Why is the COP of a heat pump so high?

Step 1 of 12 · Explain

Most of the heat comes from the outdoor air

Take a heat pump heating a house on a mild 7 °C day, with 35 °C water for underfloor heating. The box in the garden is the outdoor unit; inside it the compressor is the only part that uses much electricity. In the model it draws about 1.4 kW of electricity and delivers about 7.4 kW of heat to the house: five times as much, a COP of about 5.2.

Where do the other 6 kW come from? Not from the electricity. About 6.1 kW come out of the 7 °C outdoor air, which leaves the unit colder than it came in. The real unit the model follows shows the same in its datasheet: 7.3 kW of heat for 1.38 kW of electricity at 7 °C, and even at −7 °C about 6.6 of its 9.7 kW of heat come from the air (Viessmann Vitocal 250-A).

Step 3 of 12 · Explain

The energy balance: nothing is created

Read the heat pump's energy flows like a bill. In: about 6.1 kW of heat from the outdoor air and about 1.4 kW of electricity. Out: about 7.4 kW of heat into the house. Of the electricity, about 1.3 kW runs the compressor and the water pump and ends up in the house too; the remaining 150 W or so run the fans and the control and leave with the outdoor air.

Compare everything that goes in, air and electricity together, about 7.55 kW, with the heat that comes out, 7.39 kW, and you get about 98 %: below 100 %, as the conservation of energy demands. The "500 %" is a different ratio: it compares the heat only with the part you pay for. The heat in the air is free.

That is why the COP has its own name. A heat pump isn't a better heater; it is a pump. With a water pump you pay for lifting the water, not for the water itself. A heat pump's electricity pays for lifting heat, not for the heat.

Step 5 of 12 · Explain

The electricity pays for the temperature lift

What exactly does the electricity buy? On its own, heat only flows from warm to cold, never from 7 °C air into 35 °C water. So the heat pump lifts it. Its refrigerant boils in the outdoor coil a little colder than the air, at about 4 °C in the model, so heat flows from the air into it. The compressor then squeezes the vapour until it is hotter than the heating water, about 37 °C, and there the heat flows into the water.

The gap between the cold side and the warm side is the temperature lift: here about 28 degrees between air and water, a few more inside the refrigerant. The smaller the lift, the less electricity each kilowatt-hour of heat costs, just as carrying water up one floor takes less work than carrying it up three. Everything that follows comes down to this lift.

Step 7 of 12 · Try it

Hotter heating water costs about a third

A common assumption is that the water temperature is just a matter of comfort, or that hotter water even makes the heat pump better because it carries more heat. The opposite is true. Many older houses have radiators that need water at about 55 °C instead of 35 °C. On the same 7 °C day the lift grows from about 28 to 48 degrees. In the model the compressor then needs about 2.0 kW instead of 1.4 for slightly less heat, about 6.7 kW, and the COP falls from about 5.2 to 3.3: about a third less.

The datasheet of the real unit shows the same at −7 °C: a COP of 3.16 with 35 °C water and 2.13 with 55 °C water. As a rule of thumb, every degree less on the water saves about 2–3 % of the electricity. In the model the COP is about 4.6 at 40 °C and about 4.5 at 41 °C.

Step 6 of 12 · Predict

Why radiators need hotter water than underfloor heating

How low the water can go depends on how the heat gets into the rooms. Underfloor heating gives off its heat through the whole floor, so water at 30–35 °C is enough even on a cold day. A radiator has a much smaller surface, and its output drops steeply as the water cools. A common double-panel radiator 600 mm high and 1 m wide gives about 1.6 kW with 75 °C water, about 0.85 kW at 55 °C and only about 0.27 kW at 35 °C (EN 442 rating): about a sixth.

That is why radiators sized for an old gas boiler often need 55–70 °C. Real houses usually need less than their radiators were sized for, though: in Fraunhofer ISE field tests in existing houses with radiators, the heat pumps needed about 44–45 °C on the coldest days, on average. Larger radiators in a few rooms, or better insulation, bring the temperature down further.

Step 9 of 12 · Explain

The Carnot limit: the best a heat pump could do

Is there a highest possible COP? Yes, and it depends only on the two temperatures. A perfect heat pump, with no losses at all, would reach the Carnot COP: the warm temperature divided by the difference between warm and cold, both in kelvin (degrees Celsius plus 273). Between 7 °C air and 35 °C water that is 308 ÷ 28 = 11.

Real heat pumps reach about half of that. The model gets 5.2, and textbooks give 45–55 % of the Carnot COP for real machines. The rest is lost because heat needs a temperature difference to flow through the two heat exchangers (the refrigerant boils at about 4 °C, not 7, and condenses at about 37 °C, not 35), because the compressor isn't ideal, and because motors, fans and pump use some electricity too. With 55 °C water the ceiling itself drops to about 6.8.

Step 10 of 12 · Try it

Cold air raises the lift too

The lift has two ends, and the outdoor air is the other one. At −7 °C the gap to 35 °C water is 42 degrees instead of 28. The Carnot ceiling falls from 11 to about 7.3, and the model's real COP from about 5.2 to 3.8. The heat pump keeps heating, just at a higher price per kilowatt-hour; the separate question of how a heat pump works in winter shows why it never stops.

In the model the COP is about 4.6 at 2 °C, 4.4 at 0 °C and 3.8 at −7 °C, with floor heating at 35 °C. Hot water on a cold day is the worst case: at −7 °C with 55 °C water the model's COP is about 2.6.

Step 11 of 12 · Explain

From the moment to the year: COP, SCOP and seasonal performance

So which number is the efficiency of a heat pump? The COP changes every hour with the weather and the water temperature. On a 2 °C day in an older house with radiators at 45 °C the model's COP is about 3.7, with 6.1 kW of heat for 1.7 kW of electricity.

For a whole year you add up all the heat and all the electricity. On the label that is the SCOP, calculated for an average European climate: 5.01 at 35 °C and 3.87 at 55 °C for the real unit the model follows. Measured in real houses it is called the seasonal performance factor. In Fraunhofer ISE field tests in existing German houses it was about 3.4 for air source heat pumps (between 2.6 and 4.9) and 4.3 for ground source ones.

The year comes out a little lower than a mild day because the coldest days need the hottest water, the outdoor unit has to defrost now and then, and heating domestic hot water to about 55 °C has a lower COP. Most heating hours fall between 0 and 10 °C, though, so the year sits close to a day like this one. That is where the familiar "300 %" comes from.