The rapid development and growth of battery storage have heightened an interest in the co-location of battery energy storage systems (BESS) with renewable energy projects which enables the stacking of multiple revenue streams while reducing connection charges of BESS. To help wind energy industries better understand the coordinated operation of BESS and wind farms and its associated profits, this paper develops a simulation model to implement a number of coordination strategies where the BESS supplies enhanced frequency response (EFR) service and enables the time shift of wind generation based on the UK perspective. The proposed model also simulates the degradation of Lithium-Ion battery and incorporates a state of charge (SOC) dependent limit on the charge rate derived from a constant current-constant voltage charging profile. In addition, a particle swarm optimisation-based battery sizing algorithm is developed here on the basis of the simulation model to determine the optimal size of the co-located BESS along with SOC-related strategy variables that maximise the net present value of the wind + BESS system at the end of the EFR contract.