2014-The Economic Viability of Battery Storage For Residential Solar Photovoltaic Systems

Renewable and Sustainable Energy Reviews 39 (2014) 1101–1118
Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews

journal homepage: www.elsevier.com/locate/rser
The economic viability of battery storage for residential solar

photovoltaic systems – A review and a simulation model
Joern Hoppmann a,b,n, Jonas Volland a, Tobias S. Schmidt a, Volker H. Hoffmann a
a
ETH Zurich, Department of Management, Technology, and Economics, Weinbergstrasse 56/58, 8092 Zurich, Switzerland
b
Harvard University, Energy Technology Innovation Policy Group, 79 John F. Kennedy Street, Cambridge, MA 02138, USA
art ic l e i nf o a b s t r a c t
Article history: Battery storage is generally considered an effective means for reducing the intermittency of electricity
Received 18 February 2013 generated by solar photovoltaic (PV) systems. However, currently it remains unclear when and under
Received in revised form which conditions battery storage can be profitably operated in residential PV systems without policy
30 June 2014
support. Based on a review of previous studies that have examined the economics of integrated
Accepted 7 July 2014
PV-battery systems, in this paper we devise a simulation model that investigates the economic viability
Available online 9 August 2014
of battery storage for residential PV in Germany under eight different electricity price scenarios from
Keywords: 2013 to 2022. In contrast to previous forward-looking studies, we assume that no premium is paid for
Solar photovoltaic power solar photovoltaic power and/or self-consumed electricity. Additionally, we run the model with a large
Solar energy
number of different PV and storage capacities to determine the economically optimal configuration in
Battery storage
terms of system size. We find that already in 2013 investments in storage solutions were economically
Distributed electricity generation
Techno-economic model viable for small PV systems. Given the assumptions of our model, the optimal size of both residential PV
Simulation systems and battery storage rises significantly in the future. Higher electricity retail prices, lower
Electricity price electricity wholesale prices or limited access to the electricity wholesale market add to the profitability
of storage. We conclude that additional policy incentives to foster investments in battery storage for
residential PV in Germany will only be necessary in the short run. At the same time, the impending
profitability of integrated PV-storage systems is likely to further spur the ongoing trend toward
distributed electricity generation with major implications for the electricity sector.
& 2014 Elsevier Ltd. All rights reserved.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1102
2. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1102
3. Data and method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105
3.1. System boundaries and layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105
3.2. Model input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105
3.2.1. Technological input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105
3.2.2. Economic input parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106
3.3. Techno-economic model of integrated PV-storage-system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108
3.3.1. Self-consumption calculation module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108
3.3.2. Net present value calculation module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109
3.3.3. Storage and PV system size optimization module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109
3.4. Model output and sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109
4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109
4.1. Optimal PV system size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109
4.2. Optimal storage size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1110
4.3. Storage profitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112
4.4. Sensitivity analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112
5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113
n
Corresponding author. Tel.: þ 41 44 632 82 03; fax: þ41 44 632 10 45.
E-mail address: jhoppmann@ethz.ch (J. Hoppmann).
http://dx.doi.org/10.1016/j.rser.2014.07.068
1364-0321/& 2014 Elsevier Ltd. All rights reserved.
1102 J. Hoppmann et al. / Renewable and Sustainable Energy Reviews 39 (2014) 1101–1118
5.1. Implications for household investments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113

5.2. Implications for environmental pollution, safety and maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113
5.3. Implications for the electricity sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114
5.4. Implications for policy makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114
6. Limitations and future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114
7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115
Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115
Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116
Appendix C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117
1. Introduction storage in an environment without demand-side subsidies for PV

