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This paper presents the modelling, simulation and analysis of a 2 MW variable-speed directly-driven permanent magnet synchronous generator (PMSG) wind energy conversion and storage system (WECSS). The WECSS model presented consists of a pitch controlled wind turbine directly driving a 2 MW PMSG. The PMSG is connected to a host AC grid network via a controlled full-scale power converter system (PCS). The power converter system comprises of two back-to-back 3-level neutral point clamped (NPC) pulse width modulated (PWM) voltage source converters (VSC) interconnected by a common DC bus. The electrical energy storage system is integrated with the PCS and connected at the DC bus via a full-bridge DC-DC converter. This paper presents a model for the representation of the proposed WECSS in power system dynamic simulation software PSCAD/EMTDC. Simulation results are presented for various changes in wind speed which show the ability of the system to 'smooth' the power output and operate at the optimum coefficient of performance without the need for a wind speed sensor. The WECSS model has been developed in order to facilitate the investigation of the positive impacts of integrated electrical energy storage on stability enhancement of the host AC grid network.