Heavy Duty Truck Systems by Sean Bennett

192 Hybrid vehicles

Faradaic efficiency is the quantity of current associated with the primary electrochemical
reaction between charging and discharging, a reaction that competes with secondary reac-
tions. It depends primarily on the nature of the redox pair and the conditions of use (current
rate and SOC operating range).

Energy efficiency is the ratio between the energy recovered during discharge and the
energy supplied for a complete charge that returns the battery to its initial state of charge.
The efficiency depends on the nature of the redox pair and the conditions of use (current rate,
temperature, and SOC operating range).

4.2.1.3 Operation and Characteristics of Supercapacitors

A. Operation of a Supercapacitor [Conway, 1999; Lassègues 2001]

Operation of a supercapacitor is similar to that of a capacitor. A capacitor consists of two
electrical conductors, or "plates," that are very similar but separated by an insulator, or "die-
lectric." The electric charge stored by a capacitor energized by the electrostatic accumulation
of charges at the windings is proportional to the voltage applied across both windings:

q = C.U (4.8)

where q is the charge of the winding in coulombs (C), U is the voltage expressed in volts
(V), and C is the electric capacitance of the capacitor in farads (F). This capacitance, which
is essentially determined by the geometry of the winding and the nature of the insulators, is
often estimated by means of the simplified formula:

where S is the surface of the windings expressed in m2, e the distance between the windings
in m, ε0 the permittivity of vacuum in F/m, and 8r the relative permittivity of the dielectric
(dimensionless).

A supercapacitor consists of two porous electrodes with very high specific surface area
(several hundreds or thousands of square meters per gram of material), impregnated with an
electrolyte (a purely ionic conductor) and separated by a membrane, also impregnated with
an electrolyte, that is electrically insulating but porous to ions. At rest (zero electric field),
the electrodes are not differentiated, but a double layer of cations a few tens of nanometers
thick is spontaneously formed at the interface of each electrode opposite the electrons, thus
ensuring the assembly's electric neutrality. When an electric field is applied between the
electrodes, the cations and anions migrate in the opposite direction and the electrodes are
differentiated. The movement of ions in the electrolyte results in the accumulation of electric
charges at the interface of each electrode, a so-called double layer, forming two capacitors
that are charged until the limit of stability of the solvent is reached at one of the electrodes.
Several models of double-layer capacitor have been proposed (Figure 4.10).

- In the simple Helmholtz model, electrolyte ions are treated as nonsolvated, forming a
compact layer.

Chapter 4 · On-board energy storage systems 193

- The Graham model makes use of electrostatic forces and the specific absorption of
electrolyte species at the electrodes, since cations are generally smaller than anions
and much more solvated. The electrochemical double layer then comprises a compact
layer consisting of two layers (inner and outer) and a diffuse layer.

Figure 4.10

Models of double-layer capacitors and potential changes Φ: (a) simple Helm-
holtz model, (b) Graham model, comprising two compact layers (internal and
external) and a diffuse layer.

194 Hybrid vehicles

Once charged, the system remains at equilibrium but self-discharges after several hours,
which tends to return the system to the discharge state through the migration of ions and
through parasitic faradaic reactions at the electrodes. During discharge, ions and electrons
follow opposite directions and discharge occurs in a matter of seconds [Fuhs, 2008].

In this way, when a voltage is applied, the two electrodes of a supercapacitor behave like
two capacitors in series, with different capacitances, depending on the nature of the anions
and cations, whose mobility and solvation (surrounded by molecules of solvent) will vary.
Recall that the capacitance of the assembly in series is always less than the weakest of the
two capacitances because of the laws of association of capacitors. For a supercapacitor, the
molecules of the electrolyte solvent serve as the dielectric and the typical thickness of the
insulator is molecular (a few nanometers). Consequently, the capacitance per unit surface
of supercapacitors is very high, on the order of 0.1 F.m~2, and the capacitance of ordinary
capacitors is considerable, given the high specific surface areas. Note, however, that capaci-
tance isn't directly proportional to the specific surface area because only part of the devel-
oped surface is accessible to ions.

In 2006, P. Simon and Y. Gogotsi published work that challenged a principle that had
been accepted for decades [Chmiola et al., J. 2006; Chmiola et al., 2008; Simon and Gogotsi,
2008]. Their work showed that it is possible to use pores less than 1 nanometer (nm) to store
charges, which would allow the volume density of current double-layer supercapacitors to be
increased by more than 80%. Typically, the pores of an electrode (carbon) must be between
2 and 20 nm so that an ion surrounded by its solvation layer can penetrate it. It has been
suggested that the ions, whose size is similar to that of the pores, can penetrate micropo-
res 3 smaller than 1 nm without the solvation layer (molecules of solvent), which surrounds
them in the electrolyte. The size of the pores, their shape (tortuosity), and their accessibility
(pore opening) are factors that are currently being studied to help formulate specific types of
electrolytes.

B. Electrical Characteristics of Symmetric Supercapacitors

Because very low internal resistance allows high currents to be used during charge and dis-
charge operations, the formation or relaxation time of double layers at the electrodes is nearly
immediate (0.3 to 30 s). This is an essential difference with batteries that make use of redox
reactions and diffusion and relaxation phenomena, and results in much higher discharge
times (0.3 to 3 h) [Fuhs, 2008]. This results in specific power values that are very high, while
specific energy is low (4.2.6) and limited by surface storage and electrolyte voltage. The
energy, E, of a supercapacitor is expressed as a function of capacitance, C, and voltage, U:

(4.10)

Note that energy increases proportionally with the charge and the square of the volt-
age, which underlines the benefits of the increased capacitance of supercapacitors and, espe-
cially, the acceptable voltage limit in the solvent, for increasing the energy of symmetric
supercapacitors.

3. The IUPAC classifies pores on the basis oftheir diameter, using the following terminology: micropo-
res (< 2 nm), mesopores (from 2 to 50 nm), macropores (> 50 nm).

Chapter 4 · On-board energy storage systems 195

Because of the (theoretical) absence of faradaic reactions, charge/discharge cycles take
place with considerable efficiency and induced aging is very limited. Supercapacitors have
excellent cyclability, which can exceed a million cycles, while batteries can achieve these
values only with a very limited depth of charge/discharge. Finally, the voltage range used in
practice for a supercapacitor element is very broad (sometimes 100 to 50% of the rated volt-
age for an acetonitrile electrolyte element). Also, a pack often requires the use of a suitable
converter, which is not necessary for a battery.

4.2.2 Lead Storage Cells

4.2.2.1 Description [Robert and Alzieu, 2004b]

The oldest electric vehicles, which used a lead battery, were in operation as early as the
19th century [Kiehne, 2003]. The lead storage cell, written Pb(sJH2S04(aq)|Pb02 (s), is the
oldest single-compartment storage cell, characterized by its active materials of lead oxide

(Pb02) and lead sulfate (PbS04) immersed in an aqueous concentrated sulfuric acid (H2S04)
solution. The rated voltage of the cell is 2 V at 25 °C.

When discharging, the principal electrochemical reactions are as follows:

- at the positive electrode: (4.11)
- at the negative electrode: (4.12)
- (condensed) balance: (4.13)

Charge reactions are the reverse of these. The redox reactions involve a solution-precip-
itation mechanism. When discharging, the Pb2+ cation formed is relatively insoluble in the
sulfuric acid solution, and PbS04 precipitates at the reaction site on the surface of the elec-
trode. When charging, the lead sulfate is dissolved before being retransformed into metallic
lead. Additionally, the electrolyte helps discharge the battery by serving as a reagent and
supplying sulfate ions necessary to the production of lead sulfate. This participation of the
electrolyte solute is specific to the lead-acid storage cell.

In addition, there occurs a parasitic reaction involving the hydrolysis of water, which
leads to the generation of gas (oxygen and hydrogen) and "dries" the electrolyte:

- at the positive electrode, water is oxidized in an acid medium: (4.14)
- at the negative electrode: (4.15)

These secondary chemical reactions can result in self-discharge phenomena, but they are
at a kinetic disadvantage compared to the primary reactions.

4.2.2.2 Characteristics

The charge/discharge curve of a typical 12 V, 12 Ah lead battery (for a two-wheel vehicle)
is shown in Figure 4.11.

196 Hybrid vehicles

Figure 4.11
(a) Complete charge at C/20 to 14.2 V, maintained until I <C/100,
t max = 26 h.
(b) Discharge at constant I of C/10 to 11 V.

Industrial lead batteries are used extensively in heavy duty vehicles (handling and lifting
equipment, locomotives) as they provide relatively constant voltage, which is especially well
suited for powering and controlling electric motors. Their characteristics are highly variable,
with voltages between 12 and 240 V and unit capacity between 100 and 1,500 Ah (7 to 85 kg
per element). The specific energies range from 20 to 30 Wh/kg with tubular plates but can
reach 40 Wh/kg with flat plates. The energy density typically ranges from 60 to 75 Wh/L,
while specific power can reach 500 W/kg, depending on the corresponding P/E type for the
intended application, from hybrid to all electric (4.2.6.1). In spite of a cycle time character-
ized by deep discharging (typically 80% at C/5), their working life can reach 1,000 to 1,500
cycles. Because of the low cost, recyclability, and high durability, this technology is also
used in certain hybrid vehicles such as buses (4.2.2.4).

In practice, the weight of the technological components used (enclosure, grid, etc.)
remains high and the use of active materials (35 to 55%) partial. The ratio between the effec-
tive mass of active material and the total mass is less than 20% for this technology.

Lead storage cells can be rectangular or cylindrical in shape, the latter providing improved
power performance. Spiral shaped cells have a specific discharge power of 500 W/kg com-
pared to 200 W/kg when charging. Such elements have been used in hybrid vehicle dem-
onstrations by replacing the Ni-MH battery, as shown by A. Cooper in the Honda Insight
(4.2.2.4).

