Financial Return on an Air Source Heat Pump

Financial Return on an Air Source Heat Pump

In the autumn of 2010 our annual bill for oil had reached £2000 so we began to investigate alternatives. LPG seemed to be even more expensive, and the lack of a gas supply left electricity as the only alternative, but as it is also expensive we investigated a combination of photovoltaic solar panels to generate electricity and heat pumps to use it to heat water.

Refrigerators and deep freezers are examples of heat pumps – they pump heat from the inside of the appliance to the grill or heat exchanger at the rear where the heat escapes into the air. The heat pumps that are alternatives to boilers pump heat from outside the building to the inside. There are several different types depending on the input and output of the heat pump. The heat can be taken from the air (air source) or the ground (ground source). The latter requires either a long deep trench in the ground in which is laid a pipe containing water or a deep shaft with a vertical rather than horizontal pipe (these are called geothermal). The heat pump takes heat from the water in the pipe, the water then being warmed again by being heated by the ground. These are expensive to install and require suitable ground which we do not have. An air source heat pump takes heat from the air which is sucked by fans through a heat exchanger. The output of the heat pump can be either hot water used to heat radiators and provide domestic hot water, or warm air piped through the house (the latter can also be used as air conditioners in hot weather). As we already have radiators we went for the hot water output.

Another difference between heat pumps is in the gas used. The heat pump works by compressing a gas which increases its temperature. The hot gas flows through a heat exchanger which heats either water or air which is pumped into the house. This cools the gas which is now allowed to expand cooling it even further (typically well below 0C). The cold gas flows through another heat exchanger which warms it using either the outside air or water in the case of ground source. There are two main types of gas used. Most heat pumps use refrigerants similar to those used in refrigerators and deep freezers. However these have a limited temperature range. They are suitable for ground source where the water never gets very cold and under floor heating systems where high water temperatures can damage the piping. The size of radiators needs to be doubled from that designed for a conventional boiler as the water temperate is lower. The outside air used in an air source heat pump can be very cold. So we went for R744 as the refrigerant. This is compressed carbon dioxide which poses no danger to the environment if accidently released, and will still extract heat from air at temperatures below -25C. It also produces very high temperatures – we get over 90C after compression with an outside temperature of 0C.

The efficiency of heat pumps is compared to that of an immersion heater which has an efficiency of nearly 100% in converting electricity into hot water. The typical value for a R744 heat pump is 300% (this is also called the Coefficient of Performance or COP=3) at 15C. This means that three times as much heat is produced using the same amount of electricity as an immersion heater, or the cost of heating water is one third of that using an immersion heater. The COP value varies according to the input and output temperatures. In our case it drops to 1 with an outside temperate of -30C and exceeds 4 at outside temperatures of over 25C (giving very cheap hot water in the summer). There is a sudden fall in the COP value from 2.6 at 5C to 2.2 at -1C because ice forms on the air heat exchanger and this must be melted by a defrosting operation (diverting warm refrigerant through the heat exchanger). However at temperatures below freezing the air is usually much dryer and so the fall with temperature is less. Ground source heat pumps have a more constant COP value typically between 4 and 5 because the input temperature is more constant, and they do not suffer from icing up - in practice they often rely on immersion heaters to boost the water temperature and the practical COP value is usually about 3. We have changed the wiring to our immersion heater to give us manual control. It will only be used to provide faster heating from cold in winter (i.e. if the heating has been switched off for a week or so).

The heat pump is most efficient when raising the water temperature in the output heat exchanger by 20C, and by limiting the maximum temperature of the water in the tank to about 65C. This is hot enough to require a thermostatic mixing valve to reduce the temperature to about 45-50C for washing etc. Ideally the hot water tank should be tall enough to sustain a temperature differential of 20C - this is about 3 feet or 1 metre between the pipes to the heat pump.

We have kept our existing radiators, but replaced the hot water tank with a much larger double tank. This has an outer tank containing the heated water from the heat pump, and an inner tank containing the hot water for domestic use. The radiators get their water from the outer tank. The reason for going for a large hot water tank is that the electricity generated by the solar panels during the day is used to power the heat pump, and the hot water is then available for use at night. This means we export a minimum of electricity to the grid (we are paid 3p per unit for exported electricity but have to pay 12p to import it again when we want it – converting it into hot water saves 9p per unit).

We have kept the same target indoor temperatures of as we had for the oil boiler (18C all night, 19C during the day and 20C in the evening). However most of the eleven radiators (one per room so each room receives 900 watts if it is averaged out - total floor area is about 175 sq metres) now have thermostatic valves. The heat pump's power consumption varies from 2.86kW at 15C and above, to 4.93kW at -5C and below. The latter corresponds just over 10kW output (COP = 2.1). Our oil boiler was double this and that could just hold the indoor temperature at 20C when it was below freezing outside. Our new installation struggles to keep the indoor temperature above 17C (20C now we have cavity wall and loft insulation) when below freezing outside so extra electrical heating is then required. This could be provided by the immersion heater (the system is designed to do this automatically), but we have found an electric fan heater in the room more cost effective. This is not required when it is above freezing outside or during the night. I have read that the average 3 bedroom house uses 16,000 units per year for heating and hot water, and has 10 radiators. Over the last four years with the heat pump we have used between 7,033 and 10,850 units in a year. Our bungalow has 3 bedrooms and eight other rooms.

