Sizing of II-Life Batteries for Grid Support Applications and

Economic Evaluations

Giuseppe Graber

, Vito Calderaro

, Vincenzo Galdi

and Antonio Piccolo

Department of Industrial Engineering, University of Salerno, Fisciano (SA), Italy

Keywords: Battery Sizing, Economic Assessment, Electric Vehicles, Energy Storage Systems and Second Life.

Abstract: Power systems are facing increasing stress due to modernization changes in both supply, through the growing

penetration level of renewable sources, and demand due to the spread diffusion of electric vehicles (EVs). In

this scenario, the use of energy storage systems (ESSs) is becoming technologically attractive but problems

of economic and ecological sustainability are still evident. For these reasons, II-Life battery modules are a

possible solution for supporting power systems: they are a promising prospect for the modernization process.

We propose a method to size an ESS of exhausted plug-in EV battery packs for grid support applications. The

method estimates the residual value of cycles for II-Life battery modules, the decrease in the supplied power

due to the battery ageing and the number of EV battery packs to meet service requirements. Then, an economic

assessment is presented to compare them with an equivalent I-Life storage system.

1 INTRODUCTION

Energy storage systems (ESSs) for power system

application is attracting significant interest and

attention as an enabling solution for integrating the

growing penetration of renewable energy resources

and electric vehicles (EVs) into electrical grids,

(Calderaro, 2014 – Tejada-Arango, 2018). Likely,

ESSs are becoming an essential contributor to

modernization investments of power systems at each

voltage level. In fact, the ESSs can provide a technical

solution to face current industry challenges such as

power quality, network security, congestion

management, generator’s low utilization factor, and

fuel price volatility. Consequently, the storage

devices can propose ancillary services bringing

benefits to customers and energy operators, (Graber,

2017 – Ju, 2018).

However, two main challenges must be faced to

support the integration of ESSs into the networks: the

economic and ecological sustainability. Promising

prospects are coming from the use of II-Life battery

modules, reusing EV battery packs for alternative

uses. In particular, they still have significant

https://orcid.org/0000-0002-3474-2470

https://orcid.org/0000-0003-0868-6601

https://orcid.org/0000-0002-7768-7125

https://orcid.org/0000-0001-6405-7020

remaining capacity for grid support applications,

although this is not sufficient to provide an electric

driving range. The main advantages of these battery

modules are the supposed lower cost compared with

new battery modules and the possibility to delay the

development of the EV battery packs recycling chain

(Viswanathan, 2011).

Figure 1: II-Life battery process, (Reid, 2016).

In the literature, the relationship between II-Life

batteries and network electrical systems has been the

subject of several recent investigations. The use of

Graber, G., Calderaro, V., Galdi, V. and Piccolo, A.

Sizing of II-Life Batteries for Grid Support Applications and Economic Evaluations.

DOI: 10.5220/0007728800800088

In Proceedings of the 8th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2019), pages 80-88

ISBN: 978-989-758-373-5

II-Life battery-based ESSs for network support is

recently analysed in several papers. In particular, in

(Viswanathan, 2011) the authors propose a method

for determining the optimal rating of the modules and

the state of charge (SoC) profile during the operation.

In (Saez-de-Ibarra, 2016), an optimization study is

presented in order to maximize the value of an electric

vehicle battery to be used as a transportation battery

(in its first life) and, then, as a resource for providing

grid services (in its second life). Also in (Lacey,

2013) II-Life batteries are used for provision of

services with particular emphasis on peak shaving

and upgrade deferral of low voltage (LV) distribution

systems, while in (Gladwin, 2013) and (Koch-

Ciobotaru, 2015) a general estimation of the use of

batteries for electrical systems and a feasibility

analysis are investigated, respectively. The

integration of photovoltaic (PV) energy sources is

proposed in (Mukherjee, 2015), where studies on the

modular boost-multilevel buck converter to control

the storage systems are proposed, and in (Gohla-

Neudecker, 2015), where it is deducted an effective

control strategy for attaining maximum system

performance with minimum battery cell aging. Ref.

