In this work, a generalized optimization methodology based on Lagrange Multipliers was used to propose circulating current references in order to properly control the Modular Multilevel Converter (MMC) under different conditions. The optimization strategy finds the local minima of the objective function, which is typically the power losses of the MMC system, subject to equality constraints, which are previously defined by the desired operating condition. Furthermore, this control approach is developed in the ABC frame, giving more insight into the physical phenomena related to the MMC internal dynamics. Finally, equivalent controllers to existing ones, which can be found in the literature, are obtained by means of this methodology with the objective to demonstrate the versatility and generality of the present control approach.
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