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Profitability of Residential Battery Energy Storage Combined with Solar Photovoltaics

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Lithium-ion (Li-Ion) batteries are increasingly being considered as bulk energy storage in grid applications. One such application is residential energy storage combined with solar photovoltaic (PV) panels to enable higher self-consumption rates, which has become financially more attractive recently due to decreasing feed-in subsidies. Although residential energy storage solutions are commercially mature, it remains unclear which system configurations and circumstances, including aggregator-based applications such as the provision of ancillary services, lead to profitable consumer investments. Therefore, we conduct an extensive simulation study that is able to jointly capture these aspects. Our results show that, at current battery module prices, even optimal system configurations still do not lead to profitable investments into Li-Ion batteries if they are merely used as a buffer for solar energy. The first settings in which they will become profitable, as prices are further declining, will be larger households at locations with higher average levels of solar irradiance. If the batteries can be remote-controlled by an aggregator to provide overnight negative reserve, their profitability increases significantly.
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energies
Article
Profitability of Residential Battery Energy Storage
Combined with Solar Photovoltaics
Christoph Goebel 1,*, Vicky Cheng 2and Hans-Arno Jacobsen 1
1Chair of Business Information Systems, Technical University of Munich, Boltzmannstr. 3, 85748 Garching,
Germany; jacobsen@in.tum.de
2Munich School of Engineering, Technical University of Munich, Lichtenbergstr. 4a, 85748 Garching,
Germany; vicky.cheng@tum.de
*Correspondence: christoph.goebel@tum.de; Tel.: +49-89-289-19452
Academic Editor: Francesco Calise
Received: 9 May 2017; Accepted: 6 July 2017; Published: 11 July 2017
Abstract:
Lithium-ion (Li-Ion) batteries are increasingly being considered as bulk energy storage in
grid applications. One such application is residential energy storage combined with solar photovoltaic
(PV) panels to enable higher self-consumption rates, which has become financially more attractive
recently due to decreasing feed-in subsidies. Although residential energy storage solutions are
commercially mature, it remains unclear which system configurations and circumstances, including
aggregator-based applications such as the provision of ancillary services, lead to profitable consumer
investments. Therefore, we conduct an extensive simulation study that is able to jointly capture these
aspects. Our results show that, at current battery module prices, even optimal system configurations
still do not lead to profitable investments into Li-Ion batteries if they are merely used as a buffer for
solar energy. The first settings in which they will become profitable, as prices are further declining,
will be larger households at locations with higher average levels of solar irradiance. If the batteries
can be remote-controlled by an aggregator to provide overnight negative reserve, their profitability
increases significantly.
Keywords: lithium-ion batteries; solar photovoltaics; ancillary services; economics
1. Introduction
The generation of electricity using residential-size solar photovoltaics (PV) installations has
reached grid parity in 19 markets globally, including countries with relatively low levels of solar
irradiance such as Germany [
1
]. Today’s levelized cost of solar energy without subsidies is therefore
smaller than the cost of purchasing energy from the utility. Until recently, PV systems were mainly
installed to feed the generated electricity directly into the grid at a fixed feed-in remuneration that
is guaranteed for usually 20 years. Today, the solar PV feed-in remuneration ranges below the
end-consumer prices in many countries worldwide, which is making self-consumption of solar power
more attractive.
Although solar energy and most of the demand in households occurs in the daytime, the
simultaneity of solar power and demand is limited. Besides controlling deferrable loads, e.g., hot water
heaters and washing machines, battery energy storage is increasingly being considered as an effective
way to increase self-consumption. Several companies, including electric vehicle manufacturer Tesla
(San Carlos, CA, USA) [
2
], offer lithium-ion (Li-Ion) batteries as a buffer for solar energy so that excess
PV generation can be stored in the battery for self-consumption during times when demand exceeds
supply. Li-Ion battery cell prices are declining rapidly, while their lifetime is slowly increasing [
3
].
Therefore, investing in Li-Ion battery storage will become financially more attractive in the future.
However, it still remains an open research question how systems should be sized and operated to
Energies 2017,10, 976; doi:10.3390/en10070976 www.mdpi.com/journal/energies
Energies 2017,10, 976 2 of 17
achieve positive business cases. Moreover, considering the high cost of Li-Ion battery cells, being able
to utilize residential batteries for more than just buffering solar energy could be a major driver of
profitability. Their ability to quickly adjust (dis)charging power makes batteries a potential provider of
ancillary services. Controlled by an aggregator or directly by the system operator, distributed batteries
could, for instance, help to provide frequency reserve.
In this paper, we investigate the financial impact of coupling state-of-the-art Li-Ion batteries with
solar PV panels in residential settings. We make the following contributions:
1.
We advance beyond conventional methodology by simulating stochastically the electricity demand
of different households and PV generation at different locations in high temporal resolution.
2.
In addition to solar energy buffering, we investigate the use of batteries to provide negative
reserve and its impact on profitability, which is a largely unexplored topic.
3.
We implement a detailed model to control the operation of a residential energy system and derive
the net present value (NPV) of different system configurations.
4.
Based on the results of an unprecedented large number of experiments with different inputs, we
conduct a sensitivity study to identify optimal system configurations and the drivers of energy
storage profitability.
5.
Our study provides fresh insights that facilitate investment decisions, in particular which
system configuration should be chosen based on location, household size, and current battery
module price.
This paper is organized as follows: in Section 2, we review related literature. Section 3provides
details on the different models and data we use. In Section 4, we summarize the setup and results of
a comprehensive simulation study. Section 5discusses our work, including its limitations and possible
future work. Finally, in Section 6, we provide summarized conclusions of our study.
2. Related Work
Several recent studies [
4
6
] attempted to examine the profitability and optimal sizing of residential
PV-battery systems, but most suffer from major limitations that impede the robustness of the results.
A common shortcoming stems from the use of low time resolution electricity demand and PV
generation models, which fail to capture the short-time peaks that are intrinsic to real generation
and load curves. The time-averaging effects arise from coarse resolution models, lead to inaccurate
representation of the instantaneous matching of electricity supply and demand, and, consequently,
undermine the capacity sizing and economic assessment of PV-battery systems. Based on the
simulation of a UK household over a summer day, the authors of [
7
] reported significant errors
in the estimation of on-site solar fraction by coarse time resolution models. An hourly resolution
model overestimated the PV supply and demand matching capability by over 60% compared to
a minute-resolution model. Ried et al. [
8
] modeled the profitability of PV-battery systems for
a sample of households and reported significant underestimation of battery cycle life using coarse
time resolution models. An hourly resolution model on average underestimated the battery cycle
by 9% and overestimated the battery life by up to three years compared to a minute-resolution
model. Furthermore, past studies neglected the stochasticity in residential electricity demand and
drew conclusions merely based on simulations using standard load profiles of a single household.
