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This study introduces a multirate method for the simulation of multi-physics systems containing a wide range of time scales. This method has been designed for strongly coupled systems and is able to deal with high mutual dependency between fast and slow state variables. The proposed method based on a cycle formulation approach is applied to the ageing behaviour simulation of the energy storage unit (ESU) of an all-electric ferry. The objective is to design this ESU taking into account the electrical and thermal models, permitting to predict its ageing over the 20 years of the ferry operation. So, simulations could be excessively time consuming. The main objective behind this study is to reduce the simulation time to make possible an optimisation process. Using the proposed multirate method based on embedded extrapolation methods formulated on cycles, a speed-up factor of about 1000 compared with standard integration methods is obtained. Numerical results for the electric ferry example are presented for different tolerances in order to demonstrate the performance of the method.