(Strickland, 2014) and (Tong, 2015 – Hamidi, 2013)

suggest a more general approach for supporting the

integration of renewable energy resources. In (Saez-

de-Ibarra, 2016) the important task of II-Life batteries

sizing, is faced. It is a complex procedure due to many

uncertainty factors such as degradation factors,

calendar life, and applications.

With this in mind, here, we extend (Calderaro,

2017) by proposing a method to size the II-Life

battery-based ESSs and assess the economic

outcomes. The method is based on two main steps:

the first one allows identifying an approximate value

of the residual number of cycles and the maximum

power that battery modules of II-Life ESS can

deliver, whereas in the second one, we calculate the

annual cost of energy to compare it with an equivalent

I-Life storage system.

2 SIZING METHOD FOR II-LIFE

BATTERIES

We propose a method for sizing an ESS consisting of

II-Life lithium batteries. The method takes into

account the real calendar life of the battery modules

and the uncertainty related to the residual capacity

measurements. The sizing methodology is composed

of four steps:

• modelling of the II-Life battery model consisting

of the series of a resistance and an ideal voltage

source and their relationship with SoC and

charging/discharging cycles (CDC);

• calculation of the residual cycles of the II-Life

lithium batteries by linearizing the relationship

between the batteries residual capacity and CDC;

• estimation of the II-Life battery aging in terms

of supplied power by linearizing the relationship

between the batteries internal resistance and CDC;

• Monte Carlo (MC) analysis to compute the

number of II-Life battery modules according to the

capacity and capability requirements.

2.1 Ii Life Battery Model

The II-Life battery is modelled as an ideal voltage

source in series with a resistor. In particular, the ideal

voltage source represents the open circuit voltage

(OCV) depending on SoC of the battery module,

while the series resistor R

int

represents its overall

internal resistance.

Figure 2: Proposed II-Life battery model.

The equations (1) describes the electric model of

II-Life battery modules. Specifically, the first

equation represents the Kirchhoff's voltage law, while

the second one is the n-polynomial relation between

OCV and SoC. The third equation models the SoC

update law, according to the required current from the

battery modules.

int

( ) ( ) ( )

( ) ...

( ) ( 0) ( ) ( )

3600

BATT BATT

BATT

V t OCV t R I t

OCV SoC SoC SoC

SoC t SoC t V I d

  

  











     





   









(1)

In (1), β

… β

are the interpolation coefficients,

BATT

, V

BATT

and C

BATT

are the battery modules current,

voltage, and capacity, respectively.

Moreover, battery-aging leads to a decrease in

battery capacity as CDC increases described by the

function f as follows:

Sizing of II-Life Batteries for Grid Support Applications and Economic Evaluations

()

BATT

C f CDC

(2)

In Section 2.2, we present a method to estimate

the function f starting from EV battery datasheet. In a

similar way, the g function describes the increase of

int

by increasing CDC as follows:

int

()R g CDC

(3)

The method to estimate the function g is presented

in Section 2.3.

2.2 Residual Capacity vs. CDC

Approximation

Often, manufacturers do not provide any information

about relationships between the battery residual

capacity C

BATT

and its maximum number of CDC

performed at different depth of discharge (DoD) or

they give only some curves at certain DoD. In the

following, we describe a methodology to approximate

this relationship at different DoD.

Figure 3 shows the typical trend (in logarithmic

scale) between the calendar life in terms of maximum

number of CDC and the DoD of a battery module

(Julien, 2016). Generally, the functional dependency

between CDC and DoD can be formalized by a test

curve, a table, or a mathematical relationship based

on measured data, which allows us to estimate the

number of CDC before the battery module reaches its

end of life (EoL). The EoL identifies the maximum

acceptable reduction of the battery rated capacity and

it is strongly dependent on the battery application

(traction, energy, etc.).

Figure 3: Lithium batteries typical trend - maximum

number of CDC vs. DoD.

