This paper presents the modelling and design steps of a digital proportional multi-resonant controller used in a grid-connected photovoltaic (PV) system. It is shown that the use of only one Proportional-Resonant (PR) compensator, tuned to the system fundamental frequency, may have its effectiveness compromised due to nonlinearities in the system components. To overcome this drawback and improve the system's output current waveform, a multi-resonant controller is introduced. The performance of the discrete-time designed controller is tested on a grid-connected photovoltaic power plant. Experimental results obtained with the operation of a 30 kWp PV system connected to a distribution network, using only the leakage inductances of a connection transformer as passive filter are presented and discussed to demonstrate the performance of the designed control strategy.