Pre-Print: doi:10.17170/kobra-202103103481, 2019
Large-scale heat pumps:
market potential and barriers, classification and estimation of efficiency
Jesper, M.1,*,Schlosser, F.2,3, Pag, F.1, Schmitt, B.1, Walmsley, T.G. 3, Vajen, K.1
1 University of Kassel, Department of Solar- and Systems Engineering, Kurt-Wolters-Str. 3, 34125 Kassel, Germany
2 University of Kassel, Department of Sustainable Products and Processes, Kurt-Wolters-Str. 3, 34125 Kassel, Germany
3 Sustainable Energy & Water Systems Group, School of Engineering, University of Waikato, Hamilton, New Zealand
Heat pumps powered by renewable electricity have a significant potential to become a critical technology to
disruptively decarbonize an economy. An essential step towards this goal is the development of an accurate
understanding and model of how heat pumps in large-scale implementations perform in terms of economics,
energy, and the environment. In this study, the influence of system design and operating conditions on the
Coefficient of Performance (COP) of large-scale (> 50 kWth) electric driven mechanical compression heat pumps
is reviewed, leading to a methodology to estimate a heat pump’s performance depending on the operating
conditions. An overview of the potential scale, market size and barriers for large-scale heat pumps with a focus on
applications in industry, commerce and district heating systems is given. The review underscores the knowledge
gap in the area of large-scale heat pumps including their lack of performance testing standards given the large
window of operating conditions as well as meaningful application possibilities. Transferring a significant and
reliable dataset to practitioners (e.g. energy-managers and consultants) can close this knowledge gap. Therefore,
this study assembles a comprehensive dataset for the system configuration and performance of 33 large-scale heat
pumps from 11 different manufacturers and addresses three main objectives: (1) Classifying and evaluating the
capabilities of market available heat pumps. (2) Modelling the correlation between the COP and the operating
conditions. (3) Developing an economic and ecological evaluation method for a heat pump project. Applying the
developed models to accurately assess real-world performance and build a sound business case for large-scale heat
pumps has the potential to accelerate the uptake of renewable energy and help improve overall environmental
•Summaries the potential and capabilities of market available heat pumps
•Examines the influence of system configuration on heat pump efficiency
•Develops accurate models for estimating the COP depending on operating conditions
•Presents a short-cut method for economic and ecological feasibility assessment
Keywords: heat pump, high temperature, COP, temperature lift, state of technology, feasibility assessment
Word count: 11,163
a annuity factor [-]
A annuity [€/a]
b price dynamic cash value factor [-]
cp isobar heat capacity [kWh/(kg∙K)]
c specific Cost [€/kWh]
C costs [€]
CHP combined heat and power
DH district heating
E-mail address: email@example.com
Siehe auch: Renewable and Sustainable Energy Reviews, Volume 137, 110646, 2020, https://doi.org/10.1016/j.rser.2020.110646
SGB standard gas boiler
SHP standard electric driven mechanical compression heat pump
COP coefficient of performance [-]
CPS climate protection scenario
Eel consumed electric energy [kWh]
EF emission factor [gCO2/kWh]
f effect factor [%]
GHGE greenhouse gas emissions [gCO2]
GWP global warming potential [-]
HP electric driven mechanical compression heat pump
HTHP high temperature electric driven mechanical compression heat pump
LCOH levelized cost of heat [€/kWh]
n number [-]
N depreciation period
NBT normal boiling temperature [°C]
p pressure [bar]
pc/p0 pressure ratio [-]
electric power input [kW]
q interest-rate factor
Qdem annual reference energy demand
Qh,use usable thermal energy [kWh]
usable heat output [kW]
R² coefficient of determination
SCOP seasonal coefficient of performance [-]
SG safety group classification [-]
t temperature [°C], time [h]
T temperature [K]
VHC volumetric heating capacity [kJ/m³]
VHTHP very high temperature electric driven mechanical compression heat pump
γ heat capacity ratio [-]
∆T temperature difference [K]
εisentropic isentropic compressor efficiency [-]
η2nd 2nd law efficiency [-]
μ expected value
ρ density [kg/m³]
σ standard deviation
dr driving gradient
h heat sink
l heat source
ng natural gas
NBT normal boiling temperature
oh operation hours
ref reference system
Large-scale heat pumps (> 50 kWth), especially for waste heat recovery and powered by renewable electricity,
are an important and economically promising technology for the disruptive decarbonisation of low temperature
heat demand of industry, commerce, district heating (DH) systems and large communal or residential buildings.
Excess heat is broadly available in industrial plants, and a substantial proportion could be recovered and upgraded
to displace conventional fossil heat generation and to reduce greenhouse gas emissions (GHGE). In comparison to
environmental heat sources (ambient air, near-surface geothermal energy, lake, river or seawater), the temperature
of many excess heat sources is relatively high, which results in an increased heat pump efficiency, reduced
operating costs, and improved competitiveness to conventional fossil fuel-driven heat generators. Sequentially,
several studies stated the high potential of excess heat recovery using heat pumps to supply different industries or
DH systems (see section 1.1). The state of research regarding the technical potential of heat pumps in industry and
DH, market overview and barriers as well as the efficiency assessment of heat pumps is reviewed in the following
sections (Sections 1.1 to 1.4).
1.1 Technical potential of large-scale heat pumps in industry and DH
Due to the oil crises in the 1970s, there was a strong emergence of research work and scientific publications in
the field of large-scale heat pumps in the following years . An example of this is Eder and Moser  describing
suitable applications of heat pumps in industrial plants for drying, evaporation or distillation. They also defined
selection criteria for heat pumps and described economic application possibilities. In the late 1980s, 1990s and
early 2000s, the general interest in this topic weakened again. Due to intensified efforts to decarbonize heat supply,
the attention to large-scale heat pumps is increasing again since the late 2000s. This is confirmed by many
published case studies, of which some are presented below:
The HPTCJ-Institute of Japan investigated the heat recovery potential in the food and beverages industry in
China, USA and nine European Countries. It was found that the usage of heat pumps for heat recovery could save
up to 105 TWh/y of primary energy in total, which equals 15 % of the entire primary energy demand in this
industry in the investigated countries . Almost the same relative technical potential was indicated in another
study that investigated the French food and beverage industry. This study names an absolute technical potential of
15 TWh/a of heat recovery using heat pumps, which also equals 15 % of the industries total energy consumption
. Dupont and Sapora  compared the low temperature excess heat availability (35 – 70 °C) to the heat demand
which could be supplied by heat pumps (60 - 140 °C) for seven further industries in addition to the food and
beverage industry. One of the main findings is that the potential excess heat utilization with heat pumps in food
and beverage, dairy, transport equipment, cement, lime and plaster industries exceeds the low temperature heat
demand by 4 – 31 %.
Besides the internal use of excess heat in industrial or commercial companies, the usage of excess heat to supply
external consumers via DH is seen as a promising option to increase overall efficiency and to reduce GHGE .
Additionally, the role played by large-scale heat pumps in DH utilizing environmental or sewage water heat is
especially important. “Heat Roadmap Europe 4”, a comprehensive study by Paardekooper et al.  on the
economic and ecological share of DH, predicts it will cover around half of Europe’s heating market in 2050. With
a share of 25 % of the whole DH-demand, large-scale heat pumps utilizing environmental or sewage water heat
are seen as the second most important heat generator following biomass or natural gas-fueled combined heat and
power (CHP). This is the fact, although industrial excess heat is not considered as a heat source for heat pumps.
But similar to further studies like Reckzügel et al., which also avoid the high complexity of determining the
low temperature industrial excess heat availability and modelling the resulting potential due to the utilization with
the help of heat pumps, it is stated that this could additionally increase the importance of large-scale heat pumps
in DH significantly. Reasons for this are the high availability of low temperature excess heat sources in urban areas
and the usually higher temperatures of excess heat sources in comparison to environmental or sewage water heat.
1.2 Market overview and barriers
In contrast to the high technical potential of large-scale heat pumps, the overall market penetration is extremely
low. This is especially true for heat pumps in industry. Wolf  lists 38 realized heat pumps in European, five in
Japanese and one in Canadian industry. Laue et al.  describe 115 large-scale heat pump applications in Austria,
Canada, Denmark, Germany, Japan, Korea, the Netherlands and Switzerland of which some are also covered by
Wolf . Most of these heat pumps are internally utilizing waste heat in Industry, but some supply into DH. Still,
the overall share of heat that is provided by heat pumps in the European industry is negligible [9,11].
