How do changes in climate and consumption loads affect residential
PV coupled battery energy systems?
, Veronika Locherer, Martin Danner, Wolfram Mauser
Department of Geography, LMU Munich, Luisenstr. 37, 80333, Munich, Germany
Received 7 November 2019
Received in revised form
3 March 2020
Accepted 6 March 2020
Available online 7 March 2020
Residential battery storage system
Energy ﬂow modeling
Weather conditions and domestic consumption belong to the essential boundary conditions in the
optimal dimensioning of residential battery storage systems. In future, both factors will undergo tran-
sitions due to climate change and efﬁciency enhancement of domestic appliances. This study seeks to
assess potential developments in climate and consumption loads on the battery ﬂows and residual loads
for the near-time future. For this purpose, a land surface processes model with an integrated domestic
energy system component is applied. Three scenarios project changes in consumption loads and
meteorological conditions for the year 2040. The study area includes 4906 buildings located in the south
of Germany. The results show a general rise of grid feed-in rates between 21% and 27% due to increased
photovoltaic production. Climate change is expected to raise battery utilization during the winter
months, whereas decreasing effects from efﬁciency enhancement dominate in the summer. The self-
consumption rate declines between 4% and 12%, whereas self-sufﬁciency rises up to 6%. Consequently,
in the assessment of battery dimensioning approaches maximizing self-consumption or proﬁtability, we
recommend including the shifts in battery utilization and residual loads arising from future changes in
climate and consumption loads.
©2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND
In recent years, residential battery storage systems have gained
growing popularity among the owners of rooftop mounted
photovoltaic (PV) systems. Taking Germany as an example, already
every second newly installed PV systemwith less than 30 kWp was
coupled to a storage system in 2017 . Consequently, residential
batteries are expected to inﬂuence the ﬂows in the energy systems
Apart from the ability of increasing the PV self-consumption
rates, battery storages have the potential of reducing harmful
feed-in peaks into the local grids . Therefore, much research has
been undertaken in the dimensioning of residential battery storage
capacities for cost-effective and grid-friendly operation modes. A
variety of studies presents optimization techniques for the battery
size aiming at different goals like the maximization of economic
beneﬁts for the PV owners under different tariffs [3e6], the
reduction curtailment losses under feed-in restrictions  or the
additional utilization for frequency regulation apart from self-
consumption . In these ﬁelds of application, the proﬁtability of
a battery system is driven by the excess energy production of the
domestic PV plants and the residential consumption loads apart
from economic parameters. Apart from the future technological
development of the PV and battery systems, these two factors will
undergo severe transitions in the next decades.
Climate change will inﬂuence the operation temperature of PV
systems, but also the availabilityof the bottom-of-atmosphere solar
irradiation due to shifts in cloud cover and humidity . Several
studies have examined how far the PV production rates will be
affected by the changing meteorological conditions. In a ﬁrst
approach, the potential changes in PV energy are quantiﬁed from
daily temperature and solar radiation means of global climate
projections for 2080 . This approach has been adopted in sub-
sequent studies, which used improved climate projection data in
order to determine the future annual changes in PV production and
their variance for different spatial extents and scales [11e13]. Their
spatial resolutions of PV production scenarios originate from the
grid sizes of the underlying climatic projections. The results provide
a general estimate of potential changes in the production of
E-mail addresses: email@example.com (A. Reimuth), v.
firstname.lastname@example.org (V. Locherer), email@example.com-
muenchen.de (M. Danner), firstname.lastname@example.org (W. Mauser).
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Energy 198 (2020) 117339
residential PV systems up monthly temporal scale . In order to
increase the temporal resolution, the meteorological parameters of
the climate projections have been temporally downscaled from
monthly means to daytime values assuming sinusoidal curves of
the daily courses for temperature in Ref.  or irradiance in
Refs. . However, the impacts of changing PV production rates
resulting from the future shifts in the meteorological conditions on
the charging and discharging quantities of battery storage systems
have not yet been investigated closer.
The mitigation of global warming implies a transformation of
the residential energy sector, which belongs to the considerable
contributors of greenhouse gas emissions . Apart from the
conversion to renewable energy resources, potential measures also
include energy savings by changes in behavior or improvements in
energy efﬁciency . Signiﬁcant reductions in the electrical en-
ergy demand can be achieved if appropriate regulative instruments
are implemented . Recent research has shown that the resi-
dential consumption proﬁle has a strong inﬂuence on the self-
consumption of PV systems coupled to battery storages .
Thus, a decrease of the energy demand arising from increasing
efﬁciency rates of domestic appliances will induce changes in the
residual loads and battery utilization.
These future developments of climate and efﬁciency enhance-
ment will affect PV production and consumption loads in adverse
ways. To the authors’knowledge, the effects of changes in con-
sumption loads and climatic conditions on the residential storage
systems have not yet been analyzed.