Ried et al. [
8
] reported considerable errors in the estimation of battery cycle life and overall cost-savings
when standard load profiles as opposed to measured household demand curves are used. In the
following, we provide several detailed reviews of key papers related to our work.
Naumann et al. [
4
] investigate the costs of Li-Ion battery storage for a 4-person single family house
under the current regulatory regime in Germany. They scale and linearly interpolate a low granularity
standard load profile (15 min averages, 4-person household) to obtain one-minute household demand.
Instead of searching the optimal combination of PV and battery sizes, they fix the PV capacity (4.4 kWp)
and conduct a sensitivity study of the return on investment (ROI) of the system in three battery size
Energies 2017,10, 976 3 of 17
scenarios. With the PV size constraint, they reported an optimal battery capacity of 4.4 kWh while the
ROI varies depending on assumptions in the state of health and aging behavior of the batteries.
Weniger et al. [
5
] attempt to find optimal PV and Li-Ion battery sizes for a 3-person single family
house in Germany. They use measured data of typical daily load profiles from one household in
one minute resolution based on VDI (verein deutscher ingenieure) guideline 4655 [
9
], which they
assemble into a one year long profile. The main caveat of the study arises from the very conservative
assumptions regarding the battery modules, in particular costs ranging between 3000 EUR/kWh and
600 EUR/kWh, state of charge ranging between 20% and 80%, and a cycle life of 5000 equivalent
full cycles. As a result, PV-battery systems are found to be economically viable only in the long term
assuming PV system costs of 1000 EUR/kWp, battery costs of 600 EUR/kWh, and feed-in tariffs as low
as 0.02 EUR/kWh. The authors reported an optimal configuration consists of (per MWh of demand) a
0.8 kWp PV system and 1.1 kWh usable battery capacity.
The authors of [
6
] conduct a very detailed study of the profitability of residential lead-acid
batteries. In particular, they use several learning curve models to forecast system costs (one for each
major system component) and different price development scenarios to investigate how net present
values would evolve if investments were made anytime between 2013 and 2022. In contrast to the
authors of [
4
], they consider optimal PV panel and battery sizing. However, they use hourly solar data
and concatenated standard load profiles (15 min resolution) as input for their simulations.
Zhu at al. [
10
] investigate the use of residential batteries for exploiting time of use (TOU)
tariffs. TOU tariffs are end-customer contracts that result in different electricity prices based on when
electricity is consumed. In contrast to us, they consider two different battery types with different cost
characteristics being operated simultaneously, a lead-acid and a lithium-ion battery. This can lead to
higher cost-efficiency due to optimal coordination. Moreover, they do not consider optimal battery
sizing and combined use with solar PV, which is the focus of this paper.
The authors of [
11
] developed a method for optimally sizing PV-battery systems based on
a probabilistic (“chance constraint”) approach. Similar to [
12
], which their formal analysis is based on,
they consider autonomous energy systems without grid connection. In contrast to the grid-connected
systems investigated in our paper, such scenarios call for an investigation of how a probabilistic metric
of autonomy, i.e., how likely a certain system configuration would be able to cover all demand, can be
provided. In [
11
], such a method is proposed. However, to be used in practice, one needs to carry out
stochastic simulations based on actual data, such that the complex time-dependent system behavior
can be considered.
In this paper, we try to combine the strengths and overcome the weaknesses of the past studies.
In particular, we use recent data-driven models to simulate stochastically the electricity demand of
households and PV generation in high time resolution in an effort to accurately assess the profitability
of residential PV-battery systems. We also consider a large sample of households in different sizes and
PV generation in different locations to ensure generalizable results. In fact, our results show that these
contextual parameters are decisive to the profitability of PV-battery systems. Similar to [
5
], our work
considers the important financial trade-offs resulting from different PV panel and battery sizes by
searching for optimal configurations instead of fixing them ex ante. However, we use more realistic
input assumptions and stochastic residential load profiles that are lacking in [
4
,
5
]. Furthermore, our
paper also investigates a realistic extension of the standard residential battery use case, namely the
provision of negative reserve. This application is recognized to have growing market potential
worldwide but has not been considered in previous publications [13].
3. Models and Data
3.1. Household Load Model
We use the residential electricity demand model described in detail in [
14
] to generate random
load profiles. The model uses an activity-based modeling technique which combines data from
Energies 2017,10, 976 4 of 17
a time use survey with smart meter data of household appliances to derive realistic load profiles
on the household level at one-minute resolution. Load is computed using a bottom-up approach.
Empirical data about timing and duration of activities (e.g., cooking, watching TV, etc.) is combined
with empirical data on load distributions depending on household size to derive so-called activity
load profiles of households. These profiles are stochastic, since the use of each activity-based load is
simulated by sampling from the corresponding probability distributions. One of the special merits of
this model is that it also considers the shape of standard load profiles. It achieves this by making sure
that the mean of many simulated household load profiles converges to the standard load profile. The
authors of [
14
] have validated the generated household load traces by comparing them to actual smart
meter measurements based on critical statistical properties.
3.2. Solar PV Model
We apply models described in [
15
,
16
] to obtain realistic data traces for the DC power generated
by residential solar crystalline silicon PV panels. PV module efficiency
ηPV
can be approximated using
Equation (1) [
15
], where
Tc
and
G
are input variables denoting the PV cell temperature and incident
solar irradiance on the PV array, respectively. The remaining parameters are constants as provided
in Table 1:
ηPV =ηre f (1β(TcTc,re f ) + γlog(G
Gre f
). (1)
The PV module temperature
Tc
can be modeled according to Equation (2) [
16
], where
Ta
and
Vw
are variables representing ambient temperature and wind speed, respectively:
Tc=Ta+G
Gno
·9.5
5.7 +3.8Vw
·(Tno Ta,no )·(1ηre f
τα ). (2)
The total DC power output of a PV module can be calculated as
PDC
PV =Ac·G·ηPV
, where
Ac
is
the module area.
Table 1. Constant model parameters.
