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).Energies 2020, 13, 747 2 of 19 delivery. However, neither technology is flawless. For example, the existence of the power electronic switches in the dc circuit breakers make them more vulnerable than the HVAC transmission system, especially when a fault takes place in the converter, due to the low dc-side impedances and sensitive semiconductor power converters [1,2]. On the other hand, the HVAC system offers advantages, such as more reliability of the well-known protection schemes and the change capability of voltage levels using transformers [3]. However, the HVAC transmission system's main disadvantage is the existence of the reactive power in comparison to no reactive power in the HVDC electrical energy system. Due to that, the existence of the reactive power can be translated as losses in the grid [4].The aforementioned points have led to an alternative solution which combines both sets of HVACs and HVDC advantages, known as a low frequency ac (LFAC) transmission system, or a fractional frequency transmission system (FFTS) [5][6][7]. This system transmits the power at a lower frequency range of about 1-60/3 Hz. The LFAC has already been proposed for the offshore wind energy and has offered attractive advantages compared to both transmission solutions. For example, in the HVDC electrical energy system, the implementation of a high capacity dc circuit breaker is difficult due to the absence of the zero crossing points of the DC current [8]. On the other hand, the LFAC system has zero-crossing, thus, the protection is more advantag...