SYSTEM SIZING FOR RESIDENTIAL PV AND EES SYSTEMS
Tobias Melloh, Tristan Fehling, Gerhard Kleiss1, Bernard Nacke
Institute for Electrotechnology (ETP), Leibniz Universität Hannover
Wilhelm-Busch-Str. 4, D-30167 Hannover, Germany
1 corresponding author: email@example.com
ABSTRACT: Looking at the market for residential Electrochemical Energy Storage (EES) systems in
combination with PV systems (PV), a significant growth has been observed recently. For these systems a new
purchase motivation of the residential customers can be observed: private customers are looking for autarky in order
to avoid purchasing electricity from the grid. This is in contrast to preceding purchase motivations triggered by
comparatively high feed-in tariffs leading to installation of larger grid-connected PV systems without storage on
private households (having promised more financial benefit for the user in the past). This work determines levels of
autarky for different sizes of both PV system (PV) and storage (EES). A simplified algorithm for system operation is
applied to a standardized consumption profile that is calculated under consideration of 3 different typical European
climatic conditions. Based on these results design rules are suggested leading to comparatively small system sizes as
the economic optimum under the financial boundary conditions considered here.
KEYWORDS: PV, ESS, system sizing, autarky, cost, site-dependence
Today, there are an increasing number of residential
applications of photovoltaic (PV) solar energy systems in
combination with an electrochemical storage system
(EES). Since such systems are in most cases still
connected to the electrical grid, many users are looking
for a high level of autarky in their electricity supply in
order to reduce cost of electricity purchase from the
Distribution System Operator (DSO).
We may call this approach in the context of this text
the “user’s egocentric approach”, as no or little awareness
is given for the overall grid situation. In case all
residential users would follow exactly the scheme
proposed here, this would incur a serious burden for the
DSO. Other approaches may deliver not only benefits for
the individual customer but also for the utility operator.
This is not discussed in this paper but will be discussed
The aim to minimize private electricity consumption
directly creates a need for choosing the appropriate size
of both PV generator and EES battery. Prices and
economics of both PV and EES have seen considerable
changings recently , . This is why it is important to
re-calculate models and derive new design rules for
system sizing. The influence of climatic operation
conditions can be expected and is studied in this work by
comparing results from several climatic zones: temperate
continental, Mediterranean and temperate coastal. The
selected locations are taken from  and offer a good
broad-band view for locations in Europe.
2.1. Model of General System Set-Up and Operation
The PV-EES system investigated is based on the 4
- PV Generation (P)
- ESS Storage (S)
- Grid (G) (consumption or feed-in)
- Load requirement (L)
The scenario which has been studied has a flow of
energy following the subsequent rationale:
(a) The actual load requirement L must always be
met: in the first place (Priority 1a) through the
PV system (P), in the second rank (Priority 1b)
through the ESS (S), and in case of necessity the
grid (G) as Priority 1c.
(b) Only if the load requirement is satisfied and if
there is additional energy available from the PV
system, the ESS (S) can be loaded by PV
(Priority level 2).
(c) Only if the ESS is fully loaded under such
conditions the residual power may be injected
into the grid G (Priority level 3).
Fig. 1: algorithm for flow of energy adopted in the model.
Of course, there are many other strategies to run PV-
EES combinations , , including the possibility to
charge the EES directly from the grid under conditions of
varying tariffs . Another necessity to adapt the
operation algorithm may arise due to regulatory
requirements limiting the feed-in from the PV system into
the grid . The latter case was investigated in the frame
of the current work, but results are not presented here, as
the main trends turned out to be similar to what is
To calculate the load L, we use a Standard Load
Profile (SLP) H0 as published by the German
Distribution System Operators’ association BDEW
relevant for residential applications . This SLP is given
on quarter-hourly base and is expanded to an hourly base
for purpose of calculation within this study. Fig. 2 shows
the typical SLP yearly normalized to a yearly
consumption of 4000 kWh as investigated in this work.
Fig. 2 BDEW load profile H0 for the month of January,
scaled for a yearly consumption of 4’000 kWh
2.2. PV Specific Model
In order to simulate the PV-EES system, a module
efficiency of is assumed. Likewise, a
maximum inverter efficiency of is
considered for calculation. Both assumptions may be
considered a conservative approach. Temperature related
losses are accounted on the base of calculating the power
reduction by a temperature coefficient
with the temperature coefficient set to = -4’600
ppm/K. Operating temperatures have been
calculated by FAIMAN’s approach 
with applicable coefficients for typical
crystalline PV modules taken from . There is no
further consideration of the modules’ relative
performance with respect to irradiance and/or other
impacts. Prior studies  have shown that an influence
is existing, but it may be regarded small as within this
study the total energy produced is the leading quantity
(and corrections are of second degree). We have been
considering the thermal correction (eqn. 1 and 2) as this
will exclude any possible temperature related (AM versus
PM) asymmetry. The model contains no provision for
temperature-related de-rating of the inverter or the EES,
as those components are deemed to be operated indoors
within a controlled environment. Moreover, no
degradation effects are considered as a time frame of 10
years is considered, corresponding to typical warranty
periods for many residential EES systems promising
lawless operation. In order to attain a site-dependent
result, the meteorological data given per Table I have
been used for computation.
