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Since the indoor coil of an "all electric heat pump" can be located upstream of the electric heating elements there is no problem running the heat pump and the back up heating simultaneously. Note in the diagram how the RA (Return Air) is what enters the indoor coil, not the heated air from the electric elements. A heat pump is sized to the air conditioning load so that it has a long run cycle and can properly dehumidify the space. If it is located in a climate where the heating requirements are very much greater than the cooling requirements there will obviously be a need for additional heat. This additional heat has several names but they all mean the same thing; back up heat, auxiliary heat, AUX heat, supplemental heat. Further complicating the situation is the fact that it is harder to extract heat from colder air. (There is less heat content to be extracted) So as heat is required more, it is less available from the heat pump and there is a greater reliance on back up heat. Whereas the add on heat pump must shut off every time back up heat is required, the all electric heat pump can continue to provide some portion of the heat at a more energy efficient rate than the fossil fuel system. This layout where electric back up heat is located downstream of the indoor coil is also what is used in packaged heat pump systems.
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