The increasingly stringent emissions regulations and needs for higher power density for both turbo-diesel passenger vehicle and commercial vehicles have demanded significant alterations to the basic architecture of turbochargers. An attractive option for providing a high-boost system is the use of two-stage turbocharger which consists of two different size turbochargers connected in series that may or may not utilize bypass regulation. The exhaust mass flow is expanded by the high pressure turbine to the low pressure turbine, and on the other side the air flow is compressed through the low pressure compressor to the high pressure compressor. This increases the complexity of the air-charging system and requires new methodologies for modeling and control. A two-stage turbocharger model is presented in this paper. The total efficiency of the two-stage compressor, which poses the biggest problem in two-stage turbocharger modeling, was derived based on a second law analysis. A new parameter, compressor temperature ratio, was introduced as a linkage between the two stage compressors and also used to predict the two-stage compressor outlet temperature. Extrapolation to lower turbocharger speeds and compressor flow rates by using curve fitting methods was also discussed. The model for a two-stage turbine with a bypass valve is derived in the same way. Engine dynamometer tests have been performed to identify the model parameters and to validate the model structure. The test results show a good agreement between the model predictions and test data. In conclusion, this two stage turbocharger model is suitable for turbocharger control design and the estimation of some key turbocharger parameters.

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