Economic Assessment of Lithium-Ion Battery Storage Systems in the Nearly Zero Energy Building Environment

Abstract

Scope of this paper is to deliver a complete techno-economic model for the economic assessment of lithium-ion battery energy storage systems in the framework of the nearly zero energy buildings (NZEB). The proposed model simulates the combined operation of photovoltaics, solar thermal generators, heat pump generators, electrical and thermal storage devices in order to represent efficiently the typical characteristics of NZEBs. The model takes into account the thermal and electrical needs of the building, typical electricity prices, household electrical consumption profiles, weather data and typical costs for lithium battery energy storage systems. Using these inputs, an optimization procedure is applied and the optimal size, in terms of net present value, for the lithium-ion battery energy storage system is derived.

Full text

Economic Assessment of Lithium-Ion Battery
Storage Systems in the Nearly Zero Energy
Building Environment
Angelos I. Nousdilis, Eleftherios O. Kontis Georgios C. Kryonidis,
Georgios C. Christoforidis, and Grigoris K. Papagiannis
Abstract—Scope of this paper is to deliver a complete techno-
economic model for the economic assessment of lithium-ion
battery energy storage systems in the framework of the nearly
zero energy buildings (NZEB). The proposed model simulates the
combined operation of photovoltaics, solar thermal generators,
heat pump generators, electrical and thermal storage devices
in order to represent efficiently the typical characteristics of
NZEBs. The model takes into account the thermal and electrical
needs of the building, typical electricity prices, household elec-
trical consumption profiles, weather data and typical costs for
lithium battery energy storage systems. Using these inputs, an
optimization procedure is applied and the optimal size, in terms
of net present value, for the lithium-ion battery energy storage
system is derived.
Index Terms—Electrical storage, lithium-ion batteries, nearly
zero energy buildings, photovoltaics, thermal storage.
I. INT ROD UC TI ON
European Union’s target for 2030 include the transformation
of the existing building stock to Nearly Zero Energy Buildings
(NZEBs) [1], [2]. NZEBs are characterized by reduced net-
energy demand, since the major part of their thermal and
electrical energy needs are covered locally by renewable
energy sources (RESs), especially photovoltaics (PVs).
Consequently, in the following years, a considerable amount
of intermittent solar generators will be connected in the
existing distribution grids, posing new technical challenges
for distribution system operators (DSOs). The most important
of them include overvoltages, protection, stability and con-
gestion issues. An efficient solution to tackle these technical
Angelos I. Nousdilis, Eleftherios O. Kontis, Georgios C. Kryonidis, and
Grigoris K. Papagiannis are with the Power Systems Laboratory, School
of Electrical and Computer Engineering, Aristotle University of Thessa-
loniki, Thessaloniki, Greece, GR 54124, (e-mail: angelos@auth.gr, kontislef-
teris@gmail.com; kryonidi@ece.auth.gr; grigoris@eng.auth.gr).
Georgios C. Christoforidis is with the Western Macedonia University of
Applied Sciences, Kozani, Greece, (e-mail: gchristo@teiwm.gr ).
This work has been co-funded by the European Union and National Funds
of the participating countries through the Interreg-MED Programme, under
the project "PV-ESTIA - Enhancing Storage Integration in Buildings with
Photovoltaics".
The work of Georgios. C. Kryonidis and Eleftherios. O. Kontis was
conducted in the framework of the act "Support of PhD Researchers" under the
Operational Program "Human Resources Development, Education and Life-
long Learning 2014-2020", which is implemented by the State Scholarships
Foundation and co-financed by the European Social Fund and the Hellenic
Republic.
challenges is to store locally the excess of PV energy, using
energy storage systems (ESS) [3].
Residential ESS are mainly based on battery technologies.
Among the available solutions, lead-acid batteries are the dom-
inant technology for small scale applications [4]. Compared to
other technologies, lead-acid batteries present high reliability,
low self-discharge as well as low maintenance and investment
cost. On the other hand, they have short lifetime and low
energy and power density. Thus, it is expected that in the
near future lead-acid batteries will be replaced by lithium-ion
ones, which present higher energy efficiency and better aging
characteristics [5], [6].