The energy efficiency of lead batteries ranges from 70 to 75%. That is because 25% of
the electric energy is dissipated through parasitic electrochemical reactions that take place
during the electrolysis of water, primarily as heat associated with the recombination of water.
The loss of capacity during self-discharge varies between 2 and 5% per month at 25 °C. At
40 °C it is on the order of 15% per month. A lead battery is capable of supplying a very high
intensity current over a period of several seconds, which is useful when starting internal

Chapter 4 · On-board energy storage systems 197

combustion motors electrically, one of the reasons the technology is commonly used in auto-
mobiles. In general, the nominal characteristics are:

- for automobiles: 12 V, 30 to 100 Ah
- for trucks: 24 V, up to 600 Ah

The specific energies of a starter battery are on the order of 35 Wh/kg and 70 Wh/L, with
a working life of 4 to 5 years.

To better meet the needs for endurance, reduced maintenance, and reliability in lead stor-
age cells, a new design involving sealed gas-recombination cells was developed in the 1990s,
commonly referred to as valve-regulated lead acid (VRLA) cells. The electrolyte in VRLA
batteries is gelified through the addition of silicon dioxide (Si02), which prevents leaks in
the event the unit is upended. In VRLA batteries, oxygen given off at the end of the charge
is recombined at the positive plate (electrolysis of water). Here, the electrolyte (extremely
porous) provides a number of channels that allow oxygen gas to reach the negative plate,
where it is reduced. In this way, recombination prevents the loss of water.

4.2.2.3 Aging

Among the causes of the breakdown of lead batteries [Cugnet, 2008; Robert and Alzieu,
2004b] listed in Figure 4.12, the following affect traction batteries in particular:

- Sulfation, a phenomenon associated with the accumulation of lead sulfate on the elec-
trodes, occurs during discharge and dissolves normally when recharging. However,
under certain conditions (extended discharge or one that is too deep, high temperature,
gasification of the electrolyte), stable clusters of lead sulfate appear that are not dis-
solved when charging. Because of its low electrical conductivity, the lead sulfate gen-
erated reduces the battery's capacity by limiting reactions at the electrode.

- Electrode oxidation occurs whenever the electrolyte level is too low and the plates
come in contact with the air and are oxidized. The lack of electrolyte can occur from
heavy use (auxiliary equipment, for example), high outside temperatures (30 °C or
above), or overcharging that leads to the production of gas (oxygen and hydrogen)
associated with the electrolysis of water.

- Corrosion of the current collector can occur at the interface between the active material
and the collector, which results in an alteration of the electric properties of the collec-
tor. In open batteries, this corrosion is primarily the result of the instability of lead (an
essential element of the grid alloy) in sulfuric acid solutions in the domain defined by
the pH ranges and potentials of the positive electrode, corresponding to the different
phases of battery life. In this way, a semiconductive layer of lead oxide and a fine layer
of PbS04 develop when cycling the battery. This phenomenon is customarily referred
to as corrosion of the positive grid. In the case of VRLA batteries, the corrosion also
affects the negative grid because of the presence of oxygen, which is recombined at
this electrode.

198 Hybrid vehicles

Figure 4.12
Summary of the causes and interdependence of aging phenomena in lead
batteries.
Source: [Cugnet, 2008]

4.2.2.4 Applications
The characteristics of commercial products vary greatly, the voltage of unit packs ranging
from 12 to 240 V with capacities of 100 to 1,500 Ah. Lead traction batteries are used in buses,
microcars (Aixam), electric utility vehicles (Goupil Industrie), and stop-start systems (those
that exclude starter battery applications, handling and lifting equipment, forklifts, etc.). It
should be pointed out that this highly competitive market keeps prices low.

For applications that are not limited in terms of volume or weight but for which operat-
ing costs are key, lead, at a few hundred euros per kilowatt-hour, is an economical solution.
In France, a manufacturer like Goupil Industrie sells several hundred utility vehicles a year,
equipped with lead batteries. In North America, hundreds of hybrid buses travel across the
United States, and recent evaluations indicate that the low cost of lead batteries (purchase and
use), with a working life on the order of three years, put them, in 2005, ahead of Ni-MH and
Li-ion when considering total cost of use [Callaghan and Lynch, 2005].

Research in spiral VRLA cells, conducted primarily by Hawker Batteries, is specifically
aimed at hybrid vehicle applications [Cooper, 2004; Cooper and Moseley, 2009].

Chapter 4 · On-board energy storage systems 199

The development of new cells supporting currents of 8 C when charging and 15 C when
discharging have been realized with the introduction of a 144 V pack consisting of four 36-V
modules. This has been tested in a Honda Civic as a replacement for a Ni-MH pack. These
experiments have demonstrated the benefits of lead battery technology for HEVs; their size
is comparable to that of a Ni-MH battery but at lower cost and with a 90% recycling rate.

4.2.2.5 Outlook

Lead storage cells remain a solution for microhybrids, especially VRLA technology (Cit-
roën's Stop-Start, for example) and spiral systems, because of their ability to increase resil-
ience [Pistoia, 2007]. However, obtaining efficient rechargeability at the high power levels
required can be obtained by coupling a supercapacitor to the battery, as Valeo has done with
its StARS system (5.3.1.2).

4.2.3 Ni-MH Storage Cells

Nickel-metal hydride storage cells, Ni-MH, have been studied since the 1980s as a develop-
ment of nickel-cadmium (Ni-Cd) pairs. They were conceived as a way to improve energy
density and overcome the problem of cadmium's toxicity, especially for highway transporta-
tion applications. Their principal application is in power batteries for hybrid electric vehicles,
especially since the introduction, in late 1997, of the Toyota Prius 1, which was equipped
with a 288 V Panasonic EV Energy (PEVE) Ni-MH battery (5.5.2.1).

4.2.3.1 Description [Caillon, 2001]

A MH.JKOH/ JNiOOH.x storage cell comprises:

- A positive nickel electrode that makes use of a NiOOH/Ni(OH)2 redox couple, with an
E° of 0.49 V compared to the SHE 4.

- A negative electrode consisting of a hydrogen-fixing alloy, that is, one capable of revers-

ibly absorbing hydrogen, with an E° of- 0.83 V compared to the SHE. In practice we find

two broad families of alloys, AB5 and AB2. The most common AB5 material is LaNi5.
For economic reasons, lanthanum can be replaced in part by a mixture of rare-earth

metals (referred to as Mm, from the German misch-metal). A typical base alloy of the

AB2 type is ZrNi2. In the majority of Ni-MH batteries sold on the market, we find either
Ni3.2Col.0Mn0.6A10.llMo0.09 all°ys (AB5) or Ti0.siZr^Vo^Nij 18Cr0 12 alloys (AB2).

- an electrolyte of concentrated potassium hydroxide (typically 6 mol/L)

Its rated voltage is 1.2 V at 25 °C. During discharge, the primary electrochemical reactions are:

- at the positive electrode: NiOOH + H20 + e" -^ Ni(OH)2 + OH" (4.16)

- at the negative electrode: MH + OH" -^ M + H20 + e~ (4.17)
- balance: NiOOH (s) + MH (s) -* Ni(OH)2 (s) + M (s) (4.18)

4. SHE is the "standard hydrogen electrode" whose potential, E°, is 0 V by convention. It consists of a
platinum wire in contact with hydrogen, H2, at a pressure of 1 bar and a molar acid ([H+] = 1 or pH = 0)
at a temperature of 25 °C.

200 Hybrid vehicles

The reactions when charging are reversed. The redox reactions involve a mechanism of
proton, H+, insertion/removal between the two electrodes. However, the proton isn't trans-
ferred as such in the electrolyte but by H20 and OH~. Here, the electrolyte is invariant.

When overcharging, a secondary reaction occurs at the positive electrode:

(4.19)

followed by recombination of diffused oxygen at the negative electrode:

(4.20)

A secondary reaction also occurs during overdischarge at the positive electrode:

(4.21)

followed by recombination of diffused hydrogen in the reservoir at the negative electrode:

H2 + 2 OH" -> 2 H20 + 2e" (4.22)

To limit the production of gas (hydrogen and oxygen) associated with secondary reac-
tions at the positive electrode, the capacity of the negative electrode is conventionally overd-
esigned to ensure proper operation of Ni-MH storage cells, as shown in Figure 4.13. As a
result, the positive electrode is the limiting factor when charging and discharging.

Figure 4.13

Schematic representation of a MH.JKOH, JNiOOH.x cell.
Source: [Begum et al, 2009]

Chapter 4 · On-board energy storage systems 201

4.2.3.2 Characteristics

Ni-MH storage cells can be cylindrical or rectangular in shape. In practice, they typically
have a specific energy of 40 to 80 Wh/kg and specific power of up to 1,000 W/kg, depend-
ing on the P/E type for the intended application - hybrid or all-electric (4.2.6.1). The ratio
between the mass of active material used and the total mass is 40 to 60% for this technology.

Figure 4.14 shows an example of a charge/relaxation/discharge curve at 20 °C for a
7.2 V/6.5 Ah Ni-MH module with 6 elements in series at various skin temperatures and pres-
sures. We see that the end of charge is marked by a rise in internal pressure and temperature,
while discharge for the 1 C regime is endothermic and accompanied by a drop in pressure.

Figure 4.14

C/30 charge/relaxation/discharge curve of a 6.5 Ah NiMH module from a
Prius 2 at 20 °C and related change in skin temperature and internal pressure.
Source: [Sauvant-Moynot et al, 2009]

The equilibrium voltage at 50% charge is in the neighborhood of 1.27 V at ambient tem-
perature. It slightly changes the composition of the positive electrode, the plateau pressure of
the alloy, and the composition of the electrolyte [Caillon, 2001]. With Ni-MH technology,
the voltage level between charging and discharging, for a given SOC, differs appreciably.
This phenomenon is known as hysteresis (Figure 4.15).