In this context, the study sets out to assess their impacts on the
charging and discharging quantities of batteries. The paper seeks to
answer the following questions: Firstly, in which way will the
battery ﬂows and utilizations be inﬂuenced by changes in climate
and consumption loads in the course of the year? Secondly, how far
will the local grid ﬂows be affected that have to be managed bygrid
suppliers? Third, to which degree will self-consumption, self-sup-
ply, and battery cycles be inﬂuenced? The parameters are analyzed
as changes in the battery utilization and grid ﬂows potentially shift
the optimal dimensioning.
In order to answer these questions, a spatially distributed land
surface model with an integrated residential energy system
component is applied. This model enables the assessment of mul-
tiple residential systems on regional scale with building-speciﬁcPV
inclination angels and orientations, energy demands and battery
sizes. As currently available climate projections provide insufﬁcient
temporal resolutions needed for an assessment of battery ﬂows, a
statistical climate generator is applied, which downscales the
meteorological drivers to an hourly time step. Three different sce-
narios for the future development of climate change and efﬁciency
enhancement are assessed to gain a comprehensive understanding
of the impacts on the energy ﬂows in the residential systems in the
2. Materials and methods
2.1. Model environment
The simulation environment of the domestic energy systems is
embedded into the land surface processes model PROcesses of
Radiation, Mass, and Energy Transfer (PROMET) . The PROMET
model was originally developed for analyzing hydrological and
agricultural processes. It uses a raster-based approach, which
means that each domestic energy system is referenced to a grid
point in the simulation domain. It is spatially explicit and strictly
conserves mass and energy in all components. The presented
simulation results were carried out with a temporal and spatial
resolution of 1 h and 100 m. The basic input includes hourly
meteorological point data for air temperature, air humidity, wind
speed, cloud cover, and precipitation . These parameters are
spatially interpolated with the inverse squared distance weighting
method considering topographical conditions. The incoming direct
and diffuse radiation relevant for the hourly PV generation is
calculated according to the approaches of , and . A detailed
description of the general model and application is given in Mauser
and Bach , and Mauser, Bach et al. .
The domestic energy system simulating the residential energy
ﬂows consists of three components (see Fig. 1).
The PV model calculates the energy production rate P
solar direct and diffuse irradiation E
on the inclined PV panel area A
method of  (see Eq. (1)). Temperature effects T, and aging aare
considered by the efﬁciency parameters
. Snow coverage
exceeding 2 cm impedes the PV production.
The temporal course of the energy consumption E
from the annual consumption E
, which is downscaled by hourly
load proﬁles h
depending on season Sand day of the week doW
(see Eq. (2)).
The PV model and the consumption component were validated
with measurement data on hourly resolution obtaining determi-
nation coefﬁcients of 0.58 respectively 0.56.
The battery model includes the simulation of the ﬂows within
the accumulator as well as the grid conversion. The battery is
assumed as rechargeable, always connected to the grid, and directly
coupled to the PV module. The performance of the battery P
determined from the available energy excess or deﬁcit
E, the state
of charge SOC, the useable capacity C
, and the maximum charging
or discharging power P
(see Eq. (3)). The inﬂuences of tem-
perature and current are considered bya constant efﬁciency rate
The battery model includes self-discharge and aging effects.
The battery management is based on daily dynamic feed-in
limits (DFLs) as shown in Fig. 1. The battery starts to charge as
soon as the PV production rate, which is not immediately
consumed by the household, exceeds the DFL, and stops, when the
residual load falls below this threshold. In this way, the selected
battery charging strategy both optimizes the self-consumption rate
and decreases the feed-in peaks. The DFL thresholds have been
previously determined assuming a perfect forecast. The battery is
discharged when the hourly energy consumption exceeds the
The residual load of a domestic energy system RSL
, which is
supplied by or fed into the grid, is deﬁned as the difference between
the consumption rate and the power ﬂows of PV panel and battery.
The efﬁciencies of the MPP-Tracker
considered as shown in Eq. (4).
The degree of self-consumption (DSC) assesses the percentage
of production used by the domestic energy system (see Eq. (5)). The
degree of self-sufﬁciency (DSS) quantiﬁes the annual percentage of
the total consumption that is supplied by the domestic PV pro-
duction (see Eq. (6)). The degree of autarky (DA) represents the
changes in the grid ﬂows in comparison to the state without a
residential energy generation and storage system (see Eq. (7)). RSL
A. Reimuth et al. / Energy 198 (2020) 1173392
denotes the hourly energy ﬂow supplied by the grid.
A detailed description of the model setup and structural
embedding into the PROMET model is given in Reimuth et al. 
and in its associated technical notes [24e27].
