# Heat Pumps - Performance and Efficiency Ratings

## Rating the performance and efficiency 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*on the hot side. The maximum theoretical efficiency can be calculated by using

^{o}C*(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.

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