In Figure 4, we show the general trend of the

relationship between the residual capacity C

BATT

and

the maximum number of CDC for a fixed value of

DoD, which is given by the manufacturer (Julien,

2016). Typically, a nonlinear function describes this

relationship for lithium batteries. We observe a rapid

decrease of the battery residual capacity in the first part

of the characteristic, then, in the middle one, the trend

is almost linear and it decreases very quickly at the end

of the curve. The knee of the curve on the right of

Figure 4 identifies the battery EoL for energy

applications EoL

(typical value 60 - 70% of C

BATT

rated value) whereas the EoL for traction purposes is

defined when the residual capacity is in the range of 80

- 85% of C

BATT

rated value. For our purpose, it is not

relevant to identify battery discharge profiles (such as

DoD, CDC, etc.) before the point EoL

trac

- CDC

trac

(i.e.

the number of CDC at the EoL

trac

Figure 4: Lithium batteries typical trend - residual capacity

vs. CDC.

Figure 5: Linear approximation:residual capacity vs. CDC.

Figure 6: Linear approximation - residual capacity vs. CDC

for different DOD values.

SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems

If the battery manufacturer does not give this

curve, it is possible to take some assumptions to

estimate the parameters of interest for our study. We

use the following procedure to approximate the curve

in Figure 4 by a line for different DoD values, as

shown in Figure 5:

• select a DoD value from Figure 3 (DoD

) to

obtain a maximum number of CDC (CDC

) that

represents the number of cycles when the battery

module reaches its energy EoL

;

• draw the point B

in the plane C

BATT

/CDC

(Figure 5);

• repeat the same procedure for each value of DoD

in Figure 3 in order to obtain a set of

n-1 maximum values (CDC

, CDC

,…, CDC

)

and for each maximum value of CDC, in the

plane C

BATT

/CDC draw the points (B

, B

,…,B

)

as show in Figure 6;

• in the plane C

BATT

/CDC, identify the point A in

correspondence of 0 cycles and C

BATT

rated

capacity;

• draw a line from the point A to each point

, i=(1, 2, … , n); each line represents a specific

DoD value (Figure 6);

• calculate the coefficients of the straight lines.

It is worth noting that the constellation of points

, B

… B

) defines different number of cycles at

the energy EoL of the battery.

In particular, the yellow area in Figure 5 shows

the error obtained by using the proposed linear

approximation. It is greater in the I-Life of the battery,

but it is not important for our methodology.

Figure 7: Maximum number of CDC vs. DoD trend for

SAFT lithium-ion batteries.

Figure 8: Residual capacity vs. CDC trend for SAFT

lithium-ion batteries.

According to real data provided by batteries

manufacturers (SAFT, 2014), and showed in

Figure 7-8, the proposed linear approximation

reasonably describes the relationship between

residual capacity and the maximum number of CDC.

2.3 Aging of Internal Resistance

Approximation

The internal resistance of Li-ion batteries also

increases with use and aging. The increase in R

int

leads to a reduction of the maximum power that the

battery can deliver and therefore it is necessary to

estimate this increase so that the ESS is able to supply

the required power for a given grid service until its

EoL. Unfortunately, manufacturers of EV batteries

very often do not provide such information in

datasheets.

In our analysis, we assume that the increase of the

internal resistance during the battery life is a

synchronous process with the reduction of its residual

capacity.

Figure 9: Internal resistance vs. Residual capacity: typical

trend and linear approximation.

Sizing of II-Life Batteries for Grid Support Applications and Economic Evaluations

Figure 9 shows the typical trend of the internal

resistance reducing the battery residual capacity (i.e.

increasing the aging). In particular, the X, Y and Z

points are defined by the pair of values R

int

, C

BATT

the beginning of life (these values are provided by

battery manufacturer), at the EoL for traction, and at

the EoL for energy applications, respectively. The Y

and Z points are very difficult to estimate because we

usually do not have any data from the battery

manufacturers.

We assume that the increase in the R

int

is given by

the ratio between the nominal capacity and the

residual capacity of the battery. Therefore, to estimate

the point Y (or Z) it is necessary to multiply the R

int

nominal value (X point) for the ratio between battery

nominal and residual capacity. Finally, established

the Y and Z points, we can linearly estimate the trend

of R

int

with the aging. The yellow area in Figure 8

shows the error obtained by using the proposed linear

approximation.