2.2. Generation of the meteorological scenarios
The effects of anthropogenic emissions on the future climate are
studied extensively under the umbrella of the Intergovernmental
Panel on Climate Change (IPCC) . The IPCC established four
Representative Concentration Pathways (RCPs), which project
different future developments of the greenhouse gas concentra-
tions. The impacts of these RCP emission scenarios on the future
climatic conditions are assessed using global climate models. The
generated output data sets of the global climate models as well as
those of derived regional models often have a grid size of several
kilometers and low temporal resolutions . Since local climatic
conditions can considerably deviate from the coarse-grid model
representations, we downscale the meteorological drivers to a
resolution of 100 m and 1 h. In this way, the small-scale variation of
the weather conditions, which induce relevant differences in the
energy ﬂows within a regional system , can be adequately
considered in this study.
From the variety of downscaling processes  we chose the
statistical climate generator of Mauser , which uses the general
regional future climate change trends to rearrange measured his-
torical data sets in a way that they represent future climatic con-
ditions. This method relies on climate parameters measured by a
station network and therefore produces spatially and physically
consistent meteorological data sets with a temporal and spatial
resolution identical to the measured data. Thus, the full compara-
bility of the results for the current and future states of the domestic
energy systems is ensured and local peculiarities are preserved.
Precondition for this method is an hourly data set with a sufﬁ-
ciently high number of observation years. The approach further
assumes a continuance of the current climate regime, which can be
presumed in Central Europe for the near-time future . In this
manner, robust correlations representing the local weather char-
acteristics can be derived. Therefore, the historical weekly sums of
precipitation and weekly averages of temperature measurements
are analyzed with respect to their annual variation and covariance.
In the next step, the annual future trends in temperature and
precipitation are extrapolated for the study region from the
selected IPCC climate projection. A two-dimensional statistical
random generator is applied to mimic the natural variability of the
future climate. The ﬁnal projection is obtained by rearranging the
historical data set according to the future synthetic weeks. In this
way, the projected meteorological scenario follows the future
temperature trend of the IPCC scenario but maintains the measured
consistency of the region. A detailed description of the method and
its restrictions is presented in Ref.  and the supplementary
3. Case study
3.1. Description of the study area
The research area “Bavarian Oberland”is located in the south of
Germany and covers the administrative districts Miesbach, Bad
olz-Wolfratshausen, and Weilheim-Schongau (see Fig. 2). The re-
gion consumes 2161 GWh of electrical energy in the annual average
(2013e2016), of which 21.6% can be attributed to the private sector
[34e40]. This corresponds to a mean consumption of 5127 kWh per
building for an average household with 4.3 persons.
Between 1994 and 2016, a total of 13,940 PV systems feeding
into the local grids have been registered within the study area [43,
44]. 7522 plants mounted on residential houses could be identiﬁed
as domestic systems by using an airborne laser scanning data set
containing the building outlines . With an annual incoming
solar irradiation of 1167 kWh/m
, the study area belongs to the
regions of Germany with the highest PV potentials under the cur-
rent climate .
3.2. Basic input for the domestic energy model
To consider the variability of the energy system setups, 4906
residential buildings with existing, rooftop mounted PV systems
are selected having a nominal power between 3.0 kWp and
10.0 kWp. The inclinations and orientations of the panels are
derived from the corresponding roof pitches of the building out-
lines provided by . On average, the panels have a nominal po-
wer of 6.3 kWp, a size of 44.17m
at an inclination of 27.36
towards the southeast. The efﬁciencies are estimated from the date
Fig. 1. Structure of the domestic energy module including the energy production of the PV panels, the battery with its environment and the grid power ﬂows (left) and selected
charging and discharging strategy (right). RSL denotes the residual loads, DFL the dynamic feed-in limit.
A. Reimuth et al. / Energy 198 (2020) 117339 3
of installation and an efﬁciency curve  and range between 10.7%
and 16.4%. Further parameters for the PV model are taken from
Quaschning  (see also Table A.1).
The load curves used to determine the hourly domestic energy
consumption rates are based on standardized consumptionproﬁles
[48,49]. Three types of season and day are distinguished (see
The domestic energy storage devices are assumed as lithium-ion
accumulators, which have become the common type for domestic
applications . The battery systems are limited to a useable ca-
pacity of 60% and a maximum power of 0.3 kW/kWh at an hourly
loss rate of 6.25 ∙10
of the nominal capacity [50,51]. The con-
verter efﬁciency is set to 94% and the losses of dis-/charging to 1% of
the power ﬂow (see also Table A1).
The useable capacities of the battery systems are dimensioned
according to the nominal power of the corresponding PV systems
following Weniger et al. . Thus, the nominal battery capacities
of the domestic energy systems range between 5.0 kWh and
16.7 kWh at an average value of 10.5 kWh.