Param. Value Param. Value
ηre f 0.21 Tc,ref 25 C
Gre f 1.0 kW/m2β0.0048
γ0.12 Gno 0.8 kW/m2
Tno 25 CTa,no 20 C
τα 0.9 rc1.0
rd1.0 ηB0.95
CAPEO L
B0.74 Lcal
B20 years
Lcyc
B8.000
We use Meteonorm [
17
] to create data traces for a typical year (1991–2010) in one-minute
resolution. Meteonorm provides simulated ground measurements of solar irradiance for typical
years, i.e., it considers the short-term effect of moving clouds. Meteonorm was configured to simulate
G
over a year, assuming a south facing PV panel tilted by 30
, which represents the optimal fixed tilt
position in Central Europe. We also use Meteonorm to obtain data traces of the ambient temperature
Ta
and wind speed
Vw
. Data was generated for two locations in Germany, Bremen and Munich. We have
chosen these locations since Bremen has one of the lowest, whereas Munich one of the highest solar
irradiance levels in Germany. The results obtained for these two extreme locations enable us to estimate
the impact of solar availability on the profitability of PV-battery systems. We scale the resulting DC
power generation traces based on the maximum value observed during one year and the desired peak
power capacity, C APPV.
Energies 2017,10, 976 5 of 17
3.3. Battery Model
Our battery model can be defined using the following parameters: The battery efficiency
ηB
(charging and discharging), the nominal battery storage capacity
CAPB
, and the C-rates for charging
and discharging, rcand rd. In addition, we define the usable range of the state of charge (SOC) of the
battery via SOCmin and SOCmax .
The overall lifetime of Li-Ion batteries can be approximated based on two parameters, the calendar
lifetime
Lcal
B
and the maximum number of full battery cycles until decommissioning
Lcyc
B
. Lifetime
parameters differ depending on the battery chemistry. In this work, we consider the lithium iron
phosphate (
LiFePO4
) battery chemistry, which is used by several solar battery providers [
18
,
19
] due to
their long cycle life and operational robustness (depth of discharge, safety, temperature, etc.). The exact
specifications were based on the Sony Fortelion cell (Tokyo, Japan) [
20
]. The capacity of
LiFePO4
batteries decreases approximately linearly with time until a certain reflection point, beyond which
capacity rapidly declines. We denote the end of life battery capacity by
CAPEOL
B
. The SOC range of
these cells are not restricted in practice, because, in contrast to other battery chemistries, depth of
discharge does not play a major role in the aging process of LiFePO4cells [21].
3.4. Power Electronics Model
To transform the DC power from the solar PV panel and the battery into AC power used by
household appliances and the grid, an inverter is required. Likewise, charging the battery with grid
power requires rectification of AC grid power to DC battery charging power. Power electronics
efficiency
ηPE (Pl
,
Pr)
usually peaks at its rated output power and decreases in other load conditions.
To accurately consider this behavior, we use the following model provided in [4]:
ηPE (Pl,Pr) = p
p+0.0072 +0.0345 ·p2;p=Pl
Pr. (3)
The rated output power
Pr
is treated as a constant. In the following, we will model two power
electronic devices: the inverter that converts DC power from the panel and the battery into AC power
and the rectifier required to convert AC grid power to DC charging power for the battery. The nominal
power electronics capacity is chosen to be equal to expected peak load. Therefore,
Pr=CAPPV
in the
former and rc·CAPBin the latter case.
3.5. Battery Control
We combine the different models described above to perform a comprehensive evaluation of
state-of-the-art residential battery energy storage. In addition to using the battery as a way to store
excess solar PV energy and use the stored energy to (partially) replace power drawn from the grid,
we also investigate the case of charging the battery using grid power during times of negative
reserve deployment.
Figure 1shows the algorithm of method
control
, which takes the following inputs: the current
time
t
, solar PV generation
PDC
PV
, household demand
PAC
HH
, and the battery’s SOC. It controls the
battery power during the control time interval
S
by determining a feasible value for the DC battery
power
PDC
B
. Thus, the control frequency depends on the length of
S
, which is set to 1 min in our
evaluations. We assume that all control inputs are measured or are accurately estimated based on
available measurements. Inputs have to be provided to the algorithm at the same frequency as controls
are computed. Apart from computing
PDC
B
, the battery control algorithm also returns the remaining
power
PAC
D
that needs to be transferred to or from the grid. If
PAC
D
is positive, additional power needs
to be drawn from the grid to cover the demand. If negative, excess energy produced by the solar PV
panels that cannot be absorbed by the battery is fed back into the grid.
Lines 3–9 of algorithm
control
determine the battery dispatch, i.e., the value of
PDC
B
. The method
getReservePower
provided in Figure 2determines a feasible reserve contribution of the battery,
Energies 2017,10, 976 6 of 17
which requires the battery state, and can otherwise be based on time, reserve requirements, etc.
In Germany, there exist separate markets for positive and negative secondary reserve, from 8 a.m. to
8 p.m., and from 8 p.m. to 8 a.m. the next day. The underlying market mechanism is a pay-as-bid
auction for capacity and actual energy delivery. The corresponding Internet-based market platform [
22
]
is run jointly by the German Transmission System Operators (TSOs). Any business party able to fulfill
the technical qualification criteria (including minimum power and response time) can participate in
these markets. More details about the German ancillary services markets can be found in [
23
]. In this
paper, we evaluate negative reserve provision in
S=
15 min time intervals between
tR=
8 p.m.
and
tR=
8 a.m., which corresponds to the current rules for participating in the secondary reserve
market in Germany. Furthermore, we assume that, during each of these 12 h intervals, batteries can
charge for at most
R=
1 h, which can result in one full recharge at a charging C-rate of one. If the
battery is scheduled to deliver reserve energy, i.e., the determined reserve power level
PDC
R
is not equal
to zero, the battery is exclusively used for this purpose. Otherwise, it is used to absorb excess solar
energy or provide energy if the household demand is higher than PV generation.Figure 3specifies the
algorithm we use to determine feasible battery power based on the SOC, the required power
Preq
, and
the time interval used for charging or discharging.
1: Input: t,PDC
PV ,PAC
HH ,SOC
2: PDC
B0
3: if CAPB>0then
4: PDC
RgetReservePower(t,SOC)
5: if PDC
R=0then
6: Preq PAC
HH
ηPE (PAC
HH ,C APPV )PDC
PV
7: PDC
BgetBatPower(SOC,Preq,S)
8: else
9: PDC
BPDC
R
10: if PDC
B>0then
11: SOC SOC PDC
B·S
ηB
12: else
13: SOC SOC +ηB·PDC
B·S
14: if PDC
R=0then
15: PDC
GPDC
PV +PDC
B
16: else
17: PDC
GPDC
PV
18: PAC
DPAC
HH ηP E(PDC
G,CAPPV )·PDC
G
19: return PAC
D
Figure 1. Algorithm of control(t,PDC
PV ,PAC
HH ,SOC).
