## 1 Introduction  
The energy crisis [1] and environmental pollution [2] are the main reasons for leveraging the large-scale adoption of electric vehicles (EVs). The Chinese government has energetically supported the EV's establishment. In April 2012, the 'Energy Conservation and New Energy Vehicle Industry Development Plan (2012-2020)' formulated by the State Council pointed out that \"in 2020, pure electric vehicles and plug-in-hybrid electric vehicles will be industrialized, and their cumulative production and sales will exceed 5 million.\" The rapid growth of EVs has increased their permeability in the distribution network. The charging mode of EVs is mainly divided into slow charging [3] and fast charging [4]. Slow charging is appropriate for low-power on-board chargers [5], the charging time of which is customarily in excess of 6 h. On the contrary, fast charging is generally utilized to high-power off-board chargers, which is an attractive option over slow charging due to its potential to fully charge the EV in less than 1 h [6]. Thus, fast charging is favored by consumers thanks to economize on time [7]. However, for the power system, EVs are nonlinear loads whose frequent input and exit will provoke a negative impact on the power quality of the distribution network [8; 9; 10]. To alleviate the above problems, loads-virtual synchronous motor (VSM) technology has attracted more attention due to its ability to improve stability of frequency and voltage. On account of this superiority, some scholars put forward the application of VSM to the EV chargers [11; 12; 13; 14]. Indeed, VSM can provide inertia and damping to suppress rapid changes in voltage and frequency during transients. Furthermore, EVs autonomously participate in the primary regulation to achieve responsive interaction with the grid in the steady case. As a promising control approach, the VSM has been intensively investigated since it can resolve the EVs integration problems most flexibly. The provision of ancillary services from VSM-controlled single-phase chargers has previously been discussed [11; 12]. However, with widespread concern of fast charging, VSM-based control has gradually concentrated on three-phase power converters. If a VSM implementation designed for single-phase systems is directly applied to a three-phase converter, the control structure will be further complicated. Aiming at the three-phase EV charger composed of two-stage topology, the VSM construction method is distinct with sing-stage VSC in [12], which can take graded-control in the pre-stage AC/DC and post-stage DC/DC in accordance with its control objective [13]. In addition, if three-phase VSM continue to employ proportional resonant (PR) controller which is used in single-phase control, this implies that six PR controllers will be needed for achieving double closed-loop control. Nevertheless, this can be avoided by leading into vector control based on three-phase instantaneous reactive power theory, as mentioned in [13; 14]. The proposal for actualizing three-phase VSM has been proposed in [13]. On this basis, [14] extends to VSM control based on fast charging mode, in which the pre-stage converter implements VSM function and maintains the DC bus voltage stability, and the post-stage circuit realizes constant-voltage charging by means of double closed-loop control. However, since resistance is leveraged for emulating the power battery, the charging mode is not clear, which can be considered as constant-voltage charging due to invariance of resistance voltage. But fast charging adopts constant-current/power mode in general. Additionally, simulation results can be incapable of reflecting the primary frequency regulation characteristic of VSM owing to the application of ideal power grid model. Thus, in view of the deficiencies in [14], following the graded-control thought and the vector control based on three-phase instantaneous reactive power theory [13; 14], this paper presents a novel VSM control scheme suitable for the fast charging of the off-board chargers.