The modular multilevel cascade converter (MMCC) is a new family of multilevel power converters with modular realization and a cascaded pattern for submodules. The MMCC family can be classified by basic configurations and submodule types. One member of this family, the Hexverter, is configured as Double-Delta Full-Bridge (DDFB). It is a novel multilevel AC/AC converter with direct power conversion and comparatively fewer required components. It is appropriate for connecting two three-phase systems with different frequencies and driving an AC motor directly from a utility grid. This paper presents the dq model of a Hexverter with both of its AC systems by state-space representation, which then simplifies the continuous time-varying model into a periodic discrete time-invariant one. Then a generalized multivariable optimal control strategy for regulating the Hexverter's independent currents is developed. The resulting control structure can be adapted to other MMCCs and is flexible enough to include other control criterion while guaranteeing the original controller performance. The modeling method and control design are verified by simulation results.