David et al.  found 149 large-scale heat pumps (> 1 MWth) operated in DH, accounting for a total output
capacity of 1580 MWth. The scope of that work included the EU-28, Norway and Switzerland but large DH-heat
pumps have only been identified in 11 of those countries. With approximately 1 GWth, most of the installed
capacity is located in Sweden and was built in the 1980s. A driver for this was a legal framework that promoted
power to heat because of a temporary surplus in electricity produced by newly-built nuclear power plants.
Following the all-time high of installed heat pump-capacity in the 1980s, the newly installed capacity decreased
in the following decade. Since the turn of the millennium, the yearly installed capacity is increasing again and
mainly located in Finland (155 MWth), Italy (37 MWth), France (23 MWth) and Denmark (20MWth). The temporal
development of installed heat capacity is similar to the development of research work and scientific publications
described in Section 1.1. But even with 149 realized projects in European DH, the potential in this area is far from
There are several barriers for a wider uptake of large-scale heat pumps. The economic conditions for heat pumps
are often unfavorable, which is particularly visible in the high ratio of electricity to gas (or oil) costs in many
countries. In a European comparison, this ratio is particularly high in Germany. One reason for this is the unequal
burden of electricity in comparison to other final energy carriers caused by a levy for the cost of renewable energy
integration. This is largely responsible for the strong reduction of the potential economic share (3.4 %) in
comparison to the potential technical share (23.3 %) of useful heat demand covered by heat pumps in German
industry . For DH-heat pumps, this is practically made clear by the fact that none of the 149 listed heat pumps
in David et al. is located in Germany. Wolf  mentions more than 60 heat pumps in European DH from which
only two are located in Germany. Further reported economic barriers are relatively high payback periods (> 3
years) and cost-intensive integration into existing processes because of the need to customize the design [12–14].
Besides the economic barriers, there are also technical barriers reported. Here, the limitation of the heat sink
temperature and the availability of refrigerants with a low global warming potential (GWP) are often mentioned
[12–14]. At the same time, the technical progress and the resulting progressive debilitation of the technical barriers
are pointed out [9,14].
The third important barrier is about the missing knowledge on the topic of excess heat and heat pumps [12–14].
On the one hand, the quantity of heat demand and emitted excess heat is mostly unknown in companies. In a survey
of 7,288 German companies 86 % were not able to estimate their amount of excess heat On the other hand, the
knowledge of technical options for excess heat utilization is low. 53 % of the surveyed companies rate their
knowledge on this topic as good to very good but 50 % of the companies are still interested in more information.
This goes along with the fact that for projecting a heat pump for excess heat utilization the combined knowledge
on the capabilities of large-scale heat pumps and the process itself is needed; however, energy-managers, -
consultants and decision-makers rarely have this information [12,14]. Additionally, there is a lack of guidelines
and standards, pilot and demonstration systems and training events on the topic of excess heat utilization and large-
scale heat pumps.
1.3 Measuring and publishing of information on heat pump efficiency
One basic parameter to describe the efficiency of a heat pump is the coefficient of performance (COP). The
COP compares the usable heat output to the power input at stationary conditions (see Eq. 1-1). For electric driven
mechanical compression heat pumps (HP), the motive force is electricity and, according to the European Standard
EN 14511-1 , it includes the compressor and all auxiliary facilities like pumps and the control system.
For the measurement and publishing of the COP characteristics, most manufacturers proceed according to the
European Standard EN 14511, which is divided into four parts [15–18]. This standard defines parameters and
respective test-conditions and -methods for technical data sheets of HPs for space heating and -cooling and process
cooling. Since there is no standard available for different applications like process heating or DH, even the
technical information on most HPs, which are dedicated for applications not covered by the EN 14511, are still
tested and published on the basis to this standard with minor variations. The defined parameters include the heat
output and COP at the nominal operating point which is defined by the inlet and outlet temperatures at the
evaporator and condenser at maximum electric power intake (Figure 1). The flow rates of the heat source and sink
at the nominal operating point are a result of the nominal temperatures and the respective heating and cooling
Figure 1: Schematic of nominal test conditions of a HP according to EU Standard EN 14511 [15–18].
The prescribed heat carrier temperatures at the evaporator depend on the heat source temperature (see Table 1).
To meet the requirements of different space heating systems, the condenser temperatures must be chosen out of
four different options.
Table 1: Nominal temperatures for water/water and brine/water HPs according to EN 14511 .
of heat source
of heat sink
The seasonal coefficient of performance (SCOP) puts the seasonal (usually yearly) heat gain in proportion to
the electric energy effort (see Eq. 1-2) and is the crucial parameter to evaluate the efficiency of a projected heat
pump and sets the basis for economic and ecologic evaluation. To calculate the SCOP, detailed knowledge of the
correlation between the COP and all operating conditions occurring during a specific season must be known.
To calculate the SCOP based on the COP-characteristics as well as on the load and temperature profiles, various
methods such as simulation- or spreadsheet-software are used in practice. For more standardized applications like
space heating or domestic hot water supply, there are also simplifying methods like the VDI 4650  available,
which uses correction factors including assumptions on varying load- and temperature-profiles. Since the
temperatures of excess heat sources and process heat sinks are in many cases not influenced by the outside
temperature and any fluctuations in load profiles can be smoothed by thermal energy storages, especially industrial
HPs are often operated under almost constant conditions . In these cases, the SCOP is almost identical to the
COP under the respective operating conditions.
Since the load and temperature profiles can vary strongly from application to application, heat pump
manufacturers can not publish SCOP values which are representative for a broad range of applications. As a result,
it is reasonable to estimate the SCOP based on COP characteristics published by the manufacturers and the load
and temperature profiles for each application individually within the feasibility assessment.
According to the EU Standard EN 14511, technical data sheets which are available in public (e.g. on
manufacturers homepage) usually only contain information on the COP for one or a few nominal operating points.
Information on the COP over an entire operating range is in most cases only available for a limited number of
parties, like engineering offices or plant manufacturers, that have business relations to heat pump manufacturers.
For many applications, the estimation of the COP (or SCOP) and sequentially the undertaking of a feasibility study
is not possible for important practitioners like energy-managers or -consultants. Additionally, most actors in the
field of heat pump surveying have information on the capabilities of heat pumps limited to one or two
manufacturers. Knowledge of the capabilities of the heat pumps over the whole market is rare.
The Guideline 4646 by the Association of German Engineers (VDI), which is currently under development,
aims to close this knowledge gap on the requirements, system design and capabilities of large-scale heat pumps.
It is intended to simplify the preliminary planning for applications in industry, municipal facilities (e.g. swimming
pools), DH and large residential and non-residential buildings. The overall goal is to enable a broad audience to
do a quick feasibility assessment including an ecological and economic evaluation. The fact that no satisfactory
existing feasibility assessment method could be identified within the elaboration of the VDI 4646 was the decisive
point that initiated the development of a new method, which is presented in this work. As a result, the three main
objectives of the study are:
1. Classifying and evaluating the capabilities of market available HPs (see Section 2). For this purpose, a
comprehensive database representing market available HP technologies was assembled and is analyzed. In
that course, the market available HPs are categorized depending on their COP-characteristics.
2. Modelling the correlation between the COP and the operating conditions of the categorized HPs in a
regression analysis (see Section 4). Therefore, new approaches are developed, which are capable of higher
accuracy than the typical approach based on the Carnot-COP and a constant 2nd law efficiency (η2nd).
3. Developing an economic and ecological evaluation method for a HP project based on the derived
mathematical models for estimating the COP (see Section 5). For that purpose, nomograms are developed
comparing the levelized cost of heat (LCOH) and the GHGE resulting from the operation of a HP and a
standard gas boiler (SGB) and depending on the operating conditions.
