The Z-source inverter is a relatively recent power converter topology that has been demonstrated in the literature to exhibit voltage-buck and voltage-boost capability. The Z-source concept can be applied to two-level and multilevel inverters. However, multilevel inverters offer many benefits for higher power applications compared to two-level inverters. Previous publications have shown the control of a Z-source neutral point clamped inverter using the carrier-based modulation technique. This paper presents the optimal switching pattern for the control of a Z-source neutral point clamped inverter using the space vector modulation technique. This gives a number of benefits, in terms of implementation and harmonic performance. The adopted approach enables the operation of the Z-source arrangement to be optimised and implemented digitally without introducing any extra commutations. Simulation results are presented to verify the concepts.