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This paper presents a novel modulation strategy for a seven-phase three-level inverter, aimed at variable-speed drive applications. Developed space vector pulsewidth modulation (SVPWM) strategy is based on vector space decomposition (VSD) approach and an analysis of multidimensional space vector projections in mutually orthogonal planes. The algorithm represents an extension of a recently developed five-phase three-level SVPWM algorithm and is considerably more complex, due to the existence of three mutually orthogonal planes in a seven-phase system. The difficulties of generalization of space vector strategies, which stem from the nature of the multiphase systems, are highlighted. Increasing the number of phases from five to seven increases the number of switching states from 35 = 243 to 37 = 2187 and the number of orthogonal planes from two to three. This considerably affects the complexity of the offline calculations. However, the final implementation of the algorithm is simple. Developed SVPWM algorithm is compared to an equivalent carrier-based strategy and it is shown that they yield identical performance. The complexity of the algorithms for real-time implementation is compared. Simulation and experimental results, obtained using neutral-point clamped inverter, verify the theoretical developments.