2. Classification of market-available heat pumps and their capabilities
The market for large-scale heat pumps is complex. The system configuration of the offered heat pumps varies
strongly to meet the requirements of a broad range of applications in the best possible way. To understand the
characteristics and capabilities of the resulting diversity of system configurations would exceed the scope of this
work. A standard system configuration was defined which is intended to represent a greater part of the market for
large-scale heat pumps and the state of technology:
- Electric driven single-stage compression
- Subcritical closed-loop process
- Thermal output: ≥ 50 kWth
- Heat source: brine and water
- Heat sink: water
- Compressor: reciprocating piston, screw, scroll and turbo
(no restrictions concerning open, semi-hermetic or hermetically sealed)
- Refrigerant: azeotrope or quasi azeotrope with negligible temperature glide,
synthetic-organic or natural
- No restrictions on further system design (internal heat exchanger, economizer etc.)
Ten manufacturers have contributed information to this study. Since it was agreed with the manufacturers that
the provided data will only be published anonymously, no names or type designations will be published in this
work. For further evaluation, the gathered information was transferred to a common database. Single operating
points over the whole operating range of each HP were extracted with a minimum step size of 5 K for tl,in and th,out.
Most manufacturers offer different sizes of the same series. For most cases, the COP characteristics of the different
sizes of one series are similar. As a result, only one HP size in the middle of the range of each series was added to
the database. An exemption from this was made for one series. In this series, which is offered with a nominal
thermal output of 0.1 MWth to 0.8 MWth, major (> 10 %) variations in COP for the same operating temperatures
occur between the different sizes. In this case, one HP in the lower and one in the higher thermal output range of
this series was considered. In total, 425 operating points of 29 HPs are included in the database. The nominal heat
output of these HPs ranges from 50 kWth to 1.5 MWth, with focus on the range up to 0.4 MWth. The absolute
thermal output considering all covered operating points ranges between 25 kWth and 1.8 MWth. Additionally, 8
operating points of four HPs (Kobe Steel Kobelco SGH 120, Combitherm HWW R245fa, Ochsner IWWDS ER3b
and Ochsner IWWDS ER3c4), which fit the defined standard configuration, are taken from Arpagaus et al. .
2.1 Operating temperatures
The heat source and sink temperatures of the gathered operating points are illustrated in Figure 2. The clear
focus lies in the conventional operating range (tl,in < 40 °C and th,out < 80 °C), 76 operating points are located in
the high temperature range (40 °C≤ tl,in < 60 °C and/or 80 °C ≤th, out < 100 °C) and 37 in the very high temperature
range (tl,in ≥ 60 °C and/or th,out ≥ 100 °C).
Figure 2: Classification of the operating point database. The classification scheme is adapted from
Arpagaus et al. , which was based on [14,21–24].
Table 2 illustrates the classification of the heat pumps covered in this work. 18 out of 33 HPs only operate in
the conventional source-sink window. An additional seven HPs sit outside the conventional and within the high
temperature operating range. In total, 90 % of the gathered operating points sum under the classifications of
standard (SHP) and high temperature HPs (HTHP). Despite the relatively high number of HPs that operate in the
high and very high temperature ranges (8 out of 33 HPs), less than 10 % of the operating points can be allocated
to very high temperature heat pumps (VHTHP).
Table 2: Classification of heat pumps
Heat pump class
Temperature range of operation
High and very high
Conventional and high
The manufacturers provided information on heat pumps using nine different refrigerants (see Table 3). With 21
out of 33 HPs and 76 % of the operating points, hydrofluorocarbons (HFC) is the most dominant refrigerant class.
Hydrofluoroolefins (HFO) and hydrochlorofluoroolefins (HCFO) have usually a lower GWP and a similarly
advantageous safety classification in comparison to alternative HFC. However, since the manufacturers only
provided information on four HFO-HPs, one HCFO-HP and two HPs using R513A (HFO/HFC-mixture), it can
be concluded that the usage of these refrigerant-classes remains scarce in 2019. R717 (ammonia) is the only natural
refrigerant covered in this work. Based on manufacturers data, 18 operating points from five R717-HPs are
included in the database. Due to the high evaporation enthalpy of R717, this refrigerant is particularly suitable for
high capacities with a compact design and low refrigerant quantities. However, its toxicity and flammability
require special safety measures, which favor use outside residential buildings in large-scale industrial HPs where
tight controls can be implemented. All HP data points covered in this work with a nominal thermal output of more
than 0.8 MW use R717.
The usage of alternative natural refrigerants in large-scale heat pumps with a low GWP and a favorable safety
classification like R718 (water) or R744 (carbon dioxide) is still not state-of-the-art technology in 2019 (R718) or
not covered by this work due to its transcritical operation (R744). Hydrocarbons (HC) like R600 (n-butane) or
R601 (pentane) have a low GWP but are highly flammable. EN 378-1  limits the filling capacity of these HPs
to a maximum of 2.5 kg, making HC inappropriate for large-scale HPs and further explains why no large-scale
commercial HPs use these refrigerants.
Table 3: Refrigerants used by the heat pumps in the database.
*1 GWP for a 100-year time horizon [12,26]
*2 Safety group classification (SG) according to [25,27] and taken from [12,26]
*3 R513A is a mixture of R1234yf (56 %, HFO) and R134a (44 %, HFC) 
2.2.1 Temperature operating range
Figure 3 illustrates the operating temperature range and the maximum temperature lift (∆Tlift) of the nine used
refrigerants. For R513A, R245fa and R1336mzz(E), the operating range and ∆Tlift are equal. For the rest of the
refrigerants, ∆Tlift is smaller than the operating range, probably caused by limitations of the compressor. The
maximum ∆Tlift lies for all but one HP between 60 and 78 K. The HP “Kobe Steel Kobelco SGH 120”  is the
only exception. In a single-stage compression using R245fa, this heat pump reaches a maximum temperature lift
of 95 K by transferring excess heat from 25 °C to 120 °C.
Figure 3: Normal boiling temperature at 1.013 bar (NBT, left end of grey bar) [12,26], minimum tl,in (left
end of red/blue bar), maximum temperature lift (∆Tlift, blue bar), maximum th,out and critical temperature
(tcrit, right end of grey bar) [12,26] of the nine refrigerants.
For subcritical HPs, which are the scope of this work, the maximum th,out is limited by tcrit. Usually, a heat pump
operation below ambient pressure is avoided . Therefore, the lower operating boundary is given through the
normal boiling temperature at 1.013 bar. In Figure 3, the difference between the real operating range and NBT or
tcrit is exemplified. For R410A, R134a, R1234ze(E), R1336mzz(E), R1233zd(E) and R1336mzz(Z), the difference
of tcrit and th,out (∆Tcrit) is 9 to 19 K. When the driving temperature gradient of the condenser (Tdr,h) and a subcooling
is considered, the minimum difference to this upper operating boundary is almost exhausted for these refrigerants.
This is especially true when considering that the COP is particularly low at condensation temperatures (tc) close
to tcrit (Figure 4 (a)) because of the narrowing two-phase area.
∆Tcrit is relatively high for R717 (47 K), R245fa (34 K) and R513A (30 K). This suggests the conclusion that
higher th,out could be reached, which could extend the operating range of the HPs using these refrigerants. For
R513A, this seems to be true but, for R717 and R245fa, there are reasons to explain the relatively high ∆Tcrit:
• R717: The critical pressure is 113 bar . Currently, the maximum achievable pressure for commercial
R717-HTHPs is 76 bar . The maximum th,out recorded in the collected data is 85 °C. If a ∆Tcrit of 10
K is assumed, this equals a condensation pressure (pc) of 57 bar . By limiting the maximum pressure
below what is technically possible, costs can be saved because the construction complexity is reduced.
• R245fa: In a simulation study, Arpagaus et al.  find that R245fa reaches particularly low COP for tc
above of 100 °C. If tc is further increased towards tcrit (154 °C), the COP of R245fa deteriorates even more
compared to nine different refrigerants including R1336mzz(Z), R1233zd(E) and R1234ze(Z). To avoid
an unnecessarily low COP, R245fa is therefore not used to reach th,out above of 120 °C.
Figure 4: Qualitative development of the COP (a), the pressure ratio (pc/p0) (b), the volumetric heating
capacity (VHC) (c), all for a range of condensation temperatures (tc) (adapted from Arpagaus et al. ),
and the isentropic compressor efficiency (εisentropic ) depending on pc/p0 (d) (adapted from Maurer ).