1: Input: t,SOC
2: if t=tRthen
3: RR
4: PDC
R0
5: if Pneg
GR (t)Pne g
GR R>0ttR,tRSthen
6: PDC
RgetBatPower(SOC,,S)
7: Rmax [RS, 0]
8: return PDC
R
Figure 2. Algorithm of getReservePower(t,SOC).
Energies 2017,10, 976 7 of 17
1: Input: SOC,Preq,
2: PDC
B0
3: if Preq <0then
4: Pmax rc·C APB
5: Ptheo (SOCmax SOC)·C APB/(ηB·)
6: PDC
B← −min Pmax ,Ptheo ,Preq
7: else if Preq >0then
8: Pmax rd·C APB
9: Ptheo (SOC SOCmin )·(ηB·C APB)/
10: PDC
Bmin Pmax ,Ptheo,Preq
11: return PDC
B
Figure 3. Algorithm of getBatPower(SOC,Preq,).
Figure 4shows selected input traces and simulation results to demonstrate the effect of the
applied battery control strategies. Ten single-person household traces are plotted at once to reveal the
stochasticity of the demand and how it leads to different battery utilization patterns. One can also see
that negative reserve is required very often, i.e., the chances that batteries can be controlled to provide
it during the allowed time interval are very high.
.
Figure 4.
Selected input traces and modelled results of 10 single-person households for the simulation
case
CAPPV =
1 kWp and
CAPB=
1 kWh. Each household is represented by a different colour and
the plot illustrates the stochasticity of household electricity consumptions.
Energies 2017,10, 976 8 of 17
4. Simulation Study
To perform a comprehensive profitability evaluation of the residential battery energy storage,
we run a large number of simulations with different parameter configurations. Each simulation run
covers one entire year in one minute detail, i.e., the computational steps summarized in algorithm
control (cf. Figure 1) have to be executed 365
×
24
×
60
=
525, 600 times in each run. Since we intend
to consider a typical investment horizon of 20 years, we scale the PV module and battery capacity
to average values, i.e.,
CAPPV =CAPPV ·(
1
(rPV ·LPV )/
2
)
and
CAPB=CAPB·(
1
+CAPEOL
B)/
2,
where
rPV =
0.5% is the annual (linear) performance loss of solar PV cells according to [
24
]. Thus,
for the NPV calculations the full detail of minute calculations is considered because the energy values
EB
,
ED
,
EHH
, and
EPV
are calculated using the method described above. However, we simulate one
year per configuration, and then use the resulting energy values to estimate net present value (NPV)
for longer time periods.
To compute the figures of merit presented in the following, we collect several aggregated metrics
in each simulation run, including the total energy consumed by the household EHH , the energy from
the grid
ED
and the excess solar energy being fed into the grid,
EPV
. In addition, we compute the total
energy EBbeing provided by the battery.
4.1. Metrics
We evaluate the profitability of different combinations of solar PV panel and battery sizes by
computing the NPVs of the corresponding investments. NPV is one amongst several ways to determine
the return of an investment (ROI). In contrast to the most basic ROI formula, i.e., the difference between
the gain from an investment and the cost of investment, and the cost of investment, the use of NPV
allows us to consider the time value of cash flows in subsequent time periods, which is particularly
important for long investment horizons. In our case, significant investments are due right at the
beginning of the considered investment time period, whereas revenues are constantly being generated
during a relatively long time (20 years). Thus, even relatively low interest rates may play a crucial role
in the decision. Furthermore, the NPV method provides a monetary value instead of merely measuring
the efficiency of an investment in terms of a percentage rate and is thus more informative.
The corresponding financial parameters are summarized in Table 2. All price values exclude the
value added tax (VAT).
Table 2. Financial parameters.
Param. Values Param. Values
pPV 750 EUR/kWp [6]pPE 170 EUR/kWp [6]
pBOS 640 EUR/kWp [6]fEPC 0.08 [6]
fOP 0.015 [6]pF I 0.10 EUR/kWh [4]
pEL 0.30 EUR/kWh [4,25]iI NV 0.02 [4]
iVAT 0.19 TIN V 20 years
LPV 25 years [6]LPE 10 years
Based on these values, we calculate initial investments into the different system components based
on their respective sizes, in particular
CAPPV
and
CAPB
. The nominal capacity of the PV inverter and
grid-to-battery rectifier used during reserve provision are derived from these values. Thus, the initial
investment costs for the solar modules (Equation (4)), the battery (Equation (5)), and the additional
power electronic equipment (Equation (6)) can be calculated as follows:
C0,PV = (1+iVAT)·(pPV +pPE +pBOS )·(1+ (( fEPC)11)1)·CAPPV , (4)
Energies 2017,10, 976 9 of 17
C0,B= (1+iVAT)·pB·CAPB, (5)
C0,PE+=IRE ·(1+iVAT)·pPE ·C APB. (6)
Since both the power electronic equipment and the battery modules usually have a shorter
lifetime than the assumed investment horizon of 20 years, we consider their replacement costs in
the NPV calculation. Furthermore, since we examine a limited investment horizon, we also consider
the residual value of assets at the end of the investment period. Otherwise, the replacement of
a system component shortly before the investment horizon ends would distort the NPV. Replacement
costs and residual values include VAT, but exclude additional (de)installation costs. We denote
the annual cash flow resulting from solar PV system replacement costs and residual value in year
t
by
Ct,PV
. The cash flow resulting from the investment in the battery modules is denoted by
Ct,B
, the cash flow corresponding with the investment in additional power electronics required for
reserve provision by
Ct,PE+
. Replacement times are determined from the parameters
LPV
,
LPE
, and
LB=min nLcal
B,(Lcyc
B·CAPB)/EBo
. Residual values are determined proportionally, i.e., the residual
value of device
D
that costs
CD
EUR, has lifetime
LD
, and was installed or last replaced at time
trep
,
would be equal to
CD·(LDtend +trep )/LD
. In addition to the equally distributed replacement costs,
we consider annual PV system maintenance costs according to Equation (7):
Ct,OP =fOP ·C0,PV. (7)
Positive cash flows correspond to revenues resulting from the grid electricity cost savings and the
revenue from PV feed-in. In Germany, households are paid a fixed feed-in tariff for the PV energy they
deliver to the grid. The tariff is determined at installation time and remains valid for 20 years. More
details can be found in the corresponding Act on the Development of Renewable Energy Sources [
26
].