202 Hybrid vehicles

Figure 4.15

Change in open-circuit voltage during charge and discharge for a Ni-MH cell.
Source: [Prada, 2010a]

The energy efficiency of Ni-MH storage cells is from 85 to 90% because of voltage
hysteresis between charging and discharging. The faradaic efficiency is close to 1 for a 50%
SOC, which is important when using this technology in hybrid vehicles (absence of second-
ary reactions in its operating range).

4.2.3.3 Aging
There are three primary aging mechanisms, all of which are sensitive to the composition of
the materials used, especially the stoichiometry of metal hydrides [Forgez, 2008]:

- Absorption and desorption when cycling results in a volume change of electrode
materials leading to the fracture of hydride grains (Figure 4.16) [Castro and Milocco,
2007; Guenne and Bernard, 2002; Raju et al, 2007; Tliha et al, 2007]. The induced
increase in the exchange surface and the number of insertion sites for hydrogen has
positive short-term effects marked by increased capacity during the initial charge/dis-
charge cycles [Durairajan et al, 2000]. However, the sensitivity to corrosion of metal
hydrides in contact with an electrolyte is also increased [Geng et al, 1998; Notten et
al, 1995; Rongeât et al, 2006]. This results in a drop in rated capacity, the consump-
tion of electrolyte, and an increase in charge transfer resistance (corrosion deposits)
[Bauerlein et al, 2008].

- Degassing during overcharging and overdischarging results in a drop in capacity and
an increase in resistance of the electrolyte through the consumption of OH-·

- Self-discharge is associated with corrosion reactions.

Chapter 4 · On-board energy storage systems 203

Figure 4.16

Fractured metal hydride grains observed by scanning electron microscopy of a
negative battery electrode in a Prius after 70,000 km.
Source: [Prada et al, 2009]

4.2.3.4 Application

Construction of the PEVE Ni-MH battery pack for the 2003 Prius 2, is shown as an exam-
ple of the most widespread HEV technology in use today, with more than 1.5 million units
sold. The pack consists of 28 rectangular modules arranged in series, each module compris-
ing 6 cells, also connected in series. Their physical and electric characteristics are shown
in Table 4.3. Figure 4.17 illustrates the assembly of battery pack modules and displays the
stratification of electrodes and separators inside the rectangular casing.

HPPC tests at high current were performed at 25 °C on two Ni-MH PEVE batteries for
the Prius 2, one new and the other taken from a vehicle with 70,000 km [Prada et al, 2009].
Power values were calculated as a function of depth of discharge and current direction: DPPC
refers to discharge (Discharge Pulse Power Capability) and RPPC to recharge (Recharge
Pulse Power Capability). The results obtained, shown in Figure 4.18, reveal the range of
useful SOC limited by minimum charge and discharge power demands. So, if the minimum
power required when charging and discharging is 25 kW, battery use would have to be lim-
ited to an SOC range between 80 and 38% for an old battery. This range is larger than that
for a new battery (SOC 80 to 48%). The gain in power can be interpreted as a result of elec-
trochemical grinding of the active material of the negative electrode during cycling (4.2.2.3).

2 0 4 Hybrid vehicles

Table 4.3. Characteristics of the Ni-MH PEVE element, module, and pack in the Prius 2

Characteristics Pack Module Element
flto and 1.2
Rated voltage (V) 201.6(28x6x1.2) Ohnishi, 2003] 6.5
Rated capacity (Ah) 6.5 7.2(6x1.2)
Internal resistance (mOhm) 0.1151
45 (including modules, 6.5
Weight (kg) wires, and accessories 11.4 16x30x80
68
Dimensions (mm) BMS. cover, etc.) 1.04
Rated specific energy (Wh/kg) 370x185x700 1,960
Specific power (W/kg), (excluding BMS) 19.6x106
discharge 10 s, 60% SOC, 25 °C x285
30 46

840 1,300

1. Stacking of electrodes in a dry element (active material on collector + separator grids) excluding metallic
collectors.

Chapter 4 · On-board energy storage systems 205

Figure 4.17

Construction of the PEVE Ni-MH pack in the Prius 2: (a) top view without
cover, (b) schematic representation of the inside of a cell, (c) stacking of elec-
trode materials and separators viewed with a scanning electron microscope.
Source: [Bernard, 2010a]

206 Hybrid vehicles

Figure 4.18
Power performance comparison of old (70,000 km) and new Ni-MH packs in
the Prius 2 during a high current HPPC test at 25 °C as a function of depth of
discharge.
Source: [Prada et al, 2009]

In conclusion, it appears that a limited SOC window, targeted at approximately 50%,
provides the best performance compromise in a Ni-MH battery in a Prius 2 between charge
and discharge, and this is how it is used in the vehicle (5.5.2.3.A).

4.2.3.5 Outlook
Ni-MH battery technology has undergone considerable evolution over the last few years
[Fronzek, 2008]. The specific power of Ni-MH technology (measured at 50% SOC during
a 2 s pulse), on the order of 1,400 W/kg by the end of 2008, is very close to the maximum
potential of 1,500 W/kg. Although power performance has reached maturity, new materials
for negative electrodes are currently being developed to increase capacity and A2B7 alloys
are being developed along with AB5 alloys [Sakintuna et al, 2007; Yonesu et al, 2006]. In
the case of positive electrodes, the use of nickel hydroxide no longer appears to be in dispute.

This technology, proven in millions of HEVs, remains largely confined by automobile
manufacturers to future non-rechargeable HEV applications (energy < 2 kWh). Several mod-
els are scheduled to come to market in the early years of the decade from manufacturers such
as Toyota, GM, and Ford. Given its performance, cost, and the new awareness of Ni-MH
durability and battery management in a vehicle environment, this technology will most likely
continue to be used for future HEVs. However, rechargeable hybrid vehicles will probably be
equipped with Li-ion batteries, as illustrated by the Chevrolet Volt, the Toyota Prius Plug-in
and the Volvo V60 Plug-in.

Chapter 4 · On-board energy storage systems 207

4.2.4 Lithium Storage Cells

Describing lithium storage cells is complicated because of the number of similar models mar­
keted and sold in the form of battery packs by manufacturers, automobile manufacturers, and
equipment suppliers. Given the variety of electrode materials and electrolytes used, as well as
stacking and packaging alternatives, a number of important choices must be made. For trans­
portation applications, we will limit our discussion to storage cells and lithium-metal and
lithium-ion families, which are the most prevalent at this time. These are described below.
There is an extensive and detailed body of literature on the materials and characteristics of
lithium batteries. These include important serial publications [Tarascon and Armand, 2001],
monographs [van Schalkwijk and Scrosati, 2002], and several summaries [Caillon, 2001;
Robert and Alzieu, 2005].

4.2.4.1 Description

Metallic lithium was chosen as an electrode material because it has the twofold advantage
of having the lowest standard potential (- 3.04 V compared to the SHE), making it a strong
reducer, and very high mass capacity (3800 Ah/kg). The first developments of lithium stor­
age cells were conventional in nature, with one negative electrode of Li metal, a positive
electrode (intercalation compound) capable of reversibly inserting lithium ions, Li+, and an
electrolyte for the transfer of ionic charge carriers exclusively (LL Jsalts Li+|LizAxB ,Λ.

When discharging, the primary electrochemical reactions for this configuration are:

- at the positive electrode: (4.23)
- at the negative electrode: (4.24)
- balance: (4.25)

The crystalline structure of the ΑχΒγ insertion compound ideally possesses empty crys-
tallographic sites capable of accepting, then releasing, lithium ions with small variations in
volume (< 10%).

This potentially valuable configuration, studied as early as the 1950s, has not resulted
in further developments in secondary storage cells because of the problems caused by the
negative electrode of metallic lithium. This electrode has the disadvantage of very strong
reactivity with the electrolyte and modification of its morphology during cycling (successive
deposit and removal of metallic lithium), especially through the formation of dendrites, which
can cause short circuits. To resolve these problems, two alternative solutions were proposed.
These consisted in replacing the metallic lithium electrode with an insertion compound,
graphite (whose intercalation potential is close to that of lithium), or replacing the organic
electrolyte with a polymer. These developments led to the two approaches currently used in
the transportation field: lithium-ion storage cells and lithium-metal-polymer storage cells.

A. The Li-Ion Storage Cell

A Li-ion (LizMN , Jsalts Li+|Li1_zAxB ,§γ) storage cell uses two compound electrodes; the
Li+ ion insertion/removal mechanism is shown in Figure 4.19.

208 Hybrid vehicles

Figure 4.19

Diagram illustrating the discharge of a lithium-ion cell, involving reversible
insertion compounds at both electrodes - lithiated carbon at the negative elec-
trode and LizAxB at the positive electrode.
Source: [Robert and Alzieu, 2005]

During discharge, the electrochemical reactions are: (4.26)
- at the positive electrode: (4.27)
- at the negative electrode: '. (4.28)
- balance: L i ^ A ^ ^

This technology has been sold since the early 1990s by Sony. A classic example of a Li-
ion storage cell consists of graphite at the negative electrode (lithiated at full charge, depend-
ing on the stoichiometry of LiC6, with a theoretical capacity of 372 mAh/g), a mixed oxide
of cobalt and lithium at the positive electrode (LiCo02, emptied of half its Li+ at full charge),
and a porous separator, all of which is impregnated with a liquid electrolyte. The electrolyte
is typically composed of a lithium salt (Li+PF6~) dissociated in a polar organic solvent com-
posed of a mixture of dimethyl carbonate and ethylene carbonate, formulated for the intended
application [Xu, 2004]. The average voltage is 3.7 V (with an upper limit of 4.2 V). The
range of operating temperatures typically varies between - 20 °C and 55 °C. When the cell is
first charged (formation cycle), a solid deposit is formed by decomposition of the electrolyte
at the carbonated negative electrode (reduction). This deposit, known as a solid-electrolyte
interphase (SEI), plays a key role, for it creates a protective layer between the reducing nega-
tive electrode and the electrolyte, while allowing the reversible insertion of Li+ ions. The
storage cell can then be cycled several times, while its capacity remains unchanged.

