Jenny Rieck, Lina Taube, Frank Behrendt
Feasibility analysis of a heat pump powered by
wind turbines and PV-applications for detached
houses in Germany
Open Access via institutional repository of Technische Universität Berlin
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Journal article | Accepted version
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https://doi.org/10.14279/depositonce-12170
Citation details
Rieck, J., Taube, L., Behrendt, F. (2020). Feasibility analysis of a heat pump powered by wind turbines and PV-
Applications for detached houses in Germany. Renewable Energy, 162, 1104–1112.
https://doi.org/10.1016/j.renene.2020.07.011
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Feasibility analysis of a heat pump powered by wind turbines and
PV
- applications for detached houses in Germany
Jenny Rieck*a, Lina Taubeb, Frank Behrendtb
aTU Berlin, Department of Energy Process Engineering and Conversion Technologies of Renewable Energies Berlin,
Germany, jenny[email protected]
bTU Berlin, Department of Energy Process Engineering and Conversion Technologies of Renewable Energies Berlin,
Germany
Abstract
In this study an intelligent energy supply system is developed. Energy is obtained by wind
or solar radiation and stored to cover the electricity and heat demand of a detached house in
Germany. For this a heat pump and a storage tank is used. The simulation shows strategies
to integrate renewable energies in different regions of Germany while diminishing the need to
turn offa wind turbine or feed energy to the grid. For this, the energy consumption in a single
house is modelled. Different wind turbines and PV systems are introduced as an energy source.
The profitability of these systems is calculated and compared to conventional systems with gas
or oil. The analysis shows that at the moment small wind turbines are a feasible option for
cover the energy demand under the given conditions. On the other hand, currently PV plants are
not suitable for the heat demand coverage as the specific costs outgo the ones for conventional
systems. Further research is necessary to look at different case scenarios, taking into account
future climate developments.
Keywords: Integrated Energy, Micro Energy Systems, Space Heating, Sector-coupling, Small
wind turbines, Photovoltaic
1. Introduction1
The Climate Protection Act by the German Federal Government aims to reduce CO2emis-2
sions by 55 % in 2050. The emissions by the energy industry and the building sector even should3
be decreased by more than 60 % [1]. This is only possible by increasing the share of renewable4
energies. While their fraction in the power sector was 36 % in 2017, for the heating sector the5
share was only by 13.9 % [2]. Therefore the integration of renewable energies in this sector is of6
particular importance. This can be achieved by increased usage of biomass but also by efficient7
power-based heating devices, especially for private households. As one focus of the renewable8
energy strategy of the German Government lies on the expansion of wind and PV power plants,9
coupling the power and heating sector is consequential. While decentralised concepts for PV10
plants are already quite common (e. g. on roofs [3]), using small wind turbines for energy sup-11
ply of single households is not. For both technologies there is the challenge of high volatility,12
which means that energy demand and generation are unequally distributed. This especially ap-13
plies for decentralised plants, as it is not possible to balance this effect the same way as in larger14
Preprint submitted to Renewable Energy May 29, 2020
power distribution grids.15
16
One way to counteract the volatility is the integration of an energy storage system [4], an-17
other is to shift demand from peak hours to offpeak hours, a strategy known as demand side18
management [5]. A further option is to feed excess electricity to the grid and get rewarded for19
it. In times the electricity generated decentrally does not meet the demand, electricity from the20
grid can be used. However, currently the feed-in tariffs for wind power plants up to 750 kW are21
4.63 cents/kWh, and 11.51 cents/kWh for PV plants up to 10 kWpeak [6]. As the electricity price22
is around 29.87 cents/kWh at the moment [7], it is more attractive to use the electricity oneself.23
24
As demand side management is not as easily achieved on a decentralised level storage is25
the main option to react to renewable energy volatility. While battery storages become more26
common, they are still costly, decreasing the economic efficiency of renewable energy systems.27
Heat production from electricity and storage of this heat can be an alternative. However, there28
are some challenges connected to this too that need to be analysed: peaks in electrity generation29
by PV and those of heat demand are anticyclical and seasonal heat storage is not economically30
viable for private households yet [8]. Space for decentralised renewable energy plants is limited,31
especially for PV roof plants. Investment costs for the necessary appliances can make heat sup-32
ply economically unfavourable. This especially applies as the costs for conventional heat supply33
by fossil fuels (oil, gas) are already lower by more than a third compared to grid electrictiy.34
Electricity demand by other consumers (household appliances etc.) might compete with the heat35
demand. Finally, the mean building age is 28 years in Germany, whichs means that good thermal36
isolation does not exist comprehensively [9]. Overall, it needs to be carefully analysed, in which37
cases a system restructure towards heat generation from electricity is sensible.38
39
First, the examined house structure needs to be defined, for which the decentralised energy40
