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Accurate modelling is of key importance for the model-based design of controlled systems. The overall system complexity can be limited by using simple component models that represent only the main characteristics, where smooth characteristics are preferred to avoid unnecessary irregularities in the design optimization and in the controlled signals. This paper presents the design of such control-oriented models to describe the power dissipation in a mechanical hybrid powertrain. The two key powertrain components are the continuously variable transmission for mechanical power transmission and a flywheel system for kinetic energy storage. The power dissipation in these components is modelled by parametric functions, which are suitable for describing smooth characteristics in a relatively simple format with only a few coefficients. The functions are selected on the basis of the physical understanding of the systems, whereas the coefficients are identified from dedicated test rig experiments. The results show that the power dissipations are modelled very accurately for both the continuously variable transmission and the flywheel system, with a modelling error of less than 75 W for 80% of the operating conditions in a wide operating range between 225 kW and 38 kW. The continuously variable transmission model is also validated under dynamic driving conditions, showing an overall error for the transmission efficiency of less than 1%.