These parameters are kept constant for all scenarios to quantify
the inﬂuence of climate change and efﬁciency enhancement of
domestic appliances. The basic input needed to drive the land
surface model PROMET is described in Mauser and Bach .
3.3. Input required for the climate generator
The hourly measurement data used for the statistical analysis
and the reassembling process are taken from 377 weather stations
German and the Austrian Weather Service network covering the
The future local climate trend is developed from bias-corrected
projections for precipitation and temperature of ﬁve global climate
models from the ISIMIP Fast Track input-data catalogue for each
RCP scenario [41e43].
The mean decadal temperature increases serving as input for
the climate generator were determined from the ﬁve projections of
the grid cell representing the study area. The annual temperature
trend of each RCP scenario relevant for the study region was ﬁnally
found by ﬁtting a polynomial curve of third order to the ensemble
average of the temperature trends (see Table A.2 and Fig. A.2).
The changes of the weekly temperature averages and precipi-
tation sums were calculated from the ﬁve data sets for each RCP
scenario in the following way: First, the long-term average for
precipitation sums and temperature means were obtained from the
time spans 1961 to 1990 and 2021 to 2050. The differences between
past and future time span were smoothened by taking the moving
average over 10 weeks. The differences in the weekly temperature
means and ratio of the precipitation sums were ﬁnally determined
as the ensemble average of the smoothened values from the ﬁve
projections (see Fig. A3).
3.4. Scenario generation
The baseline scenario simulates the current state of the energy
system as reference using the year 2016. This year is characterized
by average annual energy consumption rates [34e40] and a global
irradiation sum deviating only marginally from the long-term
average . The domestic consumption is obtained in a top-
down approach from the number of buildings and the annual
consumption of the municipalities [34e40]. The simulation is car-
ried out with hourly measurement data from 79 weather stations of
the German and the Austrian Weather Service network.
Three future scenarios are applied considering potential de-
velopments of the annual domestic energy consumption and cli-
matic conditions. The year 2040 is chosen as projected year, since a
time interval of 25 years corresponds to the performance guaran-
tees of the PV manufacturers .
The ﬁrst varied component is the underlying global climate
trend, which is used to project the meteorological conditions in
2040. Three out of four available RCP pathways of IPCC are selected
RCP 2.6 represents the lower bound of a warming climate. It
assumes that the radiative forcing undergoes the lowest total
increase of 1.27 W/m
RCP 4.5 includes ambitious efforts in reducing temperature in-
crease. The scenario projects a rise of the radiative forcing by
Fig. 2. Location of the study area (left) and distribution of the 4906 selected households (right) (Data source: [41,42]).
A. Reimuth et al. / Energy 198 (2020) 1173394
The third scenario is based on RCP 8.5 assuming the highest rise
of global temperature. For the ﬁrst half of the 21st century the
radiative forcing is projected to rise by 3.04 W/m
The time span from 2038 to 2042 is simulated assuming con-
stant climatic conditions within ﬁve years. The year with median
PV production is assumed to represent average meteorological
conditions for the respective climate scenario (see Fig. A4-A.6).
In terms of efﬁciency enhancement, scenario “Strong”and
“Medium”follow the story lines developed in , who outlined
two scenarios for the energy consumption rates in Germany. These
scenarios already include the additional prospective energy con-
sumption arising from the growing use of air conditioning and
changes in behavior, which counteract the decrease in energy
consumption from efﬁciency enhancement. The differences be-
tween the residential consumption of 2040 and 2016 (obtained by
linear interpolation between 2011 and 2020) represent the future,
potential increases in energy efﬁciency used in this study. Scenario
“Strong”supposes that the goals of the ofﬁcial energy concept are
realized. This means a reduction of 17.1%. Scenario “Medium”pro-
jects the German trend of the recent years leading to 15.5% in 2040.
Scenario “No”assumes that the domestic energy consumption is
As the assumptions in the RCP scenarios already include explicit
projections of the global energy use, a consistent development of
energy enhancements and the greenhouse gas emissions is
assumed in this study (see Table 1). Scenario A is characterized by
strong efforts in climate change mitigation, which is consistent to
strong improvements in energy efﬁciency. Scenario B projects a
medium range future with major emission reductions and medium
success in raising energy efﬁciency. Scenario C assumes a business-
as-usual, non-sustainable development, which projects the current
emission path and consumption into the future.
4.1. Temporal course of the energy ﬂows
Fig. 3 shows the average annual course of the cumulated energy
ﬂows and the cumulated differences of the future scenarios in
relation to the baseline.
The energy consumption rates do not show signiﬁcant seasonal
variations in all four scenarios, as they accumulate almost linearly
during the year. The reductions of the annual consumption result in
a decline of 868.83 kWh in scenario A and 786.97 kWh in scenario B
compared to the baseline and scenario C with 5110.48 kWh.
