A mathematical model for the evaluation of the seasonal performances of electric air-to-water heat pumps for heating is used to analyze the efficiency of on-off heat pumps, multi-compressor heat pumps and heat pumps with inverter compressor, integrated by electric heaters as back-up system, in the service of several buildings located in different Italian climates.The paper points out the importance of a good dimensioning of the heat pump as a function of the building energy signature and of the climate of the city where the building is placed, in order to enhance the system seasonal efficiency