Abstract: The invention is the design of a heat pump and heating and air conditioning system that improves the performance at part loads, and lowers the operating costs by heat storage and/or modulating the output of the system to meet the heating and cooling needs of the building. The invention uses the technologies of refrigeration, thermodynamics, fluid flow, heat transfer, and solid state electronics. The output and electric power requirements of the system are modulated by an electronic controller that can vary the speed of the compressor motor by changing the frequency of the electric power to the motor of the refrigerant compressor. The two most important components of the system, that are an improvement in the state of the art of heat pumps systems, are the design and use of a modulating thermosiphon evaporator (MTSE) and a zoned heat storage system (ZHSS).