The minimum difference between th,in and NBT (∆TNBT) is for all refrigerants, except R245fa, to be at least
19 K. This is considerably more than what is necessary to ensure sufficient superheating and to consider the driving
temperature gradient of the evaporator (Tdr,l). Among others, there are three practical reasons to explain why ∆TNBT
is relatively high for most refrigerants and why the resulting limitation of the operating range is acceptable:
• The pressure ratio (pc/p0) is increasing when tc is decreasing and ∆Tlift is constant (see Figure 4 (b)). A
pc/p0 in the upper compressor operating range results in a relatively low isentropic compressor efficiency
(εisentropic) (see Figure 4 (d)) and a low COP. The relatively low COP for tc in the lower operating range is
also visible in Figure 4 (a). Additionally, the maximum pressure ratio is technically limited. For instance,
the maximum pc/p0 of reciprocating piston and screw compressors usually lies between 10 and 20 and the
optimum efficiency is around 5 .
• VHC is decreasing when tc is approaching the NBT and ∆Tlift is constant (see Figure 4 (c)). This is
opposed to the fact that a higher VHC is advantageous for reciprocating piston, screw and scroll
compressors because it leads to a smaller size at a given capacity and also to reduced investment costs
•For some refrigerants, the two-phase area in a log(p)-h-diagram is strongly overhanging. As a result, an
relatively increased superheating before suction is required to ensure a dry compression. For instance,
Arpagaus et al.  found that, for R1336mzzz(Z), superheat of 21 K before suction is needed to ensure
superheat of 5 K after compression. In contrast, for other refrigerants like R245fa a superheat obfore
suction of 5 K is sufficient.
∆TNBT is by far the lowest for R245fa (10 K). This can be explained by the fact that that the COP-tc curve for
R245fa is decreasing only slightly when tc approaches NBT . As a result, the operation of R245fa close to the
NBT is advantageous.
2.2.2 Flow and return temperatures
Regarding the difference between flow and return temperature of the heat-sink and –source, most HPs using
HFC, HFO and HCFO are operated following EN 14511-2  (see Figure 5 (a), see also Section 1.3). Almost
half of the operating points of the HPs using these refrigerants are stated with a spread between tl,in and tl,out (∆Tl)
of 3 K, which is mandatory for efficiency measurements at the respective nominal operation point. The spread
between th,in and th,out (∆Th) matches for 82 % of the operating points the nominal spread of 5, 8 or 10 K. For the
measurement of operating points which differ from the nominal ones, the EN 14511-2 also allows varying spreads
if the flow rates are kept at the nominal values. This explains the minor differences resulting from the nominal
Figure 5 (b) illustrates the spreads of HPs using the non-organic natural refrigerant R717. In contrast to the
synthetic-organic refrigerants covered in this work, ∆Tl and particularly ∆Th differ significantly from the nominal
spreads mandated by the EN 14511-2 . An explanation for this is the relatively high heat capacity ratio (γ) of
R717 . As a result, R717 reaches significantly higher temperatures after compression in comparison to the
organic refrigerants covered in this work. For instance, based on a comparison, R717 reaches 138 °C whilst R134a
stays at 42 °C after compression (theoretical dry process, no subcooling after condensation, no superheating after
evaporation, t0 = -30 °C and tc = 30 °C) . By operating R717-HPs with a high ∆Th, the high temperature after
compression can be utilized for efficiency gains. Additionally, a high spread can also be utilized for subcooling
Figure 5: Difference between flow and return temperature of heat-sink and -source according to the
2.3 Compressor type
The manufacturers provided information on HPs using reciprocating piston, screw and scroll compressors. The
distribution of these compressor types is almost balanced among the 33 HPs covered in this work (see Table 4).
Regarding the operating points, scroll compressors are more represented than reciprocating piston or screw
Table 4: Compressor types of heat pumps in the database.
Figure 6 illustrates the operating range and maximum ∆Tlift of the covered compressor types. The scroll
compressors are mainly used in smaller HPs with a nominal heat output between 50 and 170 kWth. The maximum
∆Tlift (70 K) and maximum th,out (82 °C) are the lowest among the three covered compressor types but are sufficient
for the intended utilization of environmental heat (near-surface geothermal energy, lake, river or seawater) in large
residential buildings or small companies.
When considering only organic refrigerants, HPs using screw compressors are covering the largest nominal
thermal output range (0.2 – 0.8 MWth) and are designed for versatile applications with heat sink temperatures up
to 120 °C. Screw compressors manage the highest single-stage ∆Tlift (95 K) among the covered HPs. Reciprocating
piston compressors are used in HPs with organic refrigerants with a nominal thermal capacity ranging from 50
kWth to 0.4 MWth. The HPs using this compressor type are reaching the highest heat sink temperatures (160 °C)
and medium ∆Tlift (78 K). Both, screw and reciprocating compressors are employed in R717-HPs to reach heat
outputs of more than 1 MW.
Figure 6: Minimum tl,in (left end of the red bar), maximum ∆Tlift (blue bar) and maximum th,out (right end
of the red bar) of the three compressor types.
Figure 7 visualizes the dependency of the COP on ∆Tlift for three different HP-categories which reveal clear
differences between the indicated COP curves. These categories were derived based on variances in refrigerants,
plant sizes, operation and data availability described in the previous sections and summarized below. Due to the
clear differences, these categories will be considered separately in the further course of this work.
• SHPs & HTHPs with HFC and/or HFO:
A wide range of HPs is offered in various sizes with heating supply up to 0.8 MWth and th,out up to
100°C by different manufacturers. These HPs are often produced in product series and are available
from standard stock. Due to the larger quantities sold by these HPs, manufacturers often prepare
detailed information such as planning manuals including detailed COP characteristics covering the
entire operating range. More than half (20 out of 33 HPs) of HPs and 86 % of the operating point fit
into this category. Additionally, the operation of HPs in this category is strongly oriented to the
EN14511 (see Section 2.2.2) and the distribution of nominal HP-sizes is reasonably balanced over the
whole range (50 kWth to 0.8 MWth) but has a focus to the lower and middle sizes up to 0.4 MWth. The
homogeneity of this class is also reflected in the efficiency which is illustrated in Figure 7. There is a
clear correlation between COP and ∆Tlift with a small range of variation and no obvious outliers. This
category represents the state of technology and the largest part of the market for large-scale HPs.
• VHTHPs with HCFO, HFC or HFO:
The range of VHTHPs offered is still relatively small with rarely established stock-standard solutions
by the manufacturers. Because manufacturers usually provision these HPs individually, they do not
prepare comprehensive planning manuals for resellers or plant engineers. As a result, the
manufacturers only provided information on five VHTHPs. Additionally, the database was
complemented by three VHTHPs from the literature . Eventually, 10 % of the operating points
could be accumulated in this category. Although the operation is also oriented to the EN 14511 (see
Section 2.2.2) and the offered sizes, used refrigerants and compressors types are similar to the category
listed above, the COP of VHTHPs is higher for ∆Tlift in the upper range (see Figure 7).
•SHPs & HTHPs with R717:
The properties of R717 differ from the organic refrigerants covered in this work (see Section 2.2).
R717 is used in particularly large-scale HPs which are operated with significantly higher ∆Th.
Additionally, the COP of the R717 operating points is noticeable above the remaining HPs (see Figure
7). Whether this is caused through differences in system design, operation, size or by another reason
cannot be answered based on the present data. Similar to the case of VHTHPs and due to the large-
scale, these HPs are usually built to meet an individual specification. No implementation manuals are
available and only 4 % of the operating points belong to this category.
Figure 7: COP depending on ∆Tlift for three different HP-categories.
The system configuration of the HPs within the three identified categories is still versatile. The HPs are partly
equipped with internal heat exchangers, economizers, different refrigerants or compressor types. Therefore, the
following sections examine whether a further subdivision into subcategories within three main categories is
reasonable. This is exemplified by the category SHP & HTHP with HFC and/or HFO.
In total, five different organic refrigerants (Figure 8) and three different compressor types (Figure 9) are used.
Among the five refrigerants, the COP of R513A and R1234ze(E) is particularly low for small and medium ∆Tlift
while R410A and R134a are more advantageous in this range. In the upper operating range, this pattern is not
observed as no refrigerant shows a clear advantage. The COP of R245fa is for small ∆Tlift relatively low but is the
highest for 30 K ≤ ∆Tlift ≤ 60 K.