supply is supposed be realised. It can be provided for a whole quarters, but also solely for a41
single building. This building can be a tower, an apartment house or a single family house. The42
installation of wind power plants are more suitable in rural areas as wind flow is not as restrained43
as in cities. In these rural areas detached single family houses are very common [10]. There-44
fore these building type is especially interesting for studying energy supply by wind and PV.45
Additionally, heat and warm water demand from a single-family house consist of 84 % of the46
total energy demand [11]. Therefore, the implementation of a climate friendly heat supply is of47
special importance.48
49
Several studies have been conducted on the integration of renewable energies in detached50
houses. In [12] the focus was on benefits of utilising on-site and off-site renewable energy51
sources for a single family detached house. Bracke et al. [16] researched the prerequisites for a52
self-sufficient energy supply and the necessary technologies for it. The assessment of the modi-53
fications in the German Combined Heat and Power (CHP) Act in 2016 with respect to technical,54
economic and ecological aspects is given by [17]. In [18] the requirements and consequences of55
an extensive heat transition towards a heat demand coverage based on renewable energies was56
analysed. Indicators concerning technical and economic aspects as well as energy and climate57
protection policy were identified and presented.58
59
Additionally, small wind power plants up to 10 kW for decentralised, household-specific en-60
ergy supply is not researched in great detail. Ghaith et al. studied the potential for household61
2
wind power plants in Oklahoma [13]. However, the US net metering system enables a load shift,62
making it unnecessary to implement storage options. This concept is not available in other coun-63
tries, like Germany. Heat generation using electricity was not considered. Predescu looked at the64
economics of small wind power plants for residential consumers without taking into account con-65
sumer behaviour [14]. Grieser et al. compared different regions in Germany in regards to their66
potential to install small wind turbines for household electricity supply. They found positive net67
present values for some of these regions but stated that urban areas with higher density affect the68
results negatively. They did not consider sector coupling, but rather used battery storage systems69
[15].70
71
It becomes clear that there are studies that look at the energy supply by renewable energies72
for single houses and there are those concerend with small wind power plants. However, until73
now there is hardly anything to find that compares the energy demand of houses of different74
conditions with different renewable energy supply options taking into account sector coupling75
as a mean to consider the volatility of these energy sources. This study tries to fill this void by76
looking at decentralised electricity production and electricity consumption for power and heat in77
detached houses in different regions in Germany. Chosing a detached area is compliance with the78
study by Grieser et al, expanding their scope by also considering PV as renewable energy source79
and heat as additional consumption. The focus lies on buildings built at the begin of the 21 cen-80
tury that have a higher heat demand compared to relatively new constructed buildings. At the81
same time it can be assumed that they can be representative of older but modernised buildings.82
Thereby, the results of the study have a greater significance for the integration of dezentralised83
PV and wind power plants for heating purposes in Germany and countries with similar building84
and climate structure.85
86
For the introduced model, a small wind turbine or a PV plant should provide the energy for87
electricity and heat demand of a detached house parallel to the existing grid. The possibility of88
establishing this kind of plant besides an already existing home supply system is investigated to89
design a renewable energy system for local applications. Since demand and energy generation90
can occur at different periods, an intelligent system is needed to distribute the energy in time. The91
overall objective of this study is the development of an intelligent energy supply system where92
the energy is obtained by wind or solar radiation and stored in a heat storage tank if necessary.93
For this a heat pump is used. The goal is to use the whole energy potential and diminish the need94
to turn offthe turbine or to feed energy to the grid. The study aims to reveal the conditions under95
which the most efficient power output and profitability of the system occurs.96
2. Methodology97
Following, the methodology of all calculations is presented. A so called test reference year98
given by Germany’s National Meteorological Service is used as basis for the calculation of wind99
speed and solar radiation. In this case, test reference year means that the data is synthesised of100
20 years (1988 - 2007) of measured weather data. It includes hourly data for 365 days and 15101
regions in Germany, concerning among others wind speed and direct and diffuse solar radiation102
[19]. Several data sources are used to calculate the generated electricity for every hour of the103
year. For the wind power plant system, micro and mini wind turbines up to 10 kW are considered.104
Micro wind turbines have a nominal power smaller than 5 kW, mini wind turbines operate in a105
range of 5 - 30 kW. For the PV system modelling, plants with nominal power between 2.44 and106
3
9.9 kW are taken into account. Table 1 shows all used wind turbines and PV plants with the107
nominal power and their respective data source.
