Heat Pumps  Performance and Efficiency Ratings
Performance and efficiency rating of heat pumps.
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 ^{o}C on the cold side and temperature 40 ^{o}C 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 57 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.
Related Topics

Air Conditioning Systems
Design of Air Conditioning systems  heating, cooling and dehumidification of indoor air for thermal comfort. 
Heating Systems
Design of heating systems  capacities and design of boilers, pipelines, heat exchangers, expansion systems and more.
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