In contrast, the courses of the PV production rates are charac-
terized by sigmoid shapes caused by the steeper solar inclinations
angles in the summer months. Under conditions of scenario 0, the
average PV production rate exceeds the total energy consumption
with an annual yield of 6419.26 kWh. Due to the changing climate
conditions, the electrical energy generation is further raised be-
tween 12.5% and 17.5%. The deviations to scenario 0 have different
seasonal courses. In spring, the changes in scenario A and B un-
derlie a higher variability than the scenario C. In the further course
of the year, scenario B and C are characterized by a linear daily
increases in contrast to A, which continues to ﬂuctuate.
The differences, which can be observed in the production and
consumption rates, consequently lead to varying changes of the
battery ﬂows. Scenario A is characterized by an annual, average
reduction of 105.96 kWh compared to the battery ﬂows of the
baseline scenario 0 with 2832.31 kWh. In contrast, the battery
ﬂows of the two future scenarios B and C increase by 46.81 kWh
and 280.61 kWh. In the spring and summer months, the deviations
in the battery ﬂows follow the form similar to the linear variation of
the projected consumption rates. Scenario A decreases by 6.7%,
scenario B by 4.5%, and scenario C shows more or less no deviation.
However, at the beginning and end of the year, the changes in the
battery ﬂows between scenarios and baseline converge to those of
the PV production rates. This time span is characterized by higher
ﬂuctuations as the batteries cannot always be fully charged.
The average ﬂows between the domestic energy systems and
grids are collectively raised between 717.97 kWh in scenario C and
952.11 kWh in A, compared to 4121.80 kWh in the baseline year.
The courses of the grid ﬂows are also subject to seasonality. During
the ﬁrst and last months of the year, all three scenarios are similar
to the baseline. However, the varied boundary conditions lead to
signiﬁcant changes between the scenarios in spring and summer.
Scenario A and B show the strongest increase of grid ﬂows with a
daily average of 17.05 kWh and 17.95 kWh. This is caused by the
increased PV excesses and the lower battery utilization. In contrast,
the differences in the grid ﬂows of scenario C show a more or less
constant daily increase of 15.93 kWh.
4.2. Variance of the energy ﬂows
Fig. 4 represents statistical parameters of the annual energy
ﬂows for the PV production, consumption, battery, and grid ﬂows
referenced to their PV peak performance (see Table A.3).
Scaled by the PV power, the annual consumption rates show the
largest deviations among the 4906 domestic energy systems
varying by 2.93 MWh. The high number of outliers is caused by
households with small PV plants and high annual energy con-
sumption rates. According to the efﬁciency increases of 17.1% and
15.5%, the medians of the consumption rates decline by 140.07 kWh
for scenario A and 127.10 kWh for scenario B related to the baseline
with 812.40 kWh per kWp PV. The distribution of scenarios C is
identical to 0, as no shifts in the consumptions are assumed.
The scaled PV production shows a more or less constant increase
between 12.8% and 15.3% of median and quartiles for all future
scenarios. Climate change increases the PV production but not the
variance among the domestic energy systems.
The scaled battery ﬂows are generally characterized by lowest
variance of the analyzed parameters, as the interquartile range
varies only by 63.77 kWh per kWp in the baseline year for instance.
However, in scenario A and B the spread between the annual bat-
tery ﬂows is increased under future conditions by up to
110.96 kWh. For smaller battery systems, the battery ﬂows increase,
whereas for larger systems they decline.
This is different for the residual loads: The median increases
Boundary conditions for three future scenarios concerning the IPCC emission scenarios and the progresses in energy efﬁciency.
Greenhouse gas emission path
RCP 2.6 RCP 4.5 RCP 8.5
Efﬁciency improvements 17.1% A
A. Reimuth et al. / Energy 198 (2020) 117339 5
between 26.7% in A, and 20.8% in C compared to the baseline sce-
nario. However, the future interquartile ranges are decreased. Thus,
the total grid ﬂows of the domestic energy systems rise but the
variances between the energy systems decreases under the future
4.3. Development of the residual loads
The residual loads presented in Fig. 5 are obtained from a subset
of 2505 simulated domestic systems, which exclusively occupy a
raster grid point so that the energy ﬂows can be directly linked to a
The maximum and minimum residual loads represent the range
of hourly power ﬂows per kW-peak, which are supplied by or fed
into the grid. All four scenarios show that the feed-in peaks exceed
maximum consumption. The power excesses are also raised in all
three future scenarios in their quantities. In addition, the maximum
positive residual loads decrease in scenarios A and B due to the
reductions of the consumption rates. In all scenarios, the maximum
power ﬂows of the households are deﬁned by the PV excesses.