Table 1: Wind turbines and PV plants
Wind turbines nominal data
power kW source
SW Skystream 3.7 1.9 [20]
Exmork HM 3.2−2000 2 [20]
Skyline sl −30 3 [21]
Exmork HM 4.5−3000 3 [20]
Uge −4K 4 [21]
Cyclone 4.8KW 4.8 [20]
Inclin 6000 Neo 6 [20]
Fortis Alize 10 [21]
PV plants nominal data
power kW source
Aleo Solar S19 HE Tec 2.44 [22]
Viessmann Vitovolt 300 Typ P275 AB 3.3 [23]
Viessmann Vitovolt 300 Typ P275 AB 4.4 [24]
Aleo Solar X59 HE Tec 5.58 [25]
LG325N1K-V5 NeON 2 Black Cello 5.85 [26]
BenQ Solar SunForte PM096B00 6 [27]
LG320N1K-V5 NeON 2 Black Cello 6.72 [28]
Aleo Solar X79 8.37 [29]
LG330N1C-A5 NeON 2 9.9 [30]
108
2.1. Calculation of energy demands109
The calculation of the daily heat demand is different from the other daily demand calcula-110
tions, as the heat consumption depends largely on the condition of the building. Whereas the111
electricity and the hot water demand vary mainly with the behaviour of the consumer, so for112
these two demands mean values are used. Both methodologies are explained in this paragraph,113
starting with the heat demad calculation. For that, data given by the EU project TABULAR [31]114
is used, which analysed the heat demand for a building portfolio in 13 different European coun-115
tries. The full building portfolio is represented by ten different building types. These types can116
be distinguish by the construction year and by the designated use of the building. The project117
analysed various houses for very different usage, but for this study only the characteristic energy118
values for detached houses are needed. The calculation of this characteristic energy values was119
done according to European standards, such as the EN ISO 13790 for the calculation of energy120
use for space heating and cooling and the EN 15316 for the calculation of system energy re-121
quirements. The heat demand per square meter and the living space that needs to be heated is122
considered to calculate the heat demand. By multiplying these two values with each other, the123
heat demand of the whole house for a year is obtained. Table 2 shows the overall heat demand,124
the heat demand per square meter and the heated living space for different building ages. In this125
study only buildings from 2002 to 2009 are modelled. The assumption is that modernisation126
efforts in older buildings will decrease their heat demand in future. Therefore, the focus lies on127
the newest age group as reference for older, renovated buildings.
Table 2: Characteristic energy values for detached houses [31]
Building year heat demand kW
m2aheated living space m2heat demand kW
a
1958 - 1968 211.1 242.0 51086.2
1969 - 1978 232.7 157.5 36650.3
1979 - 1983 149.3 196.0 29262.8
1984 - 1994 177.9 136.6 24301.1
1995 - 2001 134.9 110.8 14946.9
2002 - 2009 101.3 133.2 13493.2
128
4
The respective heat demand needs to be split to receive the daily heat demand. This is not129
done by just dividing the value by 365 days, as the heat demand in the winter time is much higher130
than the heat demand in spring. Instead the method of reference demand profiles introduced by131
[32] is employed. First obtained is the so called customer value CV, again a yearly demand132
value. The calculated customer value is a side specific value, whereas the values in table 2 are133
generalised demand values.134
CV =QN
PN
ih(v)(1)
The heat demand of one year QN, given in table 2, is divided by the sum of all temperature135
regression functions hof one year. The temperature regression function is influenced by the136
mean temperature v. Hence all buildings are able to store heat it is necessary to consider this137
ability in the calculation. In the method of reference demand profiles this is done by calculating138
a mean temperature considering four serial days. So if the mean temperature of a given day is139
needed, the temperature value of this given day Txand of the three days before are considered.140
v=Tx+0.5·Tx−1+0.25 ·Tx−2+0.125 ·Tx−3
1+0.5+0.25 +0.125 (2)
In addition the temperature regression function his specified by a set of coefficients, so that141
the outcome is only valid for a given wind condition, a designated use and a specific age of a142
building. The coefficients (sA,sB,sCand sD) are called Sigmoid parameters and are given in143
[32].144
h=sA
1+(sB
v−v0)sC
+sD(3)
The wind conditions at various sites in Germany can be quite different from each other, which145
also influences the heat demand of a building. The reason behind this connection between mean146
wind speed and heat demand is that during ventilation a higher air exchange rate occurs if the147
wind velocity is higher. To consider this effect in the calculation of hfive different wind classes148
are introduced ranging from very low wind speeds to high wind speeds. So first of all the mean149
wind speed of one year need to be calculated by using the hourly wind data of the test reference150
year. Table 3 presents the four Sigmoid parameters for different wind speed classes.
