The control of the status of the 3-phase power switches of an inverter is commonly carried out with classical pulse width modulation techniques due to its simplicity; these techniques compute the status of the 3-phase power switches in a pre-established way, but they do not guarantee high performance because of, for example, load variations. So, the previous techniques are replaced by current source sliding mode control computing the status for the 3-phase power switches in real time; the synchronization with the grid and the inverter management are guaranteed by applying the Park's transformation. Two novel current source vector sliding mode control strategies are described. Several simulations show the performance of the inverter control.