and storage technologies. In this case wholesale and retail electricity
Renewable energy technologies are expected to play a major market price developments will strongly affect storage profitability.
role in mitigating pressing societal challenges such as climate Second, and more importantly, existing forward-looking studies that
change and resource depletion, while contributing to domestic investigate the profitability of storage for residential PV have usually
energy security. Among the many options available, solar photo- investigated a limited number of sizes for both the PV system and the
voltaic (PV) power has been found to have a particularly large battery storage. However, especially under the assumption of no
physical potential for electricity generation [1]. However, three additional policy incentives, the chosen size of the PV system and
important barriers to a more widespread use of solar PV are that battery storage strongly affect the economic viability of the inte-
electricity generation from this source is limited to daytimes, grated PV-battery system. This is because the economic viability of
depends on local weather conditions and fluctuates strongly over storage is strongly driven by the degree to which electricity produced
the year [2]. As a consequence, there are often considerable gaps by the PV system is self-consumed, which in turn is highly sensitive
between electricity consumption and the electricity supply of PV to the aforementioned parameters. As a result, it currently remains
plants. With an increasing deployment of PV, such demand– unclear when storage investments will be economically viable for a
supply mismatches pose an increasing threat to the stability of household that optimizes the size of the PV system and the battery
the electricity system [3]. storage at the time of investment.
An effective means for reducing (and eventually eliminating) With this paper, we address the two previously mentioned
the mismatches between electricity demand and electricity supply shortcomings by investigating the question when and under
by intermittent energy sources are storage technologies. Respond- which conditions battery storage will be economically viable in
ing to the need for steadier electricity supply, several companies in residential PV systems without demand-side subsidies for an
the PV industry have started to develop and sell storage solutions economically optimized system configuration. Building upon a
based on battery technologies [4]. Yet, while the possibility of review of existing studies that have examined the economics of
shifting the supply of electricity to different times enhances the integrated PV-storage solutions, we present the outcomes of a
value of the electricity produced, adding storage technologies to a techno-economic model that calculates the profitability of storage
PV system also raises the overall investment cost to be borne by for distributed PV from 2013 to 2022. To account for uncertainties
plant operators. First countries, like Germany, have therefore in the future development of technology costs and electricity
announced programs that subsidize the use of storage technolo- prices, we draw on 8 electricity price scenarios and conduct a
gies for residential PV [5]. Considering the falling costs for both PV comprehensive sensitivity analysis. Analyzing the optimal PV
and battery technologies, however, it remains controversially system size, the optimal storage size and the profitability of
discussed whether and for how long these subsidies are necessary storage under each of these scenarios allows us to derive impor-
to drive the deployment of storage technologies. tant implications for policy making and the trend toward dis-
Currently, the academic literature provides little guidance as to tributed electricity generation.
when the advantages of combining PV systems with storage can be The remainder of this paper is structured as follows. Section 2
expected to justify the extra expenses. Existing studies on integrated reviews existing studies that have investigated PV systems with
PV-storage systems mostly focus on the additional costs rather than storage solutions and discusses existing shortcomings. Section 3
the added economic value from storage (see Section 2). The few explains the data and method underlying our techno-economic model,
studies that investigate profitability of storage for PV typically followed by a discussion of the model results in Section 4 and their
examine its potential to raise the share of electricity generated by implications in Section 5. The paper concludes with a description of
the residential PV system that is consumed by the household (so- the study's limitations, suggestions for future research (Section 6) and
called self-consumption). By investing in storage technologies house- a brief summary of the main results (Section 7).
holds can leverage the existing spread between wholesale and retail
electricity prices by reducing both the volume of electricity that is
bought at retail prices and the one to be sold at wholesale prices [6– 2. Literature review
8]. Yet, while these studies have strongly advanced our knowledge
about the role that storage can play for residential PV systems, two An overview of past studies that have investigated the eco-
main shortcomings remain. First, existing studies examine the nomics of battery storage in distributed PV systems is given in
economic viability of storage under the assumption of policy support Table 1.1 It shows that in recent years a number of articles have
in the form of feed-in tariffs for solar photovoltaic power and/or been published that examine how different input parameters, such
additional premiums for self-consumed electricity. However, feed-in
tariffs in many countries have significantly decreased over last years 1
The list of publications is limited to original papers dealing with small PV
and are expected to be phased out in the foreseeable future [9]. systems ( o 15 kW) and does not include studies of integrated PV-storage systems
Therefore, it seems important to investigate the profitability of in hybrid applications (e.g. in combination with wind power or diesel generators).
J. Hoppmann et al. / Renewable and Sustainable Energy Reviews 39 (2014) 1101–1118 1103
Table 1
Overview of studies investigating the economics of battery storage in distributed PV systems.
Ref. Author PV technology Battery technology Varied input parameters Econ. output FITa/SCb Time of
parameter premium? investment
[10] Arun et al. Not specified Not specified PV system and storage size Cost of No/No Not spec.,
(2009) electricity one year
[11] Askari and Not specified Lead-acid PV system and storage size Cost of No/No Not spec.,
Ameri (2009) electricity one year
[12] Avril et al. Crystalline Lead-acid, nickel cadmium Technology cost Cost of No/No 2011–2020
(2010) silicon (poly) electricity
[13] Battke et al. Not specified Lead-acid, lithium-ion, Storage cost, storage roundtrip efficiency, life time Cost of No/No 2013
(2013) sodium–sulfur, vanadium and cycle life electricity
redox flow
[6] Bost et al. Crystalline Lithium-ion PV system and storage size, technology cost, Cost of Yes/Yes 2010–2020
(2011) silicon (mono) consumption pattern electricity. grid
parity
[7] Braun et al. Crystalline Lithium-ion Storage size, electricity price, technology cost, FIT IRR, payback Yes/Yes 2010, 2014
(2009) silicon (mono) degression rate period
[14] Celik et al. Crystalline Lead-acid PV system size, location Cost of No/No Not spec.,
(2008) silicon (mono) electricity one year
[15] Clastres et al. Crystalline Not specified Consumption pattern Profit No/No Not spec.,
(2010) silicon (poly) one year
[8] Colmenar- Not specified Lead-acid PV system and storage size IRR, payback Yes/No 2011
Santos et al. period
(2012)
[16] Denholm and Not specified Not specified PV system and storage size Cost of No/No Not spec.,
Margolis electricity one year
(2007)
[17] Jallouli and Not specified Lead-acid Storage size Cost of No/No Not spec.,
Krichen (2012) electricity one year
[18] Kaldellis et al. Not specified Lead-acid, sodium–sulfur PV system size, energy autonomy, solar irradiation, Cost of No/No Not spec.,
(2009) discount rate, investment subsidy, electricity price electricity one year
[19] Kolhe (2009) Not specified Not specified PV system and storage size, technology cost Cost of No/No Not spec.,
electricity one year
[20] Kolhe et al. Not specified Lead-acid Discount rate, solar irradiation, technology cost, Cost of No/No Not spec.,
(2002) O&M costs electricity one year
[21] Lazou and Crystalline Lead-acid Technology cost, location Cost of No/No 1998, 2005
Papatsoris silicon (mono) electricity
(2000)
[22] Li et al. (2009) Crystalline Lead-acid PV system size, technology cost, component Cost of No/No Not spec.,
silicon (poly) efficiency electricity one year
[23] Liu et al. Thin-film Lead-acid PV system and storage size, PV panel slope, Cost of Yes/No Not spec.,
(2012) technology cost and life-time, electricity price electricity, net one year
present cost
[24] Wissem et al. Crystalline Lead-acid PV system and storage size, PV panel slope Cost of No/No Not spec.,
(2012) silicon (mono electricity one year
and poly)
a
FIT: feed-in tariff.
b
SC: self-consumption.
as PV system and storage size, affect specific economic output production, a household could profitably supply active power. In
parameters, e.g. the cost of electricity or the profitability of the contrast, similar to the focus of this study, Bost et al. [6], Braun
integrated PV-battery-system. et al. [7] and Colmenar-Santos et al. [8] see the main financial
Some authors do not specify the PV technology they model. Those incentive for investments in storage in leveraging the gap between
that do usually opt for crystalline silicon PV (for an overview of PV retail and wholesale prices. They assume that, by using storage, a
technologies and their respective merits and shortcomings see household may raise the self-consumption ratio, i.e. the share of
[25–27]). Similarly, among the different options available for battery PV electricity that is consumed by the household. Since this
storage (see [28,29] for an overview), all authors except Bost et al. [6], reduces both the amount of electricity to be fed into the grid at
Braun et al. [7] and Battke et al. [13] focus on lead-acid batteries as the wholesale prices and the electricity to be purchased at retail
currently least expensive alternative for use in residential PV [30]. prices, investing in storage may increase the household's return
To economically assess the inclusion of storage in distributed from the PV plant. Neither Bost et al. [6], nor Braun et al. [7], nor
PV systems, the majority of studies calculate the cost of electricity Colmenar-Santos et al. [8], however, find investments in storage to
that results when installing storage of a particular size. In these be profitable at the time of investigation.2 Therefore, Bost et al. [6]
studies, storage is often used as a means to reach a predefined and Braun et al. [7] additionally test profitability for future points
level of energy autonomy or self-consumption (e.g. in off-grid of investment, assuming declining investment costs for both the
applications), such that the chosen system configuration is gen- PV system and the battery storage over time.
erally not compared to a configuration without storage. So far, only
few studies, namely Bost et al. [6], Braun et al. [7], Clastres et al.
2
[15] and Colmenar-Santos et al. [8], explicitly compute economic Note that Bost et al. [6], following the logic of the ‘grid parity’ concept,
evaluate the profitability by comparing levelized cost of electricity with a mix of
revenues from storage investments. Clastres et al. [15] investigate retail and wholesale price that depends on the self-consumption ratio of the
the possibility of a household providing ancillary services and find household. Braun et al. [7] and Colmenar-Santos et al. [8], in contrast, use the
that, even when considering forecasting errors of electricity metric of internal rate of return.
3.1 System Boundaries and Layout
3.2 Model Input Parameters
3.2.1 Technological Parameters 3.2.2 Economic Parameters

• Electrcity generation • General assumptions
• Electricity storage • Photovoltaic system costs
• Electric load profile • Electricity storage costs
• Electricity prices
8 electricity price scenarios
3.3 Techno-Economic Model of Integrated PV-Storage System
Self-Consumption
3.3.1 Self-Consumption Net Present Value PV System and
Calculation
Calculation Module Calculation Storage Size
Module Module Optimization Module
3.4 Model Output and Sensitivity Analysis
Optimal Optimal Profitability index of