Therefore, there is a strong need to evaluate the profitability
of residential ESSs based on lithium-ion batteries. Towards
this objective, in [7] the economic viability of second use
electric vehicle batteries for energy storage application in
the residential sector is evaluated, while in [8] and [9] the
profitability margins of adding lithium-ion battery SSs (BSSs)
to existing residential grid-connected PV plants is investigated.
The corresponding results reveal that the present costs of
lithium-ion batteries are too high to allow economically viable
investments. However, the above-mentioned studies do not
take into account the impact of thermal storage systems (TSS),
solar thermal (ST) and heat pump (HP) generators on the
optimal size of the electrical BSS.
Concerning the above-mentioned issue, the scope of the
paper is to develop a complete techno-economic model to
evaluate the economic viability of electrical ESSs based on
lithium-ion batteries in the NZEB environment. The combined
operation of PVs, HP and ST generators, TSS and BSS is
simulated by a full set of equations, describing the coupled
behavior of each component in the NZEB context [10]. The
proposed model receives as inputs: i) technical data related
with the building energy systems and the building shell, ii)
economical data such as the typical cost of lithium-ion batter-
ies and electricity prices, iii) typical electricity consumption
profiles related with the electrical power consumed for lighting
and household appliances, and iv) weather data. Initially, the
model calculates the total thermal and electrical needs of the
building, using the available climate data. Afterwards, the
optimal size, in terms of net present value (NPV), for the
lithium-ion BSS is determined by applying an optimization
scheme.
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II. BUILDING MODEL
The adopted building model [10] takes into account PV
systems, ST and HP generators, TS and BS systems. The
mathematical description of these components as well as the
control strategies, used for the charge/discharge of TSSs and
BSSs are described in detail in the following subsections.
A. Heating and Cooling Load
The thermal power required at each time instant for the
heating of the building, Pth,H , can be estimated as:
Pth,H =Pth,des,H 1−
¯
Text −Tdes,H
Toff,H −Tdes,H !(1)
where Pth,des,H is the thermal power, required for the heating
of the building under the designed conditions, while Tdes,H
is the external temperature, used for the design of the heat-
ing system. Moreover, Toff,H is the nominal temperature at
which building losses and gains are balanced and the heating
system is switched off. Finally, ¯
Text is the effective outdoor
temperature based on the characteristics of the building and
the actual external temperature Text. The ¯
Text temperature is
defined as the simple moving average of the previous ¯
φvalues
of Text. Where ¯
φis the nearest integer of the effective time
shift of the building, defined as:
¯
φ=PN
i=1(U A)iφi
PN
i=1(U A)i+Hv e
(2)
where φiand (UA)iare the characteristic time shift, as
defined by EN ISO 13786:2007 [11], and the surface thermal
transmittance of the i-th external wall, respectively, while Hve
is the equivalent ventilation-thermal transmittance based on air
change rate.
The thermal power required for the cooling of the building,
Pth,C , is calculated as:
Pth,C =Pth,des,C 1−
¯
T∗
ext −T∗
des,C
Toff,C −T∗
des,C !(3)
where T∗is the so-called "sol-air temperature" [12], Toff,C
is the nominal temperature in which the cooling system is
deactivated, while ¯
T∗
ext is the simple moving average of the
previous ¯
φvalues of T∗
ext
B. Heating and Cooling System Terminal
In this paper, a radiant floor is considered as the heat ter-
minal unit. Water and floor temperature evolution is simulated
through a simplified resistance model [10], as presented in
(4)-(6).
∆TRF =Tw,RF −Tin =
∆TRF,nom Pth
SRF KRF,nom !
1
nRF (4)
Tf,RF,H =Tw,RF,H −Pth,H
SRF Uwf
(5)
Tf,RF,C =Tw,RF,C +Pth,C
SRF Uwf
(6)
where Tw,RF and Tin is the temperature of the water within
the radiant floor and the internal air temperature of the build-
ing, respectively. Please note that in this paper, the internal
air temperature is considered equal to the corresponding set-
point value. Additionally, ∆TRF is the nominal difference
between the mean temperature of the water and the internal
air, while nRF is the emitter exponent of the radiant floor
and KRF,nom is the nominal thermal output per surface unit.