The extreme grid ﬂows ﬂank the average loads of the four
classes of storage capacities (<8 kWh, 8e11 kWh, 11e14 kWh,
Fig. 3. Cumulated energy ﬂows of consumption, production, battery and grid ﬂows for an average domestic energy system (left), and cumulated differences between the future
energy ﬂows of Scenario A, B, and C and the baseline scenario (right).
Fig. 4. Quantiles of the domestic annual energy ﬂows for consumption, production, battery, and grid per kWp-PV power for Scenario 0, A, B, and C.
A. Reimuth et al. / Energy 198 (2020) 1173396
>14kWh). All three future scenarios are characterized by an in-
crease of hours with medium and maximum excesses. This can also
be observed when analyzing the number of hours without grid
ﬂows. In the baseline scenario, the domestic energy systems with
less than 8 kWh capacity have 47 h without grid interaction in
contrast to 1640h with systems of more than 14kWh. Under the
future scenario conditions, the hours of autarky decrease for all
sizes of the battery systems. Scenario C is characterized by the
highest decline for all battery sizes showing only 12 h without grid
interaction for the smallest and 1071 h for the largest category of
4.4. Self-consumption and self-supply
Fig. 6 shows the degrees of self-consumption (DSC), self-supply
(DSS), autarky (DA), and the number of cycles (NoC) as a function of
the domestic battery capacities (see also Table A.4-A.5). The curves
are interpolated from the subset of 2505 domestic energy systems.
In the baseline scenario 0, the degree of self-consumption
ranges between 82.2% at a storage capacity of 5.0 kWh and 39.4%
at the maximum capacity of 16.7kWh. In the future scenarios, the
DSC decreases constantly by 11.9% in scenario A, 11.1%in B, and 4.1%
Whereas the degree of self-supply varies between 49.2% and
87.5% in the baseline scenario, the DSS increases under the future
scenarios. With 79.0%, scenario B is characterized by the highest
DSS rates for an average storage size, which means an increase of
6.2% compared to the baseline scenario. However, the sensitivity of
this parameter to the capacities declines. The range of the DSS
between the smallest and largest battery sizes decreases from
38.3% for the baseline to a 29.4% in scenario A and B.
Analyzing the degree of autarky shows a high dependency of the
battery size. Whereas the inﬂuence of climate change and efﬁciency
enhancement is low for small battery systems, the DA is very
sensitive to the future developments of efﬁciency improvements
and climate change for larger systems. At the smallest battery size
of 5.0 kWh, the DA increases only up to 12.0% compared to scenario
0. For the largest analyzed battery storage size of 16.7 kWh, the DA
rises from the baseline result of 127.8%e222.3% in A, 220.4% in B,
and 163.5% in C.
The threshold of 100% is the point at which the annual grid ﬂows
of the building are equivalent to grid supply. In the baseline sce-
nario, an energy system with a peak power of 8.1 kW and storage
capacity of 13.5 kWh has the same magnitude of grid ﬂows as
without a production and storage component. Scenario A reaches
this threshold already at 9.2 kWh, Scenario B at 9.5 kWh and Sce-
nario C at 11.4 kWh.
While the DA increases under futures conditions, the cycle
numbers decline. In the baseline scenario, the NoC shows almost no
dependency on the battery size with 340.0 battery starts. In sce-
nario C in contrast, the NoC has the highest sensitivity to the battery
capacity with annual cycle numbers ranging from 321.2 to 341.9.
Scenario C is also characterized by the lowest decline of the NoC
from the future scenarios.
5.1. Battery utilization
The results obtained in this study show that the inﬂuence of
efﬁciency enhancement and climate change on the battery ﬂows is
both signiﬁcantly and strongly dependent on the season.
The summer months are characterized by the rising PV pro-
duction of up to 13.7% under RCP 4.5 (see Fig. 3). This leads to an
increased availability of excess energy in a time span, which is
already in the baseline year characterized by higher back ﬂows and
fully charged batteries. Consequently, the discharging quantities
enabling the intake of surpluses gain more inﬂuence. Since a
reduction of the consumption impedes the full discharging, efﬁ-
ciency enhancement will lead to the decrease of the battery ﬂows in
the summer months.
This is different in the winter times, when the changes in the
production rates determine the battery ﬂows. The availability of
excess PV power will continue to play the decisive role on the
battery ﬂows in winter. On the one hand, climate change will lead
to increasing precipitation events and therefore a reduced avail-
ability of solar irradiation. On the other hand, the days with snow
coverage and therefore the blocking of radiation absorption will
decrease under rising temperatures. Under a high climate change
scenario the positive effects of decreasing snow days exceed the
reduced availability of solar irradiation in the study region, which
leads to increasing PV production and battery ﬂow rates.