PV system size storage size storage investment
(2013-2022) (2013-2022) (2013-2022)
Fig. 1. Overview of the model structure.
Both studies by Bost et al. [6] and Braun et al. [7] test for storage for a given electricity consumption to achieve a minimum
potential influences of a number of input parameters on profit- cost of electricity, this is not the case for Bost et al. [6] and Braun
ability and provide interesting insights into the potential future et al. [7].3 Systematically testing for a wider range of different
profitability of storage. Yet, two questions remain open from these PV-storage-combinations is important since the self-consumption
analyses. First, in both studies it is assumed that the household ratio, and hence the financial return of the storage investment, is
receives a premium paid on top of electricity market prices for highly sensitive to the assumed PV and storage size. Choosing the
PV-generated electricity that is self-consumed or fed it into the PV system sufficiently small can lead to very high self-
grid. This assumption reflects the current regulatory situation in consumption ratios even without storage since beyond a certain
the German energy market under the Renewable Energy Sources point almost all supply is backed by household demand. Accord-
Act, which Bost et al. [6] and Braun et al. [7] investigate. However, ingly, Bost et al. [6] themselves point out that, while the size of PV
both the feed-in premiums and self-consumption incentives paid plants in Germany has risen over the last years, increasing
have been subject to considerable change in recent years [9]. The incentives to self-consume PV electricity (due to falling FITs and
feed-in tariff for PV has fallen by more than 43% from 2009 to 2011 additional self-consumption incentives) may lead to a trend
and has already reached a level that is below average retail prices. toward smaller PV plants. Currently, however, it remains unclear
PV will have to compete in a market with other sources of to which extent economic optimization of PV system and storage
electricity without policy support in the foreseeable future. Under size affects the profitability of storage over time. In particular, it
a regime with no demand-side policy support storage profitability appears interesting to investigate whether and when economic
will strongly depend on market electricity prices. In their studies optimization of PV system and storage size allows operating
Bost et al. [6] and Braun et al. [7] consider different electricity storage profitably in an environment without policy support.
retail price developments. However, as they assume the existence
of FITs, they do not investigate the effect of different wholesale
price scenarios and the possibility of the household having limited 3
In their model, Braun et al. [7] only vary the storage size and keep the PV
access to the wholesale market. system size constant. Bost et al. [6] simulate different sizes of both the PV system
Second, whereas the majority of studies listed in Table 1 and storage but do not systematically optimize these two parameters with regard
explicitly optimize the size of both the PV system and the to an economic objective function.
PV System
Inverter
Grid
AC Bus
Electricity Electric
Meter Load
Current
Controllers
Battery
Inverter
Battery
Storage
Fig. 2. Layout of integrated PV-storage system [34].
3. Data and method the most widely used one in the literature, considered economic-
ally efficient and suitable for domestic applications and producing
In the subsequent sections, we explain the design and input minimal losses [30,33,34]. The detailed mode of operation of the
parameters of our techno-economic model. Following the general system as assumed in our model will be described in Section 3.3.
logic depicted in Fig. 1, we first describe the system layout and
boundaries (Section 3.1). Next, in Section 3.2 the technological and 3.2. Model input parameters
economic input parameters of the model are presented, including
the eight electricity price scenarios we employ. We provide a 3.2.1. Technological input parameters
detailed explanation of the different modules of the model and The technological input parameters can be broadly divided into
discuss how they interact to produce the simulation results in three categories: those pertaining to electricity generation, the
Section 3.3. The model output and the sensitivity analysis we electricity storage and the electric load. In the following, each of
conducted are described in Section 3.4. the categories will be discussed separately.
3.1. System boundaries and layout 3.2.1.1. Electricity generation. The PV electricity production in kWh/
kWp is a function of the available global horizontal solar irradiation,
To investigate the economic viability of storage in distributed the outside air temperature as well as the tilt, orientation and
PV systems, we simulate electricity generation and consumption performance characteristics of the PV module. Hourly solar
for a three-person household in Stuttgart, Germany. Similar to the irradiation data for Stuttgart, Germany, was obtained from the
studies by Bost et al. [6] and Braun et al. [7], Germany was chosen EnergyPlus weather database provided by the U.S. Department of
as a country as it has the largest share of PV in its electricity mix, Energy [35]. Orientation and tilt were chosen such that the PV
operating more than 35% of the worldwide installed PV capacity in modules could operate under optimal conditions. In southern
2011. The resulting intermittency in electricity generation makes Germany, this corresponds to a southward orientation and a tilt of
Germany a potentially important market for storage solution 301 [26].
providers [31]. Although, due to falling prices for PV systems, the In line with previous studies (see Section 2) we choose crystal-
average size of PV plants in Germany has constantly risen over the line silicon as a PV technology. This choice is made as currently
years, a large share of the German PV market is still made up of crystalline silicon PV offers higher conversion efficiencies than
small-scale, residential PV systems. For example, of the more than thin-film PV and therefore has a market share in residential
73,000 PV plants installed in Germany from January to April 2012, markets that exceeds 86% [36]. To reflect inefficiencies in the PV
more than 47% had a size of less than 10 kWp and more than 85% a system, such as inversion losses, the PV system rated output is
capacity of less than 30 kWp [32]. A three-person household was multiplied with a performance ratio (PR) of 85%.5 In sum, the
chosen to make the results of this study comparable to previous chosen parameters lead to an annual electricity generation of
studies of PV systems in Germany, which have usually investigated 980.93 kWh/kWp.
households of similar sizes.
The layout of the integrated PV-storage system to be investi-
3.2.1.2. Electricity storage. Similar to the majority of previous
gated is shown in Fig. 2. It consists of the PV system, battery
studies (see Section 2), we choose lead-acid batteries as the
storage, two DC–AC inverters and an AC bus.4 This system layout is
storage technology for our model. Compared to other battery
technologies, lead-acid batteries have a short lifetime and low
4
The electricity generated by the PV system is inverted and transmitted to an energy and power density. However, currently, due to their high
AC bus where it can either be directly assigned to the loads of the household
(right), stored in the storage (bottom) or transmitted to the grid (left). To store
5
electricity, the electricity fed into the storage is tapped from the AC bus, inverted to We deliberately choose a slightly higher value than the average PR of 84%
DC and stored. When the household needs to access electricity from the storage, found by Reich et al. [37] as we separately account for losses due to temperature
the DC power in the battery is re-inverted to AC and fed into the household through and degradation. In line with Jordan et al. [38] module efficiency decreases at a rate
the AC bus. of 0.5%/year. The temperature coefficient was chosen to be 97.8% [26].
Production,
Consumption
[Wh]
4'000
3'500
3'000
2'500
2'000
1'500
1'000
500
Time
0 [hour
1 501 1001 1501 2001 2501 3001 3501 4001 4501 5001 5501 6001 6501 7001 7501 8001 8501 of year]
Adj. production [Wh] Consumption [Wh]
Fig. 3. PV electricity generation vs. electric load over year for annual consumption equaling annual production without storage.
Table 2
Economic input parameters for PV system.
Category Parameter Value Source
PV module Average module price 2013 (incl. 0.75 EUR/Wp pvXchange [44]
profit)
Learning rate PV module 20% Kost and Schlegl [45]
Wand and Leuthold [46]
Junginger et al. [47]
Module lifetime 25 Years See Table A.3 in appendix
Inverter Average inverter price 2013 (incl. 0.17 EUR/Wp Annual reports of SMA AG
profit)
Learning rate inverter 18% Annual reports of SMA AG, own
calculation
Inverter lifetime 15 Years EPIA [48]
Balance of systems Sales price BOS PV system 2013 0.64 EUR/Wp BSW solar [49]
Learning rate BOS PV system 18% Schaeffer [50]
EPCa and operations and EPCa PV system 8% of PV system cost (incl. inverter) Peters et al. [26]
maintenance Operations and maintenance cost PV 1.5% of PV system cost (incl. inverter) per Peters et al. [26]
year
a
EPC: engineering, procurement and construction.
reliability, low self-discharge as well as low investment and generation for the case that annual electricity generation of the
maintenance costs, they are the dominant technology in small PV system equals the annual consumption of the household.
scale, residential applications [30,33,39]. Several authors argue It becomes apparent that without storage there is a strong
that in the longer-term lead-acid could be replaced by lithium-ion mismatch between the electricity consumed and generated
