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This paper presents a three-stage 18-level inverter design with a novel control method. The inverter consists of a series-connected main high-voltage, medium-voltage, and low-voltage stages. The high-voltage stage is made of a three-phase, six-switch conventional inverter. The medium- and low-voltage stages are made of three-level inverters constructed by H-bridge units. The proposed control strategy assumes a reference-input voltage vector and aims to operate the inverter in one state per sampling time to produce the nearest vector to that reference. The control concept is based on representing the reference voltage in 60^-spaced two-axis coordinate system. In this system, the inverter vectors' dimensions are integer multiples of the inverter's dc voltage, and the expression of the inverter's vectors in terms of its switching variables is straightforward. Consequently, the switching signals can be obtained by simple fixed-point calculations. The approach of the proposed control strategy has been presented, the transformed inverter vectors and their relation to the switching variables have been defined, and the implementation process has been described. The test results verify the effectiveness of the proposed strategy in terms of computational efficiency as well as the capability of the inverter to produce very low distorted voltage with low-switching losses.