A number of insertion materials are used for negative and positive electrodes, some of which
are shown in Table 4.4. Each material is characterized by its redox potential compared to lith-
ium, its theoretical specific capacity, cyclability, stability, toxicity, and cost. Note that the posi-
tive electrode must be lithiated before assembly of the cell; consequently, lithiated intercalated
compounds that are stable in air must be used for the positive electrode of Li-ion batteries.

Chapter 4 · On-board energy storage systems 209

Table 4.4. Properties of negative and positive electrode materials used in commercial Li-ion storage cells

Negative electrodes Positive electrodes

Material Potential Theoretical Material Potential Theoretical
(structure) compared specific (structure) compared specific
to Li (V) capacity to Li (V) capacity
(Ah/kg) (Ah/kg)
0.140
LiC6 0.02 to 0.3 0.372 LiCo02 4.0
graphite cobalt oxide 3.9 0.200
3.4
(sheets) (layered) 4.1 0.200
3.4
Li4Ti5012 LiNi^CoAl^ 0.140
known as NCA
known as LTO 1.6 0.175 mixed oxide 0.170
titanium oxide (layered)

(spinel) LiNi^Mn Coz02
known as NMC
mixed oxide
(layered)

LiMn204
known as LMO
manganese oxide

(spinel)

LiFeP04
known as LFP
iron phosphate

(olivine)

Li-ion storage cells are generally cylindrical, rectangular, or oblong in shape, within a
steel or aluminum casing. The use of a polymer-base gelified electrolyte has been a signifi-
cant technological development in the manufacture and use of Li-ion batteries. The polymer,
which serves as a support for the liquid electrolyte, produces a gel whose mechanical strength
can, in the best of cases, eliminate the need for a porous separator. Such systems appear as
stacks of thin, flexible films (positive electrode/electrolytic gel/negative electrode), wrapped
in a flexible, water-tight metal-plastic pouch. Systems such as these eliminate the need for the
heavy, rigid metal enclosure of conventional systems, while avoiding the risks of electrolyte
leaks. Additionally, the polymer matrix can be added using conventional methods, such as
coating, which reduces costs. The first Li-ion-polymer technology, known as PliON (plas-
tic Li-ion), was proposed by Bellcore in 1999 and used a difluorinated vinylidene copoly-
mer and hexafluoropropylene. Successive developments of polymer-based electrolytes took
place through the addition of solvents (and composite electrolytes through the addition of
reactants), which improved the transport properties, mechanical properties, and interfacial
properties of gelified electrolytes in Li-ion batteries [Song et al, 1999; Stephan and Nahm,
2006]. Polymer gel electrolytes include:

- systems in which a porous polymer membrane (typically made from PVDF-HFP
copolymers) is impregnated or swollen with a solution rich in Li+ ions (solution of
LiPF6 in a carbonate solvent);

210 Hybrid vehicles

- systems in which the liquid organic solution is directly gelified by a polymer
matrix (e.g., poly(acrylonitrile), PAN, poly(methylmethacrylate), PMMA, or
poly(vinylidenefluoride), PVDF).

Although the Li-ion-polymer batteries that have been developed so far satisfy the criteria
for increased safety, light weight, and optimized design required for transport applications,
there remains the problem of extending the operating range to low temperatures (ideally,
down to - 20 °C) compared to liquid electrolyte systems.

Recently, a new technological stage in the development of lithium batteries has been
reached with the use of liquid ionic salts at room temperature as electrolytes for Li-ion bat-
teries. Ionic liquids (consisting of cations and anions) are nonvolatile and nonflammable
organic compounds that are relatively conductive (conductivity can reach 25 mS/cm at 20
°C) and possess remarkable chemical (in air or water in some cases), electrochemical (up to
approximately 5 V), and thermal stability (between - 90 °C and 400 °C). This combination
of properties makes them the solvents of choice for a number of applications, especially as
electrolytes in electric storage systems [Armand et al, 2009]. They are especially valued for
their safety, but still suffer from high instability at low potential and significant viscosity,
which limits their use in cold environments.

B. Characteristics of Li-Ion Storage Cells

In practice, conventional Li-ion storage cells have a specific energy of 70 to 200 Wh/kg,
while specific power ranges from 300 to 1,500 W/kg, depending on the P/E type (determined
by the electrode thickness) for the target application, from the hybrid to the all electric vehi-
cle (4.2.6.1). The ratio between the mass of useful active material and total mass ranges from
45 to 60%, depending on the Li-ion technology used. In the case of Li-ion-polymer storage
cells, the construction of the solid cell results in a specific energy of 130 to 200 Wh/kg,
an energy density of 300 to 640 Wh/L, and specific power as high as 1800 W/kg. Lithium
storage cells also benefit from very low self-discharge rates, high energy efficiency, and a
faradaic efficiency close to 1.

C. Aging of Li-Ion Storage Cells

There are several aging mechanisms that occur in Li-ion storage cells. Some are associated
with the electrode materials and specific to the type of electrode and its electrolyte, others
with the aging of electrode-electrolyte interfaces, electrolyte and separator, and phenomena
such as corrosion of the collectors, separation of electrode and collector, pore obstruction,
etc. Additional information on the aging of Li-ion storage cells can be found in the literature.
See, for example, Broussely (2002), Broussely et al (2005), Delacourt (2008), Vetter and
al (2005).

The principal mechanisms involved in the aging of lithiated-carbon negative electrodes
include:

- Destabilization of the SEI passivation layer in carbonated materials, which triggers
decomposition of the electrolyte in contact with the negative electrode by reduction,
together with an irreversible loss of capacity. This degradation is promoted by high
temperatures.

Chapter 4 · On-board energy storage systems 211

- The growth of dendrites of Li metal on carbonated materials if the diffusion of Li+ ions
within the carbon is too slow, accompanied by a loss of capacity. This mechanism is
favored by low temperatures or rapid charging.

However, these aging mechanisms do not affect Li4Ti5012 spinel, an alternate nega-
tive electrode material, which possesses exceptional mechanical (no deformation during the
reversible insertion of Li+ ions) and thermal stability to 60 °C [Zaghib et al, 1999], but
which has low theoretical capacity. In the case of lithium oxide positive electrodes, there are
three degradation phenomena that result in a loss of capacity:

- reversible insertion of Li+ ions when cycling, which leads to a change in the volume
of electrode materials and possible microfissures; excess delithiation of the crystal-
lographic structure can destabilize the electrode;

- partial dissolution of electrode materials in the electrolyte;

- the formation of a film through electrolyte degradation on the positive electrode (oxi-
dation), leading to increased impedance.

Note that LiFeP04 olivine, a positive electrode material valued for its nontoxicity and sta-
ble three-dimensional structure during delithiation, follows the same aging mechanisms but
to a lesser extent [Bernard et al, 2009; Zaghib et al, 2006; Zaghib et al, 2008]. In general,
the state of charge, cycling conditions, and temperature are factors that influence the kinet-
ics of aging mechanisms. High current regimes significantly accelerate aging [Takei et al,
2001], as do elevated charge/discharge amplitudes. Because chemical and diffusion reactions
are activated by heat, high temperatures promote decomposition reactions of the electrolyte
and dissolution of the SEI.

During the life of the vehicle (10 to 15 years), electric and thermal management of on-
board storage cells must be implemented, depending on vehicle use and the chemistry of the
electrodes, in order to minimize and control aging and the associated drop in performance
(4.2.9). Aging tests are conducted in laboratories to determine aging mechanisms and kinet-
ics under conditions intended to represent vehicle use, generally accelerated over a period of
several months to several years. Because a vehicle will alternate periods of use and rest, we
generally make a distinction between cycled aging, where the battery is connected on a test
bench using simulated or actual usage profiles, and calendar life aging, where no voltage is
applied to the battery at a given SOC level. Given the variety of aging factors and mecha-
nisms in Li-ion storage cells, it is reasonable to consider accelerated aging test protocols in
terms of intended vehicle use. Broad-scale research-and-development programs are regularly
conducted to study the effects of aging on new storage cells under a maximum number of test
conditions [Badin, 2009; Howell, 2009; Van den Bossche et al, 2006].

D. The Li-Metal-Polymer Storage Cell

Here, a solid polymer-based electrolyte is used with a negative electrode of lithium metal,
which helps limit the formation of dendrites at the negative electrode when cycling and the
risk of short circuits in the presence of a liquid electrolyte. However, the range of service tem-
peratures of Li-metal-polymer batteries is limited to high temperatures (T > 60 °C, approxi-
mately) because of the low intrinsic ionic conductivity of polymers at room temperature.

212 Hybrid vehicles

Although good ion solvents with conventional salts, they provide poor dissociation between

Li+ cations and anions (low dielectric permittivity). For example, the conductivity of a poly-
mer electrolyte like PEO is 10~5 S.cm-1 at room temperature, while the ionic conductivity of
an ethylene carbonate liquid electrolyte (EC/DMC) is around 102 S.cm-1. Nonetheless, the
use of strongly dissociated lithium salts like Li+TFSI~has contributed to the development of
lithium batteries with polymer electrolytes (TFSI-' the anion, bis-(trifluoromethanesulfonyl)-
imide, is also written (CT^SC^^N-).

By using a metallic Li electrode as the negative electrode, the positive electrode does not

necessarily need to be lithiated before assembly of the cell, unlike Li-ion batteries. Also, the

use of air-stable lithiated intercalation compounds is not required for the positive electrode;

rechargeable Li-metal-polymer batteries currently use vanadium oxides for the positive elec-

trode (Table 4.5).

