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# Heat pump performance when outside air temperature below water temperature

I am developing a simplified model of an air-to-water reversible heat pump in Modelica. The model is based on a curve-fitting approach for the calculation of the COP with data retrieved from the technical documentation of a heat pump unit. The COP is a function of evaporator and condenser temperatures. I am using a bi-quadratic function (as EnergyPlus does for example for chiller models)

My doubt refers to the cooling mode. In particular, I can't understand what exactly happens to the COP of the machine when the outside air temperature (temperature entering the condenser) goes below the water temperature (temperature leaving the evaporator). This situation can happen for example when a building needs cooling during a cold day.

Depending on the set of data that I use for the curve-fitting approach, I found two different behaviors: in graph1, the COP continuously increases

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In graph2 the COP reaches a maximum approximately in correspondence with the value of the water temperature (it was 14 °C in this case)

Theoretically, whenever the outside air is lower than the water temperature, almost 100% free cooling could be achieved, however I am not really sure about the reality.

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In cooling mode, the system capacity will continue to increase as the condensing (water-side) temperature decreases. This is because the sub-cooling at the condenser increases yielding more capacity, and at a lower compressor head pressure which reduces power consumption (higher COP). This agrees with graph 1.

On the air-side, as entering air temperature decreases, the system SHR reduces. Meaning that less sensible capacity is available while more latent capacity is available (lower "sensible" COP, don't confuse this with "total" COP). Something else also happens at lower condensing and entering air conditions. The compressor suction temperature/pressure is lower. This translates to a lower refrigerant density, which for a volumetric pump (compressor), means the refrigerant side mass flow rate is lower.

So multiple things are happening as the operating temperatures are reduced. I can't tell from these graphs where the data came from. But I would lean towards graph 2 as being more representative, although the magnitude is still in question at this point.

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