Air Source Heat Pump

A simple model for estimating Air Source Heat Pump performance

The Building Research Establishment carried out tests BRE Test Report on a Mitsubishi PUHZ-W90VHA air-to-water heat pump and the test results presented in table 3 of that document were analysed against a reverse-Carnot cycle (as original work by FLUKE ). The Carnot cycle describes the maximum theoretical efficiency of ANY thermodynamic process and has the advantage that it can be calculated without any knowledge of the device, but simply from two temperatures expressed in degrees Kelvin: the cold and hot limits of the process, in this case the outside air heat source temperature and the supply temperature to hot water for space heating. So the two equations are

COP_ACTUAL = Heat output (kW) / Electrical power input (kW) … as reported

COP_CARNOT = 1 / ( 1 - T_COLD / T_HOT ) … T in Kelvin

which when expressed in Celsius and rearranged gives:

COP_CARNOT = (t_HOT + 273) / (t_HOT - t_COLD) … t in Celsius

The average value over 30 tests for COP_ACTUAL/COP_CARNOT is 0.342 so the COP value for the Mitsubishi heat pump can be estimated simply from the outdoor air temperature and the hot water supply temperature from the equation:

COP_CALC = 0.342 * (t_HOT + 273) / (t_HOT - t_COLD) … t in Celsius

Other makes and models of ASHP may be expected to have factors slightly higher or lower than 0.342. To assess the validity of the model, calculated versus actual (test) values of COP are presented below:

Application of the model to a case study

Armed with a simple equation to calculate COP and 'degree day' data averaged over 20 years (method discussed elsewhere) , a case study 'typical' house can be modelled based on providing heat for space heating and domestic hot water using the heat pump instead of a gas boiler that would otherwise have a 'medium' gas consumption of 12,000 kW-h per year (OFGEM). The supply temperature is 55°C so that the ASHP can be used as a retrofit to a normal central heating system for economy (compared to say, replacing with brand new low-temperature underfloor heating). The outside temperature is assumed to be constant at the monthly average and heat demand is weighted accordingly

Month	20-year average degree days	Days/month	Mean temperature below 15.5C	Mean temperature	Thot K	Tcold K	COPCARNOT	COPCALC	Mean monthly heat demand kW	Mean monthly motor power kW
January	362	31	11.7	3.8	328	276.8	6.41	2.19	2.43	1.11
February	318	28	11.4	4.1	328	277.1	6.45	2.21	2.13	0.97
March	299	31	9.6	5.9	328	278.9	6.67	2.28	2.00	0.88
April	235	30	7.8	7.7	328	280.7	6.93	2.37	1.57	0.66
May	156	31	5.0	10.5	328	283.5	7.37	2.52	1.05	0.42
June	90	30	3.0	12.5	328	285.5	7.72	2.64	0.60	0.23
July	45	31	1.5	14.0	328	287.0	8.01	2.74	0.30	0.11
August	52	31	1.7	13.8	328	286.8	7.97	2.72	0.35	0.13
September	95	30	3.2	12.3	328	285.3	7.69	2.63	0.64	0.24
October	183	31	5.9	9.6	328	282.6	7.22	2.47	1.23	0.50
November	270	30	9.0	6.5	328	279.5	6.76	2.31	1.81	0.78
December	348	31	11.2	4.3	328	277.3	6.47	2.21	2.33	1.05
Totals	2453								11,967	5,147
	°day								kW-hth/year	kW-he/year

Economics

According to the Money Advice Service the average cost to the UK consumer in 2018 of gas was 4.5p per kW-h and of electricity 18.4p per kW-h. 12,000 kW-h of heat would therefore cost £540 from a conventional gas boiler compared to £947 from an ASHP. However, under the Renewable Heat Incentive (RHI) a government subsidy scheme designed to encourage uptake of renewable technologies, applicants can claim 10.71p per kW-h or £1,285 per year, for 7 years.

Indicative cost for a complete ASHP system is £5,000-£10,000 see Centre for Sustainable Energy Appendix C. Taking the mid-value (£7,500) costs over a 20 year period can be compared:

Status quo (gas boiler); cost of gas = £10,800 ASHP (equipment cost + electricity - RHI payments) = £17,445

Conclusions

In original work by FLUKE performance test results (by BRE) for an Air Source Heat Pump (ASHP) were modelled with reasonable accuracy (R² = 0.928). The derived equation depends only on outside temperature, heat supply temperature and one empirically determined constant.

Using the equation, for the case study conditions described above the ASHP could deliver 12,000 kW-h of heat per year, as space heating and domestic hot water to the house for the expenditure of 5,150 kW-h electrical power. This would represent a COP value of 2.33 rather less the figure 3 to 3.5 sometimes claimed for the technology

Even allowing for the RHI subsidy payments, ASHP is more expensive than a gas boiler. If the ASHP were supplied free-of-charge and RHI payments were received, the cost is about the same