Figure 8: COP depending on ∆Tlift for SHPs & HTHPs, highlighting the refrigerants
18.104.22.168 Compressor type
In general, differences of the efficiency between the various compressor types are marginal. Still, the COP of
HPs using screw compressors tends for the whole operating range to be slightly higher than the COP of scroll-
HPs. HPs using reciprocating piston compressors show small disadvantages for low ∆Tlift and small advantages
for ∆Tlift in the higher operating range. Nevertheless, all three types are overlapping and no clear advantage of one
type is recognizable.
It can be summarized that there are differences between refrigerants and compressors regarding the COP but,
in most cases, these differences exist for a few operational conditions and are not applicable for the whole operating
range. The same belongs to further differences in system design. For instance, some HPs are equipped with internal
heat exchangers or economizers but no systematic differences concerning the COP are discernible. Therefore, no
further categorization by system configuration is made and the scope of the mathematical models developed in
Section 4 covers the three HP-categories defined in Section 2.4.
Figure 9: COP depending on ∆Tlift for SHPs & HTHPs, highlighting the compressor type
In Section 2, the database, which is the base of this work, was presented and analyzed. In the further course of
this work, the categorized database is used to mathematically model the correlation between the operating
conditions of HPs and the COP. These models are used to derive a methodology for a quick feasibility assessment
including economic and ecological evaluation. The methodology used for these purposes is presented below.
3.1 Regression analysis
Sections 4.1.1 to 4.1.3 present a regression analysis using the method of the least-squares approximation.
Several theoretical, semi-empirical and empirical approaches to estimate the COP for the HP-category SHPs &
HTHPs with HFC and/or HFO are derived. This approximation aims to reduce the residuals (deviations) between
the estimated COP and the real COP calculated with the help of the different approaches or given by the gathered
operating points, respectively. All examined approaches are evaluated individually. Therefore, important statistical
indicators like the standard deviation (σ) and the coefficient of determination (R²) are used. Additionally, the
correlation between the real COP and the estimated COP as well as the distribution of residuals are illustrated and
The development of the approaches starts with a theoretical approach based on the Carnot-COP. To increase
the quality of regression, the development of the following approaches successively incorporates the results of the
evaluations of the previous.
Finally, a recommendation for one of the derived approaches is made (see Section 4.1.4). Therefore, the results
from the individual evaluations as well as the trends of the estimated COP and the trend of η2nd derived from the
estimated COP are illustrated and compared. In addition, for a plausibility check, these trends are compared to the
literature as well as to the expected trend based on a statistical evaluation of the gathered operating points. In
Sections 4.2 and 4.3, the previously presented methodology of the regression analysis for SHPs and HTHPs is
transferred to the other two derived HP-categories (VHTHPs and R717-HPs).
3.2 Economic and ecological evaluation
High accuracy of the COP estimation is a prerequisite for a reliable feasibility assessment of heat pump
applications regarding their economic and ecological efficiency compared to conventional reference systems
facing the knowledge gap on meaningful application possibilities of stakeholders, especially decision-makers. Heat
pumps are often designed for stationary nominal operating conditions. Non-continuous process behavior can be
smoothed by thermal energy storage. For this reason, the evaluation of an implementation based on the stationary
COP at full load compared to the considerable effort of a dynamic simulation of a SCOP using software tools is
an appropriate compromise. During the detailed planning phase, the SCOP is than to be estimated by the load and
temperature profiles for each application individually.
To gain an impression of how important the accurate assessment of a COP is for the design and evaluation of
economic and environmental efficiency compared to a reference system, and what other framework conditions
influence the efficiency, a comparison is made based on a nomogram. A nomogram enables the approximate
reading of key performance metrics through the graphic representation of mathematical functions.
3.2.1 Economic evaluation
Economic efficiency describes the ratio between profit and the effort required to achieve it. Wolf et al 
provide a graphical orientation aid with a nomogram that shows the economic efficiency of a heat pump as a
function of a constant η2nd, ∆Tlift and final energy price ratio of electricity to natural gas cel/cng compared to a
common reference system, based on a standard gas boiler (SGB). Arpagaus  indicates the range of possible η2nd
between 0.4 and 0.6 with a typical value of 0.45, which is also confirmed by the results of this work, shown in
Figure 11. The economic operation of heat pumps depends on cel/cref,fu and the reference system efficiency ηref and
is given for the fulfilment of Eq. 6-1 which is taken from Schlosser et al. :
To make a sound investment decision between the two systems, investment ratios, depreciation period and
interest-rate factor q must be considered. VDI 2067  explains the calculation of LCOH of technical building
equipment based on the annuity method. Annuity, A, contains capital-related costs (Ccap), operation-related costs
(Cop) and demand-related costs (Cdem).
The annuity factor combines one-off investment costs, CI, and current payments and distributes the net present
value of an investment with a calculation interest-rate factor q over the depreciation period N.
Here, price rises represented by the price dynamic cash value factor bi is neglected due to the uncertainty of
price inflation that is strongly influenced by both policy and economic climate. In this case, bi is the inverse of a
and the product a x b is equal to 1. The factor fm,C affects the Cop considering maintenance costs. Cdem for the yearly
heat gain arises as a function of the final energy costs for a corresponding fuel and the efficiency η of the
concerned conversion technology. The yearly heat demand is calculated by integrating a constant over the
operating hours toh. The LCOH is the ratio of annuity to annual reference energy demand Qdem.
To determine the cost parity (LCOEHP = LCOEref) for a heat pump compared to a SGB, the LCOHHP and
LCOHSGB are equated (LCOEHP/LCOESGB,ng =1) for the same heat demand over different cel/cng. The nomogram
displays cost ratios LCOEHP/LCOESGB,ng for different ∆Tlift and cel/cng. ∆Tlift influences the COP regression
function underlying the nomogram as η in Eq. 3-2. Since the standard deviation also records possible efficiencies
below and above the regression the sensitive range (COP regression ± σ) must be specified for a sensitive
assessment of possible economic viabilities.
3.2.2 Ecological evaluation
The ecological nomogram is based on the same principle, representing the ecological efficiency in terms of
GHGE. GHGE correspond to the specific emissions of CO2-equivalents (CO2-e) per consumed quantity of final
energy source. Within this framework, only energy-related GHGE during operation and not upstream and
downstream emissions are taken into account. The ecological feasibility depends on the ratio of emission factors
(EF) EFelgrid/EFfu,ref of the electricity grid and the reference system fuel.
Since the EFng, as the reference fuel used in this case, is physically constant the nomogram displays the cost
ratio GHGEHP/GHGESGB,ng for different ∆Tlift and EFel,grid. Analogous to 3.2.1, the COP function is specified in its
4. Heat pump model development through regression analysis
Section 4.1 presents a detailed regression analysis to mathematical model the correlation between the COP and
the operating conditions of SHPs & HTHPs with HFC and/or HFO. Sections 4.2 and 4.3 are building upon this
and transferring the derived models to VHTHPs with HCFO, HFC or HFO as well as to SHPs and HTHPs with
4.1 Standard and high temperature heat pumps with organic refrigerants
In the following different mathematical approaches to estimate the COP of a SHPs or HTHPs with organic
refrigerants for any possible operation point within the given operation range are presented (see Sections 4.1.1 to
4.1.3), compared and a recommendation for one of these regressions is made (see Section 4.1.4 ).
4.1.1 Theoretical approach
The scope of this work covers subcritical HPs which use refrigerants without a temperature glide. The
anticlockwise Carnot process is the comparison process for these HPs. According to the 2nd law of
thermodynamics, the COP cannot exceed the Carnot-COP (see Eq. 4-1).
η2nd compares the real COP of a HP and the Carnot-COP (see Eq. 4-2). In many feasibility assessments, the
assumption is made that η2nd is constant over the entire operating range. Depending on the type of HP, different
values are given in the literature. For instance, van de Bor and Infante Ferreira  suggest 0.5 for industrial HPs
in general. Wolf  recommends 0.45 to 0.50 for industrial water/water-HPs and 0.35 to 0.40 for industrial
air/water-HPs. Arpagaus et. al.  recommend 0.45 for industrial water/water and water/steam HTHPs and
In practice, most heat sources and sinks provide or respectively use sensible heat. Thus, the heat source (Tl) and
sink (Th) temperatures are not constant when heat is transferred to or from the HP. In contrast to this, the Carnot
process requires constant source and sink temperatures. To get closer to the Carnot process and achieve a high
COP, ∆Th and ∆Tl are usually chosen to be as small as practicable (see Sections 2.2.1 and 2.2.2). If this condition
is met, ∆Th and ∆Tl are usually ignored. Based on this, Eq. 4-3 can be used to estimate the COP.