2.4 Equivalent Sizing of II-Life ESS

In order to size the II-life ESS (i.e. define the number

of II-Life battery modules), we have to identify the

service that the ESS must perform. Let us assume that

this application has a fixed DoD (e.g. DoD

The proposed procedure is based on a preliminary

sizing obtained by using a conventional methodology

computing the number of I-Life battery modules M,

fixed the application (i.e. the necessary power and

energy for the service, the DoD value and thus the

maximum number of CDC). M is equal to the

maximum value between the ratio of the energy

requirement and the energy of one I-Life battery

module, and the ratio of the power requirement and

the power of one I-Life battery module. In order to

consider the II-Life of the modules, we assume, for

each one of them, a reduced capacity (battery capacity

equal to the EoL

trac

value multiplied C

BATT

) and an

increased R

int

value: in this way, the number of II-Life

modules is greater than the one obtained by using

I-Life battery modules.

Afterwards, we bring into the problem the

uncertainties due to an incorrect estimation of the

residual capacity and maximum power. We assume

M as the number of II-Life battery modules needed

for the application in case of uncertainty is not

considered. According to the available data, it is

possible to consider the points B

, C and Z as random

variables with a given probability distribution (e.g.,

uniform, Gaussian, etc.) to in order to bring into

account their uncertainties. We use a MC approach to

calculate: i) a distribution of residual cycles of II-Life

battery for the application; ii) a distribution of battery

maximum power at the EoL for the application.

We assume for our studies two Gaussian

distributions (μ

=CDC

trac

, σ

=1, μ

=CDC

and

=1), to tackle the uncertainty due to a wrong

estimation of points B

and C. In a similar way, a

Gaussian distribution (μ

=1.66*R

int

, σ

=1) is

assumed at the point Z.

For these reasons, we consider m II-Life battery

modules in addition to M, able to guarantee a number

of CDC equal to CDC

≥ CDC

trac

- CDC

, and

maximum battery power at EoL

, P

BATT

≥ P

. In such

a way, the remaining life of the II-Life ESS and its

maximum power at the EoL

can be designed. In

particular, we introduce m

and m

that represent the

additional capacity necessary to the II-Life ESS for

satisfying the required CDC and the additional power

necessary for satisfying the maximum required

power, respectively. We calculate the parameter m

and m

by implementing an iterative procedure based

on a MC approach. Our procedure starts with

=0 and ends when it finds the smaller value of

that ensures

 Pr (CDC of M modules ≥ CDC







m

modules) > 

90%

 (4)

and the smaller value of m

that ensures

 Pr (P

BATT

of M modules ≥ P







m

modules) > 

90%

 (5)

where 

90%

is the percentile of the resulting

distribution.

The number m of battery modules satisfying the

CDC

and the P

requirements is the maximum value

between m

and m

. Then, we are able to define the

final number of II-Life battery modules (M+m

with

i=1 or 2 depending on the m

maximum value)

necessary to achieve an equivalent I-Life ESS and to

perform an economic assessment.

3 ECONOMIC METRIC

We use the net present value (NPV) as economic

metric to examine costs and revenues while

accounting for the time value of money (Masters,

2013). If the NPV of a system is positive, then the

investment should may be profitable. A negative

NPV indicates that the returns are worth less than the

cash outflows and the investment does not show a

financial benefit, although unquantified benefits may

be present. Annual cost of energy (ACOE) in [$/year]

represents the present value of total cost C

tot

multiplying by the capital recovery factor CRF. The

CRF converts a present value into a stream of equal

SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems

annual payments over a specified lifetime N [year], at

a specified interest rate r. It is defined as follows:

(1 )

(1 ) 1

CRF







(6)

and the C

tot

is given by:

 

&tot I M O REP

C C C C  

(7)

where C

is the storage capital cost, C

M&O

is the net

present value of the total operations and maintenance

costs and C

REP

is the present value of the replacement

costs.