Table 4.5. Properties of some electrode materials used in Li-metal-polymer storage cells

Negative electrode Positive electrode

Material Potential Theoretical Material Potential Theoretical
(structure) compared specific (structure) compared specific
to Li (V) capacity to Li (V) capacity
(Ah/kg) (Ah/kg)

Li metal 0 3,800 V205, LiV308 2.7-3.6 0.240
vanadium oxides 3.0
0.200
Mn02
manganese oxides

E. Characteristics of the Li-Metal-Polymer Storage Cell

In practice, solid LMP technology is much less widely used than Li-ion technology. For
example, the Li-metal-polymer battery pack in the Blue Car, approved in 2007, has an energy
density of 100 Wh/kg and a peak (30 s) specific power of 150 W/kg. It should be pointed out,
however, that a Li-metal-polymer battery cannot meet the power needs of a hybrid vehicle.

4.2.4.2 Applications

A. Examples of Li-Ion Storage Cells

To meet the growing popularity of hybrid, plug-in, and electric vehicles, which will make
extensive use of Li-ion technologies, a diversified commercial market for Li-ion storage cells
has developed. Li-ion storage cells available from Kokam and Saft are shown in Figures 4.20
and 4.21.

Chapter 4 · On-board energy storage systems 213

Small & Medium Capacity

1. H i g h p o w e r cell

2 High energy density cell

Figure 4.20

Examples of Li-ion storage cells from Kokam (small, medium, and large capac-
ity, high energy density, high or ultra-high power).
Source: www.kokam.com.

The Mercedes S400 was the first mild hybrid vehicle sold on the European market in
2008 with a Li-ion battery pack (118 V rated voltage, 0.82 kWh, 25 kg). Located under the
hood and liquid cooled, the battery pack used SAFT storage cells [Back, 2008]. In addition
to storing electricity in chemical form for traction, it was used to start the vehicle, replacing
the conventional lead battery.

214 Hybrid vehicles

Figure 4.21
Li-ion storage cells manufactured by SAFT (www.saftbatteries.com).
B. Example of a Li-Metal-Polymer (LMP) Storage Cell
In France, batScap, a subsidiary of Bolloré, has been working to develop LMP batteries for
15 years. The basic cell, which is entirely solid, is assembled from layers of ultrathin film. It
contains a negative electrode of lithium metal, a solid polymer electrolyte (poly[oxyethylene])
containing dissolved lithium salts, a positive electrode of vanadium oxide, electrolyte and
carbon, which, when mixed, form a plastic composite, and a current collector to provide an
electrical connection (Figure. 4.22). The films are stacked, wound, and compressed to form
a prismatic design.

Chapter 4 · On-board energy storage systems Next Page

215

Figure 4.22

Solid cell of a Li-metal-polymer storage cell made by batScap
(www.batscap.com/la-batterie-lithium-metal-polymere/technologie.php).

BatScap designed the Blue Car, a small electric vehicle equipped with Li-metal-polymer
battery technology, which is used for its fleet of self-service Autolib' electric vehicles in and
around Paris. Each module, whose characteristics are shown in Table 4.6, is equipped with
an electronic system that provides thermal management (controls internal temperature) and
electrical operation (discharging and recharging and alarm management).

Table 4.6. Characteristics of the Li-metal-polymer batScap EV pack for the Blue Car

Energy 30 kWh Volume 300 L
Nominal voltage 410V Mass 300 kg
Voltage range 300 V - 4 3 5 V Communications bus CAN
Capacity at C/4 75 Ah Internal temperature 60 °C to 80 °C
Peak power (30 s) 45 kW Ambient temperature - 20 °C to +60 °C
Specific energy 100Wh/kg Energy density 100Wh/L

Source: www.bluecar.fr.

The battery made from these modules (mini/maxi voltage = 243 V/374 V, weight
= 240 kg, recharge time to 100% = 4 h, air cooled) gives the Blue Car a range of approxi-
mately 200 km.

Previous Page Hybrid vehicles
216

4.2.4.3 Outlook

Li-ion and Li metal batteries are promising reversible storage systems for on-board applica-
tions, especially those that require a certain type of energy (PHEV and EV). These tech-
nologies provide better specific energy and power than the Ni-MH technology used in the
majority of commercial HEVs. Moreover, appreciable progress is expected in the area of
electrode materials (Figure 4.23) and the foreseeable designs are also more flexible (see inset
below). In the next decade, Li-ion batteries are expected to experience considerable growth
as on-board storage systems.

Figure 4.23

Potential materials for use in future Li-ion storage cells.
Source: [Tarascon, 2008]

Perspectives for lithium batteries
(M. Morcrette, LRCS France)

We must stress the versatility of the lithium battery technology, since there are no
less than 6 different materials in the positive and negative electrodes of the batteries sold.
This means that any innovation concerning the materials is "relatively" easy to transfer in
an accumulator. Given the complexity of an accumulator, improvements can be sought
in a number of areas: materials, safety and architecture of the electrodes:

- Concerning the materials, to improve the energy density of an accumulator, either
its output voltage, or its faradaic capacity (mAh/g of electrode) must be increased.
Figure 4.23 illustrates some of the options being investigated. While materials
already exist for the first solution (LiNi0 5Mn1 504), they require an even more stable

Chapter 4 · On-board energy storage systems 217

electrolyte, which remains a very open challenge. To increase the faradaic capac­
ity, the number of lithium ions per formula unit must be increased (> 1 electron
per transition metal). In the very large polyanion family to which LiFeP04 belongs,
this type of mechanism has already been identified, for example with Li3V2(P04)3.
Currently, the development of new synthesis tools (ionothermal, microwave, etc.)
has opened the way to numerous materials (sulphate, fluoride) which should allow
this objective to be reached while adjusting the intercalation potentials. Other elec­
trochemical mechanisms can also be tested. For example, in the alloy reaction of
silicon with lithium, there is a huge change in volume. This problem can be con­
trolled through electrode engineering and the silicon-based electrode therefore
seems to be a promising solution, although it still requires adjustments. Numerous
studies are also in progress to use metallic alloys other than silicon.

- Concerning the safety aspect, it seems quite obvious that the fluorine-based lith­
ium salt, which produces toxic hydrofluoric acid in case of thermal runaway, must
be replaced. Some alternatives are available, for example LiFSI which exhibits
less aluminium corrosion than LiTFSI, mentioned previously. Clearly, the "all solid"
technologies (polymer, ceramic) are extremely competitive in this respect.

- Concerning electrode architecture, improvements can be made to increase the
exchange area between the two electrode materials without penalising the gravi­
metric energy density. Numerous research programmes are currently underway
to manufacture 3D batteries, as opposed to the traditional architecture which is
generally two-dimensional.

Apart from lithium ion, it is important to plan for the future. This is a risky exercise
since numerous automobile manufacturers have drawn up roadmaps for the deployment
of the fuel cell. Note, however, that the theoretical capacities of the Li/S and metal/air
technologies are highly attractive. For Li/S (theoretically, a figure of 350 Wh/kg can be
reached), both the operation of a lithium-based electrode and the solubility of polysul-
phides in the electrolyte must be controlled.

In Canada, L. Nazar obtained excellent results, which revived the interest for this
technology [Ji et al., 2009]. Numerous research teams are conducting studies on the
metal/air technologies. The zinc/air, aluminium/air or Li/air technologies are the most
well-known and the most promising. Once again, although many challenges are to be
faced (metallic lithium, fuel cell type electrode, etc.), there is much at stake since energy
densities of between 500 and 1000 Wh/kg could be obtained.

4.2.5 Supercapacitors

Supercapacitor technologies can be divided into electrostatic supercapacitors, where the ions
are confined to the electrolyte, electrochemical supercapacitors, which make use of redox
reactions at the electrodes in addition to electrostatic processes, and a hybrid category that
exploits both principles, either within the same electrode or in asymmetric systems, where
each electrode uses a different technology. The materials involved are summarized here, but
specialized monographs provide additional details [Conway, 1999; Lassègues, 2001].

218 Hybrid vehicles

4.2.5.1 Electrostatic Supercapacitors

A. Description

In an electrostatic supercapacitor, both electrodes, generally identical, consist of an active
material that contains mostly activated carbon with a large specific area (up to 3,000 m2/g),
together with additives to improve conductivity and percolation (carbon black or graphite).
The active material, bound by a polymer binder, is placed on the surface of aluminum sheets
that serve as a current collector and support. The electrodes are assembled on either side of
an ion-permeable separator consisting of a fine membrane (typically a polyethylene or poly­
propylene polymer). The multilayer assembly is 250 to 350 μιη thick. An electrolyte, liquid
in most cases, impregnates the electrodes and the separator.

Both aqueous and organic electrolytes are in commercial use today. Aqueous liquid elec­
trolytes have low toxicity but a low operating voltage window, limited to 1.23 V by the
breakdown potential of water. Organic liquid electrolytes [Ue et al, 1994] have a greater
window of electrochemical stability (up to 3 V), which significantly increases the energy
stored compared to aqueous electrolytes. However, this window decreases at high tempera­
ture. Additionally, their resistivity is around a hundred times higher than it is for aqueous
solvents, which reduces the response time to a charge or discharge peak. At present, the
most efficient electrolyte for carbon/carbon supercapacitors uses acetonitrile as a solvent and
Et4NBF4 as the salt. Unfortunately, acetonitrile is somewhat toxic, which makes its use in
transportation applications problematic, in addition to its very low boiling point (80 °C). A
number of more marginal electrolytes are also available or currently being researched. They
include the polymer electrolytes that have been used in storage-cell and fuel-cell research and
ionic liquids, which are especially promising due to their excellent electrochemical stability
(> 5 V) [Arbizzani et al, 2008; Balducci et al, 2007].

B. Applications

Used for transport, especially in hybrid and electric buses, streetcars, and trolley buses, sym­
metric electrode supercapacitors containing carbon and an organic electrolyte are mature
technologies [Tertrais, 2009]. Supercapacitor packs consist of modules containing a tempera­
ture and voltage measuring device and balancing electronics, like the batScap module shown
in Figure 4.24. These supercapacitors are often used in streetcars to travel short distances
whenever electricity can't be provided by the network [Rechenberg and Meinert, 2009].