Since households have to pay VAT on self-consumed electricity, the complete annual revenue can be
obtained using Equation (8):
Rt= (1+iVAT)·EPV ·pFI +pEL ·(EH H ED). (8)
The net present value of an investment into a residential energy system that is composed
of PV module, battery, and power electronic equipment is given in Equation (9). If this value
is positive, the investment would be beneficial compared to the non-investment alternative,
and disadvantageous otherwise:
NPV =C0,PV +C0,B+C0,PE++
TIN V
t=1
RtCt,OP Ct,BCt,PE+
(1+iI NV )t. (9)
In addition to net present values, we compute the number of annual storage cycles according to
Equation (10) and the self-sufficiency rate according to Equation (11):
ASC =EB/C APB, (10)
SSR =100 ·(1ED/EH H ). (11)
In the case of reserve provision, i.e.,
IRE =
1, the total energy drawn from the distribution grid
includes the reserve energy. Thus, we still define self-sufficiency as the percentage of used energy
that is produced on-site, even if charging during reserve provision is assumed to be free. We do not
assume that the aggregator pays the home owner extra for being able to control battery charging,
i.e., the NPVs computed for
IRE =
1 represent lower bounds. Market participation operations of the
aggregator, in particular the control of many batteries in concert with other energy resources forming a
virtual power plant, are beyond the scope of this paper [
27
]. Provided that the aggregator fulfills the
Energies 2017,10, 976 10 of 17
requirements for participating in the reserve market, it should be able to obtain (positive) revenues
from the participation. However, based on historical price data, these revenues should be rather
limited today [
28
]. The deployment bids would have to be sufficiently low, such that the aggregator
would be instructed to deliver reserve energy relatively often, which, in turn, is required to recharge
the batteries overnight.
4.2. Setup
Table 3lists the sensitivity parameters considered in this study. All parameters except the battery
module price pBrequire independent simulations. To account for the stochasticity of household load
and its impact on self-consumption and battery operation, we perform ten independent simulations
for each parameter configuration and report the mean metrics.
Table 3. Sensitivity parameters.
Param. Input Range Param. Input Range
CAPPV 1, 2, ..., 6 kWp CAPB0, 1, ..., 10 kWh
nHH 1, ..., 4 LOC Munich, Bremen
IRE 0, 1 pB800–100 EUR
4.3. Implementation
Our simulation and data processing procedures can be divided into three phases.
In the first phase, we use appropriate models to generate the input data traces. We use the
original implementation of the household load model described in Section 3.1 to generate a large
number of year-long household consumption traces in one-minute resolution for different household
sizes. Using the weather data traces generated by Meteonorm, we compute corresponding PV power
generation using our own Python implementation of the models described in Section 3.2. The reserve
traces were obtained from [29].
In the second phase, we simulate the PV-battery systems over the course of a year in one minute
detail. Even at 1 kWp increments of PV capacity and 1 kWh increments of battery capacity, we still need
to perform 1056 simulation runs. Due to the high time granularity, the inclusion of many independent
household demand traces per run (cf. Figure 4), and the required computation in each simulation
step (cf. Section 3.5), each simulation run takes several hours on commodity hardware. Using two
powerful computer servers with 32 cores each, we were able to parallelize simulations such that the
full experimental setup was feasible in reasonable time.
In the final phase, we calculate the figures of merit, in particular, net present value, annual
storage cycles, and self-sufficiency rates using Python scripts. This enables us to perform sensitivity
studies using different financial parameters (cf. Table 2) without having to repeat the computationally
expensive simulations of the second phase.
4.4. Results
Figure 5contains plots of net present values and number of annual storage cycles for two-person
households in Munich. These plots only represent a fraction of the total results we obtained. The figures
reveal several important facts about the optimal sizing of system components and the influence of
battery prices and reserve provision, which are outlined in the following. At current battery prices
of 800 EUR/kWh and without reserve provision, it would be optimal to invest only into a system
consisting of a small PV module without a battery. Investing into energy storage would only reduce
profitability in this case. Even at very low battery prices of 200 EUR/kWh, NPV peaks at rather small
storage capacities in the range of 1 kWh–4 kWh. The possibility of a free overnight recharge resulting
from negative reserve provision significantly increases profitability, despite approximately doubling
Energies 2017,10, 976 11 of 17
the number of annual storage cycles. In this case, the optimal energy storage capacity also increases,
but still peaks well below 10 kWh.
Across all cases, it becomes clear that relatively small PV module capacities (1 kWp–2 kWp) are
more beneficial from a financial perspective. Although additional energy storage capacity can, as
expected, significantly increase the value of PV capacity, system configurations with more than 2 kWp
of PV capacity will remain less profitable than smaller systems, irrespective of energy storage. Similar
trends are observed in other household scenarios and for Bremen.
In Figure 6, colors refer to different household sizes (1 person–4 persons), whereas solid and
dashed lines designate different metrics, including NPV, battery capacity and self-sufficiency rate.
Figure 6a–d show the best NPVs (solid lines) within the search space defined in Table 3, as battery prices
decrease from 800 EUR/kWh to 100 EUR/kWh. The figures reveal at which price levels investments in
energy storage become profitable in the studied cases. Taking Figures 6a as an example, for a 3-person
household, it is more profitable to have a solar PV system without a battery when the battery price is
above 600 EUR/kWh. This can be observed as the optimal battery capacity (red dash line) stays at zero
when the value of the x-axis is beyond 600. When the battery price drops to between 300 EUR/kWh
and 600 EUR/kWh, a small battery of 1 kWh capacity is optimal (red dash line reaches 1). The optimal
battery capacity increases in steps up to 6 kWh as the battery price drops to 100 EUR/kWh. The
contextual factors also play a crucial role as NPVs increase substantially with larger household size
and higher solar availability.
Interestingly, irrespective of how low the prices per kWh of energy storage capacity become,
capacities greater than 6 kWh are never an optimal choice in the regular self-consumption use
case. If the batteries deliver negative reserve, however, optimal battery sizes approximately double.
Furthermore, although battery owners are not financially compensated directly, reserve provision
significantly increases profitability.