The heat pump looks like an air conditioning unit which either stands on the ground or is attached to an outside wall. It does make some noise, but not enough to be noticeable. The fan speed is much lower than air conditioners, and it can only be heard from a few feet away.

The heat pump was installed at the start of January 2011 and completed on 11 January so the values before that in the spreadsheet are not reliable. As I have no accurate measurement of either the amount of oil used or the electricity consumed I have made the following assumptions. The amount of oil used per day is assumed to be constant throughout the year. I have assumed purchases at the start of the year and mid summer taking those prices from the internet using the approximation that the cost per day is ten times the price per litre (which was correct in 2010 and 2011). I have also assumed that the heat pump and the additional heater use all the power in excess of 15 units per day – measurements in October-December 2010 showed that our average consumption without the heat pump was 15 units.

An idea of the efficiency can be obtained from the number of units required to heat two bathfulls of water (which is more than enough for our daily use) - on a hot (over 25C) summer's day 2 units while on a cold (less than 0C) winter's day about 8 units. A similarly cold winter's day uses about 65 units for central heating. Our bungalow has eleven heated rooms, each with one radiator.

We would have had the oil boiler serviced for £80 at the start of September - the heat pump does not require servicing so this is reflected in the savings on the first of the month in the Spreadsheet. We also had cavity wall insulation installed at the end of March 2012 at a cost of £165 and this is added in as an additional capital cost.

The house temperature is 17C at night, 18C during the day and 19C in the evening. A detailed breakdown of units used and costs per day is given in this spreadsheet.

The cost of running the heat pump increased significantly during late 2013 (10,850 units at a net cost of £1558) and on 12 January 2014 we disconnected it and found that the water pump, pipe work and heat exchanger were blocked with debris. The water pump was replaced and the rest flushed through and cleared resulting in warmer radiators and lower consumption of electricity.

At the end of 2015 (after five years) we had used 42910 units with 4615 of those coming from the solar panels so the running cost was £5244 for the five years compared to an estimated £10063 for oil. Even with the current low oil price we are still saving money.

At the end of 2020 we had used 82360 units with 9332 coming from the solar panels at a cost of £10424 or £1042 per annum, and a total estimated saving over the cost of oil of £18310 over the ten years.

The cost of electricity and oil increased sharply during 2022, and we reduced the indoor temperature on 23 November 2022 by 1C so after that date it was 16C at night, 17C during the day and 18C in the evening, and on 1 December 2022 these were reduced by another 1C to 15,16,17C.

The following explains the values in a spreadsheet which has detailed day by day values:
Date: The date of the readings, normally taken at 6am of the next day (i.e. the value for 1 January is taken at 6am on 2 January), but occasionally corrected to be approximately what would have been the values at 6am. There are also columns for the previous month's total, the total at the end of the previous month, the total for the current month, and the total at the end of the current month.

The first section covers the units used and the estimated savings over oil.
Units imported: The number of units imported less 15. I have assumed that the first 15 units imported are used for lighting, cooking, and other domestic appliances, and that all units over the 15 (if any) are used by the heat pump. In summer the heat pump is only used around midday so all its electricity comes from the solar panels and hence this value is zero. In the winter very little if any comes from the solar panels, and so this value is closer to the amount actual used. The maximum value is about 90 units, around 50 is typical in winter.
Cost of units: The number of units imported times the cost per unit (12-15p) - about £7 on a typical winter's day, £14 on a very cold day.
Hot water units used: An estimate of the number of units used to heat the domestic hot water. Some of these are imported and the rest generated by the solar panels - the former dominates in winter and the latter in summer.
Central Heating units used: An estimate of the number of units used for central heating - virtually all of these are imported with very few from the solar panels, but on sunny winter days it may reach 5 units out of 6 generated.
Saving on oil: Prior to installing the heat pump we used about 3,600 litres per year so the average cost per day is about 10 times the price per litre (which can be obtained from Boiler Juice). Oil was delivered twice a year in June and December so I have used prices in those months for the next six months. This obviously over estimates the daily cost in the summer and under estimates it in winter so a true comparison between the cost of the heat pump and oil can only be made at the end of the year.
Overall saving in day: This is just the the average daily cost of oil less the cost of units imported, and is only meaningful at the end of the year.

The next section estimates the financial return.
Cost plus 0.013% per day: The installation cost was £8629.98, increasing by £165 in April 2012 due to the cost of cavity wall insulation. This is increased by 0.013% per day compound to allow for inflation and lost of interest on the money invested.
Gain/loss in day: The savings on oil less loss on depreciation and inflation. Positive is a gain, negative a loss.
Total gain/loss to date: The gain/loss in this day added to the previous days value. When this equals the cost plus 0.013% per day we will will have covered the full cost.
Overall gain/loss This is the gain/loss based on the original price or the gain/loss to date - £8629.98 up to March 2012 and £8794.98 from April 2012. Positive is a gain, negative a loss. When zero we will have covered the original purchase price but this will not take inflation into account.

The final section gives the minimum and maximum temperatures measured in the shade on the NE wall near the heat pump.

Note that from October 2022 to March 2023 there was a government rebate of £400 spread over the six months - the daily figures ignore this, but the rebate is included in an additional column at the end of the month and the rebated cost per unit is calculated.

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