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The generalized modulation strategy of the conventional matrix converter (MC), i.e., three-leg MC, was previously developed using the duty-cycle space vector (DCSV) representation of switch duty cycles. This paper uses the DCSV representation of switch duty cycles to develop a new formulation of the generalized modulation strategy for one-, three-, and four-leg MCs. The four-leg MC, unlike the three-leg MC, is capable of providing a neutral connection at the output side of the MC. The neutral connection enables the four-leg MC to operate as a power supply providing a balanced, regulated, and fixed-frequency voltage for balanced and unbalanced loads, including the single-phase load. The generalized modulation strategy of the four-leg MC in this paper is developed in the context of power supply applications. Using the new formulation of the generalized modulation strategy, the direct duty-cycle modulation strategies based on DCSV calculation are developed for one-, three-, and four-leg MCs, which are referred to as the DCSV-based modulation strategy of the MC. Part I of the paper formulates the DCSV-based modulation strategy of the three- and four-leg MCs.