Heating
Heat pumps in cold climates: balance point and backup heat
A heat pump sized for summer can heat most of a northern winter. The question is what happens below the balance point, and the answer is a few lines of arithmetic.
Two lines that cross
A house loses heat in proportion to the difference between the indoor and outdoor temperature. Plot that heat loss against the outdoor temperature and it is a straight line, zero at about 65 to 70 °F and rising as it gets colder. A heat pump’s heating capacity runs the other way: it moves heat from the outdoor air, and the colder that air is, the less it can move. Its capacity line falls as the temperature drops.
Where the two lines cross is the balance point. Above it, the heat pump can supply all of the house’s heat and cycles on and off like any other heater. Below it, the heat pump runs continuously and still falls short, and something else, usually electric resistance strips in the air handler, makes up the difference.
How fast capacity falls
A heat pump’s nominal capacity is measured at 47 °F. Manufacturers also publish its capacity at 17 °F and, for cold-climate models, at 5 °F. The heat pump size calculator uses a straight-line approximation of those published figures:
| Outdoor temperature | Standard heat pump | Cold-climate heat pump |
|---|---|---|
| 47 °F | 100% | 100% |
| 30 °F | 78% | 89% |
| 17 °F | 61% | 81% |
| 5 °F | 45% | 73% |
| −5 °F | 32% | 66% |
These are typical shapes, not a particular model. A cold-climate unit, such as one on the NEEP cold-climate heat pump list, keeps much more of its capacity at low temperatures, which is the point of buying one. Real units also need occasional defrost cycles below about 40 °F, which cost a few percent more.
Finding the balance point
The calculator works out the house’s heat loss per degree from its design load, then finds the temperature at which the heat pump’s capacity equals the loss:
A standard heat pump in Chicago
A 2,000 sq ft house in zone 5, average insulation, a 5 °F design temperature, a 3-ton standard heat pump sized for cooling.
- Heating load at 0 °F: 2,000 × 45 = 90,000 BTU/hr, so 1,286 BTU/hr per °F
- Heat needed at 5 °F: 1,286 × 65 = 83,571 BTU/hr
- Capacity at 5 °F: 36,000 × 45% = 16,344 BTU/hr
- Backup needed: 83,571 − 16,344 = 67,227 BTU/hr, or 19.7 kW, so 20 kW of strips
- Balance point: about 40 °F
A cold-climate model of the same size would keep about 73% at 5 °F and cut the backup to about 57,000 BTU per hour.
The balance point matters more than the backup size, because it decides how many hours of the winter the strips run. In Chicago a 40 °F balance point means the heat pump alone covers the shoulder months and the milder winter days, and the strips carry a growing share as the temperature falls. In Atlanta, the same calculator gives a 3.5-ton cold-climate unit a balance point of about 33 °F and only 7.4 kW of backup at its 20 °F design temperature, so the strips run on a handful of nights a year.
Why backup heat is expensive
Electric resistance turns one kWh into 3,412 BTU of heat, a coefficient of performance of 1. A heat pump on a mild day delivers three or four times as much heat for the same electricity. Every hour the strips carry the house costs about three times as much as an hour on the compressor. At 17 cents per kWh, resistance heat is $49.82 per million BTU delivered, against $17.79 for a heat pump at a seasonal COP of 2.8 and $15.79 for gas in a 95% furnace, from the fuel cost per million BTU calculator.
That is why the share of the season that runs on backup has such a large effect on the bill. The heat pump versus furnace cost calculator takes the backup share into account in an effective COP:
With a COP of 2.8 and 10% of the season’s heat on strips, the effective COP is 2.37. In the calculator’s zone 5 example, that makes a gas furnace at $1.50 per therm cheaper by $439 a season, with a break-even electricity price of 12.8 cents per kWh. A cold-climate unit with 3% backup raises the effective COP to about 2.65 and cuts the gap to about $230.
Three ways to cover the cold end
Strips. The simplest and cheapest to install. The air handler carries electric elements, often 5, 10, 15 or 20 kW, and a two-stage thermostat or the heat pump’s controls bring them on below the balance point. The electrical service has to carry them: 20 kW is over 80 A at 240 V.
A cold-climate heat pump. Costs more and keeps working far lower. It pushes the balance point down and shrinks the backup, often to a single small strip for emergencies.
Dual fuel. A gas or propane furnace serves as the air handler and takes over below a switch-over temperature, usually set where the heat pump’s cost per BTU rises above the furnace’s. It makes most sense where there is already a gas furnace in good condition. The heating cost by fuel calculator shows which fuel is cheaper at your prices, which is where the switch-over temperature should sit.
Sizing up for heating
In climate zones 5 to 7 it is tempting to size the heat pump for the heating load instead of the cooling load. Manual S allows heat pumps up to 125% of the cooling load in heating-dominated climates for this reason. Going further brings back the oversized-air-conditioner problem every summer. A variable-speed or cold-climate unit sized near the cooling load, with a modest backup, usually beats a large single-speed unit. The guide to BTU per square foot by climate zone shows where heating overtakes cooling, and the guide to comparing fuels per million BTU sets the running costs side by side.
What the seasonal rating hides
A heat pump’s HSPF2 is a seasonal average for a standard climate. In a cold climate the real seasonal COP is lower, because more hours are spent at low temperatures and on backup. Read HSPF2 as a way to compare models, as the guide to efficiency ratings explains, and use the balance point to judge how a model will do in your winter.