Moreover, Tf,RF stands for the floor temperature, while SRF
is the total surface of the radiant floor and Uwf is the thermal
transmittance between the circulating water and the flood
surface.
C. Domestic Hot Water Production
The power required for the production of domestic hot water
(DHW) can be evaluated as:
PDHW =dwcw(TD HW −Taqua )(7)
where dwis the supply of domestic hot water in Kg/s, while cw
is the specific heat capacity of the water. TDHW is the desired
temperature of the DHW, whereas Taqua can be considered
equal to the outdoor temperature.
D. PV System
The power produced by the PV system can be efficiently
calculated using the following set of equations [10]:
PP V =nP V ηinvηP V SP V Isol (8)
ηP V =ηP V,ref [1 −βPV (TP V −Tref,P V )] (9)
TP V −Text = (219 + 819Kt)N OC T −20
800 (10)
where, ηinv is the efficiency of the inverter, nPV is the number
of the installed PV modules, while SP V is the surface of each
module. Moreover, ηPV is the actual efficiency of the PV
modules at the operational temperature TP V , while ηPV ,ref is
the efficiency of the PV modules at the reference temperature
Tref,P V . Additionally, βPV is a temperature penalization factor
depending on the PV technology and NOCT denotes the
nominal operating cell temperature. Finally, Isol is the clear
sky irradiation and Ktis the clearness index.
E. Heat Pump Generator
In this paper, air to water electrically-driven HPs are con-
sidered. To ensure that the thermal load of the building is
covered under any conditions, the nominal capacity of the
HPs is chosen to be equal with the peak thermal load. The
performance of the HPs can be evaluated using the following
equations:
COP =ηHP,H
Tcond
Tcond −Teva
(11)
EER =ηHP,C
Teva
Tcond −Teva
(12)

The HP efficiency ηHP can be considered with sufficient
accuracy as a constant value [10]. Additionally, in this paper,
the same ηHP is adopted for both the heating mode and the
production of DHW. The values of Tcond and Teva depend
on the provided service [10]. At the indoor of the HP heat
exchanger (water side), a temperature droop equal to 5 K
is considered. Moreover, a drop of 10 Kis assumed at the
outdoor of the HP heat exchanger (air side).
F. Solar Thermal Generator
The operation of the ST generator is simulated using the
following mathematical model [10]:
Pth,ST =nST ηS T SST Isol (13)
ηST =FR(τ α)nA−B(14)
where
A= (1 −b0(1/cosθ −1)) (15)
and
B=FRUL(TST ,in −Text)
Isol
(16)
In the above equations, nST and ηST denote the number of
solar collectors and their efficiency, respectively. SST is the
surface of each collector, while FRis the solar thermal removal
factor. Furthermore, (τα)nis the transmittance-absorptance
product for normal incidence irradiance, while b0is the inci-
dence angle modifier coefficient for single-cover solar thermal
collectors, and θis the angle between the beam radiation and
the normal to the solar thermal collectors. Finally, ULis solar
thermal frontal losses and TST ,in is the temperature of the
thermal storage.
G. Thermal Storage System
For the adopted TSS, the thermal power balance equation
at the j-th time step of the analysis can be written as:
VT S ρwcw(Tj
T S −Tj−1
T S ) =Pth,S T +Pth,HP,T S −
Pth,DHW −Pth,T S,H −
Pth,T S,ls
(17)
where VT S is the total volume of the TSS, while ρwis
the density of the water. Moreover, Tj
T S and Tj−1
T S are the
temperatures of the water at the TSS at the jand j−1time
step of the analysis, respectively. Pth,ST and Pth,H P,T S are the
powers provided by the ST generator and the HP to the TSS,
respectively. On the other hand, Pth,T S,H denotes the power
exported from the TSS for heating purposes, while Pth,DHW is
the power used for the production of DHW. Finally, Pth,T S,ls
stands for the power losses of the TSS and can be calculated
as:
Pth,T S,ls =ST S
λT S
sT S
(TT S −Text,T S )(18)
In the above equation, STS ,λT S and sT S are the total
surface, the thermal conductivity, and the thickness of the
TSS. Moreover, Text,TS is the TSS room temperature. Further
information concerning the control strategy of the TSS can be
found in [10].