The capital cost C

is the one-time investment,

which brings the ESS into an operable status. It

contains two subsystems: the first one is the power

sub-system whereas the second one is the energy

storage sub-system. The cost of the two sub-systems

should be added together to get the overall capital

cost. C

can be formulated as

I P R E R FC

C C P C E C  

 (8)

where P

[kW] and E

[kWh] are the ESS rated

power and capability; C

[$/kW] and C

[$/kWh] are

the specific costs mainly related to the electronic

interface to the network and to the size of the ESS,

respectively. C

[$] is the fixed cost (building cost,

landing cost, construction cost, etc.).

There are at least four elements in the C

M&O

cost:

1) labour associated with plant operation, 2) plant

maintenance, 3) equipment wear leading to its loss-

of-life, and 4) disposal and decommissioning cost.

The C

M&O

cost is defined as follows:

(1 )







 (9)

where C

[$] is the annual operation cost on n years

and it is defined as a function of two main parts: a

fixed one related to the ESS rated power, and a

variable part depending on its annual discharged

energy E

year

[kWh].

n f R v year r

year

r CH

C C P C E C



  



 (10)

The annual operation cost is split in variable cost

) and charging cost (C

): where η

is the battery

charging efficiency and C

[$/kWh] is the electricity

cost coefficient for charging the ESS.

Battery modules have to be replaced one or more

times during the project lifetime. The NPV of

replacement cost is:

[(1 ) (1 ) ...]

REP RP

C C r r



    

 (11)

where C

[$] is the future value of replacement cost

and L is the replacement period that can be estimated

by using the battery modules datasheet such as

(Julien, 2016).

4 SIMULATION FRAMEWORK

We apply the introduced methodology for the sizing

of II-Life ESSs to a real distribution system. We

consider the implementation of a peak shaving

service for the microgrid that supplies the Campus of

the University of Salerno (UniSA).

4.1 Case Study

The UniSA microgrid is a 12 bus 20 kV distribution

system with two feeders configured in closed loop

(Figure 10). Connected to the grid, there are several

distributed generators (DG). Two combined heat and

power (CHP) units, with a rated power of 580 kW

each one at bus 11, and eight PV power plants for a

total PV rated power of 1076 kW installed on the roof

of the campus buildings (bus 2, 3, 4, 5, 6, 8, 9 and 12).

CHP units produce both electricity used to supply the

loads and thermal energy used to heat water of the

campus sport facilities.

Figure 10: Power grid of the UniSa Campus.

In Figure 11, we show the typical daily profiles of

the net active power drown from the main external

PCC by the UniSA network (bus 1). Blue and green

lines depict the active power absorption with and

without internal PVs and CHPs, respectively. Finally,

yellow and pink lines show the average (calculated

every 15 minutes) active power generated by the PV

and CHP units.

Sizing of II-Life Batteries for Grid Support Applications and Economic Evaluations

Figure 11: Active power drown from the UniSA microgrid.

Furthermore, the study in (Graber, 2017), based

on the CO.S.MO. (Cooperative Systems for

Sustainable Mobility and Energy Efficiency)

European research project, allows us to consider the

additional demand due to the connection of EVs to

charging stations (CSs) into the Campus.

Figure 12: Active power drown from the UniSA microgrid

by adding the EVs charging load.

The study assumes that the users behaviour and

their mobility needs highlighted by the COSMO data

analysis, do not change moving from ICE-based

(internal combustion engine) vehicles to battery EVs.

Moreover, different types of CSs (AC level 2,

CHAdeMO, SAE Combo, Tesla Supercharger, etc.),

each of them characterized by different values of

charging power, are considered in the analysis. EV

charging demand profile is depicted in Figure 12.

4.2 Economic Assessment

We consider one II-Life battery ESS supporting CSs

in the UniSA parking area and implementing a peak

shaving based control. More in detail, during the day,

the ESS acts when the power demand of the UniSA

Campus is greater than a given threshold working in

load following mode. At night, the ESS charge itself

in constant charging power mode.

In our analysis, we consider two different size of

the ESS according to the imposed maximum power

drown from the main external grid, P

max

. More in

detail, by imposing P

max

=3.00 MW we need an ESS

of 0.55 MW, 1.6 MWh (ESS

), while by imposing

max

=2.75 MW we need an ESS of 0.80 MW,

2.0 MWh (ESS

), (Graber, 2017).

