Analysis of MMC Dynamics in dqz Coordinates for Vertical and Horizontal Energy Balancing Control

This paper presents a control system implementation in dqz-coordinates for equalizing the average energies stored in each arm of a Modular Multilevel Converter (MMC); a control objective that is typically referred to as horizontal and vertical energy balancing. The proposed control scheme is obtained from analysis and simplification of a detailed time-invariant dqz-frame state-space representation of the MMC. The state variables of the model are the equivalent arm capacitor energies and the current components, and it will be shown that this representation is very suitable for designing outer-loop energy controllers in dqz coordinates that rely on linear inner current control loops. Moreover, a series of justified assumptions on the energy dynamics will be presented, providing significant insight that simplifies the control design. Finally, by proving that the unbalances of the average values of the converter equivalent arm capacitor energies in abc coordinates appear as undesired oscillations in dqz coordinates, active filtering is proposed as a mean to dissipate them and, therefore, achieve the desired balanced operation. Operation of the proposed control strategy is demonstrated by time-domain simulation of a 1 GW MMC-based HVDC converter terminal.