Algorithm 1 Pseudocode for the control strategy of the BSS
1: Define upper/lower SOC limits, i.e. SOCuand SOCl.
2: if PP V > Pload && SOC < SOCu
3: Battery charges
4: elseif PP V > Pload && SOC ≥SOCu
5: No action
6: elseif PP V < Pload && SOC > SOCl
7: Battery discharges
8: elseif PP V < Pload && SOC ≤SOCl
9: No action
10: end if
H. Battery Storage System
The electrical power balance equation can be written as:
PP V +Pgrid +Pbat =Pload (19)
where
Pload =PHP +Pel (20)
In the above equations, Pgrid denotes the electrical power
imported from the main utility grid, Pbat is the electrical power
of the BSS, and Pel is the electrical power, used for lighting
and household appliances. Finally, PHP is the electrical power
of the HP, which can be easily computed using the following
equations:
PHP,H =Pth,H
COP (21)
PHP,C =Pth,C
EER (22)
Concerning the control strategy of the BSS, a simple scheme
that maximizes the self-consumption ratio is adopted. More
specifically, in case the PV power exceeds the total load
demand, the BSS starts the charging procedure by absorbing
the surplus of the generated power up to the maximum
permissible value. On the other hand, if the PV generated
power is lower than the load demand, the BSS discharges.
During this process, the upper and lower limit of the state of
charge (SOC) of the BSS is taken into account. The adopted
control strategy is analytically presented in Algorithm 1.
III. ECONOMIC EVALUATI ON O F BSS
Nowadays, the majority of PV installations in the residential
sector are operated under net-metering (NeM) schemes [13],
[14]. In these policies, prosumers can offset the imported
energy from the grid with electrical energy generated from
a local PV system. The prosumers are then charged for a
certain billing period according to their net energy consumed.
The time period during which the produced PV energy can
be netted against the imported energy is characterized as
netting period [14]. In case the generated energy exceeds the
consumed throughout the netting period, a compensation may
be provided for the excess energy at a certain sale price (sp).
In this paper, the economic viability of lithium-ion BSS
is investigated assuming a full NeM scheme [14]. In the
examined scheme, the netting period is considered equal to

one hour. This paper examines two cases in which excess
energy is either compensated using the system marginal price
(SMP) of the Greek electricity market or not compensated at
all. Moreover, the billing is performed assuming two distinct
charge categories: i) The fixed cost (fc), that includes trans-
mission and distribution systems constant charges, standing
fees, etc, and ii) the netted-cost (nc), which is the prosumer
charge calculated using the net energy consumed during the
billing period.
A 20-year economic analysis is performed based on the
following procedure: Initially, the exported energy to the grid
(Eexp) and the netted energy (Enet ) are calculated. For a
typical day, these energies can be defined by the aid of Fig. 1
as follows:
EP
exp =B+D(23)
EP
net =A+F+E−B−D(24)
EP B
exp =B(25)
EP B
net =A+F−B(26)
Eq. (23) - (24) stand for the case in which only the PV system
is considered, while Eq. (25) - (26) refer to the case of an
integrated PV-BSS.
For a specific year of investment (t), the NPV of the
installed BSS (npvt) is computed as:
npvt=
N
X
n=1
cft,n
in −cft,n
out
(1 + i)n−capexB(1 + a)t−1(27)
Here Ndenotes the lifetime of the lithium-ion batteries. A
typical system with a depth of discharge equal to 80% can
perform more than 8000 cycles of operation [15]. Therefore,
assuming a full operation cycle during each day of the year, N
is considered equal to 22 years and no replacement is foreseen
for the batteries during the analysis period. Moreover, in (27),
iis the discount rate, while astands for the inflation rate.
cft,n
in and cft,n
out are the cash in and out flows, respectively.
Finally, capexBis the capital investment cost of the BSS.
The cash flow out is related with the operation and mainte-
nance costs of the BSS (opexB) and is calculated according to
(28). On the other hand, the cash flow in represents the profit
from the use of the BSS and can be derived using (29).
cft,n
out =opexB(1 + a)t−1(1 + a)n−1(28)
Fig. 1. Typical household consumption and generation profiles.