However, the potential development of the battery ﬂows is also
dependent the capacity. The battery ﬂows will rise under the
conditions of high efﬁciency improvements and low climate change
only for small capacities. This is also reﬂected by the decrease of the
cycle numbers, which is caused by fewer and longer lasting energy
surpluses of the small systems.
Fig. 5. Distribution of the hourly residual loads of 2505 selected domestic energy systems with the minimum and maximum extrema enclosing the average ﬂows for the battery
systems having capacities of less than 8 kWh, 8e10.99 kWh, 11e14.99 kWh, and larger than 14 kWh.
A. Reimuth et al. / Energy 198 (2020) 117339 7
The projected developments of the battery ﬂows suggest that
the analysis of the future utilization requires scenarios containing
both the changing climate conditions and efﬁciency improvements
as their inﬂuences are subject to opposing temporal courses: The
effects of climate change dominate in the winter months, whereas
those of efﬁciency enhancement prevail in the summer.
The spatial patterns of the meteorological drivers are less rele-
vant, as the annual ﬂows of battery systems are characterized by
the smallest regional variance. The results indicate that a sufﬁcient
temporal resolution of the energy efﬁciency and climate pro-
jections plays a more important role in the regional assessment of
the changes in the future battery utilizations than the choice of the
5.2. Residual loads
Similar to the battery ﬂows, the projected deviations in the grid
ﬂows underlie seasonal effects. In the winter months, all three
future scenarios are characterized by only small differences.
Despite the reductions in energy demand under scenario A and B,
the grid ﬂows do not decline at the same magnitude as the energy
consumption. This indicates that also in winter the grid suppliers
have to deal with rising power excesses.
In the summer months, the feed-in rates are signiﬁcantly raised
when compared to the baseline scenario 0. These shifts arise from
several factors: Despite adverse effects of rising temperatures, the
PV production rates will increase due to more stable high-pressure
systems, which lead to reduced cloudiness and intensiﬁed short-
wave irradiance. The buffering function of the batteries balancing
PV production and consumption remains more or less constant or
even declines if the consumption is reduced. Therefore, the
increasing energy excesses have to be fully balanced by the grid
suppliers. Consequently, scenario A with the strongest reduction of
the battery ﬂows is characterized by the highest increase of the grid
power ﬂows. Scenario C assuming no efﬁciency improvements and
the climatic conditions of RCP 8.5 shows the lowest rise of grid
ﬂows, as the increased PV production can be better balanced under
the higher consumption rates.
The distributions of the residual loads, which shift to more
extreme PV excesses, also reﬂect this development. Stresses in the
local grids caused by high PV production rates will further intensify,
if no countermeasures are taken. The annual grid ﬂows scaled by
kWp PV show a high spread between the domestic energy systems,
which is caused by the variance in the consumption rates (see
Fig. 4). This can be explained by the divergence of PV sizes, which
were primarily dimensioned to maximize the grid-feed in recent
The average increase of the PV production obtained in this study
Fig. 6. Degree of Self-Consumption (DSC), Degree of Self-Supply (DSS), Degree of Autarky (DA), and Number of Cycles (NoC) in dependency of the battery capacity. The lines
represent the ﬁtted curves, which are in logarithmic form for DSC and DA, and exponential form for DSS and NoC.
A. Reimuth et al. / Energy 198 (2020) 1173398
exceeds the projected rates of the discussed literature ﬁndings
[11,12,14]. One reason for this divergence could be that the selected
study area belongs to a part in Germany with high PV potential but
also large sensitivity to climate change. Lying at the fringe of the
Temperate and Mediterranean climate, it will increasingly come
under the inﬂuence of Mediterranean climate with milder winters
and dry, hot summers. This effect may be generally underrepre-
sented in climate models with larger grid sizes.
The deviations are further reasoned in the lower temporal res-
olutions of the climatic projections used in previous studies (1h in
our study vs. 3h in Ref.  or 1d in Ref. [11 ]). Temperature rise and
irradiation conditions, but also the inﬂuence of the continuously
changing inclination angles between panels and sun are not
distributed linearly during daytime. Temporally coarser meteoro-
logical drivers using daily or even monthly values for assessing
changes in PV production rates cannot capture these effects due to
their coarse simulation of atmospheric processes. Consequently, we
recommend the utilization of climate data with a sufﬁciently high
temporal resolution or downscaling methods when analyzing po-
tential effects on residual loads.
5.3. Limitations of the study
The study is subjected to several limitations concerning the
temporal and spatial variability of the consumption loads. As the
annual energy consumption is averaged on municipal scale and
temporally downscaled by standard load proﬁles, the variance be-
tween the individual buildings cannot be represented with high
precision. That means that the obtained results for battery utiliza-
tion and grid ﬂows are valid for residential buildings constructed in
recent decades but not new buildings like zero-energy homes.
