Content uploaded by Angelos Nousdilis

Author content

All content in this area was uploaded by Angelos Nousdilis on Jul 10, 2018

Content may be subject to copyright.

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.

2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republising this material for advertising or

promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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.

REFERENCES

[1] European Union, On the Energy Performance of Buildings. Directive

2010/31/EU of the European Parliament and of the Council (recast),

Ofﬁcial Journal of the European Communities, Brussels, May 2010.

[2] European Commission, "Green Paper: A 2030 climate and energy

framework", Communication COM(2013) 169, 27/03/2013.

[3] J. Moshovel, K.-P. Kairies, D. Magnor, M. Leuthold, M. Bost, S. Gahrs,

E. Szczechowicz, M. Cramer, and D. U. Sauer, “Analysis of the maximal

possible grid relief from pv-peak-power impacts by using storage

systems for increased self-consumption,” Applied Energy, vol. 137, pp.

567 – 575, 2015.

[4] N.-K. C. Nair and N. Garimella, “Battery energy storage systems:

Assessment for small-scale renewable energy integration,” Energy and

Buildings, vol. 42, no. 11, pp. 2124 – 2130, 2010.

[5] K. Divya and J. Ostergaard, “Battery energy storage technology for

power systems. an overview,” Electric Power Systems Research, vol. 79,

no. 4, pp. 511 – 520, 2009.

[6] J. Hoppmann, J. Volland, T. S. Schmidt, and V. H. Hoffmann, “The

economic viability of battery storage for residential solar photovoltaic

systems. a review and a simulation model,” Renewable and Sustainable

Energy Reviews, vol. 39, pp. 1101 – 1118, 2014.

[7] R. Madlener and A. Kirmas, “Economic viability of second use electric

vehicle batteries for energy storage in residential applications,” Energy

Procedia, vol. 105, pp. 3806 – 3815, 2017, 8th International Conference

on Applied Energy, ICAE2016, 8-11 October 2016, Beijing, China.

[8] S. Barcellona, L. Piegari, V. Musolino, and C. Ballif, “Economic

viability for residential battery storage systems in grid-connected pv

plants,” IET Renewable Power Generation, vol. 12, no. 2, pp. 135–142,

2018.

[9] K. Uddin, R. Gough, J. Radcliffe, J. Marco, and P. Jennings, “Techno-

economic analysis of the viability of residential photovoltaic systems

using lithium-ion batteries for energy storage in the united kingdom,”

Applied Energy, vol. 206, pp. 12 – 21, 2017.

[10] D. Testi, E. Schito, and P. Conti, “Cost-optimal sizing of solar thermal

and photovoltaic systems for the heating and cooling needs of a nearly

zero-energy building: Design methodology and model description,”

Energy Procedia, vol. 91, pp. 517 – 527, 2016, proceedings of the 4th

International Conference on Solar Heating and Cooling for Buildings

and Industry (SHC 2015).

[11] EN ISO 13786:2017 Thermal Performance of Building Components -

Dynamic Thermal Characteristics. Brussels: European Committee for

Standardization (CEN), 2008.

[12] P. O’Callaghan and S. Probert, “Sol-air temperature,” Applied Energy,

vol. 3, no. 4, pp. 307 – 311, 1977.

[13] I. Koumparou, G. C. Christoforidis, V. Efthymiou, G. K. Papagiannis,

and G. E. Georghiou, “Conﬁguring residential PV net-metering policies

a focus on the mediterranean region,” Renewable Energy, vol. 113, pp.

795 – 812, 2017.

[14] G. C. Christoforidis, I. P. Panapakidis, T. A. Papadopoulos, G. K.

Papagiannis, I. Koumparou, M. Hadjipanayi, and G. E. Georghiou, “A

model for the assessment of different net-metering policies,” Energies,

vol. 9, no. 4, 2016.

[15] Datasheet Fronius Energy Package. Available online:

http://www.fronius.com/ /downloads/Solar

[16] D. Parra and M. K. Patel, “Effect of tariffs on the performance and

economic beneﬁts of pv-coupled battery systems,” Applied Energy, vol.

164, pp. 175 – 187, 2016.