The resulting η2nd (see Table 5) from the regression analyses corresponds to the values from the literature listed
above. Figure 10 (a) illustrates the quality of this approximation. With a perfect regression, all points would lie on
the bisector between the estimated COP and the real COP and R² would be 1. In contrast to that, the real regression
shows a variance and a localized bias. While for low COP the real value and estimation are almost equal with low
variance, there is a notable negative bias for medium COP and a distinct positive bias for COP in the upper range.
Figure 10 (b) visualizes the distribution of the residuals. As the primary peak of the distribution lies in the
negative values and a second peak in the positive residuals (> 0.95), the localized bias of the estimation is
recognizable. Globally, the expected value (μ) is 0.00 and σ is 0.80.
Figure 10: - comparison of estimated COP and real COP (a) and frequency
distribution of the residuals (b)
As shown above, the usage of a constant η2nd for estimating the COP leads to a bias. As a result, η2nd must be
varying for operating conditions. To visualize this, Figure 11 presents a boxplot of η2nd for ascending sorted
categories of ∆Tlift. At first, η2nd rises strongly, reaches its maximum at 35 K ≤ ∆Tlift <45 K and then drops
relatively weakly down again. The median of η2nd ranges for the depicted ∆Tlift-categories from 0.25 to 0.49.
Consequentially, the assumption of a constant η2nd is only conditionally suitable for the COP-estimation.The trend
which is discernible in Figure 11 strongly reminds to Figure 4 (d). As εisentropic is a major influence on the COP and
pc/p0 is strongly correlated to ∆Tlift, it is logical that these trends have a similar appearance.
Figure 11: Boxplot of η2nd for classified ∆Tlift
4.1.2 Semi-empirical extensions of the theoretical approach
Second law efficiency, η2nd, includes all efficiency losses of a HP which occur in a certain operating point. The
largest share of losses can be attributed to one of the following causes [33,35]:
- Compressor efficiency
- Heat losses to the environment
- Pressure drop
- Temperature driving forces at heat exchangers (condenser/ evaporator)
- Throttling losses
As already mentioned, the Carnot process is based on constant source and sink temperatures. Furthermore, the
Carnot process ignores temperature difference between Th and Tc as well as between Tl and T0. To consider that
the difference between T0 and Tc is larger than ∆Tlift, Eq. 4-3 can be extended by a constant factor Tdr (see Eq. 4-
4). To reduce the number of fit-parameters and to prevent overfitting, Tdr is assumed to be equal for condenser and
evaporator. However, other influences like superheating or subcooling which may enlarge the difference between
Th and Tc or Tl and T0 cannot be excluded when Tdr is fitted. According to the VDMA 24247-2 guideline , ηKC
is intended to include all further loss mechanisms besides the temperature driving forces.
Figure 12 visualizes the quality of the regression of Eq. 4-4 to the operating points. In comparison to Eq. 4-3
(see Table 5) σ has almost been halved and R² was significantly increased from 0.78 to 0.89. Still, the same pattern
of locally occurring bias is recognizable: Low COP values are slightly overestimated, medium COP are
underestimated and COP values in the upper range are strongly overestimated (see Figure 10).
Figure 12: - comparison of estimated COP and real COP
(a) and frequency distribution of the residuals (b)
Eq. 4-5 provides a further extension of Eq. 4-3. By adding an exponent to both, the two main influencing
variables of the Carnot-COP, ∆Tlift and Th, out, can be weighted differently.
When fitting Eq. 4-5 to the operating points, R² and σ are slightly poorer in comparison to Eq. 4-4. Additionally,
the same pattern of localized bias occurs (see Figure 13 (a)). However, besides a few extreme outliers in the upper
COP range, the general deviation appears to be smaller. The outliers all result for operating points with a ∆Tlift of
10 K and overestimate the COP by more than two. When these outliers are ignored, a nearly normal distribution
of residuals is recognizable around a residual of zero, as shown in Figure 13 (b).
Figure 13: - comparison of estimated COP and real COP (a) and frequency
distribution of the residuals (b)
The regression parameter c is fitted with 0.01, which means that the absolute temperature does not affect the
COP. To further simplify Eq 4-5, a second fit with a given c = 0 was done. All parameters describing the quality
of regression are almost similar for both fits. Differences can be identified at the fourth significant digit. For this
work, only the second fit (c = 0) is presented (see Table 5).
The fact that the absolute temperature has practically no influence on the COP of real HPs stands in sharp
contrast to the theoretical approach based on the Carnot-COP, what is illustrated in Figure 14. While the result of
Eq. 4-3 (η2nd∙COPCarnot) rises for all ∆Tlift and especially for low ∆Tlift, the trends of the real COP are almost constant
when th,out is rising. A possible way to explain this behavior is presented below:
Figure 14: Comparison of the theoretical and practical influence of the absolute temperature on the COP
for constant ∆Tlift. Notes: the dotted lines is Eq. 4-3 with η2nd=0.45; straight lines are the linear trend of the
several groups of operating points with constant ∆Tlift; and, to improve the clarity only a selection of data is
Although the absolute deviation of the real COP between the individual HPs is low, it is quite high in
comparison to the theoretical rise of the COP. Therefore, the theoretical increase of the COP, if it does occur for
individual heat pumps, is difficult to detect. Furthermore, the COP of real HPs is influenced by various refrigerant
properties. Many of these properties are affected by the absolute temperature. For instance, the absolute pressure,
pressure ratio, heat capacity ratio, density and volumetric heating capacity are to be named. The resulting
correlation between the COP and the absolute temperature for a constant ∆Tlift is schematically illustrated in Figure
4 (a). HPs are usually operated close to the COP peak if possible. On the left side of this optimum, an increase of
the absolute temperature leads to a higher COP, which then peaks and begins to decrease with further absolute
temperature increments. The relationship between absolute temperature and COP for a fixed ∆Tlift is a
characteristic of the refrigerant, such that different refrigerants peak at different temperatures. The different
temperature-COP relationships make it difficult to develop a single correlation for all refrigerants and all
underlying operating points.
Eq. 4-6.1 combines the approaches of Eq. 4-4 and Eq. 4-5 into one equation. According to Eq. 4-5, c is set to
zero without a significant loss of accuracy and b is limited to -1 ≤ b ≤ 1. Without this limit, the regression
parameters are fitted with values that are not physically reasonable (see Eq. 4-6.2 in Table 5), which does not
follow the semi-empirical approach. Nevertheless, when comparing the values of Tdr for Eq. 4-4 and Eq. 4-5 (see
Table 5) major differences occur. Therefore, it must be assumed that the value of Tdr is mainly influenced by the
respective mathematical equation and should not be physically interpreted or used for any kind of technical
The quality of regression, which can be reached with Eq. 4-6.1, is the best so far. Still, a localized bias is visible
in Figure 15 (a). Even if the operating points with very high COP (∆Tlift = 10 K) are ignored, low and high COP
values are overestimated and medium COPs are underestimated. The same applies to the distribution of the
residuals (see Figure 15 (b)). Although the residuals are almost normally distributed, the main peak is shifted to
negative values and a second peak is visible for very high positive residuals (> 0.95), which results from the
operating points with ∆Tlift = 10 K.
Figure 15: – a comparison of estimated COP and real COP
(a) and frequency distribution of the residuals (b).
4.1.3 Empirical approaches
As the theoretical and semi-empirical approaches struggle to adequately model the correlation between the
operating temperatures and the COP without a bias, new empirical approaches are developed in this section. In the
first step, the limitation of the exponents of Eq. 4-6.1 is removed. In doing so, the fitting parameters are not
physically representative anymore and are renamed (see Eq. 4-6.2). Additionally, and similar to Eq. 4-5 and 4-6.1,
the exponent of the second brackets (d) of Eq. 4-6.2 is set to zero without a significant loss of accuracy.