batteries that possess better aging features and a higher energy which varies over the year.
efficiency [7,29,40]. At present, however, lithium-ion batteries are
still in a relatively early phase of development and about 3.5 times
as expensive as lead-acid [30]. Furthermore, in the case of 3.2.2. Economic input parameters
stationary use, the lower energy and power density of lead-acid In the following we present the economic input parameters of
batteries are not as critical as, for example, in electric mobility. the model. We first review some general assumptions and discuss
Based on a comprehensive literature review (see Table A1 in the assumptions regarding the costs of the PV system, the battery
Appendix A), the round-cycle efficiency of the battery system system and electricity prices. It is important to note that, while we
was set to 81% and the self-discharge per day to 0.03%. conducted a comprehensive review of previous studies and market
data to identify the input values for our model, often the range of
possible values remains relatively broad. For this reason we use
3.2.1.3. Electric load profile. We use standard load profiles for 8 scenarios for electricity prices. In addition, we performed a
household electricity consumption in Germany at a resolution of sensitivity analysis to test the robustness of the model against
15 min [41]. The load profile was scaled to an annual consumption changes in the other input parameters (see Section 3.3).
of 3.908 kWh to reflect the pattern of a three-person household in
Germany [6]. Moreover, to be consistent with the electricity
consumption profile, the data was transformed from a resolution 3.2.2.1. General assumptions. Since we are modeling a household
of 15 min to one hour by adding up the values within every hour. in southern Germany, we choose Euro as the currency and assume
Fig. 3 juxtaposes the resulting electricity load with electricity inflation to be the one of the Euro zone, i.e. 2.1% [42]. Based on a
1.70 2,325
8% 7%
1.43 12%
1,813
8%
15% 7%
38% 1.19 11%
8% 1,327
38% 17%
6%
10%
10% 39%
19%
10% 66% Engineering. procurement
and construction storage
10% 66%
Engineering, procurement Balance of system storage
and construction PV 64%
44% Inverter storage
43% Balance of system PV
43% Battery
Inverter PV
PV module 2013 2017 2022
2013 2017 2022 Fig. 5. Assumed investment costs (nominal) in EUR for 5 kWh storage for annual
PV electricity generation equaling annual household consumption.
Fig. 4. Assumed PV investment costs (nominal) in EUR/Wp.
review of previous studies, 4% is chosen as a value for the nominal As a wholesale price we chose 0.042 EUR/kWh. The latter value
discount rate. was also obtained from BDEW [51] and constitutes the average
wholesale price during peak hours, i.e. weekdays from 8 a.m. to
3.2.2.2. Photovoltaic system cost. Table 2 lists the model input 8 p.m. Since the time of PV net electricity production falls into this
parameters related to the PV system costs that were retrieved time range, the price was considered a valid starting point for our
from the literature, annual reports of technology producers, analysis.
industry reports and expert interviews. The overall PV system The future development of both wholesale and retail electricity
costs consist of the costs for the PV modules, the inverter, balance prices is highly uncertain. To evaluate a range of possible devel-
of system and engineering, procurement and construction. To be opments in our model, we applied eight electricity price scenarios
able to assess the economic viability of storage for distributed PV (see Table 4).
in the future, we applied a learning curve approach that allows The first five scenarios (S1–S5) assume that the household has
estimating future investment costs based on the cumulative global unlimited access to the wholesale market and contain three
deployment of PV. The learning rates used for the PV module, possible developments for each wholesale and retail prices.
inverter and balance of system (BOS) are listed in Table 2, data for In scenarios S2 and S5 wholesale prices are assumed to fall, which
future PV deployment is obtained from EPIA [43] (see Fig. A1 in would reflect the current observation that an increasing supply of
Appendix A).6 Learning rates were applied to the cost, not the renewable electricity sources with low variable costs tends to
price, of the PV system components, assuming a long-term EBIT lower wholesale prices (so-called ‘merit order effect’). However,
margin of 10%. Fig. 4 exemplarily shows the resulting PV due to the intermittent nature of the former technologies a change
investment cost for 2013, 2017 and 2022. in the structure of the entire electricity market might become
necessary to incentivize the provision of additional, flexible
3.2.2.3. Electricity storage cost. The economic parameters for lead- capacity with higher variable cost (e.g. through so-called ‘capacity
acid storage used in our model are summarized in Table 3. The markets’). As the latter might lead to rising, rather than falling
battery investment cost is calculated by adding up the energy and wholesale prices, we include scenarios in which wholesale prices
power cost of 171 EUR/kWh and 172 EUR/kW respectively [13]. rise by 1.5% (S3) and 3% annually in real terms (S1 and S4). Apart
This procedure was recommended by experts we consulted on this from electricity generation cost, retail prices in Germany include
issue. While studies differ considerably with regard to their grid fees, the utility's profit margin, taxes and the ‘EEG apportion-
assessment of future cost decreases, it has been pointed out that, ment’, the latter containing the cost of the feed-in tariff that is
in general, lead-acid batteries still offer significant potential for redistributed to the consumer. The increasing deployment of
cost improvements. Therefore, in line with VDE [40], a constant renewables in Germany is likely to raise retail prices in the
decrease in battery investment costs of 7.6%/year is assumed. foreseeable future through the EEG apportionment and additional
Furthermore, similar to the PV system, inverter costs are investments in the electricity grid. Since the exact amount of
modeled as a function of the maximum power input to or increases in retail prices is uncertain, based on a literature review
output of the storage. The resulting investment costs for the (see Table A4), we investigate three possible developments,
storage system are displayed in Fig. 5. Since the battery is namely real increases of 2% (scenarios S1 and S2), 1% (scenario
assumed to have a lifetime of 8.3 years, it is replaced twice S3) and 0% (scenarios S4 and S5).
during the life of the PV system. Currently, it remains uncertain to what extent households will
be able to directly sell their electricity on the wholesale electricity
market.8 Moreover, wholesale prices fluctuate considerably during
3.2.2.4. Electricity prices. As discussed in Section 2, the economic
the day with dips occurring when many renewable plants simul-
viability of storage in a regime without policy support is likely to
taneously feed in their electricity, e.g. during noon. To consider
be strongly affected by the present and future level of retail and
these possibilities, we test three extreme scenarios at which
wholesale electricity prices. According to BDEW [51], the average
wholesale prices are assumed to be 0 EUR/kWh (S6–S8). Since
retail price in Germany in 2013 amounted to 0.2884 EUR/kWh.7
6 8
We take the average of EPIA's [43] ‘moderate’ and ‘policy-driven’ scenarios in In the short term, the assumption that households can sell their electricity on
which PV deployment grows at an annual rate of 18% and 25% respectively. the wholesale market requires a preferential feed-in of PV as established under the
Considering that PV deployment since 1994 has grown at an average rate of 35%, German Renewable Sources Act since the handling of a large number of inter-
our assumed market growth of 22% is rather conservative. mittent electricity sources on the market is difficult. In the longer-term, when
7
In accordance with the majority of private electricity contracts in Germany, electricity costs of solar PV have fallen further and intermediary institutions have
we assume that the retail price is the same for the entire day, i.e. there is no special been established that bundle and market solar PV power, it seems possible that
night tariff. solar PV can be marketed on the wholesale market without preferential treatment.
Table 3
Economic input parameters for battery storage system.
Category Parameter Value Source
Battery Battery investment costs in 2013 171 EUR/kWh þ172 EUR/kW Battke et al. [13]
Battery investment cost decrease 7.6%/year VDE [40]
Battery life time 8.3 Years Battke et al. [13]
Inverter See Table 2
Balance of systems BOS storage 70 EUR/kW Battke et al. [13]
EPC and operations and maintenance EPC battery system 8% of battery system cost (incl. inverter) See Table 2
Operations and maintenance cost battery 22 EUR/kW/year Battke et al. [13]
Table 4
Electricity price scenarios used in model simulations.
Scenario Assumption Electricity wholesale price scenario Electricity retail price scenario
S1 Unlimited access of household to wholesale market High: þ3%/year (real) High: þ 2%/year (real)
S2 Low: 1%/year (real) High: +2%/year (real)
S3 Medium: þ 1.5%/year (real) Medium: þ 1%/year (real)
S4 High: þ3%/year (real) Low:þ 0%/year (real)
S5 Low: 1%/year (real) Low: +0%/year (real)
S6 No access of household to wholesale market Constant: 0 EUR/kWh High: þ 2%/year (real)
S7 Constant: 0 EUR/kWh Medium: þ 1%/year (real)
S8 Constant: 0 EUR/kWh Low:þ 0%/year (real)
Electrcity generation,
Consumption in Wh
Electricity generation
Storage (3)
capacity
(2)
Electricity consumption
(5)
(4) (1)
(1)
Time
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 [hour of day]
load unload
storage storage
(1) From grid (4) Direct self-consumption