Chapter 4 · On-board energy storage systems 219

Figure 4.24

A batScap supercapacitor module (20 elements of 3000 F, total capacity 150 F,
total weight 151.1 kg, output power 14 kW @ 10 s and 50% DOD).
Source: [Tertrais, 2009]

4.2.5.2 Electrochemical Supercapacitors

Electrochemical supercapacitors combine the operating principles of electrostatic superca-
pacitors with electrochemical storage cells by using redox electrodes distributed across large
surface areas. They consist of two symmetric carbon electrodes, catalyzed by a transition
metal oxide (typically ruthenium oxide, Ru02), which is subject to rapid reversible redox
charge transfers. As a result, the capacity of the carbon electrodes is increased. Conduc-
tive polymers that make use of redox processes involving reversible doping have also been
studied as electrode materials in supercapacitors, but these systems have been shown to be
somewhat unstable [Mastragostino et al, 2002].

4.2.5.3 Hybrid Supercapacitors

Most hybrid systems are asymmetric systems whose electrode technology differs from that
of supercapacitors or is borrowed from other storage systems. It is, for example, possible to
combine an activated carbon electrode as the negative electrode with a conducting polymer
electrode for the positive [Arbizzani, 2001]. Systems that combine a supercapacitor and stor-
age cell have also been introduced, with a positive carbon electrode and a negative electrode
made of a material into which lithium ions (Li4Ti5012) are inserted [Pasquier et al, 2003].
There are many such examples, and hybrid systems are the subject of much current research.
These innovations demonstrate that the frontier between supercapacitors and power storage
cells is diminishing, primarily because of the needs of hybrid vehicles.

4.2.5.4 Summary

Table 4.7 provides the comparative characteristics of various supercapacitor technologies
currently being sold or in the prototype stage. At present, supercapacitors are still considered
to be expensive as storage systems.

2 2 0 Hybrid vehicles

Table 4.7. Characteristics of different supercapacitor technologies [Marquet et ai, 1998]

Characteristics Active Active Active Metal oxide Conductive
carbon carbon carbon Aqueous polymer
Energy density Aqueous Organic Solid electrolyte Organic
(Wh/kg) electrolyte electrolyte electrolyte electrolyte
Power density
(kW/kg) 0.2 to 2 lto5 lto5 2 to 10 2 to 10
Voltage (V)
Cyclability lto5 0.2 to 2 0.1 to 0.5 ltolO 0.1 to 0.5
Cost (relative)
0.8 to 1.2 2 to 3 2 to 3 0.8 to 1.2 0.8 to 1.3
> 100,000 > 100,000 > 10,000 > 50,000 > 10,000
Average Average
Low Low High

4.2.6 Comparison of Electrical Energy Storage Technologies

As an essential component of electric vehicles, the reversible electrical energy storage sys-
tem is characterized by its operational voltage range, its power and energy performance,
working life, cost, recyclability, and its need for rare materials in terms of overall automobile
demand (Section 7.3). Direct comparison of such systems is far from simple. These technolo-
gies are constantly evolving and the figures provided soon outdated. Additionally, a range of
values must be given for each technology family due to the variety of materials, designs, and
applications. A comparison of the characteristics of storage systems used in HEV and EV
applications is provided, using bibliographic data. To round out the discussion, an original
comparison of the energy efficiency of the different technologies will be provided, using
simulations, in order to describe the advantages and disadvantages of batteries and superca-
pacitors in hybrid electric vehicles.

4.2.6.1 Characteristics of Energy Storage Systems (ESS) for Different Applications

The Ragone diagram is frequently used to compare the characteristics of specific power and
energy density in batteries (Figure 4.25). The ranges associated with each technology cover
different P/E types specific to a given HEV, PHEV, or EV application. In particular, the Li-
ion range is not continuous because different technologies are used in power storage cells
and energy storage cells.

In particular, to meet the electric range requirements of each application, battery energy is
designed as a function of use and over relatively large SOC ranges, as shown in Figure 4.26
for the American FreedomCAR program.

Chapter 4 · On-board energy storage systems

Figure 4.25
Comparison of the technical performance of traction batteries.
Source: [Broussely, 2007]

Figure 4.26
Comparison of SOC ranges and customary battery characteristics in HEV,
PHEV, and EV applications.
Source'. [Howell, 2007]

222 Hybrid vehicles

Note that HEV batteries are used for an intermediate state-of-charge of approximately
30% of the energy at full charge (SOC between 40% and 70%). This corresponds to their
"useful" energy. The amount of unused on-board energy (SOC < 40% and SOC > 70%),
which is greater in HEVs than useful energy, is greatly reduced in rechargeable hybrid vehi-
cles, where the battery is cycled between an approximately 30% SOC and nearly full charge.

In spite of the broadening of the SOC range used, if we move from a HEV to a PHEV (or
to an EV), we find that the capacity and number of elements also increase in order to meet
the needs of electric vehicle range. As mentioned in section 4.1, power elements (high P/E
ratio) are used in HEV, while largely energy oriented components (low P/E) are preferred
for PHEV and EV.

These developments are reflected in the use of a greater amount of raw materials. For
example, an estimate of the weight of lithium required per Li-ion pack for an electric range
of approximately 6 to 60 km, has been proposed by L. Gaines [Gaines, 2010] for four main
Li-ion technologies intended for use in electrified vehicles (Table 4.8). The NCA/G pair
indicates the use of LiNi0 8Co0 15A10 05O2 at the positive and graphite at the negative; LFP/G
corresponds to LiFeP04 at the positive; LMO/G uses LiMn02 for the positive; while the
combination of LiMn02 at the positive and LiTi5012 at the negative is shown as LMO/LTO.
We have also calculated the total on-board energy and the amount of Li required per kWh,
assuming a useful SOC range of 30% and 65% for HEVs and PHEVs respectively.

The table shows that the Li content varies from approximately 100 g to nearly 300 g
per kWh of total battery energy. These figures agree with the study by Rade and Andersson
[Rade and Andersson, 2001], which indicates a range of 100 to 140 g/kWh for NCA/G and
LMO/G Li-ion batteries. We also see that the mass of Li per pack varies from 0.2 to 0.7 kg for
a HEV, which has a short electric range, while the mass extends from 1 to 3 kg in a PHEV,
with a range of 60 km, if the negative electrode is graphite. But we also need to consider that
approximately 5 kg of Li is required when a negative electrode of titanate is used in a PHEV,
which appreciably increases the need for Li. However, recycling should help reduce the pres-
sure on lithium production requirements.

Table 4.8. Estimate of the amount of Li (kg) per pack required for a lightweight v

Battery type 6 NCA-G 64 6 LFP-G
32 32
Vehicle range (km) 4 40 4
with consumption 1,200 20 12,000 1,200 20
ofl86Wh/km 4,000 6,000 18,462 4,000 6,000
0.335 9,231 2.753 0.196 9,231
Vehicle range (mile) 0.035 1.36 0.202 0.045 0.796
with consumption of 0.104 0.136
300 Wh/mile 0 0 0
0.37 0 2.955 0.241 0
Useful energy (Wh) 1.464 0.160 0.932
0.159 2.043 0.060 0.101
Total energy (Wh) 1.088 0.471 1.162
60
Li at the positive 60 140.1 60 60
electrode (kg) 75.9 0.021 34.6 81.6
0.019 0.007 0.011
Li in the electrolyte
(kg)

Li at the negative
electrode (kg)

Mass of Li in the
pack (kg)

Mass of Li per unit 0.093
of energy (kg/kWh)

Total mass of cells 0.424
(kg)
Number of cells/pack 60
31.2
Mass of pack (kg) 0.012

Mass of Li/kg pack

Source: based on [Gaines, 2010].

vehicle, depending on the Li-ion technology used and the electrical range

LMO-G LMO-TiO

64 6 32 64 6 32 64

40 4 20 40 4 20 40

12,000 1,200 6,000 12,000 1,200 6,000 12,000 Chapter 4 · On-board energy storage systems
18,462 4,000 9,231 18,462 4,000 9,231 18,462

1.608 0.145 0.587 1.183 0.287 1.155 2.311

0.264 0.029 0.087 0.17 0.049 0.167 0.335

0 0 0 0 0.301 1.213 2.426

1.872 0.173 0.674 1.352 0.637 2.535 5.071

0.101 0.043 0.073 0.073 0.159 0.275 0.275

2.17 0.483 1.534 3.062 0.347 0.888 1.671

60 60 60 60 60 60 60
150.2 35.6 106.2 209.1 26.1 62.6 115.4
0.012 0.005 0.006 0.006 0.024 0.040 0.044

bo
bo

224 Hybrid vehicles

4.2.6.2 Comparison of Energy Efficiency in a Hybrid Vehicle
As we have seen, in a hybrid drive mechanism the reversible storage system must continu-
ously onload and offload energy. Consequently, its energy efficiency will be an important
element when considering the overall efficiency of the system. In terms of reversible electric
storage, we can use Ni-MH or Li-ion batteries, or supercapacitors (EDLC). Additionally, the
power level at which the energy can be stored or restored must be taken into consideration in
any comparison. Our simulation was conducted on the basis of the following assumptions:

- PEVE 6.5 Ah Ni-MH cell, A123s 2.3 Ah Li-ion cell, and Maxwell 3500 F EDLC ele-
ment; the effect of a converter was considered for the supercapacitor so it could oper-
ate in the same voltage range as the batteries.

- The elements are run with an average value of 50% SOC, with microcycles of a few
percent.

- The faradaic yield is assumed to be one, which is very close to the actual value for the
three cases.

In Figure 4.27, we illustrate the energy efficiency of the different storage systems
described in Section 4.2.1.2.