Table I: sample data sets provided in the Committee
Draft of IEC 61853-4  for different climatic regions
Type (example in country)
(UK – Scotland)
2.3. ESS parameters and example calculation
It is assumed that the EES is exclusively operated at
state of charge (SOC) between 10% and 90% of the
nominal capacity. Degradation effects are not accounted
for. Results in this report are considered for a time-of-use
of 10 years, typically corresponding to less than 10.000
loading / unloading cycles. Moreover, no thermal
derating is considered, since it is assumed that the EES is
placed in a cool and dry place of a residential home.
To calculate the results a time series for one year is
determined (results are later multiplied by 10 to study the
10 years frame), where at every time step a decision of
the energy flow is made on the base of the algorithm
shown in Fig. 1.
Fig. 3 typical result for a partially sunny winter day:
temperate continental location, PV-size 5 kWp, ESS
capacity 2 kWh
Fig. 4 typical result for a partially sunny winter day:
temperate continental location, PV-size 5 kWp, ESS
capacity 8 kWh
Fig. 3 and Fig. 4 show simulation results for different
ESS sizes (2 kWh and 8 kWh) obtained for a partially
sunny winter day at the temperate continental location,
where the size of the PV system is 5 kWp. It is obvious
that the smaller storage (in comparison to the larger
storage) reaches faster its state of maximum charge and
can contribute less to the load requirement: More
“surplus” energy must be fed into the grid and the level
of autarky (as defined in the next section) is smaller.
Autarky (self-sufficiency) is defined as the
normalized share of cumulated actual supply of a PV ESS
system to the energy requirement (L) from either the PV
system (P) or the ESS (S):
If the autarky factor was 100% the energy
requirement (L) would be met under any circumstances at
any time by the PV ESS system (“Priority 1a” and “1b”
of Fig.1) and no consumption of grid energy (“Priority
1c”) would be necessary. We are deliberately not
applying the term “self-consumption” in this work, since
the definition is often not consistently defined in
literature and it is often related to PV-systems without
Fig. 5: degree of self-sufficiency (autarky) for a combined
PV ESS system in dependence of the PV system size for
several possible storage sizes. Assumed yearly
consumption of the residential household: 4’000 kWh. PV,
location: temperate continental
Fig. 6: degree of self-sufficiency (autarky) for a
combined ESS system in dependence of the PV system
size for 2 possible storage sizes at different locations.
Assumed yearly consumption of the residential
household 4’000 kWh
Fig 5. shows the degree of autarky for a 4’000 kWh-
per-year-consumption household with PV and ESS,
whereas various sizes of ESS and PV generator sizes for
the temperate continental location are given. A certain
saturation can be seen for both higher PV generator sizes
and ESS sizes. In particular, there is only little additional
contribution to the self-sufficiency factor once a
threshold of 8 kWh of ESS size is exceeded.
It is instructive to look at the effect of differences
between ESS’s of capacities of 4 kWh and 8 kWh for the
described total system and to compare the projected
performance under different climatic environments. This
is depicted in Fig. 6. It can be seen, that the degree of
higher autarky (self-sufficiency) can be attained at a
higher level in regions with more solar energy supply (in
this case the Mediterranean region). Interestingly enough,
the split between the 4 kWh and the 8 kWh ESS
contribution is higher at the high-irradiance region
compared to the other regions.
3.2. Economic consideration
The economic considerations are based on the
Table II: price assumptions (i.e. cost for residential
used) considered in this study.
Specific Cost of PV
1’000 EUR / kWp
Specific Cost of ESS
1’250 EUR / kWh
Cost of electricity
0.28 EUR / kWh
It is assumed that a primary motivation for the
residential customer is the intention to save energy
expenditure by means of a combined PV ESS system.
With the autarky as given in Fig. 3 and 4 above, the
private customer can avoid a yearly payment of
, which is in our example
In order to calculate economic results, it is assumed
that the system has a life time of 10 years and that the
savings per year (eqn. 3) can be realized during
every year on equal level. The net benefit is the total
savings during 10 years ( ), while depreciation
and inflation are neglected .
Fig. 7: Box Plot for specific end-customer prices
researched in February 2017 for residential German
ESS of size up to 10 kWh. A median of 1’250 EUR / kWh
is used for further calculation.
