This paper proposes a new control scheme for the low frequency AC transmission (LFAC) system aiming at extending the point-to-point configuration to form a multi-terminal electrical energy network. The multi-terminal low frequency ac (MT-LFAC) system configuration is based on the use of modular multilevel matrix converters (M3Cs) and virtual synchronous generator (VSG) control. The M3C is the next ac/ac converter generation, which is used as an interface with the conventional AC network and the LFAC electrical energy system. Application of VSG control is proposed to enable proper power sharing, to provide synchronization of each terminal, and frequency stabilization, thus, to offer multiterminal forming capability. Two different operation modes are applied in the system to damp the frequency deviation after a dynamic perturbation, which provides additional stabilization feature to the VSG. Frequency restoration mode and commanded mode of power sharing are applied as dynamic states to validate the robustness of the VSG control system. Besides, to solve the negative impact of low X/R ratio in the LFAC electrical energy system, we enhance the VSG control by proposing a virtual-impedance-based solution, which increases the output total impedance on the low frequency side and prevents the coupling between P and Q. The operation of the proposed system is examined by simulation results with a precise model of M3Cs in the PSCAD/ EMTDC software environment (version 4.2.1, Winnipeg, MB, Canada).