Figure 4.27

Comparison of energy efficiency as a function of specific power for Ni-MH,
Li-ion (LFP/C), and supercapacitor (EDLC) systems.

As shown in the graph, the energy efficiency of the three storage systems is very different
and tends to diverge whenever power requirements increase. In supercapacitors, the energy
efficiency determined by the fraction of stored energy that is actually usable during discharge
assumes relatively high values (> 90%). However, it cannot reach 100% because of the inevi-
table presence of internal resistance, Rs, in the supercapacitor. Part of the stored energy is then
dissipated as Rs and part ofthe available power is lost. Li-ion technology is close to or somewhat

Chapter 4 · On-board energy storage systems 225

lower than that of supercapacitors, while Ni-MH has much lower efficiency. These simulations
illustrate the need to introduce energy efficiency when comparing different storage systems.

4.2.7 Modeling

In hybrid vehicles, the combination of different drive mechanisms and storage systems makes
their architecture particularly complex. Simulation of hybrid systems is required to design and
optimize their architecture, using behavioral models of their various components. But modeling
the electrical and thermal behavior of storage systems is also required for other applications:

- the design of battery elements, battery packs, and their cooling systems;
- the understanding of physical-chemical mechanisms involved in storage systems

(especially degradation factors), the identification of the kinetics of aging, and the
prediction of behavior while in service;
- diagnosis of the system state while in use to better anticipate its real-time management;
- the initial design of electrode materials for a given electrolyte or, reciprocally, to opti-
mize performance.

These applications involve different levels of physical modeling, from molecular scale to
vehicle system simulators based on component models (Figure 4.28).

Figure 4.28

Modeling levels for storage systems.
Source: [Lynch, 2006]

226 Hybrid vehicles

4.2.7.1 Modeling Batteries

In the following sections, we examine three types of the most currently used models of the
electrical or thermal behavior of batteries.

- Models by analogy with electrical circuits, or equivalent electrical circuits, consisting
of electrical elements arranged in series or in parallel. These models, with concentrated
parameters (solely time-dependent), seek to represent the dynamics of the electrical
or thermal behavior of a battery based on an experimental database introduced in the
form of a map or as analytic functions.

- Electrochemical models inspired by the principles of thermodynamics, which rely on
a mathematical description of the physical-chemical phenomena that take place on a
microscopic scale in the battery cell. These models can be multidimensional, with ID,
or even 2D, spatial sampling, or reduced to the OD order (concentrated parameters) to
reduce processing time and simplify the calculations involved.

- Thermal models based on the physical principles of heat transfer, which incorporate
the balance of energy exchanges with the exterior. In addition to the energy balance
generated by the storage system, these models, generally multidimensional, can be
coupled to a OD model of the electric behavior of an equivalent electric circuit or an
electrochemical model.

A. Models by Analogy with Electrical Systems

Modeling the electrical behavior of a battery by electric analogy is commonplace, for it
makes use of intuitive models with concentrated parameters (solely time-dependent), which
require relatively little processor time.

a. Static Models
The simplest model is a static model that expresses the voltage, U, of the battery as a function
of the current, I, in the form:

(4.29)

where U0 represents the vacuum voltage and R the internal resistance of the battery. These
variables are conventionally determined by experiment and parameterized as a function of
the state of charge, temperature, and sometimes the current value. Here, predictive accuracy
depends on the use of maps, which can quickly represent a number of tests. Consequently,
these models have difficulty accounting for battery dynamics under conditions of nominal and
extreme use, under strong or zero currents, because relaxation phenomena in the battery are
staggered over the course of several hours before the return to thermodynamic equilibrium.

b. Dynamic Models
In dynamic electric models of a battery, voltage is expressed by the following general formula:

(4.30)

where Z*, a complex variable, is the electrical impedance of the battery, measured by elec-
trochemical impedance spectroscopy. This reflects the contributions of physical phenomena

Chapter 4 · On-board energy storage systems 227

with fast (electromigration), intermediate (electrochemical reactions), and slow (ionic dif-
fusion in materials in the storage system) dynamics. The impedance diagram for a battery
can be reproduced using relatively simple equivalent electric circuit models that make use
of commonly employed electric elements (Table 4.9) to better reflect the different physical
phenomena taking place within the battery. As with the static model, these elements are
parameterized by the state of charge, the temperature, and the current value. The state of
health (SOH) can also be used for parameterization [Huet, 1998].

Table 4.9. Example of electric equivalent circuit elements

Element Symbol Impedance
Resistance R R
Capacitance C
Inductance L 1/jCco
CPE {Constant Phase Element) jLco
CPE l/(YO(jœ)n)forO<n<l

Warburg W

Based on electrochemical impedance spectroscopy measurements with 2 electrodes (con-
nected to the terminals of a storage cell, module, or pack), we develop an equivalent electrical
model of the "black box" type, which provides a representation of experimental developments
without distinguishing phenomena taking place at each electrode, especially if it involves a
module of n cells in series, comprising 2n electrochemical systems in series, or a pack.

A number of electric equivalent circuits have been proposed to better understand the elec-
trochemical impedance of a battery over a wide range of currents and frequencies, and espe-
cially for the diffusive part at low frequencies [Oustaloup, 1995; Kuhn et al, 2006; Sabatier et
al, 2006]. Montaru and Pelissier [Montaru and Pelissier, 2010] have recently proposed a model
of the isothermal electrical behavior of a Li-ion battery, illustrated in Figure 4.29. An original
method of calculation was developed to account for non-linearity phenomena. The parameters
of the equivalent electrical model have been partially identified by impedance spectroscopy for
the high-frequency portion and by chronopotentiometry for the low-frequency portion, over
a wide range of current intensities. The model has been confirmed for high-intensity current
ranges and a current profile that was simulated using hybrid vehicle simulation software.

To account for the influence of temperature during normal and extreme operation, E.
Prada has developed a hybrid electric/electrochemical model of the electrical behavior of a
Li-ion battery [E. Prada, 2010c]. It includes:

- the dependence ofthe thermodynamic equilibrium potential, U0, on SOC and temperature;
- the kinetics of thermally activated redox reactions of the electrochemical system;

- the nonlinearity of charge transfer resistance as a function of current and its tempera-
ture dependence;

- low-frequency diffusion phenomena and their dependence on SOC and temperature.

228 Hybrid vehicles
Additionally, an energy balance for the cell was introduced to simulate reversible and

irreversible heat losses in the system, coupled with electrical demands. Functions describ-
ing the dependence on temperature, SOC, or even current, of the different parameters of the
model were calibrated on the basis of impedance measurements with two electrodes con-
ducted at different SOC under isothermal conditions (Figure 4.30).

Figure 4.29
Equivalent electric circuit and electrical impedance in the Nyquist plane, used
to model a Li-ion battery.
Source: [Montaru and Pélissier, 2010]

Figure 4.30
Electrochemical impedance measurements at two electrodes of a 2.3 Ah Li-ion
battery, shown in the Nyquist plane as a function of SOC at 20 °C.
Source: [Prada etal, 2010c]

Chapter 4 · On-board energy storage systems 229

In order to be able to compare experimental and simulated voltage (Figure 4.31) and
temperature values (Figure 4.32), the system must be in the same state at the initial instant.
Because of this, we begin at thermodynamic equilibrium at a given SOC, that is, concentra-
tion overvoltages are zero when initializing the simulation, and the experiment is launched
after approximately two hours of battery relaxation.

Figure 4.31

Change in simulated and measured voltage of an A123 Systems 2.3 Ah Li-ion
element (a) during discharge at 0.5C/1C/2C, and (b) during discharge/charge
current pulses of 20 A every 10% of SOC between 90% and 10% SOC.
Source: [Prada, 2010a]

Figure 4.32

Change in simulated and measured skin temperature of an A123 Systems 2.3 Ah
Li-ion element (a) during discharge at 0.5C/1C/2C, and (b) during discharge/
charge current pulses of 20 A every 10% of SOC between 90% and 10% SOC.
Source: [Prada, 2010a]

230 Hybrid vehicles

The comparison of measured and simulated voltages through the cell at weak and strong
currents (Figure 4.31) indicates the excellent predictability of the model throughout the SOC
range, with a relative error on the order of 1%. The heat balance also reveals good correlation
between the model and the experimental results (Figure 4.32). These results emphasize the
need to consider the influence of system temperature in behavioral models of batteries, as
well as the production of irreversible and reversible heat within the electrochemical system.

Modeling by electric equivalent circuit is also used to adjust and understand the electro-
chemical impedance spectra obtained by measurement at three electrodes of a storage cell
[Huet, 1998]. Here, a reference platinum pseudo-electrode is inserted into the system. It is
then used to record impedance diagrams for the positive and negative electrodes, whose sum
must correspond to the impedance diagram obtained by direct measurement at the terminals
of the storage cell (Figure 4.33).

Figure 4.33

Left, Apparatus for measuring EIS at three electrodes of a Ni-MH cell (Prius 2).
Right, Impedance diagrams obtained at SOC = 50%, I = 0, 20 °C. Positive
(diamonds), negative (circles), complete cell (rectangles), positive + negative
(triangles).
Source: [Bernard et al, 2010b]

Equivalent electric models of the "grey box" type have been developed, in which each
physical process is distinctly represented by electrical analogy (Figure 4.34). A Randies cir-
cuit, composed of a dual-layer capacitor (Cdl) in parallel with a charge transfer resistor (R^,
and a Warburg element (Wd), represents electrochemical, polarization, and diffusion phe-
nomena at the negative electrode. This circuit is connected to a high-frequency resistor (RHF)
in series, representing the internal resistance of the cell, and a circuit with a resistor (RL) and
an inductor (L) in parallel to introduce inductive effects due to the electrode geometry and
the cell's connecting parts.