(2) To storage (5) From storage (indirect self-
(3) To grid consumption)
Fig. 6. General logic of self-consumption calculation module (illustrative).
we model investment decisions from 2013 to 2022 for a PV system 3.3.1. Self-consumption calculation module
with a lifetime of 25 years, electricity prices are extrapolated until As the basis for the economic calculations, in a first step the
2047 in all eight scenarios. Compared to previous studies, our self-consumption ratio (SCR), i.e. the share of electricity generated
maximum price increases are chosen rather conservatively. Never- by the PV system that is consumed by the household, is calculated.
theless, it should be noted that under our assumptions in the high Fig. 6 portrays the general logic underlying the calculation. It is
price scenarios, retail and wholesale price in 2047 reach a level of assumed that whenever electricity demand during the day can be
0.57 EUR/kWh and 0.11 EUR/kWh in 2013 prices respectively (see met by the concurrent electricity generation of the PV system, the
Fig. A2 in Appendix A). household consumes its own electricity (see number 4 in the
figure). If electricity generation exceeds household consumption,
electricity is either stored for later consumption (2) or sold to the
3.3. Techno-economic model of integrated PV-storage-system grid if the storage is loaded (3). The ratio between electricity that
is directly self-consumed (4) or taken from storage later (5) and
The following sections describe how the values are processed the total electricity generated by the PV system (2 þ3 þ4) defines
in the model to generate our results. We first present the three the self-consumption ratio. For a given electricity consumption,
main modules of the model – (1) the self-consumption calculation this ratio is directly dependent on the size of the PV system and
module, (2) the net present value calculation module and (3) the the size of the battery storage. In the model, the self-consumption
storage and PV size optimization module. ratio is calculated by simulating the electricity flows of the system
over the year at an hourly resolution. The self-consumption ratio the quotient of the NPV of the storage investment and the storage
serves as an input to the second module of the model which investment cost at the time of investment.10
calculates the net present value of the integrated PV-battery To investigate the robustness of the model with regard to
system for the household. variations in the input parameters, a sensitivity analysis was
conducted. As part of this analysis the 13 most important input
3.3.2. Net present value calculation module parameters that had not been modeled as scenarios were aug-
For a given investment year t, the net present value (NPV) of mented and lowered by 33% of their original value one at a time
household investments is calculated as the sum of the discounted for scenario S3 (which assumes medium increases of both retail
cash in- and outflows over the 25 year lifetime of the PV/battery and wholesale price). The results of this analysis will be presented
system.9 As shown in detail in Appendix B, cash outflows comprise in Section 4.4 after describing the general simulation results.
the investment costs for the PV system and battery system as well
as the operations and maintenance expenses (see Section 3.2). For
the cash inflow it is assumed that with consuming electricity from 4. Results
the own PV system, the household substitutes electricity that it
would otherwise have to purchase from the electric utility at retail In the following, we describe the model outcomes, i.e. the
prices. Excess electricity that is neither self-consumed nor stored optimal PV system size (4.1), the optimal size of storage (4.2) and
is sold at wholesale prices. The revenues of the household are then the profitability of storage for a rationally optimizing household
calculated as the sum of (1) the self-consumed electricity (i.e., the for the years of investment from 2013 to 2022 and the eight
product of electricity generated during each year of system life- electricity price scenarios (4.3). Finally we present a sensitivity
time multiplied and the SCR) multiplied with the retail electricity analysis of the key input parameters (4.4).
price and (2) the electricity sold (i.e., the product of the electricity
generated during each year of system lifetime and 1-SCR) multi-
4.1. Optimal PV system size
plied with the wholesale electricity price.
The development of the optimal PV system size as well as the
3.3.3. Storage and PV system size optimization module corresponding electricity production/consumption ratio for an
The third module draws on the inputs from the ‘self-consump- economically rational household under the 8 electricity price
tion calculation module’ and the ‘net present value calculation scenarios is shown in Figs. 7 and 8. The production/consumption
module’ to find the optimal storage and PV system size for the ratio describes the quotient of the annual electricity generated by
household. For each investment year from 2013 to 2022 and each the PV system and the annual electricity consumption of the
of the eight electricity price scenarios (see Table 4 in Section 3.2) household.
the module calculates the net present value for 1435 different As can be seen, under a medium electricity retail price, medium
combinations of PV system and storage sizes (35 PV system sizes electricity wholesale price scenario (S3) the optimal size of the PV
times 41 storage sizes). Based on these values, the PV system and system the household invests in rises strongly over time. Most
storage size are identified that maximize the NPV of the overall importantly, investments in the PV system are profitable for the
PV-storage system (see Appendix C for a more detailed description household throughout the period of investigation, which is indi-
of the calculation procedure). Tested PV system sizes range from cated by the fact that the size of the PV system is always different
0.4 kWp to 14 kWp and are incremented at steps of 0.4 kWp. from zero.11 In early years, however, the optimal PV system size is
14 kWp was chosen as the maximum since the PV capacity that chosen such that the PV system generates less electricity than the
can be installed on village houses in Germany was, on average, household consumes (i.e. the production/consumption ratio is
found to be limited to this value [52]. The storage sizes tested by smaller than 1). This is due to the fact that investment costs for
the model range from 0 kWh (i.e. no storage) to 20 kWh and are both the PV and the storage system are relatively high, requiring
increased at intervals of 0.5 kWh. Note that the model assumes a the household to have a high rate of direct self-consumption
depth of discharge of the battery of 80%, i.e. the usable battery which can only be reached when choosing a small PV system size.
capacity is lower than the nominal values indicate. With falling investment costs, however, the optimal production to
consumption ratio increases to reach a point where after 2017
3.4. Model output and sensitivity analysis annual PV electricity generation exceeds the electric load of the
household. Subsequently, the optimal PV system rises further until
Overall, for each investment year from 2013 to 2022 and each in 2022 under the S3 scenario its size reaches the maximum PV
of the eight electricity price scenarios the model generates three system size of 7 kWp.
main outputs: As shown in scenarios S1, S2, S4 and S5 in Fig. 7, the optimal PV
plant size is very sensitive to both future retail and wholesale
(1) the economically optimal size of the PV system, electricity prices. Stronger increases in retail prices (scenarios S1
(2) the economically optimal size of the storage system and and S2) favor larger PV plant sizes since they enhance the value of
(3) the profitability of the storage investment.
10
As described in the previous section, the optimal PV system and We use the profitability index to measure storage profitability instead of the
NPV since we optimize the storage size for different points in time of investment.
storage size are those that maximize the NPV of the integrated
The differences in optimal storage size over time would make the profitability of
PV-storage system. As a measure for profitability of the storage storage hard to compare if we used an absolute measure of profitability. Therefore,
investment, we use the profitability index (PI) which is defined as we report the storage profitability as the NPV per EUR invested. The optimal
storage size over time is reported as a separate output variable.
11
It should be emphasized that our finding that already in 2013 PV systems in
9
Since in Germany, households have access to low-interest loans from ‘KfW Germany were profitable without policy support hinges on a number of assump-
bank’, in general the availability of capital does not constrain the size of PV systems tions: (a) the household needs to optimize the size of the PV system since only
and storage to be invested in. As a result, the households can be considered to small systems are profitable in early years, (b) electricity prices need to develop as
maximize the absolute return from the integrated PV-storage system, irrespective indicated in our scenarios and (c) costs for engineering, procurement and
of its size. In our model, we therefore use (and maximize) the NPV as a measure of construction depend mostly on the size of the system (i.e. they do not contain a
profitability. large fixed component which may be the case for very small PV systems).
Optimal Electricity generation/

