This paper presents a novel comprehensive discrete-time model of a three-phase single stage grid-connected photovoltaic generation system. The detailed model is carried out on synchronous reference frame. It is shown that both converter's AC and DC-side discrete time model differs from the continuous time one. The main differences are the AC-side current and voltage cross coupling, and the DC-side voltage non-minimum phase behaviour for small active power injected into the grid. Based on the new model, digital internal current and external DC-link voltage controllers are designed. Experimental results show that the proposed controllers provide fast transient response and disturbance rejection. Small errors obtained comparing experimental and simulation waveforms for both DC-side voltage and AC-side current corroborate to validate the model and the designed controllers.