Table 3: Sigmoid parameter for different wind classes [32]
Wind speed class m
ssAsBsCsD
0 - 1 3.0779823254 -37.4550564205 6.1084050390 0.1230000000
1 - 2 2.9273090522 -37.3533845914 5.8471730774 0.1470000000
2 - 3 2.7941105885 -37.1764144159 5.4034460226 0.1713913947
3 - 4 2.6279078804 -37.1327012568 5.2719372668 0.1950000000
>4 2.4785575976 -37.0075093695 4.9566020451 0.2190000000
151
In the next step the daily demand value will be obtained, by using this costumer value. The152
temperature regression function h in respect of a given daily mean temperature represents the153
daily variation over a year of the heat demand. So this h value is multiplied by the costumer154
value to obtain a daily heat demand value, which is done for the whole year to obtain 365 daily155
demand values.156
QD;heat =h(v)·CV (4)
5
Moreover the VDI 4655 [33] provides a set of normalised energy demand profiles to calculate157
a demand value for every minute of a day. These profiles Fheat,nare called typical day profiles158
and are ratios of the instantaneous energy demand over the daily energy demand, which means159
that the profile symbolises the percental distribution over one day. The sum of this percental160
distribution is always 100 %, but the specific values of the vector Fheat,nvary for different types of161
days. These different days exist due to the fact that during workdays most of the consumption will162
be in the morning and the evening, while at Sundays the consumption is more equally distributed163
over the whole day. So the daily demand values are then multiplied by the a vector of the164
percental distribution of the heat demand.165
Qheat(t)=Fheat,n·QD;heat (5)
By summing up these values for every hour the hourly heat demand can be calculated.166
167
To summarise this paragraph it is possible to determine the heat demand of every hour in a168
year by using the method of reference demand profiles in combination with the VDI 4655. But it169
need to be stressed that by combining these two methods the overall heat demand of this obtained170
profile may be smaller then the yearly demand given in table 2. This issue occurs due to the fact171
that the daily demand value is multiplied by the energy demand profiles (see equation 5). In172
the summer time the heat demand profile only contains zeros, as no heating is necessary if the173
outside temperature is above 15 ◦C. At the same time it could happen that the daily demand value174
QD;heat is very small but not zero, for the simple reason that this value is calculated according to175
the temperature of the last three days and not according to the temperature of the precise day.176
The yearly hot water and electricity demand of a detached house mostly depends on the177
number of people living in it. To ensure comparability of the different sites, it is assumed that178
two people are living in every house. VDI [33] proposes a yearly energy demand QY;water of179
1000 kWh to supply hot water and a yearly electricity demand WYof 4000 kWh for a detached180
house with Npers =2. The standard also includes equations to calculate the daily energy demand181
for hot water QD;water and electricity WD(equations 6 and 7).182
QD;water =QY;water ·(1
365 +Npers ·Fwater) (6)
183
WD=WY·(1
365 +Npers ·Felec) (7)
The parameter Felec and Fwater are given in the standard [19]. The calculated daily values are184
multiplied by the typical day profiles for electricity and hot water demand, as it is done above to185
assess the heat demand for each hour.186
2.2. House heating system187
A measure of the efficiency of a heat pump is the coefficient of performance (COP), which188
is defined as the ratio of heat delivered by the heat pump QHand the electricity demand of the189
compressor Pcomp.190
COP =QH
Pcomp
(8)
To facilitate comparisons the heating capacity COP for a heat pump is given for specific con-191
ditions. An air-water heat pump that works at ambient temperature of 7 ◦C and aims at a flow192
6
Table 4: Specifications of modelled heat pump
Name A7/W55 A-10/W55 expenditure data
COP power COP power source
Ochsner Eagle 717 3.3 11 kW 2.3 14 kW 20,639 e[34]
temperature of 55 ◦C has the acronym A7/W55. The specifications of the chosen heat pump are193
given in table 4.194
For the hot water, a storage tank with three incoming and three outgoing connections is195
modelled. Two heat exchangers are needed in the tank. The first one is connected with the heat196
pump and enables an individual mass flow that is not influenced by the mass flow of the heating197
circuit. The second heat exchanger is necessary to divide the fresh hot water (hot water - HW)198
from the water that flows inside the heating system (heat circuit - HC). Only with a disconnection199
of these two water flows an adequate quality of fresh water is given. In case the heat provided200
by the storage is not sufficient to fulfil the needs of the house heating/hot water system each201
circuit includes an additional heating element to increase the temperature if necessary. Using a202
controler the heat pump can be operated in full time or part time load according to mass flow and203
temperature of the outgoing circuits. A schematic figure is given in figure 1.204
HC
Heating
Element
HW
Heating
Element
Heat
Pump
Controler
T and m signal
Full- or part load signal
Mass flow
Cold Water
Figure 1: Schematic circuit diagram for the heating system
2.3. Profitability calculation205
