Modeling and Energy Balancing Control of Modular Multilevel Converters Using Perturbation Theory for Quasi-Periodic Systems

The most common modular multilevel converter (MMC) balancing solution uses the circulating current to generate additional powers in conjunction with the terminal voltages including the common-mode voltage, relying on distinct frequencies. Usually, the energies affected by each frequency component are identified assuming constant amplitudes, which neglects the inevitable impact on the other energies that inherently arises from the amplitude variation caused by the feedback. Two issues have received insufficient attention: 1) the approach does not provide a dynamic model of the converter variables suitable for model-based balancing control design, and 2) studies are missing that explore the limitations caused by the usually neglected mutual interactions of the energies. Thus, an MMC model is derived using perturbation theory for quasi-periodic systems that lends itself to balancing control design, as it solely describes the average of the energies. Moreover, the impact of the mutual interactions is evaluated, revealing the characteristics of a tradeoff between model accuracy and balancing speed, that is inherent to any similar scheme. Further contributions are the calculation of the energy ripple and the proposal of a three-step procedure to tackle the design of the balancing feedback. The findings are supported by simulations and experimental results.