Multilevel converters use series/parallelled semiconductor switching devices to synthesise switched waveforms at power levels that are well above individual device ratings. To date, most multilevel inverter research has focused on voltage source structures, primarily because these topologies address the more common high power converter limiting factor of device voltage ratings. However, multilevel current source converters can have advantages in lower voltage, very high current applications, or in situations where, despite their higher losses, DC inductors have reliability benefits compared to electrolytic capacitors. This paper presents an integrated three phase 5-level Current Source Inverter topology that requires only two intermediate link inductors, and shows how it can be controlled by mapping modulation control signals from a multilevel VSI controller. This allows the wealth of existing knowledge relating to modulation of multilevel VSI's to be immediately applied to the multilevel CSI. The mapping process matches space vectors created by the VSI modulation process to equivalent CSI space vectors, and then selects between redundant space vector alternatives to maintain the current balance of the intermediate link inductors. The converter operation has been verified in a detailed circuit simulation taking account of all second order effects.