Abstract Grid forming control of converter interfaced generation (CIG) requires some form of energy storage to be coupled with the generation. Energy storage systems (ESSs) can be coupled to the CIG either on the DC or the AC side of the power converter. When placed on the DC side, the ESS can provide damping of the variability in the generation but would require significant modification to the wind turbine hardware. The solution with an ESS connected to the AC side is simpler to implement with existing wind turbines but fails to provide damping of the CIG generation. This paper proposes a grid forming control strategy, based on virtual synchronous generator (VSG) control, which allows the ESS installed at the AC-side of the converter to have the same features and dynamic behaviour as those obtained from placement on the DC-side of the converter. In addition, the proposed control can also limit the exchanged power of the ESS within its rating for a safe operation. The proposed control is validated via a detailed Electro-Magnetic Transient (EMT) model and its impact on the grid is quantified via the case study of the All-Island Irish transmission system. Simulation results show that only a small ESS capacity can ensure that the frequency variance satisfies the grid code requirement even in the situation of a very high CIG penetration.