The removal of the limitation of the fit parameter c leads to significant improvement in the quality of regression
in comparison to all previous approaches. The bias of the estimation almost completely disappears (Figure 16).
Only the very high COP for operating points with ∆Tlift = 10 K tend to continue to be overestimated. However, the
overestimation of the COP of these operating points is significantly reduced but is still > 0.95 for some of these
points. The substantially increased quality of regression is also underlined by the improved R² and σ (Table 5).
Figure 16: – a comparison of estimated COP and real COP (a)
and frequency distribution of the residuals (b).
Besides the power function (Eq. 4-6.2) that was derived from the semi-empirical approaches, several further
empirical approaches were tested to see if a further increase in accuracy can be reached. The most promising of
these are outlined in the following. As shown above, there is no significant correlation between Th,out and the COP
within the examined HP category. Eq. 4-7 and Eq. 4-8 do not include a factor to consider the absolute temperature.
Eq. 4-7 is an exponential function with the base e. The advantage of this equation is the small number of two fit
parameters, which keeps the equation simple and prevents overfitting. Eq. 3.8 is a polynomial function of degree
two. A polynomial of a higher degree is avoided to prevent an inflection point which would not fit the general
trend of the COP (Figure 8 or Figure 9).
Both equations lead to a quality of regression almost identical to Eq. 4-6.2. This becomes visible by comparison
of R² and σ (Table 5). Graphical illustrations of the quality of regression of Eq. 4-7 and Eq. 4-8 according to Figure
16 do not show any significant differences and are therefore not included in this work.
Table 5: Regression analysis for SHPs and HTHPs with HFC and HFO (all values are inserted unitless).
4.1.4 Comparison and recommendation
The empirical approaches, in comparison to the semi-empirical and theoretical approaches, achieve
significantly better R² and σ values (see Table 5). There are only marginal differences between the three empirical
approaches. With the help of these approaches, the COP of a SHP or HTHP within the given temperature range
can be estimated with a σ of less than 0.3 and an R² of 0.96.
Figure 17 visualizes the COP-estimation of all approaches presented in the previous. The standard deviations
of the respective trends are not pictured but should be considered when the COP of a projected HP is estimated.
The empirical approaches result in an almost linear trend that is slightly curved and fits the operating points well.
In contrast to that, the theoretical and semi-empirical approaches result in a more strongly curved trend which
causes the locally changing bias described in Sections 4.1.1 and 4.1.2.
Figure 18 visualizes the trend of η2nd which is calculated for a constant th,out of 60 °C. This figure illustrates the
deviations between the different approaches, which are not visible in Figure 17 due to the scaling which is
necessary to visualize the whole operating range. This is especially true when considering the upper end of the
∆Tlift-range where the maximum deviation between the approaches is 0.7 but the absolute COP is approximately
Figure 17: COP-estimation for different approaches. Notes: if the respective equation includes th, out, a
value of th,out = 60 °C is used; and, to keep the graph clear, the illustration of σ is omitted.
The theoretical and semi-empirical approaches lead to a constant or monotonically rising trend of η2nd. This
contradicts the previous finding that η2nd has a maximum for medium ∆Tlift after which declines for further rising
∆Tlift (see Section 4.1.1). This underlines the conclusion that the theoretical and semi-empirical approaches are not
appropriate for estimating the COP.
In contrast to the theoretical and semi-empirical approaches, the empirical approaches show a maximum of η2nd
for medium ∆Tlift and are in line with the expected trend derived from the literature and also the real trend which
is visible in the boxplot of η2nd (see Section 4.1.1.). For Eq. 4-8, a minimum occurs for a ∆Tlift of approximately
66 °C, which is not reasonable and suggests an overfitting of this equation. As a result, only the trends of Eq. 4-
6.2 and Eq. 4-7 are fully plausible.
Figure 18: η2nd-estimation for different approaches. Notes: th,out = 60 °C is used for estimation of COP (if
necessary) and COPCarnot; and, to keep the graph clear, the illustration of σ is omitted.
When comparing all previous findings, Eq. 4-6.2 and Eq. 4-7 have little discernible difference. The trends of
both equations are almost congruent for low and medium ∆Tlift, showing only a minor deviation in the upper range.
As a result, both equations are appropriate for estimating the COP of SHPs and HTHPs with HFC and/or HFO
which are represented in this section. When using this equation to fit another group of HPs, Eq. 4-6.2 could show
advantages because it includes a factor to consider the influence of th,out. If fewer refrigerants or more similar
refrigerants concerning the COP-optimum are used by the respective HPs, the influence of th,out should be more
relevant than was shown for the HPs covered in this section (see aslo Section 4.1.2).
4.2 Very high temperature heat pumps
In comparison to SHPs and HTHPs, the COP of the VHTHPs with organic refrigerants (HCFO, HFC or HFO)
is on a similar level in the lower ∆Tlift-range and shows relative advantages in the upper ∆Tlift-range. Some of the
VHTHPs covered in this work are designed to allow especially high single-staged ∆Tlift of up to 95 K. These HP
use individually developed compressors which can handle higher absolute pressures and higher pc/p0 in comparison
to the compressors operated in the remaining HPs (see Figure 4 (d)). The isentropic compressor efficiency optimum
is also shifted to higher pc/p0, which explains why the COP of VHTHPs decreases less when ∆Tlift is increased.
However, it must also be considered that the absolute operating temperatures of the VHTHPs are significantly
higher in comparison to SHPs and HTHPs. Consequently, the fitted value of η2nd of the VHTHPs is slightly lower
in comparison to SHPs and HTHPs (η2nd Table 6 and Table 7).
Figure 19: COP-estimation for different approaches. Notes: if the respective equation includes th, out, a
value of th,out = 130 °C is used; and, to keep the graph clear, the illustration of σ is omitted.
In contrast to the more diverse HP-category examined in Section 4.1, the influence of the absolute temperature
on the COP is relevant for the HPs considered here. This is made clear by the fact that the parameter c in Eq. 4-5,
4-6.1 and 4-6.2 is fitted with a value not equal to zero (see Table 6). Additionally, Eq. 4-7 and Eq. 4-8, which do
not include a factor to consider th,out, result in the least favorable quality of regression. This is probably because
the refrigerants, which are covered here, have similar operating zones. As a result, the COP-characteristics of the
refrigerants are more congruent and a correlation between the COP and the absolute temperature can be derived
for this HP-category (compare to Section 4.1.2).
The trends of all approaches are almost congruent for VHTHPs (Figure 19). For the upper and lower end of the
∆Tlift-range, minor deviations between some of the approaches are visible which also cause minor differences in
the quality of regression. Eq. 4-6.1 and Eq. 4-6.2 are completely identical fitted. Additionally, the trends and
quality of regression of Eq. 4-4, Eq. 4-6.1 and Eq. 4-6.2 are completely identical. Therefore, these three approaches
are recommended for the estimation of the COP for this HP-category and the given range of validity. However, it
must be considered that the upper and lower ∆Tlift-range is crucial to show differences in the quality of regression
(see Section 4.1), but only a few operating points below a ∆Tlift of 35 K and above of 65 K, while no operating
points below a ∆Tlift of 25 K are covered. As a result, the validity of the regression analysis in the upper and lower
∆Tlift-range is low. If more operating points in the lower and upper ∆Tlift-range could be gathered, the assumption
is reasonable that the COP-trend of these would be similar compared to SHPs and HTHPs, and Eq. 4-6.2 would
be most advantageous.
Table 6: Regression analysis for VHTHPs with HCFO, HFC or HFO (all inserted values are unitless).
Eq. 4-6.1 = Eq. 4-6.2
4.3 R717-heat pumps
This HP-category covers only 18 operating points from five different SHPs or HTHPs that use the natural
refrigerant ammonia (R717). The range of validity and the validity of the regression analysis presented in the
following are limited. Major differences of the COP of these HPs in comparison to HPs using HFC and/or HFO
can be observed (Figure 20). The COP of most R717-operating points is clearly above of the COP of SHPs and
HTHPs with HFC and/or HFO. But, as the operation of all R717-HPs covered in this work differs strongly from
the rest of the HPs (see Section 2.2.2), no conclusion on a general advantage of this refrigerant in terms of
efficiency can be drawn. Furthermore, the thermal output range of the covered R717-HPs is significantly larger
than that of the rest of the HPs. As a result, the cost-benefit of R717-HPs, which results from scale effects, could
lead to specifically larger designed components and what could be another reason for the relatively increased COP.