PV system size electricity consumption
in kWp ratio
14 3.5
13
12 3.0
11
10 2.5
9
8 2.0
7
6 1.5
5
4 1.0
3
2 0.5
1
0 0.0
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Year of
investment
S1: High retail, high wholesale price scenario
S2: High retail, low wholesale price scenario
S3: Medium retail, medium wholesale price scenario
S4: Low retail, high wholesale price scenario
S5: Low retail, low wholesale price scenario
Fig. 7. Optimal PV plant size under electricity price scenarios S1–S5.
Optimal Electricity generation/

PV system size electricity consumption
in kWp ratio
14 3.5
13
12 3.0
11
10 2.5
9
8 2.0
7
6 1.5
5
4 1.0
3
2 0.5
1
0 0.0
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Year of
investment
S6: High retail price scenario, wholesale price = 0 EUR/kWh
S7: Medium retail price scenario, wholesale price = 0 EUR/kWh
S8: Low retail price scenario, wholesale price = 0 EUR/kWh
Fig. 8. Optimal PV plant size under the assumption that the household cannot sell electricity on the wholesale market (electricity price scenarios S6–S8).
the electricity produced by the PV system – which substitutes the wholesale market, the optimal PV system size is considerably
electricity purchased from the grid. Similarly, for a given retail smaller than the one for scenarios where the household can not
price scenario, the optimal PV system size is higher for higher only consume but also sell its electricity (see S6–S8 in Fig. 8). As
wholesale prices (S1 and S4) since excess electricity can be sold on could be expected, the household chooses the PV system size such
the market at higher prices. Interestingly, while retail prices are that the electricity it produces almost never exceeds the electricity
the factor that influences PV system size most strongly in early the household consumes.
years, wholesale prices become more important during later
periods. This can be explained by the fact that with falling 4.2. Optimal storage size
technology costs, the size of PV plants rises over time which leads
to a situation where households, despite using storage, need to sell Figs. 9 and 10 display the development of the optimal storage
an increasing share of their electricity on the wholesale market. size. Under the medium electricity retail price, medium electricity
Under the assumption that the household does not have access to wholesale price scenario (S3), the optimal storage size amounts to
Optimal
storage size
in kWh
8.5
8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Year of
investment
Fig. 9. Optimal storage size under electricity price scenarios S1–S5.
Optimal
storage size
in kWh
8.5
8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0 Year of
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 investment

Fig. 10. Optimal storage size under the assumption that the household cannot sell electricity on the wholesale market (electricity price scenarios S6–S8).
4.5 kWh storage in 2013 and rises significantly to reach 7.0 kWh in scenarios S4 vs. S5). At a first glance, this result seems counter-
2021. The fact that the optimal storage size levels out is due to the intuitive since one might assume that storage becomes particu-
fact that our model includes a constraint for the maximum PV larly important when wholesale prices are low such that a
system size which dampens the size of storage that is installed household does not have to sell electricity on the market at low
under economic considerations. prices. Yet, this finding can be explained by the fact that higher
Similar to the optimal PV system size, the optimal storage size wholesale prices trigger investments in larger PV plants (see
in early years depends particularly on the assumed retail price previous section), which in turn raises the optimal storage
developments. Under the assumption of strong increases in future capacity. Overall, however, the impact of wholesale prices on the
retail prices, the household invests in 4.5–5 kWh storage as early optimal storage size is relatively small. Even when assuming a
as 2013 (scenarios S1 and S2), whereas when assuming a stagna- constant wholesale price of 0 EUR (i.e. no possibility for house-
tion in retail prices (real) only 3–5 kWh storage is added (scenarios holds to sell their electricity on the wholesale market) the optimal
S4 and S5). Interestingly, given a particular retail price increase, storage is almost identical to a scenario where the household can
the optimal storage size is slightly larger for scenarios that assume sell the electricity at a medium wholesale price (see scenarios S6–
a stronger increase in wholesale prices (see scenarios S1 vs. S2 and S8 in Fig. 10).
4.3. Storage profitability wholesale electricity prices raise the profits to be gained from storage
investments in later years when PV systems are large and households
The development of storage profitability over time (excluding tend to sell a higher share of their electricity on the market (see
the PV system) is shown in Figs. 11 and 12. Investments in storage scenarios S2 and S5). Correspondingly, investments in storage remain
are already profitable in 2013 under all electricity price scenarios. profitable even under the assumption of a constant wholesale price
Furthermore, due to falling investment costs, the profitability of of 0 EUR, i.e. no access of households to wholesale markets (see
storage continuously rises over time in an almost linear fashion. scenarios S6–S8 in Fig. 12).
Under the assumptions of our model, in the S3 scenario, the
storage PI rises from 0.4 in 2013 to 2.66 in 2022. 4.4. Sensitivity analysis
Like the optimal storage size, storage profitability depends mostly
on retail prices. Assuming a higher retail price scenario raises the Fig. 13 shows a tornado graph on how the profitability index
profitability for all years under investigation (see scenarios S1 and (i.e. the NPV of the storage investment per EUR invested in
S2), whereas a low retail price scenario lowers it (scenarios S4 and storage) changes when varying the most important input para-
S5). Under the assumption of a stronger increase in future retail meters, that are not covered by the scenarios, by 33% and þ 33%.
electricity prices, storage is profitable as early as 2013. Lower It becomes obvious that of all input parameters, the nominal
Net present value of storage

per EUR invested in storage
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0 Year of
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 investment

Fig. 11. Storage profitability under electricity price scenarios S1–S5.
Net present value of storage

per EUR invested in storage
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Year of
0.0
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 investment

Fig. 12. Storage profitability under the assumption that the household cannot sell electricity on the wholesale market (electricity price scenarios S6–S8).
-30 -20 -10 0 10 20 30 Change in NPV of

Variable Starting value storage per EUR
invested in storage [%]
Nominal discount rate 4%
Battery investment cost

-7.6% p.a.
decrease
Battery investment cost 2013 171 EUR/kWh + 172 EUR/kW
Increase in global installed PV

22% per year
capacity
BOSStorage 70 EUR/kW
Learning rate inverter 18%
O&M cost PV 1.5% of PV system cost p.a.
O&M cost battery 22 EUR/kW per year
Inverter EBIT margin 10%
Module EBIT margin 10%
EPC PV System 8% of PV system cost
Learning rate PV module 20% -33%

