Turbo-compressors are an alternative compression technology to ordinary piston and scroll compressors and are currently investigated for several areas of application. A dynamic high-speed turbo-compressor model for high temperature heat pumps with water vapor as a cycle media has been developed and successfully validated. The potential for using new high temperature heat pumps in the industry is enormous and can be a cost effective way to reduce the energy consumption and carbon dioxide emissions. However more research needs to be performed in regard to the performance of the turbomachinery. The turbo-compressor model was written in object-oriented Modelica code and implemented into an existing model library. Three different approaches for modelling a turbo-compressor were investigated and compared with regard to the quality of their predictions. The basic equations and unique features of the particular approaches were elaborated and discussed. The validation was conducted with real world measurement data from an actual test rig. The utilization of the turbo-compressor within an industrial application was examined. The performance of the turbo-compressors was assessed in connection to a multi-stage compression set-up for a steam compression cycle. Various multi-stage set-ups were compared in matters of characteristically parameters like the thermalcapacity or the coefficient of performance.