3.3. Cost of Autarky
Fig. 8 shows possible maximum degrees of autarky at
the different sites for combinations of the EES-PV system
ranging between 1 kWp … 10 kWp (PV) and 2 kWh …8
kWh (EES). The maximum possible autarky can be
reached at high cost (large EES and large PV generator)
at more than 99% for the Mediterranean location.
Obviously these high levels of autarky cannot be easily
met for the two temperate locations at reasonable effort
due to the lower irradiation.
Fig. 8: Maximum attainable autarky in the studied
PV-ESS System for the 3 locations. Results are shown for
groups of systems comprising of 2 kWh, 4 kWh, 6 kWh
and 8 kWh system at each location for different sizes of
the PV system (between 1 kWp and max. 10 kWp).
Dashed lines show trends for the different locations.
As there has been shown that the level of autarky can
be chosen for each site within certain limits, it is
interesting to study which level of autarky will deliver the
best economic result for the residential user. Under the
assumptions as given in the preceding section, it can be
shown that for a 10 years period positive results will be
achieved for the Mediterranean and the temperate
continental location. However, due to the comparatively
weak irradiation level, the chosen temperate coastal
location (UK / Scotland) does not show a positive gross
margin after 10 years operation yet. The results are
summarized in Fig. 9.
Fig. 9 level of autarky with respect to the
extrapolated gross margin ( ) for different
PV-EES configurations at the three climatic sites.
Calculation for 10 years lifetime – no interest rate
4. DISCUSSION AND CONCLUSION
A straight model to work out a design rule for PV
EES systems under today’s relevant boundary conditions
(price / system sizing) is established for a residential
system (private residential user). This leads to the
conclusion that a comparatively small PV system with a
comparatively small ESS will deliver under today’s
pricing situation favorable results, whereas the optimum
level of autarky does not exceed 50% … 60%. It is a
statement of major importance, that PV-ESS systems are
deemed to be economically viable on a 10 years scale
without any other subsidy and also without a “penalty”
for self-consumption. Investigations for different climate
zones within the EU show that a higher solar irradiation
is contributing to the profitability of this scenario.
In conclusion, the economic optimum is found for
comparatively small system sizes and only medium
degrees of autarky. This finding does not necessarily
reflect today’s PV / ESS market, but has been described
earlier  with application of different methods.
 David Wedepohl (Bundesverband Solarwirtschaft),
“Preise für solarstromspeicher halbiert,” Press
 T. B. Randall, “World Energy Hits a Turning
Point: Solar That’s Cheaper Than Wind,”
published online 2016-12-15. [Online]. Available:
s-cheaper-than-wind. [Accessed: 19-Sep-2017].
 IEC TC 82 WG 2, “CD IEC 61853-4 Ed. 1.0
Photovoltaic (PV) module performance testing and
energy rating - Part 4: Standard reference climatic
profiles,” 82/1067/CD, vol. 82/1067/CD, 2016.
 J. Weniger, T. Tjaden, and V. Quaschning, “Sizing
of Residential PV Battery Systems,” Energy
Procedia, vol. 46, pp. 78–87, 2014.
 A. U. Schmiegel and A. Kleine, “Optimized
Operation Strategies for PV Storages Systems
Yield Limitations, Optimized Battery
Configuration and the Benefit of a Perfect
Forecast,” Energy Procedia, vol. 46, pp. 104–113,
 A. Sani Hassan, L. Cipcigan, and N. Jenkins,
“Optimal battery storage operation for PV systems
with tariff incentives,” Appl. Energy, vol. 203, pp.
 J. Bergner, J. Weniger, T. Tjaden, and V.
Quaschning, “Feed-in Power Limitation of Grid-
Connected PV Battery Systems with Autonomous
Forecast-Based Operation Strategies,” in 29th
European Photovoltaic Solar Energy Conference
and Exhibition, 2014, pp. 2363–2370.
 BDEW, “Standardlastprofile Strom.” BDEW
Bundesverband der Energie- und Wasserwirtschaft
e.V., Berlin, 2002.
 D. Faiman, “Assessing the outdoor operating
temperature of photovoltaic modules,” Prog.
Photovoltaics, vol. 16, no. 4, pp. 307–315, 2008.
 M. Koehl, M. Heck, S. Wiesmeier, and J. Wirth,
“Modeling of the nominal operating cell
temperature based on outdoor weathering,” Sol.
Energy Mater. Sol. Cells, vol. 95, no. 7, pp. 1638–
 G. Kleiss, H. Schülbe, and B. Nacke, “Energy
rrating of crystalline solar modules: investigation
of uncertainties due to binning in mass
production,” in Proc. 32nd EC-PVSEC, pp. 2239 –
 G. Kleiss, “Methode zur dynamischen Auslegung
eines PV Systems mit Elektrischem
Energiespeicher,” Presentation, August 2016,
DOI: 10.13140/RG.2.2.35664.71680, 2016.