MMC circulating current reference calculation in ABC frame by means of Lagrange Multipliers for ensuring constant DC power under unbalanced grid conditions

This work presents a general approach for calculating the circulating current references of Modular Multilevel Converters (MMC) based on mathematical optimization by means of Lagrange Multipliers in the ABC frame. The resulting control method is especially suitable for operation of MMCs in multi-terminal HVDC systems, under both balanced and unbalanced AC grid voltages, since it is designed for eliminating oscillations in the DC power flow independently from AC grid voltage conditions. Furthermore, it has been shown that the power flow in the DC side of the MMC is most effectively decoupled from transients in the AC grid if the main power reference of the MMC is established by the circulating current control instead of with the grid current.