Figure 20: COP-estimation for different approaches. Notes: if the respective equation includes th, out, a
value of th,out = 80 °C is used; and, to keep the graph clear, the illustration of σ is omitted.
In contrast to the HPs examined in Section 4.1 and similar to the ones examined in Section 4.2, the influence of
the absolute temperature on the COP is relevant for R717-HPs (see Table 7). The conclusion that this correlation
becomes visible only for a group of HPs using refrigerants with similar COP characteristics is strengthened.
The trends of all approaches for estimating the COP of R717-HPs are almost congruent (Figure 20).
Additionally, when comparing the quality of regression of these approaches, no significant difference is detectable
(Table 7). This will probably be caused due to the low number of operating points. Moreover, as seen in Section
4.1 the largest absolute deviations between the different approaches appear within the ∆Tlift-range below 30 K.
The fact that no operating points of R717-HPs in the lower ∆Tlift-range are covered in this work will additionally
cause similar regression-quality of all approaches. Although no advantage of one approach for estimating the COP
can be proved within this HP-category, Eq. 4-6.2 is recommended because it shows advantages in section 4.1 and
Table 7: Regression analysis for SHPs & HTHPs with R717 (all inserted values are unitless).
5. Economic and ecological evaluation
The recommended mathematical model Eq. 4-6.2 is used for comparison of LCOH and GHGE for different
operating conditions at cost parity of HP and a conventional reference system represented by a SGB. As Eq. 4-6.2
is independent of the absolute sink temperature, the nomogram (see Figure 21) is valid for the whole range of
validity of SHPs and HTHPs with HFC and/or HFO (see Table 5). The lines illustrating the standard deviation
(Eq. 4-6.2 ± σ) record the possible range of variation. This can be used in terms of a sensitive assessment of
possible economic and ecological viabilities.
Since 60 °C is in the middle of the validity range, it is selected as the sink temperature for calculating the 2nd
law efficiency curves for constant η2nd. To demonstrate the influence of η2nd, the parity curves based on 2nd law
efficiencies of 0.3, 0.45 and 0.6 are delineated.
5.1 Economic evaluation
Figure 21 illustrates ratios LCOEHP/LCOES GB,ng based on 3-2 to 3-4 and depending on different ∆Tlift and cel/cng.
The model parameters are summarized in Table 8:
Table 8: Selected nomogram parameters.
CI (incl. integration; without planning)
420 €/kWth (300 kW)
60 €/kWth (300 kW)
Operating hours toh
Interest-rate factor q
Depreciation period N
Maintenance factor fm,C
Full load efficiency η100
0.96 (300 kW)
Not surprisingly, the localized bias of Eq. 4-3 (see section 4.1) is also reflected in Figure 21. While the mean
2nd law efficiency parity curve (η2nd = 0.45) underestimates the economic efficiency in the range of 30 to 65 K, it
overestimates the regression parity curve (4-6.2) for small (<30 K) and larger (>65 K) ∆Tlift.
Figure 21: Nomogram of cost parity between SHP or HTHP and SGB for different ∆Tlift and cel/cref..
The price ratio has a major impact on profitability. The grey-dotted lines represent country-specific price ratios
for the second half of 2018 considering all taxes and levies for consumption of electricity between 500 and 2000
MWh and of natural gas between 2778 MWh and 27,780 MWh. For non-electricity-intensive industrial companies
in Germany (cel/cng = 5.3), only implementations below a ∆Tlift of 15 K are economically recommended. The
European average price ratio is 3.9:1, which allows economic integration concepts for ∆Tlift up to 25 K. In the
Netherlands (2.7:1), Austria (3:1) or France (2.3:1), economical HP integration is possible up to a ∆Tlift of
approximately 40 K. In Sweden (1.1:1), almost the whole technically ∆Tlift range is economically suitable .
Unfortunately, a two-dimensional nomogram represents only a small selection of general conditions. Besides
the COP and the price ratio, the depreciation period, interest rate, investment costs and especially the operating
hours influence the economic efficiency .
5.2 Ecological evaluation
In Figure 22, the GHGE of SGB and HP are compared using the developed method for COP estimation or
respectively a constant full load efficiency (Table 8). The average German EFel,grid electricity mix is 474 gCO2-
e/kWh in 2018 and EFng is approximated by constant 202 gCO2-e/kWh . Additionally, a possible future value
of EFel,grid is depicted by considering the climate protection scenario 95 (CPS95) that involves the reduction of
GHGE by 95 % till 2050 compared to 1990 [39,40].
Already in 2018, a ∆Tlift of up to 60 K is ecologically reasonable in Germany. Based on the depicted scenario
of a progressive decarbonisation of electricity, all future SHP or HTHP projects will be ecologically advantageous
compared to the SGB by 2030 at the latest.
Figure 22: Nomogram of GHGE parity between SHP or HTHP and SGB for different ∆Tlift and
Large-scale HPs (> 50 kWth) are an essential technology for the decarbonisation of the heat supply of industry,
commerce and DH. Nevertheless, an information deficit on the capabilities of this technology is existing amongst
important practitioners like energy-managers, and -consultants. To close this knowledge Gap, the capabilities of
market available HPs are assessed within this work based on a comprehensive HP database. Especially for heat
sink temperatures of up to 100 °C, the variety of available heat pumps from various manufacturers is particularly
large. In this range, the offered HPs are covering a heat output from 50 kWth up to several 1 MWth and the options
of different system configurations, for instance concerning the usage of low GWP refrigerants, are versatile. Still,
HPs using HFC with a relatively high GWP like R134a dominate the HP-market. HPs designed for heat sink
temperatures of more than 100 °C up to 160 °C are less frequently offered but are also available. Regarding
differences of the COP-characteristics of the evaluated HPs, a categorization concerning the designated range of
Th,out and ∆Th, which is depending on the refrigerant type (synthetic-organic or natural), is reasonable. A further
characterization using criteria like compressor type or the specific refrigerant within the respective refrigerant-
class does not reveal any significant differences of the COP characteristics.
The correlation between the efficiency and the operating conditions of market available HPs is also a crucial
point, for which usually insufficient information is available among practitioners. The efficiency of a HP is usually
published by manufactures by specifying the COP at a nominal operating point. Since in most cases the real
operating conditions deviate from the published nominal operating point, the COP is usually estimated based on
the Carnot-COP and η2nd. Depending on the heat source and sink medium, η2nd-values ranging from 0.35 to 0.6
can be found in literature and are assumed to be constant over the whole operating range. In contrast to that, the
evaluation of the assembled database reveals that η2nd is not constant as it is ranging from roughly 0.25 to 0.5
depending on ∆Tlift, even though only water as the heat source and sink medium is covered. Within the regression
analysis, the correlation of the operating conditions and the COP of a HP was modelled. As R² is increased from
0.78 to 0.96 and σ is reduced from 0.80 to 0.28, the newly developed model is significantly more accurate and
additionally eliminates a bias which is occurring when the COP is estimated based on Carnot-COP and a constant
η2nd. This bias leads to the fact that the economic and ecologically reasonability of HP projects is strongly
overestimated for ∆Tlift in the lower range of up to 30 K, underestimated in the medium range from 30 to 65 K and
overestimated in the upper range above of 65 K.
Within the economic evaluation, the importance of the electricity to gas price ratio is underlined as the main
parameter that determines the economic suitability of a HP project. Whilst under German conditions (cel/cng = 5.3),
a SHP or HTHP project is scarcely economical at present, almost every SHP or HTHP project will be economically
feasible in Sweden (cel/cng = 1.1). In strong contrast to economics, the ecological evaluation finds that almost
every SHP or HTHP project is already positive in Germany. Considering the progressive decarbonisation of
electricity in the framework of the energy transition, the ecological advantage of future HP projects will become
This work was supported by the German Federal Ministry for Economic Affairs and Energy within the
framework of the 6th Energy Research Program [project: “SolarAutomotive”, grant number 0325863A]. The
authors would like to thank all heat pump manufacturers for contributing to this work by providing data and
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