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The first comprehensive three-phase state-space dynamic phasor model (DPM) for the emerging class of dc/dc/ac modular multilevel converters (MMCs) is presented that accounts for both dc/dc and dc/ac power transfer mechanisms. The phasor model is derived in the $\alpha \beta ~0$ -frame and includes frequency components from dc to third harmonic, which is shown to yield a high degree of matching for both steady-state and transients when compared against switched and time-averaged models, the latter of which is also derived in this work. An analytical solution procedure is then proposed that takes advantage of the phasor model time-invariance to find the full state solution at any operating point including the requisite open-loop modulating signals. Several analyses are carried out for two different dc/dc/ac MMC case study designs to explore the utility and versatility of the proposed DPM and solution procedure. Results show the patterns of internal current stresses and capacitor voltage ripples for the arms can vary significantly and in a nonsymmetrical manner, which is in stark contrast to the traditional dc/ac MMC. [ABSTRACT FROM AUTHOR]