0 1 2 3 4 5 6
Battery capacity [kWh]
6000
5000
4000
3000
2000
1000
0
1000
Net present value [EUR]
nHH = 2,pB= 800 EUR, IRE = 0, Munich
(a)
0 1 2 3 4 5 6
Battery capacity [kWh]
3000
2500
2000
1500
1000
500
0
500
1000
Net present value [EUR]
nHH = 2,pB= 200 EUR, IRE = 0, Munich
(b)
0 2 4 6 8 10
Battery capacity [kWh]
10000
8000
6000
4000
2000
0
2000
Net present value [EUR]
nHH = 2,pB= 800 EUR, IRE = 1, Munich
(c)
0 2 4 6 8 10
Battery capacity [kWh]
3000
2000
1000
0
1000
2000
3000
4000
5000
Net present value [EUR]
nHH = 2,pB= 200 EUR, IRE = 1, Munich
(d)
1 2 3 4 5 6
Battery capacity [kWh]
50
100
150
200
250
300
350
400
450
Annual number of storage cycles
nHH = 2,IRE = 0, Munich
(e)
1 2 3 4 5 6 7 8 9 10
Battery capacity [kWh]
200
300
400
500
600
700
800
Annual number of storage cycles
nHH = 2,IRE = 1, Munich
CAPP V = 1 kWp
CAPP V = 2 kWp
CAPP V = 3 kWp
CAPP V = 4 kWp
CAPP V = 5 kWp
CAPP V = 6 kWp
(f)
Figure 5.
NPVs (
a
d
) and annual number of battery cycles (
e
,
f
) for different solar PV and battery capacities.
Figure 6e,f show self-sufficiency rates for the cases without and with reserve provision (solid and
dashed lines, respectively). Whereas the use of additional energy storage capacity at decreasing
Energies 2017,10, 976 12 of 17
battery prices leads to higher self-sufficiency, the opposite is true if batteries deliver negative reserve.
The reason is that the amount of energy being charged into the battery in response to reserve provision
starts dwarfing the amount of solar energy being buffered. A self-sufficiency rate of 0% indicates that
it is financially optimal not to invest in either solar PV modules or battery storage.
100200300400500600700800
Battery capacity price [EUR/kWh]
0
500
1000
1500
2000
2500
Best net present value [EUR]
IRE = 0, Munich
nHH = 1
nHH = 2
nHH = 3
nHH = 4
0
1
2
3
4
5
6
Optimal battery capacity [kWh]
(a)
100200300400500600700800
Battery capacity price [EUR/kWh]
0
100
200
300
400
500
600
700
Best net present value [EUR]
IRE = 0, Bremen
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Optimal battery capacity [kWh]
(b)
100200300400500600700800
Battery capacity price [EUR/kWh]
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Best net present value [EUR]
IRE = 1, Munich
1
2
3
4
5
6
7
8
9
10
Optimal battery capacity [kWh]
(c)
100200300400500600700800
Battery capacity price [EUR/kWh]
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Best net present value [EUR]
IRE = 1, Bremen
0
2
4
6
8
10
Optimal battery capacity [kWh]
(d)
100200300400500600700800
Battery capacity price [EUR/kWh]
0
10
20
30
40
50
60
70
Self-sufficiency rate [perc.]
Munich
(e)
100200300400500600700800
Battery capacity price [EUR/kWh]
0
10
20
30
40
50
60
70
Self-sufficiency rate [perc.]
Bremen
nHH = 1,IRE = 0
nHH = 1,IRE = 1
nHH = 2,IRE = 0
nHH = 2,IRE = 1
nHH = 3,IRE = 0
nHH = 3,IRE = 1
nHH = 4,IRE = 0
nHH = 4,IRE = 1
(f)
Figure 6.
Best NPVs (
a
d
) and corresponding self-sufficiency rates (
e
,
f
) for different household sizes
and locations.
5. Discussion
Using a high resolution stochastic electricity demand model, we are able to quantify the effects of
household size and solar availability on the profitability of PV-battery systems. Although these
contextual factors have proven to be important in our findings, they were largely neglected in
previous studies.
Furthermore, we explore the impact of providing negative reserve using the batteries (cf. Section 1),
which is a timely topic in Europe. The way the aggregator controls the batteries to provide reserve in
our use case is simple but realistic. The optimization problem of scheduling large numbers of energy
storage devices in accordance with German market rules has been studied in another publication [
27
],
and would exceed the scope of this work. In this paper, we thus make the simplifying assumption that
batteries can be charged at nominal charging power as long as there is actual demand for negative
reserve (usually many MWs). We used a real one year long trace of negative reserve to make sure that
our results could actually materialize in practice. Given the case we consider, i.e., reserve provision
during a 12 h long time interval with a maximum charging time of 1 h, batteries would almost certainly
be able to recharge every night. The required switching and metering infrastructure on the customer
side would be basic and inexpensive.
Since the power output of lithium-ion batteries can change almost instantaneously based on
the attached load or power supply, considering the ramp rate of the modeled energy storage is not
required here. However, it could be an issue if other types of energy storage are modeled or if the time
granularity of our analysis were much higher. Moreover, considering different reserve provision use
cases, including ones involving the discharge of batteries, could be valuable future work.
Energies 2017,10, 976 13 of 17
The data and assumptions adopted in this study have been carefully selected to cover
a representative range of values in reality in order to ensure generalizable results. Furthermore,
by leveraging an advanced method for generating representative household load traces [
14
], we are
able to take stochastic effects into account. Whereas these features distinguish our study from previous
work, they also lead to high computational complexity, which we manage by deploying our code on
large servers and taking advantage of full parallelization. The results clearly show that the stochasticity
of household consumption patterns are important to consider as they have significant impacts on the
NPVs, and in turn, the optimal system configurations. In this paper, we have not explicitly shown the
impact of data granularity on the matching of solar PV energy production and household demand
because we feel that this is beyond the scope of this paper. The general importance of data granularity
in the context of our study has already been shown in the literature [7].
We do not consider learning curves in this work, which form an integral part of related works [
6
].
Learning curves represent the impact of learning over time, e.g., on costs or prices. In the context of
our study, the prices of residential energy generation and storage systems may decrease over time, e.g.,
due to economies of scale and increasing competition. Instead, we implicitly assume that PV panel and
power electronics prices will not dramatically decrease in the future. Energy storage price, however, is
treated as a sensitivity parameter in our study without making explicit predictions about when which
price level will be reached, since we believe that such predictions are highly speculative at this time.
Our sensitivity study can also be used to assess the impact of subsidies for residential energy
storage. A recently prolonged subsidy program supporting residential battery energy storage
in Germany promises a payment
sB
depending on the size of the solar PV module
CAPPV
and
battery module initial investment cost
C0,B
, which can be calculated according to
sB=CAPPV ·
min n0.25·C0,B
CA PPV , 500o
EUR [
30
]. Thus, assuming the current battery cost of 800 EUR/kWh, the subsidy
for a 1 kWp PV module with a 1 kWh battery would be approximately 200 EUR. Considering the
results shown in Figure 6a,b, this subsidy would be sufficient to make battery investments for larger
households (three and four persons) at locations with high irradiance levels, like Munich, profitable.