+33%
Learning rate BOSPV 18%
Fig. 13. Sensitivity analysis of the most important input parameters under scenario S3.
discount rate and the battery investment cost reduction have the prices fluctuate significantly and the future development of both
greatest effect on the model outcome. Moreover, the model is wholesale and retail prices remains unclear, future cash flows are
sensitive to changes in the assumption of future battery cost difficult to predict. This is especially true if one considers that
decreases and the assumed increase in the global installed PV policy makers may take measures in the future that change the
capacity (the latter determining the technological learning and profitability of PV and storage investments. At the moment, for
hence the investment costs of PV). example, households in Germany that consume self-generated
electricity do not have to pay electricity taxes, the EEG apportion-
ment and grid fees. Since this puts an increasing burden on
5. Discussion electricity consumers that do not own a PV system, it seems likely
that policy makers will take measures to have owners of PV
In the following we discuss the implications of our findings for systems carry some of these costs in the future. Moreover, the
private households, the broader electricity sector and policy individual load patterns of households deviate from the standard
makers. load pattern used in our analysis. In our analysis the household
optimizes the size of both the PV and storage system to maximize
5.1. Implications for household investments its revenues. In reality, such optimization will be very hard to do as
load patterns may be unknown or change over time and PV/
The findings presented in the previous section demonstrate storage systems will be offered in standardized sizes. The uncer-
that already now battery storage is economically viable for small tainties regarding future electricity prices and difficulties in
PV systems under all electricity price scenarios. Especially those assessing the benefits from storage may prevent households from
scenarios that, in line with current trends in Germany, assume a investing in PV and storage technologies. Second, apart from
decrease in electricity wholesale prices and a concurrent increase economic considerations, the adoption of PV and storage technol-
in electricity retail prices lead to a high economic viability of ogies by households strongly depends on social factors. Household
storage investments. Moreover, if households are assumed to have investments are strongly driven by the knowledge about invest-
limited access to the wholesale market in the future, this does not ment opportunities and the ability to overcome behavioral
undermine but may even bolster storage profitability. barriers.
The early profitability of storage for residential PV without
policy support is striking and can be assumed to have a major 5.2. Implications for environmental pollution, safety
impact on household investments. Nevertheless, we caution to and maintenance
conclude that a high profitability of integrated PV-storage systems
will automatically imply a strong adoption of these technologies Solar photovoltaic plants generate considerably less emissions
by households starting at this point in time. Despite being profit- over the life-cycle than plants fueled by coal or gas [53]. However,
able, PV systems (with and without storage) may not be installed the increasing profitability of battery systems for residential PV
for several reasons. First, in stark contrast to investments under a systems raises concerns about environmental pollution that may
feed-in tariff scheme, returns from investing in PV are much less result from a wider diffusion of batteries. Lead-acid batteries
certain under a regime without policy support. Given that market contain sulfuric acid as well as toxic lead and generate carbon
emissions particularly during lead mining and polypropylene combination with residential PV systems in Germany appear
production [54,55]. This environmental impact of lead-acid bat- necessary only in the short term. This result is of importance
teries can be significantly reduced when recycling the lead. Yet, since several institutions in Germany, such as the German Solar
while in Germany nearly 100% of the lead in commercial-scale Photovoltaic Industry Association (BSW), have called for additional
lead-acid batteries is recycled [40], the use of batteries is more incentives for battery storage in past [30]. Recently, the German
problematic in countries which do not yet possess a working government has responded to this call by announcing a 50 million
recycling infrastructure. An additional challenge lies in producing EUR demonstration program that provides investment subsidies to
battery systems that allow operation without safety threats from buyers of storage for residential PV system [5]. Our findings
short circuits, deep discharge, over-discharge and over- indicate that the incentives provided under this program can be
temperature [56]. Preventing the occurrence of such threats will phased out relatively soon as rising electricity retail prices and
require mandatory safety tests and certification procedures for the falling technology costs raise the profitability of storage.
producers of battery systems. Moreover, a maintenance infrastruc- Third, our findings allow us to derive some insights into how
ture will have to be set up that ensures the reliable operation and different political interventions affect the economic viability of storage.
timely replacement of batteries. In essence, all political measures that raise the retail price can be
expected to also raise the profitability of storage investments for
5.3. Implications for the electricity sector residential PV in the short-term. In the longer-term, measures that
lower the wholesale price can additionally contribute to increasing the
Besides providing insights into potential changes in household NPV from storage investments. In this sense, electricity taxes and grid
investments, our analysis has important implications for the elec- fees that are only included in retail and not wholesale prices will
tricity sector. As discussed in Section 4.1, it can be expected that even provide an incentive for households to invest in storage technologies.
without policy support households will raise the amount of elec- Premiums for self-consumption will generally raise the profitability of
tricity they produce themselves. The use of battery storage supports storage investments. From the sensitivity analysis, it can further be
this trend as it allows households to consume a larger share of self- derived that measures which reduce the investment cost of PV and
produced electricity, reducing the amount of electricity to be bought storage, such as deployment policies or investments in R&D, con-
from utilities. Moreover, if households are also able to sell their tribute to enhanced storage profitability. Moreover, an important
electricity on the wholesale market in the future, an ever increasing means for raising the profitability of investments in storage lies in
number of households will move from being electricity consumers to lowering the interest rate at which households can obtain capital at
becoming net electricity producers. This trend has the potential to financial markets. In this sense, low-interest loan programs, such as
drastically alter the existing market structure. Electric utilities are the KfW program in Germany, are likely to be very effective means at
likely to be confronted with a growing number of households that fostering storage investments.12 For measures like feed-in premiums,
produce and sell their own electricity which fundamentally under- the effect on storage profitability is less clear since, on the one hand,
mines their current business model. At the same time, a shift toward they raise the price at which households can sell the electricity on the
a system of strongly distributed electricity generation will probably market (negative effect on storage profitability). On the other hand,
require major adaptations in the technical infrastructure of the however, feed-in premiums increase the deployment of PV, potentially
electricity system, such as distribution grids. In fact, the observation reduce wholesale prices in the longer term and may raise the retail
that storage is economically viable for a private household does not prices in the short-term (positive effect on storage profitability – see
imply that implementing battery storage systems is also beneficial Section 3.3). In Germany, FIT premiums have fallen significantly in the
from the perspective of overall stability of the electricity system. It recent past while, simultaneously, the increasing use of renewables
currently remains open to what degree implementing small-scale, has raised retail and lowered wholesale prices. Interestingly, therefore,
distributed storage reduces throughput and required capacity of the in Germany the policy-induced deployment of PV itself has driven the
electricity grid. Hollinger et al. [57] find that battery storage for profitability of storage as a complementary technology.
residential PV systems can reduce the burden on the electricity
distribution grids by around 40%. In contrast, Büdenbender et al. [58]
find no positive effect of storage on alleviating the stress on the 6. Limitations and future research
distribution grid that is created by distributed PV. Some authors even
argue that instead of enhancing grid stability, small-scale storage Our study has several limitations that lend themselves as
may add to instabilities [30]. It is suggested that, if the implemented avenues for future research. First, as for any model, our results
storage solutions are small, electricity feed-in patterns of PV systems are limited by the input parameters chosen for our simulation. To
could become less predictable with irregular peaks in distribution keep the scope of the paper within reasonable boundaries, we
grids occurring when storage systems are loaded before noon. restricted the choice of technologies to one PV and one battery
technology. As described in Section 3, strong research and devel-
5.4. Implications for policy makers opment efforts that are currently being undertaken on other
battery types (e.g., lithium-ion or sodium sulfur) could lead to
Finally, our results allow us to draw some conclusions for policy significant cost decreases in next years which would warrant a
makers. First, we find that residential PV systems of small sizes closer investigation of these technologies in residential PV appli-
(with and without storage) are profitable without policy support cations. Moreover, assuming cost decreases in PV to follow the
under all scenarios in Germany in 2013. Nevertheless, policy pattern of learning curves, of course, paints a simplified picture of
support, e.g. in the form of feed-in tariffs may be necessary for technological change. While for our model the accuracy reached
at least an intermediary period since in an environment without using learning curves is probably sufficient, a more detailed model
policy support (a) the PV systems that are built tend to be rather of technological change would have to consider a wider range of
small, leading to a suboptimal use of roof-space and (b) uncer- drivers of technological change than deployment [59] and should
tainties and the inability of households to determine the profit-
ability of PV systems may prevent households from investing (see 12
Currently, the low-interest loans from the KfW bank are only available for PV
Section 5.1). systems. However, there are plans to introduce specific loan programs for storage
Second, the findings of our analysis imply that additional which according to our analysis appears an effective way of fostering storage
economic incentives to foster the use of small scale storage in investments.
also take into consideration the rate at which technologies are profitability of battery storage from 2013 to 2022 under eight
deployed [60]. Since investment costs for technology, solar irra- different scenarios for PV investment costs and electricity prices in
diation, electricity prices and electricity consumption patterns Germany. In contrast to previous forward-looking studies, we
differ between countries [61], it would be valuable to repeat our assume that no feed-in or self-consumption premium is paid for
analysis for households in other geographic locations. Further- electricity generated using solar PV. Moreover, for each year of
more, in future studies different household characteristics, such as investment and each scenario, our model tests more than 1400
the number of persons living in the household, should be varied to combinations of PV system and storage sizes to determine the one
provide a more comprehensive picture of the economic viability of that yields the highest net present value. We find that, given an
storage under different conditions. Ideally, when doing so, the economically rational household, investments in battery storage
resolution of the data regarding both, electricity generation and are already profitable for small residential PV systems. The optimal
consumption, should be enhanced to account for short-term peaks PV system and storage sizes rise significantly over time such that
that are leveled out when using hourly data. Although Wille- in our model households become net electricity producers
Haussmann et al. [62] find that changing the resolution from 10 s between 2015 and 2021 if they are provided access to the
to 15 min alters the self-consumption ratio only by 2–3%, a higher electricity wholesale market. Developments that lead to an
resolution becomes important when conducting a more detailed increase in retail or a decrease in wholesale prices further
analysis of storage use for specific days, e.g. least or most sunny contribute to the economic viability of storage. Under a scenario
days during the year. where households are not allowed to sell excess electricity on the
Second, we restrict our economic analysis to investigating how wholesale market, the economic viability of storage for residential
storage can be used to leverage the existing price spread between PV is particularly high. Our findings have important implications
wholesale and retail prices. Beyond increasing self-consumption, for the electricity sector and regulators that wish to shape its
however, storage can generate economic value in a range of future. We conclude that, under the assumptions of our model
different applications, such as ancillary services or arbitrage deal- additional policy incentives to foster investments in battery
ing, e.g. buying electricity at night and reselling it to the grid at storage for residential PV in Germany seem necessary only in the
daytime when electricity prices tend to be higher [13]. Combining short-term. At the same time, the increasing profitability of
different applications can potentially further increase the eco- integrated PV-storage-systems may come with major challenges
nomic viability of storage compared to the findings in this paper for electric utilities and is likely to require increased investments
[63]. In this context, it should be kept in mind that in our model in technical infrastructure that supports the ongoing trend toward
we assume the electricity consumption of the household to be distributed electricity generation.
invariant to electricity prices. It seems likely that in reality,
especially with the emergence of demand-side management
systems, households may alter their consumption pattern depend- Acknowledgments
ing on the prices they face.
The authors would like to thank Laura Diaz Anadon, Benedikt
Battke, Joern Huenteler and Michael Peters for their valuable
comments on earlier drafts of this article. Moreover, we would
7. Conclusion like to acknowledge the helpful feedback we received by two
anonymous reviewers.
In this paper we investigate when and under which conditions
battery storage will be economically viable in residential PV
systems without policy support. Building upon a review of Appendix A
previous studies on the economics of battery storage for distrib-
uted PV, we develop a techno-economic model that simulates the See Figs. A1 and A2 and Table A1–A4.
Cumulative global
installed PV
capacity [GW]
900
844
800
700 689
600 562
500 459
400 376
322
300 272
227
200 183
139
100
0
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Year
Fig. A1. Global PV deployment underlying the PV investment cost development.
Electricity price
in EUR/kWh
(real)
0.60
0.55
0.50
0.45
0.40 Retail price
0.35
0.30
0.25
0.20
0.15
Wholesale price
0.10
0.05
0.00
2013 2017 2022 2027 2032 2037 2042 2047
Fig. A2. Assumed electricity price developments.
Table A1 Table A4
Overview of lead-acid technology parameters in the literature. Overview of electricity price forecasts for Germany in the literature.
Author (year) Self-discharge [%/day] Roundcycle Author (year) CAGR retail price (%) CAGR wholesale price (%)
efficiency [%]
Bhandari and Stadler [73] 2–4 3–6
Burke et al. [64] 0.3 EPIA [48] 0.9 4
Chen et al. [65] 0.1–0.3 70–90 Berger and Prognos [75] 1.7 3.2–5.1
Divya and Østergaard [29] 0.06–0.17 72–78 Nitsch et al. [76] 0–2.5
Dunn et al. [66] 75–90 Nagl et al. [77] 0–0.4
EPRI and DOE [67] 0.033 75–85
Gonzalez et al. [68] 81
Hadjipaschalis et al. [28] 2 85–90
Sauer et al. [30] 80–90
Schoenung and Hassenzahl [69] 0.1 70–80
Appendix B
VDE [40] 80–90
Wu et al. [70] 80
The net present value of the integrated PV system is calculated as
N C IN; t;n C OUT;t; n
NPV t ¼ C t þ ∑
n ¼ 0 ð1 þ iÞn
where
Table A2
CAPEX BAT;t þ 9
Overview of interest rates in the literature. C t ¼ CAPEX PV;t þ CAPEX BAT;t þ ð1 þ iÞ9
Author (year) Interest rates (%) C IN; t;n ¼ ½SCRt RP n þ ð1 SCRt Þ UWP n kWht ð1 DRÞn
C OUT; t;n ¼ OPEX PV ;t;n þ OPEX BAT;t;n
BMU [71] 5–8
Branker et al. [72] 4.5 and
Bost et al. [6] 0
NPV net present value of integrated PV-storage system
t year of investment (2013, ..., 2022)
n year of system lifetime (0, …, 25)
N system lifetime (25 years)
Table A3 i interest rate (4%)
Overview of module lifetime parameters in the literature. CIN cash flow in
COUT cash flow out
Author (year) Module lifetime [years]
SCR self-consumption ratio
Bhandari and Stadler [73] 25–40 RP retail price
Denholm and Margolis [16] 30 WP wholesale price
EPIA [48] 25–35 kWh electricity generated by PV system
Sauer et al. [30] 20
Van der Zwaan and Rabl [74] 25
DR module degradation rate
CAPEXPV capital investment cost PV system
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2014-The Economic Viability of Battery Storage For Residential Solar Photovoltaic Systems