It is assumed that all houses which were built after 2002 are equipped with a condensing206
boiler. As these houses are not older than 20 years according to [35] investment costs for a new207
boiler can be neglected and only the fuel costs are considered. For evaluation of the profitability208
of the systems, the annuity method [35] is used. The price for the heat pump can be found in209
[36]. The costs for the wind turbines are shown in [20, 21], those for the PV plants are given by210
[22, 23, 24, 25, 26, 27, 28, 29, 30]. The investment costs of a boiler according to the living space211
of the house (Ahouse) are specified by equation 9 [35].212
Paboiler =2253.6·
Ahouse
A0.7349
house
(9)
7
For the 1500 litre storage tank the price is defined as 1700 e. Before the annuity of the investment213
is calculated, first all prices need to be set to one point in time. As all researched prices are spread214
in time, it is necessary to consider the inflation of the prices. All the prices are then totalised for215
each system (symbolised with Call) to calculate the annuity of the investment.216
Ainvest =Call ·a(10)
The annuity factor a is determined as followed:217
a=(1 +i)−1
1−(1 +i)−T(11)
The interest rate i is 4 %.218
Before starting with this calculation of the heating cost annuity it is necessary to specify the219
heating system which is already existing in the house. As there are various types of heating220
systems implemented in detached houses all over Germany it would be unrewarding to calculate221
this annuity for all of these heating systems. So for the reason of a concise overview the two222
most common heating systems are chosen, which are gas and oil fired heating systems [37]. The223
annuity of the heat demand is determined by the generated heat Qf uel of a given heating system224
and the respective fuel prices Cf uel.225
Af uel =Qf uel ·Cf uel ·a·b(12)
The price dynamic annuity factor bexpresses the issue that there will be price changes during226
the observation time.227
b=1−(1+r
1+i)T
(1 +i)−(1 +r)(13)
The price change factor r differs with the respective energy source (see table 5).228
The energy effort for the heat generation (Qf uel in equation 12) is not the same as the energy
Table 5: Price change factor and price for oil, gas and electricity
Type price change factor %/a expenditure cents/kWh data source
Oil 6.24 6.73 [38]
Gas 5.06 7.24 [38]
Electricity 5.13 28.73 [38, 40]
229
which is needed to fulfil the heat demand. The reason for this is that the generation of heat is not230
an ideal process and some energy can not be used due to losses. To obtain the value of Qf uel the231
heat demand of the respective house type is divided by the efficiency of the heating device. This232
efficiency varies with the respective fuel type and is given as followed for a condensing boiler233
[41]:234
•102 % for oil235
•105 % for gas236
8
The annuity of the demand for electricity is calculated using the electricity costs given in table 5.237
The sum of these three annuities is the overall annuity. The levelized cost of electricity (LCoE)238
is calculated by dividing the annuity by the relevant demand (see equation 14). So the LCoE of239
the conventional system is calculated by the sum of the LCoE of the conventional heating system240
and the LCoE of the electricity demand. For the renewable systems the annuity of the system,241
containing the annuity of the capital and operational cost, is divided by the electricity demand of242
the house and the electricity demand for heating purposes.243
LCoE =Ai
Edemand,i
(14)
Whenever a profitability analysis is performed it is important to carry out a sensitivity anal-244
ysis, for the simple reason that such an analysis reveals the range of the costs. Furthermore it245
determines which factor is highly influencing the system and which factor is neglectable because246
the influence on the system is small. In this study a sensitivity analysis is conducted for the prof-247
itability analysis using the Monte Carlo method. The reason for applying a Monte Carlo instead248
of a standard sensitivity analyses is the benefit of varying all parameters at the same time. In the249
standard sensitivity analyses usually one parameter is varied while the others are kept constant.250
Such an analyses reveals the highly influencing parameters but does not illustrate probable future251
cases as the aspect of only one changing parameter is not likely. In this study the sensitivity anal-252
yses is used to present the cost range rather than identifying the most influencing factor, which253
is why the Monte Carlo simulation is used.254
255
The used Monte Carlo simulation is a statistical method, in which random numbers uniformly256
distributed between zero and one are generated to represent the risk that a given value can vary257
in a distinct range. This range is fixed in the analysis to a minimum and maximum value. The258
reason for fixing the range is that all considered values, like the interest rate or the expenditure259
of a distinct component, will not change unlimited in time. All factors that are changing during260
the simulation and their respective ranges are shown in table 6. With the help of the aforemen-261
tioned random number Nrand,ithe values Yiof the factors are calculated in between their ranges262
[Xmin,iXmax,i].263
264
Yi=Xmin,i+Nrand,i∗(Xmax,i−Xmin,i) (15)
In the simulation 5000 cycles are performed and in every cycle for all factors equation 15 is265
