In the next years, air-source heat pumps may become an important renewable-energy heating system in the temperate countries. These machines may be subject to changes in the operation conditions in order to maintain their performance in the face of variations in the outdoor climate and these changes may impact on the heat pump at the cycle level. In order to optimize the control of such machines, a dynamic model is mandatory. Therefore we illustrate the potentialities of a dynamic, lumped-parameter model, which is composed of moving-boundary exchanger sub-models and static compressor and expansion valve sub-models. Firstly, it is seen that the model succeeds in designing the installation as well as in controlling the superheating. Secondly, simulation results illustrate how a change of system parameters could affect the transient behaviour of the machine, thus requiring some adaptation of the controller parameters. Future developments will be devoted to model validation through experience, to design of a robust superheating controller and to model utilization towards fault diagnosis.