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Renewable and Sustainable Energy Reviews 39 (2014) 1101–1118

Contents lists available at ScienceDirect

Renewable and Sustainable Energy Reviews

The economic viability of battery storage for residential solar

5.1. Implications for household investments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113

1. Introduction storage in an environment without demand-side subsidies for PV

3.1 System Boundaries and Layout

3.2 Model Input Parameters

3.2.1 Technological Parameters 3.2.2 Economic Parameters

8 electricity price scenarios

3.3 Techno-Economic Model of Integrated PV-Storage System

3.4 Model Output and Sensitivity Analysis

Optimal Optimal Profitability index of

Fig. 1. Overview of the model structure.

Fig. 2. Layout of integrated PV-storage system [34].

Adj. production [Wh] Consumption [Wh]

Category Parameter Value Source

Category Parameter Value Source

(1) From grid (4) Direct self-consumption

Fig. 6. General logic of self-consumption calculation module (illustrative).

Optimal Electricity generation/

Fig. 7. Optimal PV plant size under electricity price scenarios S1–S5.

Optimal Electricity generation/

Fig. 9. Optimal storage size under electricity price scenarios S1–S5.

S6: High retail price scenario, wholesale price = 0 EUR/kWh

Net present value of storage

S1: High retail, high wholesale price scenario

Fig. 11. Storage proﬁtability under electricity price scenarios S1–S5.

Net present value of storage

S6: High retail price scenario, wholesale price = 0 EUR/kWh

-30 -20 -10 0 10 20 30 Change in NPV of

Battery investment cost

Battery investment cost 2013 171 EUR/kWh + 172 EUR/kW

Increase in global installed PV

Learning rate inverter 18%

O&M cost PV 1.5% of PV system cost p.a.

O&M cost battery 22 EUR/kW per year

Inverter EBIT margin 10%

Module EBIT margin 10%

EPC PV System 8% of PV system cost

Learning rate PV module 20% -33%

0.40 Retail price

Fig. A2. Assumed electricity price developments.

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