Heat Pumps - Performance and Efficiency Ratings

Several methods can be used to rate heat pump performance and efficiency:

COP - Coefficient of Performance

The Coefficient of Performance - COP - is the ratio of heat output to the amount of energy input for a heat pump.

COP can be expressed as

COP = h_h / h_w                                            (1)

where

COP = Coefficient of Performance

h_h = heat produced (Btu/h, J, kWh)

h_w = equivalent electric energy input (Btu/h, J, kWh) = 3413 P_w

where

P_w = electrical input energy (W)

If a heat pump delivers 3 units of heat for every unit of energy input - the COP is 3.

• 1 kW = 1000 W = 3413 Btu/h

Example - COP Heat Pump

Cooling Cycle

A heat pump deliver 60000 Btu/h with a total electric input of 9 kW:

COP = (60000 Btu/h) / (3413 (9 kW))

       = 1.95

Heating Cycle 

A heat pump deliver 50000 Btu/h with a total input of 7 kW:

COP = (50000 Btu/h) / (3413 (7 kW))

       = 2.1

Maximum COP

Maximum theoretical efficiency for a heating process is

COP_heating = T_h / (T_h - T_c)                                               (1b)

COP_heating = Coefficient of Performance - heating process

T_h = absolute temperature on the hot side (K)

T_c = absolute temperature on the cold side (K)

Maximum theoretical efficiency for a cooling process is

COP_cooling = T_c / (T_h - T_c)                                             (1c)

COP_cooling = Coefficient of Performance - cooling process

Note! - the efficiency of a cooling or heating process can be increased by reducing the temperature difference (T_h - T_c) between the hot and cold side.

A heating process with a lower hot temperature - like achievable in a piped floor system - will increases the efficiency compared to a system with higher hot temperature - like a heating panel system. The opposite for a cooling process - a lower cold temperature will increase the efficiency.

Example - Maximum Heat Pump Efficiency

An air to air heat pump operates between temperature -5 ^oC on the cold side and temperature 40 ^oC on the hot side. The maximum theoretical efficiency can be calculated by using (1b) as

COP_heating = (40 + 273) / ((40 + 273) - (-5 + 273))

                = 6.95

The typical practical value for a heat pump is in the range 2 - 4.

EER - Energy Efficiency Ratio

The Energy Efficiency Ratio - EER - is a measure of the cooling efficiency of a heat pump.

EER can be expressed as

EER = h_c / P_w                                                     (2)

where

EER = Energy Efficiency Rating

h_c = cooling heat (Btu/h)

P_w = electrical power (W)

Example - EER

An air conditioner or heat pump in cooling mode draws 1000 W of electric power to produce 10000 Btu/h of cooling. The EER can be calculated as

EER = (10000 Btu/h) / (1000 W)

    = 10

HSPF - Heating Season Performance Factor

The Heating Season Performance Factor - HSPF - is a measure of the overall heating efficiency of a heat pump during the season.

HSPF = h_s / 1000 P_ws                                               (3)

where 

h_s = heat produced during the season (Btu)

P_ws = electrical power consumed during the season (kWh)

The HSPF can be regarded as an "average" COP for an entire heating season. It is common to compare BTUs of heat output to watts of electrical energy input. HSPF of 6.8 can be compared with an average COP of 2. A HSPF in the range of 5-7 is acceptable.

Example - Heat Pump Heating Season Performance Factor

For a heat pump deliver 120,000,000 Btu during the season when consuming 15,000 kWh the HSPF can be calculated as 

HSPF = (120000000 Btu) / (1000 (15000 kWh))

       = 8

SEER - Seasonal Energy Efficiency Ratio

Seasonal Energy Efficiency Ratio is a measure of the seasonal cooling efficiency of a heat pump or a consumer central air conditioning system.

The SEER should be at least 13 to be sold in the United States. SEER above 20 is a very efficient system.