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This paper presents the implementation of a vehicle and powertrain model of the parallel hybrid electric vehicle which can be used for several purposes: as a model for estimating fuel consumption, as a model for estimating performance, and as a control model for the hybrid powertrain optimisation. The model is specified as a multi-domain physical model in MATLAB Simscape, which captures the key electrical, mechanical and thermal energy flows in the vehicles. By applying hand crafted boundary conditions, this model can be simulated either in the forwards or backwards direction, and it can easily be simplified as required to address specific control problems. Modelling in the forwards direction, the driver inputs are specified, and the vehicle response is the model output. In the backwards direction, the vehicle velocity as a function of time is the specified input, and the engine torque, and fuel consumption are the model outputs.