The efficiency of a heat pump
The Coefficient of Performance (COP) is a key metric for large heat pumps that describes the efficiency of the system. It indicates the ratio of usable heating power ($Q_{\text{h}}$) to the electrical drive power ($P_{\text{el}}$) used.
$$COP = \frac{Q_{\text{h}}}{P_{\text{el}}}$$
For example, with a COP of 3, three times the input drive power is provided as usable heating power.
COP Calculator
The COP calculator helps you estimate the efficiency of a large heat pump for your application.
Large heat pumps are particularly efficient when operating within an optimal temperature range. The COP is significantly influenced by the temperature difference between the heat source (e.g., geothermal energy, waste heat, or ambient air) and the heating system (e.g., district heating network or process heat). The smaller this difference, the higher the COP will be.
Furthermore, efficiency depends on operational behavior, so aiming for operation close to the design point is advisable. To achieve the highest possible COP, it is important to design the heat pump to optimally match the given conditions of the heat source and sink. The choice of compressor technology, the refrigerant used, and the Circuit Configurations play a crucial role in this. To assess the actual efficiency under real operating conditions, the annual performance factor is additionally used as a practical parameter. It represents the COP averaged over a year.
Determination of the COP
For an estimation of the COP, information about the temperature levels of the source and sink is sufficient. There are two common approaches to determining the COP:
The theoretically maximum possible efficiency of a heat pump is derived from the ratio of the sink temperature TS to the temperature lift $\Delta_{\text{Hub}}$ between the source and sink. This is referred to as the Carnot COP:
$$COP_{\text{Carnot}} = \frac{T_S}{\Delta T_{\text{Hub}}}$$
Alternatively, the COP can be determined using the Lorenz approach. In this case, the temperature changes on the sink and source sides in the heat exchangers are taken into account, enabling a more accurate exergy analysis. Based on the mean temperatures $T_{i,m}$, which result from the supply and return temperatures, the Lorenz COP can be calculated as follows:
\(COP_{\text{Lorenz}} = \frac{T_{S,m}}{T_{S,m} - T_{Q,m}}, \text{ mit } T_{i,m} = \frac{T_{i,\text{ein}} - T_{i,\text{aus}}}{\ln\left(\frac{T_{i,\text{ein}}}{T_{i,\text{aus}}}\right)}\)
The losses that occur in a real heat pump are captured by the efficiency \(\eta\). This results in the actual performance factor: \(COP = \eta \cdot COP_{\text{Carnot}} \text{ or } COP = \eta \cdot COP_{\text{Lorenz}}\). Most large heat pumps on the market have efficiencies ranging from 40% to 60%, with systems using open stages tending to exhibit higher efficiencies.
