Air Source Heat Pump
A simple model for estimating Air Source Heat Pump performance
The Building Research Establishment BRE Test Report carried out tests 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, which 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
COPACTUAL = Heat output (kW) / Electrical power input (kW) … as reported
COPCARNOT = 1 / ( 1 - TCOLD / THOT ) … T in Kelvin
which when expressed in Celsius and rearranged gives:
COPCARNOT = (tHOT + 273) / (tHOT - tCOLD) … t in Celsius
The average value over 30 tests for COPACTUAL/COPCARNOT 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:
COPCALC = 0.342 * (tHOT + 273) / (tHOT - tCOLD) … 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:
| 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 |
| Total | 2453 | 11,967 | 5,147 | |||||||
| Total | °day | kW-hth/year | kW-he/year |