However, our results show that it is insufficient to foster storage adoption in other cases.
Time-of-use (TOU) tariffs, i.e., contracts that result in different electricity prices based on when
electricity is used, are common in some countries, in particular in the US [
31
]. Typically, TOU tariffs lead
to higher charges at times of peak demand, i.e., at mid-day, and lower charges otherwise. They require
“smart" meters capable of time-based demand measurement and vary in terms of specified pricing
periods and levels. In Germany, smart meters have not yet been rolled out at the household level,
thus German utilities do not offer TOU tariffs so far. Since residential energy storage reduces electricity
usage during times of potential peak demand (cf. Figure 4), we expect TOU pricing to have a positive
effect on its profitability. However, since TOU can be very different based on the demand shifting
goal of the utility and a significant study is therefore beyond the scope of this paper, we recommend
a self-contained follow-up study that specifically investigates this issue.
We can confirm that financially optimal system configurations for self-consumption scenarios
imply relatively small solar PV and battery capacities. Even if battery prices halved from today’s
800 EUR/kWh price level to 400 EUR/kWh, optimal battery sizes would still range at approximately
1 kWh (cf. Figure 6a), although much larger residential batteries are offered already today
(e.g., Tesla’s Powerwall has a storage capacity of 6.4 kWh [
2
]). This result generally corresponds
with the findings of previous studies, in particular [
5
]. Furthermore, we find that battery module prices
would have to further decrease from today’s levels to make first investments in residential energy
storage profitable. For instance, at locations near Munich, initial investments into energy storage would
become profitable at prices lower than 550 EUR/kWh for all household sizes (cf. Figure 6a), whereas
prices would have to decrease below 200 EUR/kWh to lead to profitable investments near Bremen
(cf. Figure 6b). However, as our detailed results have shown, the exact “break even” battery prices
and the optimal system configurations vary substantially depending on factors such as household
Energies 2017,10, 976 14 of 17
size and solar availability. We thus believe that it would be dubious to quote such numbers without
considering these contextual features.
The weather and time use data used as input to the household load model assume siting in Central
Europe, which determines the results of the second phase of the simulation procedure (cf. Section 4.3).
Furthermore, several financial parameters (in particular
pFI
and
pEL
) are Germany specific. Therefore,
quantitative results assuming other climate zones and jurisdictions would likely differ from the results
presented in Section 4.4. The method itself, including the tools for generating the required input data,
are replicable to any location worldwide.
6. Conclusions
In this paper, we have described a method to investigate the profitability of residential battery
energy storage at the necessary detail, i.e., modeling stochastic demand profiles at high time resolution
and considering the monetary trade-offs resulting from different system configurations. In addition to
the standard solar energy buffering use case of residential batteries, we investigate the intermittent
provision of negative reserve, which turns out to be attractive for home owners, even without direct
financial compensation.
In summary, our results confirm the potential of residential battery storage highlighted in previous
studies, but at the same time indicate the need for further battery cost reductions to achieve profitability
under all considered circumstances, e.g., household sizes and locations.
Acknowledgments:
This work was supported by funds from the Alexander von Humboldt Foundation and the
Energy Valley Bavaria Program of the Bavarian State Ministry for Education, Science and the Arts. Its publication
was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the
framework of the Open Access Publishing Program.
Author Contributions:
Christoph Goebel and Vicky Cheng conceived the study and performed the simulation
work. Christoph Goebel wrote the first draft of the paper. Vicky Cheng and Hans-Arno Jacobsen reviewed the
paper. Christoph Goebel and Vicky Cheng revised the paper for final submission.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
AcSolar PV module area.
AC Alternating current.
ASC Number of annual storage cycles.
βSolar PV module temperature coefficient of power.
C0,BInitial investment cost of battery.
C0,PE+Initial investment cost of additional power electronic equipment.
C0,PV Initial investment cost of solar PV module.
Ct,BAnnual cashflow resulting from battery.
Ct,OP Annual solar PV system maintenance cost.
Ct,PE+Annual cashflow resulting from additional power electronic equipment.
Ct,PV Annual cashflow resulting from solar PV panel.
CAPBNominal energy capacity of battery.
CAPBAverage battery energy capacity during lifetime.
CAPEO L
BEnd of life battery capacity.
CAPPV Peak power capacity of solar PV module.
CAPPV Average peak power capacity of solar PV module during lifetime.
DC Direct current.
SDuration of control time interval.
RDuration of remaining reserve provision for current reserve interval.
RMaximum duration of reserve provisioning per reserve interval.
Energies 2017,10, 976 15 of 17
EBEnergy provided by battery.
EDGrid energy consumed.
EHH Energy consumed by the household.
EPV Excess solar energy fed into the grid.
ηBBattery efficiency (charging and discharging).
ηPV Solar PV module efficiency.
ηre f Solar PV module efficiency.
fEPC Fraction of engineering, procurement, and construction (EPC) cost.
fOP Fraction of annual PV system operations cost.
GSolar irradiance on the PV array.
Gno Incident solar irradiance when normal operating temperature is measured.
Gre f Incident solar irradiance when ηre f is measured.
γSolar PV module solar irradiance coefficient of power.
iIN V Annual interest rate.
iVAT Value added tax (VAT) rate.
IRE Variable indicating whether battery provides reserve.
Lcyc
BCycle life of battery.
Lcal
BCalendar life of battery.
LPE Lifetime of power electronic equipment.
LPV Lifetime of solar panel.
LOC Household location.
nHH Number of household members.
NPV Net present value.
pBBattery price (excl. VAT).
pBOS PV balance of system (BOS) cost.
pEL End-consumer electricity price.
pFI Solar PV feed-in tariff.
pPE Power electronics cost.
pPV Cost of PV module.
PDC
BDC power of battery.
PAC
DAC power to be transferred to or from the grid.
PDC
GDC power generated by household (solar PV plus battery).
Pneg
GR (t)Negative grid reserve required in time interval [t,t+S].
Pneg
GR Reserve provision threshold.
PAC
HH AC power demand of household.
PlActual power load of power electronic component.
Pmax Maximum power the battery is able to provide.
PDC
PV Solar PV DC power generation.
PrRated power capacity of power electronic component.
PDC
RReserve power delivered by battery.
Preq Maximum power required from battery.
Ptheo Theoretical power the battery is able to provide.
TcSolar PV module temperature.
Tc,ref PV cell temperature when ηre f is measured.
Tno Normal operating PV cell temperature.
