Performance figure

The coefficient of performance (abbreviated LZ), also known by the English names Energy Efficiency Ratio (EER short, ) for mechanical refrigeration systems and primary energy ratio ( english Coefficient of Performance , shortly COP ) for mechanical heat pumps , is the ratio of generated refrigeration or Thermal output in relation to the electrical output used. It must be distinguished from the heat ratio for thermal heat pumps or for thermal refrigeration systems, which does not refer to the mechanical power used, but to the drive heat flow used . ${\displaystyle \varepsilon }$ ${\displaystyle \varepsilon _{\rm {KA}}}$ ${\displaystyle \varepsilon _{\rm {WP}}}$ ${\displaystyle \beta }$ ${\displaystyle \beta _{0}}$ ${\displaystyle {\dot {Q}}_{\rm {B}}}$

The COP depends on the operating point, which is why it is not sufficient to state the COP alone. So achieved z. B. a heat pump with a low temperature difference has a high efficiency or high coefficient of performance, while an air / water heat pump for heating buildings, especially in winter, only has a low coefficient of performance. Several performance figures have therefore been defined specifically for air conditioning, which take into account the partial load and also climatic influences.

The mean over a year with heat pump heating is called the annual performance factor (JAZ). It corresponds to the English name SEER ( Seasonal Energy Efficiency Ratio ).

Heat pumps

In the case of electrical heat pumps (HP) with refrigerant, the coefficient of performance or COP indicates the ratio of the heat output of a heat pump to the electrical output of the compressor. A performance figure of z. B. 4.2 means that the electrical power used by the compressor provides 4.2 times the thermal power. In other words, this heat pump can provide 4.2 kW of heat output from one kilowatt of electrical power.

For a heat pump with heating output , the coefficient of performance is defined as: ${\displaystyle {\dot {Q}}_{\rm {H}}}$

${\displaystyle \varepsilon _{\rm {WP}}={\frac {{\dot {Q}}_{\rm {H}}}{P_{\rm {el}}}}}$

When considering the heat pump adiabatically, the heat output is the sum of the externally absorbed heat output (e.g. from a deep, warm geothermal probe) and the electrical output of the heat pump's compressor, which means that the coefficient of performance is, by definition, greater than one. However , the use of a heat pump can only be economically and ecologically sensible with performance figures or annual performance figures that are greater than the primary energy factor of the electricity used. ${\displaystyle {\dot {Q}}_{\rm {H}}}$ ${\displaystyle {\dot {Q}}_{\rm {u}}}$ ${\displaystyle P_{\rm {el}}}$

${\displaystyle \varepsilon _{\rm {WP}}={\frac {{\dot {Q}}_{\rm {u}}+P_{\rm {el}}}{P_{\rm {el}}}}=1+{\frac {{\dot {Q}}_{\rm {u}}}{P_{\rm {el}}}}}$.

The Carnot efficiency for a reversible heat pump with the absolute evaporation temperature (lower temperature at which the medium absorbs heat at low pressure) and the liquefaction temperature (higher temperature at which the compressed medium gives off heat at higher pressure) is: ${\displaystyle T_{min}}$ ${\displaystyle T_{max}}$

${\displaystyle \eta _{c}={\frac {T_{max}-T_{min}}{T_{max}}}=1-{\frac {T_{min}}{T_{max}}}<1}$

The reciprocal value of the Carnot factor thus represents the borderline case for the achievable coefficient of performance:

${\displaystyle \varepsilon _{\rm {WP}}<{1 \over \eta _{c}}={\frac {T_{max}}{T_{max}-T_{min}}}}$

Refrigeration systems

The coefficient of performance of refrigeration systems (KA) indicates the ratio of the resulting refrigeration output to the electrical output used: ${\displaystyle {\dot {Q}}_{0}}$

${\displaystyle \varepsilon _{\rm {KA}}={\frac {{\dot {Q}}_{0}}{P_{\rm {el}}}}}$

For real power heating machines, the EER is smaller than the COP of the Carnot process minus 1:

${\displaystyle \varepsilon _{\rm {KA}}={\frac {{\dot {Q}}_{0}}{{\dot {Q}}_{\rm {H}}-{\dot {Q}}_{0}}}<{\frac {T_{min}}{T_{max}-T_{min}}}={\frac {1}{\eta _{\rm {c}}}}-1}$

It follows from this that high COP or EER can be achieved with small temperature differences. In the area of ​​air conditioning with a small difference between the temperature of the cooled air and the environment, COPs of up to 7 can be achieved, for example.

Relationship between and ${\displaystyle \varepsilon _{\rm {KA}}}$ ${\displaystyle \varepsilon _{\rm {WP}}}$

In the case of a heat pump, the heating output is the sum of the heating output absorbed by the cold reservoir (environment) and the technical work, so that:

${\displaystyle \varepsilon _{\rm {WP}}={\frac {{\dot {Q}}_{\rm {H}}}{P_{\rm {el}}}}={\frac {{\dot {Q}}_{0}+P_{\rm {el}}}{P_{\rm {el}}}}=\varepsilon _{\rm {KA}}+1}$

Individual evidence

1. ↑ Energy saving in buildings: state of the art; Trends at Google Books , page 161, accessed on August 16, 2016

See also

• Performance figure for turbo machines