calculated to obtain changing values for the investment costs, the interest rate, the price change266
factor of oil, the price change factor of gas and the price change factor of electricity. It is neces-267
sary to emphasise that the factors are not changing in the same pattern, which means the interest268
rate could be very high while the price change factor of one fuel type is very low in the same cy-269
cle. This is realised by calculating an individual random number for every factor, which enables270
a decoupled simulation. In every cycle the whole profitability calculation, as described above, is271
performed with the random generated factors to estimate the probable distribution of the LCoE.272
3. Results and discussion273
The LCoE for oil or gas is between 5.1 and 5.2 cents/kWh for all regions. This reflects the274
pure fuel prices for fulfilling the heat demand. The electricity demand is fully fulfilled by elec-275
tricity from the grid. In the paragraph below the named LCoE always include electricity and276
9
Table 6: Parameters for Monte Carlo simulation
Factor Yiunit data source default minimum maximum
interest rate % assumption 4 2 6
roil %/a [38] 6.24 -18.5 33.5
rgas %/a [38] 5.06 -20.8 33.7
relec %/a [38] 5.13 2.3 12.1
investment % assumption 100 90 100
heat demand. In comparison, the costs for a system with a heat pump and a PV plant are above277
20 cents/kWh for all plant options. There are several reasons for the higher prices. While the in-278
vestment costs of the PV plant are not neglegtable, it does not influence the system costs to such279
level. However, the heating pump influences the system in two ways. On the one hand, the in-280
vestment costs are considerable. On the other hand, especially in winter the heat demand cannot281
be covered by the power of the PV plant alone, but the heat pump also has to be driven by grid282
electricity. As the prices for this power are more than four times higher than those of gas and oil,283
the majority of the heat demand in the new system is covered by comparatively expensive energy.284
285
However, there are diversions of costs between different regions. Figure 2 shows the results286
for the LCoE of all PV plant types in regions four (Potsdam) and five (Essen). There is a generally287
higher LCoE in region five, the city of Essen, compared to all other cities, lying between 24 and288
26 cents/kWh. On the one hand the PV plant with the lowest nominal power is the most suitable,289
on the other hand this PV plant is still more expansive than the conventional system. This means290
that the investment costs are to high in comparison to the money saved by the generated electric-291
ity. Apparently, the cities direct solar radiation, that is 31 W/m2, is not sufficient to contribute to292
the suggested system adequately. However, for regions with similar radiation as region five, the293
LCoE is still the lowest for PV plant nine. Therefore, also the distribution within the year plays294
an important role. For region four, the city of Potsdam, the PV plant with the highest nominal295
power leads to the lowest LCoE. The influence of a higher direct solar radiation is visible (yearly296
total 61 W/m2). The LCoE for this configuration is between 20 and 22 cents/kWh. While this is297
more economic than the systems in other regions, it still cannot compete with the analysed fossil298
fuel based systems. Overall, the new systems fluctuate between 20 and 26 cents/kWh.299
300
Generally, lower average direct radiation lead to higher LCoE, which can be attributed to301
the influence of the necessary grid electricity that rises and falls with the solar potential of each302
region. One option to counteract this is the implementation of a battery storage. Generated elec-303
tricity from the PV plant can be stored and the consumption of grid power reduced. Drawbacks304
are not only the the current high storage prices that influence the LCoE negatively. Also, the305
times of high electricity demand, winter, are the ones, when there is not much solar energy to306
store. Therefore, a battery storage is not considered helpful for decreasing the LCoE.307
308
The Monte Carlo analyses shows a high range of possible LCoE. Figure 3 presents the results309
for the lowest LCoE (Potsdam, PV system nine) and the highest one (Essen, PV system six). It310
is visible that the latter spreads wider. This means that the real LCoE is more likely to divert311
from the calculated one. However, it is also shown that even the most profitable combination of312
10
Figure 2: Comparison of LCoE of PV systems for region four and five
PV system and region is not able to undercut the costs for oil and gas in any case. Additionally,313
there is an increased sensitivity for higher prices. While the LCoE can be maximum 5 cents/kWh314
lower than the base case, there is an increase up to 10 cents/kWh possible with the given assump-315
tions for the sensitivity.316
317
What was not considered is the influence of the PV position on the roof as well as the general318
building design. For this model a South-East direction of the modules was assumed. A position319
in South direction is positive for the capacity, while a sattle roof with tiles showing in the line of320
West-East might increase the LCoE even further. Also, there is the possibility of shading due to321
trees or chimneys. Additionally it cannot be assumed that all roofs have the capacity for a 9.9 kW322