TaAmbient temperature.
Ta,no Ambient air temperature when normal operating temperature is measured.
TIN V Investment horizon.
τα Transmittance and absorbance product.
rcBattery charging C-rate.
rdBattery discharging C-rate.
rPV Solar PV peak power capacity deterioration rate.
RtTotal annual household revenue.
Energies 2017,10, 976 16 of 17
SOCmin Minimum battery state of charge.
SOCmax Maximum battery state of charge.
SOC Actual battery state of charge.
SSR Self-sufficiency rate.
tTime index.
tRStart of reserve provisioning time interval.
tREnd of reserve provisioning time interval.
tend Last period in investment horizon.
trep Last replacement time of device.
VwWind speed.
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... In [25,26], it is demonstrated that utilizing batteries and storage systems will improve the efficiency and reliability of the grid. Other studies have focused on combined utilization of batteries and renewable energy sources in order to compensate for the stochastic characteristics of these resources and to help utility companies with peak shaving [27][28][29]. However, none of the available articles have addressed how the installation, operation, and maintenance costs of each of these batteries might affect the utility's and customer's decision in adopting these battery technologies. ...
... where (27) represents the active rectangular power flow model and (28) represents the reactive rectangular power flow model. It can be seen that even the rectangular model has some quadratic terms which leads to a lengthy optimization process. ...
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... However, Munzke et al. [44] and Weniger et al. [45][46][47] have shown, that the actual efficiency curve in combination with the load distribution can have a considerable influence on the economic efficiency of PV home storage systems. Efficiencies in the form of efficiency curves are only considered by a smaller number of papers [10,12,14,26,38,42,48,49]. In this study, the efficiency of the inverters is considered in the form of efficiency curves. ...
... Studies, in which the dimensioning of PV storage systems is investigated and a more complex charging strategy is used at the same time, are rather few. For example, the studies by [15,28,33,36,40,48,49,54] consider more complex charging strategies. Table 1 shows how these differ from each other. ...
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PV in combination with Li-ion storage systems can make a major contribution to the energy transition. However, large-scale application will only take place when the systems are economically viable. The profitability of such a system is not only influenced by the investment costs and economic framework conditions, but also by the technical parameters of the storage systems. The paper presents a methodology for the simulation and sizing of PV home storage systems that takes into account the efficiency of the storage systems (AC, DC standby consumption and peripheral consumption, battery efficiency and inverter efficiency), the aging of the components (cyclic and calendar battery aging and PV degradation), and the intelligence of the charging strategy. The developed methodology can be applied to all regions. In this paper, a sensitivity analysis of the influence of the mentioned technical parameters on the dimensioning and profitability of a PV home storage is performed. The calculation is done for Germany. Especially, battery aging, battery inverter efficiency and a charging strategy to avoid calendar aging have a decisive influence. While optimization of most other technical parameters only leads to a cost reduction of 1–3%, more efficient inverters can save up to 5%. Even higher cost reductions (more than 20%) can only be achieved using batteries that age less, especially batteries that are less sensitive to calendar aging. In individual cases, a small improvement in the efficiency of the storage system can also lead to higher costs. This is for example the case when smaller batteries are combined with a large PV system and the battery is used more due to the higher efficiency. This results in faster ageing and thus earlier replacement of the battery. In addition, the paper includes a detailed literature overview on PV home storage system sizing and simulation.
... Goebel et al. (2017) investigated residential energy storage system which containing Lithium-ion (Li-Ion) batteries combined with solar photovoltaic (PV) panels, and they concluded that the residential battery storage system need for further battery cost reductions to achieve profitability under all considered circumstances, e.g., household sizes and locations [43]. Li et al. (2014) compared between hybrid solar-wind power system with a solar power system and a wind power system. ...
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... If multiple individual batteries increase the self-consumption of each agent, [Roberts et al., 2019] has shown that self-consumption is further increased with the installation of shared batteries instead of individual ones. Shared batteries have also the advantage of reducing the investment, maintenance, operational and replacement costs per end-user [Tascikaraoglu et al., 2019], whereas individual batteries still represent an overall cost as long as they do not provide additional services [Quoilin et al., 2016, Goebel et al., 2017, Roberts et al., 2019). Further, it has been shown by [Koirala et al., 2018] that shared batteries foster social benefits beyond monetary gains, including reinforced social cohesion and local economy, compared to a collection of individually owned and operated batteries. ...
Thesis
This thesis addresses the problem of maximizing the self-consumption of residential photovoltaic power though the optimal control of household appliances.In the first part of the thesis, the optimization problem is restricted to the control of a unique electric water heater, and is formulated as an unconstrained problem. A novel and computationally efficient optimization algorithm is proposed, and is shown to perform better in a deterministic setting than other heuristics. In order to assess the impact of photovoltaic power production uncertainties on the control algorithms performances, the algorithms are evaluated under a large number of scenarios. A novel methodology is presented to generate these scenarios ensuring that each individual scenario presents a realistic intra-day variability, and that the set as a whole represents with proportionality the range of possible production outcomes. Numerical experiments show that at a 30-minute timestep, the impact of a "perfect'' photovoltaic production forecast is negligible compared with the impact of the choice of the control algorithm. In the second part of the thesis, the problem is extended to the optimal control of a diversity appliances located in several households forming a local energy community and sharing the use of a community battery. A mixed integer linear programming formulation of the problem is adopted in order to ease the appliances modeling. The constraint of preserving the private data of the microgrid participants leads to proposing three privacy-preserving communication protocols. These protocols are used to communicate the individual households constraints for the microgrid energy management system to be able to concatenate them into a centralized microgrid optimization problem aiming to minimize the cost of providing energy to the whole community, while preserving privacy.
... Cela permet à l'Agrégateur et au DG d'avoir le support du réseau et la valeur de la flexibilité plus importants, et le réglage d'équilibre plus fin [82]. La rémunération du possesseur final du BESS prend en compte la capacité d'énergie chargée et déchargée (capacité BESS à la hausse et à la baisse) et aussi le fait d'être disponible pour cette SS [83]. La description graphique est sur la Figure 19. ...
Thesis
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... National tax deductions and incentive systems for the coupling with photovoltaic plants up to 20 kW, increased residential size plants installations up to over 18.000 units in the beginning of 2019 [1]. The decreasing national incentive on RES production made self-consumption more attractive [2] and a driver for BESS growth. This emergent application is mostly based on Li-ion batteries, a well-known technology with a strong penetration in portable systems and nowadays in the automotive sector, consequently reducing the cost of the investment with market expansion. ...
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