Model inputs
Building model,
Eq. (1) – (22)
S ≤ Smax
Battery size (S)
S=0.5 kWh
npv calculation, Eq. (27)
Optimal BSS size
Step 1
Step 2
Step 3
Step 4
Step 5
Fig. 2. Proposed techno-economic model.
cft,n
in = (ct,n
P−ct,n
P B )−(prt,n
P−prt,n
P B )(29)
Where, ct,n
Pis the electricity cost of the base scenario,
where only the PV system is considered, while ct,n
P B is the
corresponding cost when an integrated PV-BSS is assumed.
These values are obtained using (30) and (31), respectively.
Moreover, prt,n
Pand prt,n
P B correspond to prosumer profit due
to the compensation for excess energy and are obtained using
(32) and (33), respectively.
ct,n
P="K
X
k=1
(Ek,P
net nct) + fct#(1 + a)n−1(30)
ct,n
P B ="K
X
k=1
(Ek,P B
net nct) + fct#(1 + a)n−1(31)
prt,n
P="K
X
k=1
(Ek,P
exp spt)#(1 + a)n−1(32)
prt,n
P B ="K
X
k=1
(Ek,P B
exp spt)#(1 + a)n−1(33)
Here, Kis the last billing period of year n. For different
investment periods, all values, i.e., nc,fc, and sp can be
calculated as:
[nctfctspt] = [nc fc sp](1 + a)t−1(34)
IV. PROPOSED TECHNO-ECONOMIC MODEL
The proposed techno-economic model is presented in Fig. 2
by means of a flowchart. The model consists of 5 main steps,
described in detail below:
Step-1:.Initialization phase. In this step, several technical
and economical data are provided as inputs to the model. More
specifically, the required inputs include: i) technical parameters
related with the building shell and the energy systems of
the building, ii) economical parameters such as the typical
cost of lithium-ion batteries and electricity prices, iii) typical
electricity consumption profiles related with the electrical
power consumed for household appliances and lighting, and
iv) historical weather data, used to evaluate the thermal energy

TABLE I
TECHNICAL AND ECONOMICAL PARAMETERS
Building Cell Radiant Floor PV Generator
A=300 m3∆TRF,nom=20 K SP V =1.5 m2
U=3.56 W/(m2K) SRF =80 m2nP V =40
φi=8 h KRF,nom=60 W/(m2)ηinv =0.85
Hve=0 W/(m2K) nr f =1.1 ηPV ,ref =0.13
Tdes,H =-3 oCU=6 W/(m2K) βT,P V =0.004 1/K
Tdes,C =47 oCToff ,H =17 oCTref ,P V =25 oC
Pth,des=3.75 kW Toff ,C =26 oCN OC T =45 oC
TSS ST Generator HP Generator
VT S =0.5 m3sST =3 m2PH P,max=4.125 kW
ST S =3.5 m2nST =1 nH P,H =0.45
TT S,set=50 oCFR=0.8 nH P,C =0.35
TT S,up=60 oC (τ a)n=0.7 BSS
TT S,down=42 oCUL=5 W/(m2K) S OCu=90%
TT S,max=90 oCb0=0.1 SOCl=20%
λT S =0.04 W/(mK) θ=0.3839 costbattery =600 e/kWh
sT S =0.08 m costinverter =200 e/kW
Economical Parameters
a=2% nc1=0.174 e/kWh fc=35 e/year
i=5% nc2=0.165 e/kWh
needs of the building. Weather data and consumption profiles,
used in this paper, are presented in Fig. 3. Technical and
economical parameters are summarized in Table I. Concerning
electricity costs, typical values of the Greek System are used.
Based on the netted energy (whether it is over or below 2000
kWh), the netted-cost receives two separate values, namely
nc1and nc2, respectively. Finally, in the presented analysis
opexBis neglected [16].
Step-2:.Evaluation of thermal and electrical energy needs.