PV plant. This shows that the analysis of a PV plant plus heat pump system is always influenced323
by individual factors.324
325
(a) PV system nine in Potsdam (b) PV system six in Essen
Figure 3: Results of Monte Carlo analysis for PV
11
In comparison, a wind turbine system together with the same heat pump as applied to the326
PV system could generate for some regions prices below the conventional systems. As before,327
also the profitability of the renewable system highly depends on the wind resources and there-328
fore on the location of the system. Figure 4 shows the LCoE for the different wind turbines in329
Bremerhaven, which was one of the best region, and in Garmisch Patenkirchen, the region with330
the worst wind situation. It needs to be emphasised that the turbines two, four and six can be331
characterised as low wind turbines as these turbines are reaching a high portion of the nominal332
power already at low wind speeds. Compared to wind turbines two and six the wind turbine333
four has higher specific cost, which is the reason why the two wind turbines two and six appear334
out of the trendline in a positive perspective. This is not only the case for Bremerhaven. For335
all regions, except for Garmisch Patenkirchen and Fichtelberg, turbine six always generates the336
lowest LCoE. For Garmisch Patenkirchen the LCoE are all high compared to the conventional or337
to the PV system.338
339
Figure 4: Comparison of LCoE of wind turbine systems for Bremerhaven and Garmisch-Patenkirchen
When the wind system is placed in a location with very good wind resources the wind turbine340
generates enough electricity to fulfil the electricity demand, the demand of the heat pump and341
on top feeds electricity into the grid. The feed in tariffis assumed with 4.56 cents/kWh [6]. In342
the case of Bremerhaven these revenues are so high that negative LCoE are generated. From the343
15 analysed regions only for three regions all wind turbine systems were more expensive than344
the conventional systems. For all other regions there was at least one wind turbine system which345
was cheaper than an oil conventional system. Why are small wind turbines capable of fulfilling346
the demands more economically than conventional systems and PV systems not? The reason for347
this is the seasonal variation of the resources. In Germany the PV resources are much better in348
the summer than in the winter time. For the wind resources this situation is upside down, so the349
best wind conditions usually occurring in the winter time, where also the highes heat demand is350
needed.351
352
A sensitivity analysis for the best wind turbine of each region is conducted and presented in353
table 7. It can be seen that the economic feasibility of such a system could be sensitive. Con-354
12
sidering the case of Kassel, the system is under the normal condition not competitive with the355
conventional systems, but under minimum condition even a negative LCoE occurs. It is im-356
portant to stress that the wind data in the test reference year is originally coming from wether357
stations. These wether stations are usually placed in an area without big buildings, which is why358
nearly no wind shading effect is occurring. The surrounding of the wind turbine is relevant, for359
the simple reason that larger objects in the direct proximity to the wind turbine provoke turbu-360
lence and shading effects. The magnitude of the turbulence depends on the shape of the object,361
namely the hight and width. As the towers of small wind turbines are usually not so high the362
issue of the surrounding might be of greater importance for small wind applications. Especially363
in housing estates this could be a limiting factor.364
365
Table 7: Monte Carlo simulation for the best wind turbine of each region
Region wind turbine unit LCoE LCoEmin LCoEmax
Bremerhaven 6 e
kWh -2.58 -2.66 -2.49
Rostock 6 e
kWh -1.39 -1.46 -1.30
Hamburg 6 e
kWh -1.27 -1.34 -1.17
Potsdam 6 e
kWh -0.08 -0.15 0.01
Essen 6 e
kWh -0.98 -1.05 -0.89
Bad Marienberg 6 e
kWh -0.35 -0.42 -0.27
Kassel 6 e
kWh 0.13 -0.05 0.21
Braunlage 6 e
kWh -0.19 -0.25 -0.10
Chemnitz 6 e
kWh -1.63 -1.70 -1.54
Hof 6 e
kWh -0.18 -0.24 -0.09
Fichtelberg 8 e
kWh -4.91 -4.98 -4.83
Mannheim 6 e
kWh 0.17 -0.09 0.26
Muehldorf 6 e
kWh -0.29 -0.36 -0.20
Stoetten 6 e
kWh -2.05 -2.12 -1.96
Garmisch Patenkirchen 4 e
kWh 0.25 0.19 0.33
One major aspect that influences the results is the price for the heat pump. As most heat366
pumps are configured for room heating purposes, their optimum lies at a flow temperature of367
35 ◦C. This temperature is not sufficient to generate hot water. The simulated heat pump was368
chosen because the COP at A7/W55 is 3.3 and therefore comparatively high. However, the in-369
vestment costs are up to double of those for other kind of heat pumps. This inflates the total370
costs. Choosing another heat pump might reduce the costs at the expense of the COP. Another371
option is to set the flow temperature at 35 ◦C and use direct heating to get to the necessary hot372
water temperature. As the needed energy for room heating is more than ten times higher than the373
one for hot water, the system should be configured more to optimise the former trading offthe374
efficiency of the latter.375
376
13
Another aspect is that there is a decrease in heat demand for newer buildings, enforced by377
regulations on the maximum primary energy demand that is allowed in newly constructed build-378
