimental and simulations results are presented.