In this step, the thermal and electrical energy needs of the
building are calculated on a 15 minute basis using the profiles
of Fig. 3. Thermal needs are estimated using (1) - (18), while
electrical needs are calculated from (19) - (22) assuming a
specific size Sfor the BSS. Concerning the first algorithm
iteration, it is assumed that Sis equal to 0.5 kWh. During the
first iteration, the base scenario, where only the PV system is
installed, is also simulated in order to evaluate (30).
Step-3:.npv calculation. Here, (23) - (26) are computed
and the npvtof the investment is derived using (27). The
corresponding result is stored to a vector, named as P Ss.
Step-4:.Stopping criterion. If the size Sof the BSS
is greater than a maximum user-defined value (Smax), the
algorithm proceeds to Step 5. Otherwise, the procedure moves
back to Step 2, by setting S=S+0.5.
Step-5:.Optimal BSS size. In this step, a search algorithm
is used to determine the maximum value of P Ss. This value
actually corresponds to the optimal size of the BSS.
0 4 8 12 16 20 24
0
0.2
0.4
0.6
0.8
1
Hour
Irradiation (kW/m2)
January
February
March
April
May
June
July
August
September
Octomber
November
December
a)
0 4 8 12 16 20 24
0
10
20
30
Hour
Temperature (oC)
b)
0 4 8 12 16 20 24
0
0.5
1
1.5
2
Hour
Pel (kW)
c)
Fig. 3. Typical daily: a) irradiation, b) temperature, and c) consumption
profiles.
V. SIMULATION RESU LTS
In this Section, indicative results for the proposed model are
presented. More specifically, a 20-year economic analysis is
performed assuming a typical three-phase house installation,
located in the central Greece. The total floor area of the house
is considered equal to 100 m2, while its height is assumed

0 2.5 5 7.5 10 12.5 15 17.5 20
Battery size (kWh)
-500
0
500
1000
1500
2000
2500
3000
3500
npv1 (euros)
100 euros
200 euros
400 euros
600 euros
Fig. 4. NPV under a full net metering scheme. Excess energy is compensated
with SMP.
0 2.5 5 7.5 10 12.5 15 17.5 20
Battery size (kWh)
-1000
0
1000
2000
3000
4000
5000
6000
npv1 (euros)
100 euros
200 euros
400 euros
600 euros
Fig. 5. a) NPV and b) IRR under a full net metering scheme. Excess energy
is not compensated.
equal to 3 m. The internal air temperature of the house is
assumed to be constant and equal to 26 oC and 20 oC during
the cooling and the heating mode, respectively. The supply
for DHW is considered constant and equal to 10 kg/min. The
temperature of the DHW is 45 oC.
Indicative results for the two examined NeM policies are
presented in Figs. 4 and 5, respectively. As shown, under
the examined NeM policies and with the current prices,
the installation of BSS is not profitable for the prosumer.
Therefore, a parametric analysis for different BSS prices
is conducted. The analysis reveals that the installation of
BSSs can become profitable if the corresponding prices are
reduced. Additionally, it is worth noticing that the profitability
is considerably increased for prosumers operated under NeM
policies in which the excess of energy is not compensated.
VI. CONCLUSIONS
In this paper, a techno-economic model is developed to
facilitate the economic assessment of lithium-ion BSSs in the
framework of NZEBs. The proposed model simulates the com-
bined operation of PVs, thermal and battery storage systems
as well the operation of ST and HP generators to represent
efficiently the typical characteristics of NZEBs. It receives as
inputs several technical and economical parameters, typical
consumption and weather data. Initially, using these inputs,
the model evaluates the thermal and electrical energy needs of
the building. Afterwards, an optimization procedure is applied
and the optimal size for the lithium-ion BSS is derived.
Using the proposed model, the economic viability of
lithium-ion BSSs for a typical household installation, located
in the central Greece, is evaluated. The simulation results
reveal that with the current market prices, the installation of
BSSs is not recommended, since standalone PV systems can
generate more profits. However, the conducted analysis reveals
that as the BSS prices decrease, the profitability is increased,
outperforming the NPVs of standalone PVs. Therefore, in the
next few years a high number of BSSs is expected in the
building environment. In this context, the proposed method can
be a valuable tool for the economic analysis and the optimal
sizing of household BSSs.
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