ings. This means that for these kind of buildings the total heat demand is lower but also the379
diversion in demand between summer and winter is reduced. This means that the VDI standard380
used in this study might not be applicable for newer buildings and the results for both technolo-381
gies, but especially for PV could be more favourable.382
383
Oil and gas as an energy source has both a highly volatile price and a high price change fac-384
tor, which, in a poor constellation, could provoke very high annuities by considering 20 years of385
operation. Moreover the oil or gas reference system depends on two energy sources, namely oil386
or gas on the one hand and electricity on the other hand. Therefore, the oil or gas system is more387
economical according to the given calculation but there is some uncertainty. Also, it is not taken388
into account that in future subsidies might decrease investment costs for the heat pump. Schemes389
for building modernisation are already in place. This will decrease the heat demand and thereby390
decrease the influence of this sector compared to the power sector.391
392
The climate change is also of relevance. The reference model by [19] additionally gives393
the expected climate data for a synthesised year in the time frame 2021 to 2035. This data394
shows an increase in direct radiation by around 10 %. This will influence the capacity of PV395
plants positively. Together with the increase in average temperature, that is also forecasted, and a396
resulting decrease in heat demand, this might affect the efficiency of PV-based heating systems.397
Especially in regions that are already windy the wind speed is forecasted to increase in future,398
while a region as Garmisch-Patenkirchen will remain a windless area. Therefore, mainly regions399
that already profit from wind at the moment will be affected positively. Finally, it has to be400
empathised that other aspects are relevant for putting the model into reality, e.g. the question of401
space and land use to build up a small wind turbine.402
4. Conclusion403
The case study shows that at the moment small wind turbines are a feasible option for cover404
the energy demand of a detached house with an integrated heat pump in many German regions,405
mainly those with high wind resources. In a lot of cases even an overproduction of electricty can406
be achieved leading to negative LCoE. However, the high sensitivity of this systems needs to be407
considered. It can be shown that low wind turbines improve the system efficiency. However, for408
some regions, e.g. Garmisch-Patenkirchen, the LCoE is 0.25 cents/kWh, which is around five409
time higher than the one of an oil or gas system. Even considering the sensitivity of the results,410
it is clear that in those regions small wind turbines are not favourable.411
412
PV plants are not suitable at the moment for the heat demand coverage as the specific costs413
outgo the ones for oils and gas by far. Even in the best case, the city of Potsdam, the LCoE is414
22 cents/kWh, four times higher than a conventional system. While the sensitivity analysis shows415
that numbers as low as 14 cents/kWh are possible, it is still not sufficient to be a competition in416
the economical point of view. Modifications might increase the economic efficiency of PV based417
systems, e.g. lower flow temperatures. However, this is only applicable if building isolation418
improves. For older buildings this means that modernisation needs to be done on such extensive419
level that their efficiency standard compares to the one of recently constructed houses.420
421
14
It needs to be emphasised that maybe there are more suitable devices available on the market,422
which were not analysed for the simple reason that exact data for these devices were not obtain-423
able. This insufficient data in combination with the enormous number of available devices may424
reduce the willing to invest in such systems, as the engineering effort is higher then choosing an425
oil or gas system.426
427
In general it was demonstrated that for some sites an implementation of a wind system is428
profitable. This shows the ability of small wind turbine applications to contribute to cover the429
heat and electricity demand of houses, without using conventional energy sources. On the one430
hand this enables the owner of the house to generate a given share of the electricity consump-431
tion by himself and therefore life partly autarchic. On the other hand such a system improves432
the security of supply as the house no longer depends on two energy sources. Especially the433
prices of oil and gas are highly volatile and additionally depending on the political situation.434
Another important issue which was not addressed in the analysis but a motivation of this study is435
the ecological benefit of such a system. Considering the recent discussions on CO2pricing this436
ecological aspect could correlate with economic ones in the near future. This will have further437
influence on the cost comparison of renewable energy systems compared to fossil ones.438
439
The model will be used to look into the relevance of wind and solar based renewable energy440
sources to cover local energy demands in future climate scenarios. Furthermore, research will be441
done on other house age groups, older as well as very new ones and especially passive houses.442
443
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