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Modular multilevel converters are playing a key role in the present and future development of topologies for medium–to–high–power applications. Among this category of power converters, there is a direct AC–AC modular multilevel converter called “Hexverter”, which is well suited to connect three–phase AC systems operating at different frequencies. This topology is the subject of study in this manuscript. The complete Hexverter system is composed of an Hexverter power converter and several control layers, namely, a “virtual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>V</mi><mi mathvariant="normal">C</mi><mn>2</mn></msubsup></semantics></math></inline-formula> controller”, a branch current controller in a two–frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>q</mi></mrow></semantics></math></inline-formula> reference frame, a modulator, and a voltage balancing algorithm. The paper presents a thorough description and analysis of the entire Hexverter system, providing research contributions in three key aspects: (<i>i</i>) modeling and control in a unified two–frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>q</mi></mrow></semantics></math></inline-formula> framework; (<i>ii</i>) developing a “virtual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>V</mi><mi mathvariant="normal">C</mi><mn>2</mn></msubsup></semantics></math></inline-formula> controller” to dynamically account for Hexverter’s active power losses allowing to achieve active power balance on the fly; and (<i>iii</i>) a comparative evaluation of modulation strategies (nearest level control and phase disposition–sinusoidal pulse width modulation). To this end, a detailed switched simulation was implemented in the PSCAD/EMTDC software platform. The proposed “virtual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>V</mi><mi mathvariant="normal">C</mi><mn>2</mn></msubsup></semantics></math></inline-formula> controller” is evaluated through the measurement of its settling time and calculation of active power losses. Each modulation technique is assessed through total harmonic distortion and frequency spectrum of the synthesized three–phase voltages and currents. The results obtained suggest that the control scheme is able to properly regulate the Hexverter system under both modulation strategies. Furthermore, the “virtual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>V</mi><mi mathvariant="normal">C</mi><mn>2</mn></msubsup></semantics></math></inline-formula> controller” is able to accurately determine the active power loss, which allows the assessment of the efficiency of the modulation strategies. The nearest level control technique yielded superior efficiency.