Figure 13 shows the flattening effect of the II-Life

battery ESSs on the UniSA power demand when the

electric load is greater than P

max

. The results for the

max

=3.00 MW and P

max

=2.75 MW case studies are

presented. In particular, the ESS reduces the peak

load acting in load following mode from 9:00 a.m. to

12:00 p.m. and from 16:00 p.m. to 19:00 p.m., while

the ESS charges itself from the external grid in

constant power mode, from 21:00 p.m. to 7:00 a.m.

Figure 13: Daily trends of active power drawn by UniSA

Campus from the external grid with EVs charging load and

second life ESS.

Table 1: Parameter for the Economic Assessment.

Parameter

Value

Unit

Years

125

$/kW

470

$/kWh

9.2

$/kW

0.0011

$/kWh

year

for ESS

440

MWh

year

for ESS

550

MWh

0.114

$/kWh

SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems

Figure 14: Comparison of ACOE for I-Life and II-Life

battery ESS.

We calculate the ACOE for I-Life and II-Life

battery solutions based on the parameters in Table 1.

We, also, assume that C

is zero and the C

REP

is equal

to 80% of C

In Figure 14, we compare the ACOE of the I-Life

ESS and that of the II-Life ESS, assuming the

max

=3.00 MW case study. The aim is to give a

competitive price to the II-Life ESS compared to the I-

Life solution. In our case study, the sensitivity analysis

has pointed out that the price of II-Life battery modules

should be reduced at least of 55% compared to the I-

Life battery modules, in order to obtain an ACOE value

for the II-Life ESS comparable to that of the I-Life

ESS. It is worth to note that 100% cost reduction of II-

Life battery modules leads to an ACOE of the II-Life

ESS not equal to zero due to O&M costs.

Table 2: II-Life ESS Sizing by using Different Battery

Packs (0.55 MW, 1.6 MWh).

Model

Module

energy

Module

power

Nissan leaf

24 kWh

90 kW

Tesla

Model S

75 kWh

285 kW

BMW i3

33 kWh

125 kW

Renault Zoe

22 kWh

65 kW

Citröen C0

14 kWh

49 kW

114

Table 3: II-Life ESS Sizing by using Different Battery

Packs (0.8 MW, 2.0 MWh).

Model

Module

energy

Module

power

Nissan leaf

24 kWh

90 kW

Tesla

Model S

75 kWh

285 kW

BMW i3

33 kWh

125 kW

Renault Zoe

22 kWh

65 kW

Citröen C0

14 kWh

49 kW

143

In Table 2, we show the number of I-Life battery

modules (M) and II-Life battery modules (M plus the

maximum value between m

and m

) needed to satisfy

the load following application (P

max

=3.00 MW case

study) and whose economic evaluation is shown in

Figure 13. The number M, m

, and m

are calculated

by using different EV battery packs of the best-selling

EV models for tackling the uncertainty due to residual

capacity estimation and increase of the internal

resistance. A similar analysis is carried out for the

max

=2.75 MW case study and it is proposed in

Table 3. It is worth to note that the additional II-Life

battery modules needed to satisfy the power

requirement of the peak shaving service is always less

binding than that concerning the maximum number of

CDC requirement.

5 CONCLUSIONS

We present a sizing method for the economic

assessment of II-Life ESSs in providing energy

services. A linear approximation is assumed to deal

with the degradation and aging of lithium-ion

batteries. We propose a methodology to calculate the

number of battery modules able to guarantee the

power service requirements at the EoL for energy

applications and to tackle the uncertainty due to the

estimation of the residual capacity in II-Life batteries.

We calculate the ACOE of two different II-Life

battery solutions able to provide a peak shaving

service on the UniSa Campus MV network by

reducing the imposed maximum power drown from

the main external grid. We compare them with the

I-Life ESS in order to identify a competitive price of

II-Life battery modules.

ACKNOWLEDGEMENTS

The authors gratefully thank UE and all technological

partners who have contributed to the success of the

CO.S.MO. research project.

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