Compression heat pump and chiller

Simple calculations for compression heat pumps and chillers.


This module was developed to provide COP calculations based on temperatures for energy system optimizations with oemof.solph.

A time series of pre-calculated COPs can be used as input for a transformer (an oemof.solph component) in an energy system optimization. Discover more possibilities to use this module with our examples:


Compression heat pumps and chillers increase the temperature of a flow using a compressor that consumes electric power. The inlet heat flux comes from a low temperature source (T_low) and the outlet has the temperature level of the high temperature sink (T_high). The same cycle can be used for heating (heat pump) or cooling (chiller).


Fig.1: The heat pump cycle and its two temperature levels.

The efficiency of the heat pump cycle process can be described by the Coefficient of Performance (COP). The COP describes the ratio of useful heat \dot{Q}_\mathrm{useful} (\dot{Q}_\mathrm{in} or \dot{Q}_\mathrm{out}) per electric work P_\mathrm{el} consumed:

COP = \frac{\dot{Q}_\mathrm{useful}}{P_\mathrm{el}}

The Carnot efficiency COP_\mathrm{Carnot} describes the maximum theoretical efficiency (ideal process). It depends on the temperature difference between source and sink:

COP_\mathrm{Carnot, HP} = \frac{T_\mathrm{high}}{T_\mathrm{high} - T_\mathrm{low}}

for heat pumps and

COP_\mathrm{Carnot, chiller} = \frac{T_\mathrm{low}}{T_\mathrm{high} - T_\mathrm{low}}

for chillers.

To determine the COP of a real machine a scale-down factor (the quality grade \eta) is applied on the Carnot efficiency:

COP = \eta \cdot COP_\mathrm{Carnot}


0 \leq \eta \leq 1

Typical values of quality grades are 0.4 for air-source heat pumps, 0.55 for ground-source (“brine-to-water”) heat pumps using a ground heat exchanger, and 0.5 for heat pumps using groundwater as source. [1]

For high temperature heat pumps Arpagaus finds quality grades between 0.4 and 0.6. [2]

Fig.2 illustrates how the temperature difference affects the COP and how the choice of the quality grade allows to model different types of heat pumps.


Fig.2: COP dependence on temperature difference (Output of example


These arguments are input to the functions:

symbol attribute explanation
COP cop Coefficient of Performance
T_\mathrm{high} temp_high Temperature of the high temp. heat reservoir
T_\mathrm{low} temp_low Temperature of the low temp. heat reservoir
\eta quality_grade Quality grade
T_\mathrm{icing} temp_threshold_icing Temperature below which icing occurs
f_\mathrm{icing} factor_icing COP reduction caused by icing

The Coefficient of Performance (COP) is calculated using `calc_cops()`

COP = calc_cops(temp_high,


COP = \eta \cdot \frac{T_\mathrm{high}}{T_\mathrm{high}
- T_\mathrm{low}}

COP = f_\mathrm{icing} \cdot\eta
\cdot\frac{T_\mathrm{high}}{T_\mathrm{high} - T_\mathrm{low}}


COP = \eta \cdot \frac{T_\mathrm{low}}{T_\mathrm{high}
- T_\mathrm{low}}

The maximum cooling capacity can be calculated using `calc_max_Q_dot_chill()`.

Q_dot_chill_max = calc_max_Q_dot_chill(nominal_conditions, cops)
\dot{Q}_\mathrm{chilled, max}
= \frac{COP_\mathrm{actual}}{COP_\mathrm{nominal}}

The maximum heating capacity can be calculated using `calc_max_Q_dot_heat()`

Q_dot_heat_max = calc_max_Q_dot_heat(nominal_conditions, cops)
\dot{Q}_\mathrm{hot, max}
= \frac{COP_\mathrm{actual}}{COP_\mathrm{nominal}}

The quality grade at nominal point of operation can be calculated using `calc_chiller_quality_grade()`

Do NOT use this function to determine the input for calc_cops()!

quality_grade = calc_chiller_quality_grade(nominal_conditions)
\eta =
\frac{\dot{Q}_\mathrm{chilled,nominal}}{P_\mathrm{el}} /
\frac{T_\mathrm{low, nominal}}{T_\mathrm{high, nominal}
- T_\mathrm{low, nominal}}


[1]VDE ETG Energietechnik, VDE-Studie “Potenziale für Strom im Wärmemarkt bis 2050 - Wärmeversorgung in flexiblen Energieversorgungssystemen mit hohen Anteilen an erneuerbaren Energien”. 2015. (
  1. Arpagaus, Hochtemperatur-Wärmepumpen - Marktübersicht, Stand der Technik und Anwendungsbeispiele. Berlin, Offenbach: VDE-Verlag, 2019.