The validity of the study is further restricted to buildings
without electrically based heating or cooling systems. Their elec-
trical consumption is additionally dependent on the supply with
thermal energy, which is driven by the heat demands, insulating
properties of the building materials and outside temperatures.
Consequently, the hourly consumption rates of buildings with heat
pumps strongly vary from the load proﬁles used in this study.
Apart from this, the modeling of the efﬁciency enhancement
applied to scenario A and B leads to further shortcomings. The
hourly decline of the consumption rate is depending on the single
efﬁciency improvements of the running devices. However, the
progresses in efﬁciency enhancement will differ between the
electrical goods. The varying developments in the improvements
will possibly induce unsteady changes of the hourly load proﬁles.
The assumption of a temporally constant decrease insufﬁciently
reﬂects these shifts. Nevertheless, the approach applied in this
study offers a concise assessment on the battery and grid ﬂows.
5.4. Implications for the battery dimensioning
The obtained results indicate that the current assumptions in
terms of battery utilization and grid ﬂows will have to be adjusted
to the future developments when investigating optimal storage
Climate change and efﬁciency enhancement will reduce the
self-consumption rates between 4% and 12% depending on the
scenario conditions. The independency from the battery size is
reasoned in the point that climate change rises the PV production
constantly for all PV sizes as described in chapter 4.2. In contrast,
the development of the self-supply is strongly inﬂuenced by the
scenario assumptions, which thus have to be carefully selected.
When applying dimensioning approaches with the goal of a high
self-consumption or self-supply in the future, we recommend
considering these future changes of the boundary conditions in the
Another important factor for the system sizing under economic
constraints is the magnitude and time of the residual loads as the
cost savings are also indirectly dependent on the charging and
discharging amounts of the batteries. The results of this study
indicate that the balancing effect of the batteries will be weakened
for the majority of the systems. Especially during the summer time
with high PV excesses, the battery ﬂows of the systems will be
generally reduced if consumption declines. At these times, a sig-
niﬁcant increase of excessive grid feed-in rates has to be expected.
This will further raise curtailment losses if feed-in limits are
imposed by the government. These changes can have crucial im-
pacts on the proﬁtability apart from the future development of
economic parameters and technological improvement of the PV
and battery systems.
In recent years, small-scale battery storage systems have been
increasingly installed in households with rooftop mounted PV
systems. In the development of appropriate dimensioning ap-
proaches with different optimization goals, weather conditions and
energy consumption belong to the essential boundary conditions.
However, climate change and efﬁciency enhancement of domestic
appliances affect PV production and consumption rates, which
consequently induces changes in battery and grid ﬂows. We con-
ducted a regional model simulation study of three future scenarios
for the year 2040, which combines projected changes in climate
and consumption loads to assess the annual course of their impact
on 4906 spatially distributed households with PV systems and
The results of the study show a rising PV production and a
reduction of the charging cycles but rising battery ﬂows for small
battery systems. However, a decline in the utilization of larger
residential batteries has to be expected with increasing sustain-
ability of the boundary conditions. The changes in the battery ﬂows
are subject to a strong seasonal inﬂuence: In summer with higher
PV production, they are driven by the reduction of the energy
consumption. In winter, they are induced by the changes of the PV
production rates, due to the lower availability of energy excesses. A
decrease of the self-consumption between 4% and 12% indepen-
dently from the battery and PV size has been found in this study,
which is reasoned in the constant increases of the PV production
The reduced buffering effect of the batteries and the increasing
PV-production also affect the grid ﬂows. The residual loads are
shifted to more and higher energy excesses under future climate
change and efﬁciency scenarios. Especially the summer months are
characterized by high PV excesses, which cannot be stored by the
residential energy systems. This will increase the probabilities of
bottlenecks in the grids and therefore the need for grid adjustment.
The projected changes should be considered in the application
and development of dimensioning approaches optimizing self-
consumption and cost-efﬁciency. For a robust sizing, we recom-
mend the usage of scenarios, which include the potential de-
velopments of both weather conditions and consumption apart
from economic parameters.
Apart from the impact of climate and energy efﬁciency analyzed
in this study, residential energy ﬂows will also be affected by rising
rates of electrically based heating and cooling systems and the
launch of electric vehicles. These future developments highlight the
need for further research in the assessment of challenges and op-
tions for the grid integration of residential PV systems under a
A. Reimuth et al. / Energy 198 (2020) 117339 9
Declaration of competing interest
The authors declare that they have no conﬂict of interests.
This study was carried out in the framework of the project
“INOLA eInnovationen für ein nachhaltiges Land- und Ener-
giemanagement auf regionaler Ebene”(grant code 033L155AN),
sponsored by the German Federal Ministry of Education and
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