In this study, the inertial response characteristics of the permanent magnetic synchronous generator (PMSG)-based wind energy conversion system (WECS) with different virtual synchronous generator (VSG) schemes are analysed and compared in detail. It is found that the dynamic coupling between the VSG active power control loop and the other control function, e.g. maximum power point tracking control and direct current bus voltage control, in VSG-controlled WECS (WECS-VSG) is inevitable. The coupling would result in the variations of the equivalent inertia constant and damping coefficient. The frequency support capability of the WECS-VSG is thus weakened and the WECS-VSG is even harmful to grid frequency support under some conditions. Besides, the requirement of the smooth energy recovery stage is usually put forward by the power system operator for the characteristics of the energy sources for inertial response (ESIRs) in WECS. To regain the expected synchronous generator alike inertial response characteristics and follow the ESIR property, a generalised optimal WECS-VSG control strategy which can be embedded into different WECS-VSG schemes is proposed and two examples for different ESIRs are designed. Finally, the effectiveness of the analysis and the proposed strategy are verified by simulation results.