We also have a phase supply for our (17 Kw) GSHP. The specifications claim:
°C Kw
In Out In Out COP
------------ ------------- ---
0 35 3.84 16.8 4.4
0 45 4.8 15.7 3.3
0 50 4.9 16.2 3.3
I have no way of knowing whether we achieve that in reality. Nor do I care. For most of the heating season our incoming brine temperature is below 0 degrees so that would throw the figures off, but even ignoring that the COP is not the measure I am interested in. Rather, the cost of running the systemis what I care about.
Before fitting the heat pump we heated the house with oil and used electricity for everything else. The heat pump replaced the oil burner and is purely used for heating the house. (Not for hot water, or anything else). For the first winter with the heat pump our electricity bill, for the GSHP, cooking, lighting hot water, everything, was about 15% lower than the oil had been just for space heating over the previous winter. Hence we saved money, which was the objective. We installed the GSHP in 2007 so I imagine the savings are greater now, given the way oil prices have changed.
Regards trying to get more energy out of the system than we put in, that is indeed the goal. The important thing is to get more out that we put in; we cannot get more out than goes in in total. It is just that the energy we put into the system is not the only going into the system. The energy we put into the system is used to extract energy from the ground, and no laws of physics are challenged.