The operation of single-phase Modular Multilevel Converter (MMC) is analyzed in the paper. A mathematical model of the converter is developed and described, based on which the structure and selection of parameters for Classical Control and Optimal Switching State Model Predictive Control (OSS-MPC) are defined. Additionally, the procedure for the determination of circuit parameters, such as submodule capacitance and arm inductance, is described and carried out. The listed control methods are designed and evaluated in Virtual Hardware-in-the-Loop together with single-phase MMC power circuit, regarding three control objectives: AC current control, voltage balancing control and circulating current control. Control methods are evaluated for both steady-state and transient performance and compared based on nine criteria: AC current reference tracking, THD of AC current and voltage, submodule capacitor voltage balancing, total submodule voltage control, circulating current magnitude and THD, number of control parameters and computational complexity. This is the first time that a fair comparison between Classical Control and MPC is considered in literature, resulting in superior performance of both control methods regarding four different criteria and the same performance regarding AC current reference tracking.