Classical pulse width modulation (PWM) techniques are replaced by current source sliding mode control (SMC) computing the status for the three-phase power switches in real time. Synchronization with the mains and inverter management are guaranteed by Park vector transformation. Three novel sliding strategies for current source inverters are described, and the existing equivalence between the control of phase currents and phase to phase currents is shown. Several simulations show the performance of the inverter control.