The power take-off (PTO) system is a core component of a wave energy converter (WEC) that significantly influences its power performance. Careful design and testing of PTO systems are essential in WEC development. Numerical simulations have largely replaced physical testing, accelerating the PTO system design process. However, one major obstacle still prevents numerical modelling of the PTO system from achieving its full capability: integrating the PTO system model into the global simulation of the WEC system to include the effects of all subsystems. This paper uses a co-simulation approach based on the Functional Mock-Up Interface (FMI) standard to integrate a detailed PTO system model into a global WEC model that includes hydrodynamic, mechanical, and mooring subsystems. The approach is compared against a model incorporating a simplified linear-damper PTO system. The results indicate that a higher-fidelity PTO system model can have a significant impact on predictions of WEC motion, mooring fatigue damage accumulation, and power performance. For example, it is observed that a simplified PTO model can lead to a tenfold underestimation of mooring fatigue damage under some environmental conditions.