Semi-empirical power dissipation modelling of mechanical hybrid powertrain components

Accurate modeling is of key importance for the model-based design of controlled systems. The overall system complexity can be kept limited by using simple component models that capture 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 (CVT) for mechanical power transmission and a Flywheel System (FS) for kinetic energy storage. The power dissipation in these components are modeled by parametric functions, which are suitable to describe smooth characteristics in a relatively simple format with only a few coefficients. The functions are selected based on physical understanding of the systems, whereas the coefficients are identified from dedicated test rig experiments. Results show that the power dissipations are modeled very accurately for both the CVT and the FS, with a modeling error of less than 75 W for 80% of the operating conditions in a wide operating range between -25 kW and 38 kW. The CVT model is also validated under dynamic driving conditions, showing an overall error for the transmission efficiency of less than 1%.