Chapter 4 · On-board energy storage systems 231

Figure 4.34
Impedance diagram of the negative electrode of a Ni-MH module (Prius 2),
SOC = 50%, I = 0,20 °C (measured at 3 electrodes) adjusted with an equivalent
electric circuit of the "grey box" type.
Source: [Bernard et ai, 2010b]

c. Summary
Unlike static models, dynamic models based on equivalent electric circuits can be used to
reproduce the nonlinear nature of storage cells (Figure 4.35).

Figure 4.35

Comparative simulation using static and dynamic electric equivalent circuit
models of the voltage of a Ni-MH pack from a Prius 2 during an NEDC profile
atl0°C.

232 Hybrid vehicles

This approach, which was developed for lead, Ni-MH, and Li-ion storage cells, can be
used to reveal the electrochemical and other mechanisms (diffusion, relaxation, etc.) taking
place at each electrode. However, it can also be used to identify aging factors and kinetics
by means of electrochemical impedance spectroscopy [Aurbach et al, 2006; Bernard et al,
2010b; Dolle et al, 2001; Sauvant-Moynot et al, 2010].

B. Electrochemical Models of the Battery

Applied to battery technology, electrochemical models establish a connection between
microscopic data in an element, such as the molecular concentration of active species, and
macroscopic data, such as voltage or temperature. The general mathematical expression of
the voltage of a cell is given by:

(4.31)

where A(|)pos and A(|)neg represent overvoltages at the positive and negative electrodes asso-
ciated with redox reactions, Tlohmic r e P r e s e n t s t n e ohmic overvoltage, and ^ concentration m e
overvoltage associated with polarization. Underlying these models, the kinetic equations for
the primary and secondary electrochemical reactions taking place at the electrodes, together
with the mass, charge, and energy balances of an element, constitute a system of nonlinear
algebraic-differential equations. A detailed description of the equations used in electrochem-
ical models can be found in J. Newman [Newman and Thomas-Alyea, 2004; Thomas et al,
2002] and H. J. Bergveld [Pop et al, 2002].

Using an appropriate technique, the numerical resolution of the system of equations pro-
vides the instantaneous concentration of active species, the voltage of the cell, the heat flow
generated, and its temperature. It must, however, be emphasized that calibrating electro-
chemical models is difficult. Experimental determination of the geometric, thermodynamic,
electrochemical, and kinetic characteristics of a storage cell [Doyle and Newman, 1995] is
far from straightforward, more so as some variables depend on composition and temperature,
and can vary with battery aging. Additionally, if the electrochemical system is not at ther-
modynamic equilibrium in the initial state (which takes several hours), the simulation may
encounter difficulties in identifying a state that is not necessarily well defined, as described
above (4.2.7.1.A).

The results given by the electrochemical model may also depend on their coordinates in
space, if it is discretized. However, the electrochemical modeling of a storage cell rapidly
becomes extremely complex when the spatial distribution of active species is taken into
account in each region of the storage cell (positive electrode, negative electrode, separator,
gas collection compartment). Here, the mass and energy balances must be applied locally
using a three-dimensional approach. Several approximations have been proposed in the
literature:

- a pseudo-2D model [Botte et al, 2000] with a discretization of parameters in a direc-
tion x perpendicular to the cell's collectors (concentration, potential, etc.) and along
the radius, r, of solid spherical particles of active material (Figure 4.36);

- a ID model of the porous electrode [Santhanagopalan et al, 2006b; Zhang and White,
2007], where only the x direction is discretized while radial diffusion in solid particles

Chapter 4 · On-board energy storage systems 233

is ignored (however, the discontinuity between average concentration in the solid par-
ticle and concentration at the interface is taken into account);
- a OD model [Wu et al, 2001a; Wu et al, 2001b], where the cell is considered to be a
homogenous medium and the concentration of species in the electrolyte constant.

Figure 4.36

Schematic representation of a pseudo-2D electrochemical model of a Li-ion
cell with x-axis discretization and a concentration gradient of Li+ ions in parti-
cles of active materials.
Source: [Smith et Wang, 2006]

A number of electrochemical models of electrical behavior, with or without thermal
coupling, have been developed in the literature and validated experimentally, primarily for
Ni-MH [De Vidts et al, 1995; Gu et al, 1999; Paxton and Newman, 1997] and Li-ion [San-
thanagopalan and White, 2006a; Zhang et al, 2005] batteries. Multidimensional models are
preferred for design applications at the scale of a battery cell or pack, for they can be used
to predict the spatial distribution of potentials or temperature. Concentrated parameter mod-
els, however, provide the advantage of real-time calculation of system variables. Among
those variables, the state of charge is highly useful, for it is very difficult to predict solely
by observing the external variables of the battery. In an electrochemical model, the SOC is
defined from the concentrations of active materials at the electrodes and serves as an internal

234 Hybrid vehicles

variable, which can provide a precise and reliable estimate of the SOC of a battery element.
The electrochemical approach can also be used to integrate the equations associated with
aging phenomena, for predictive simulation of the long-term performance of a battery based
on vehicle use or to improve the precision of estimating the SOC of an old battery.

Recent developments in OD electrochemical models that couple the electrical and ther-
mal behavior of the battery have been used to reproduce, with considerable precision, the
dynamic voltage and thermal behavior of a power battery at different temperatures for strong
and zero currents. The first example is a new Ni-MH battery pack for the Prius 2 (202 V,
6.5 Ah) [Sauvant-Moynot et al, 2009]. Simulations with an electrochemical model with
concentrated parameters coupled to a thermal model have been compared in Figure 4.37
to measurements made on a 500 A/500 V power bench at 25 °C, 0 °C, and - 25 °C, using a
high-current HPPC test profile 5.

5 10 15
Time (s)(x 104)

Figure 4.37

Comparison of measured (solid line) and simulated (dotted line) voltage at
25 °C on a Ni-MH battery pack for a Prius 2 using a high-current HPPC profile.
Source: [Sauvant-Moynot et al, 2009]

The predictions of the model are very good between a 30% and 80% SOC, which defines
the operating range of the Ni-MH pack in the Prius 2, since the relative error is less than
± 3%. The deviation is further reduced by at least 1% during periods of high dynamic stress
when discharging (- 25 kW) and charging (+17 kW). Predictions at low temperature are also
satisfactory because the relative error at 0 °C and - 25 °C is less than ± 3% between a 30%
and 80% SOC for a low-current HPPC profile (- 7.5 kW and + 5.5 kW).

5. The Hybrid Pulse Power Characterization (HPPC) test profile [FreedomCAR Program Electro-
chemical Energy Storage Team, 2003] is applied isothermally to a charged battery that is discharged
in 10% increments. The HPPC high-current profile for the Prius battery comprises 10 sequences =
discharge peak (- 130 A, 10 s)/relaxation 30 s/charge (+ 85 A, 10 s)/discharge at C/5 to the next SOC.

Chapter 4 · On-board energy storage systems 235

Concerning lithium applications, a second example of electrochemical modeling at con-
centrated parameters is shown in Figure 4.38. The system is a Li-ion element using iron
phosphate/graphite technology sold by A123 Systems.

Figure 4.38

Comparative changes in simulated and measured voltage in a 2.3 Ah Li-ion
element from A123 Systems during HPPC tests between 90% and 10% SOC:
at 20 °C and at 0 °C.
Source: [Prada, 2010a]

Comparison of simulations to experimental measurements during an HPPC test indicates
an error of less than 1% at room temperature and at 0 °C. Note that dynamic performance is
appreciably altered in cold environments as the power pulses during discharge cause the volt-
age of the pack to fall even further, while the recharge pulses are less effective.

C. Thermal Models of the Battery

Battery packs consist of a large number of cells, especially those used in rechargeable hybrids
and electric vehicles. The behavioral homogeneity of the cells requires good control of their
thermal management, which conditions their state of charge, health, and safety. In this con-
text, simulation is a very efficient tool for optimizing the size and geometric design of a
battery pack while taking these criteria into account. Thermal modeling of a storage cell is
useful for designing an element or battery pack, and can help estimate internal temperature
gradients during charge and discharge operations, under given conditions of cooling and
geometry. The temperature of a cell can be calculated from an energy balance that takes into
account:

- the internal heat flow j generated by the cell's activity, associated with reversible
and irreversible losses from electrochemical reactions;

- the flow j t r a transferred to the surrounding environment at temperature Ta.

236 Hybrid vehicles

The net heat flow through a storage cell, φ, can easily be calculated as the balance between
internal and external flows, that is, φ = φ - cptra. The quantity of heat stored in the battery,
obtained by integrating the heat flow over time, can then be used to calculate the temperature
of the battery with the following equation:

(4.32)

where C is the average specific heat capacity of the cell and Mcell its mass.
At this point it is worthwhile discussing the distribution of the irreversible and revers­

ible contributions of heat generation. Al Hallaj [Al-Hallaj et al., 2000] has shown, using a
thermal model with concentrated parameters, that the (reversible) entropie contribution from
electrochemical activity of a Sony US 18650 Li-ion cell represents approximately 50% of
the total heat generated for weak charge/discharge regimes (C/6, C/3), whereas irreversible
contributions become preponderant for higher regimes. Consequently, if we consider only
the irreversible contribution of heat in a simulation, we will underestimate the heat flow
generated, especially at low regimes, which can be detrimental when designing a cell or pack.

Depending on user needs and the methods of calculation, we distinguish fine multidimen­
sional models, nD, and concentrated parameter models, 0D, where the parameters are aver­
aged over the system (and, thus, depend only on time). The mathematical coupling between
electrical and thermal models is not systematic, for they both require considerable time and
processing power. The user can choose to decouple electrical and thermal factors by making
an approximation of the physics of the system (assumptions about isothermal operation of the
battery, for example). These different approaches are illustrated in the following examples.

a. Semi-Empirical Uncoupled Approach

The simplest approach consists in using experimental data from calorimetry to determine
the heat flows generated in different operating modes and reintroducing them into 2D or 3D
finite-element models. Recall that the finite-element modeling technique consists in solving
the physical equations at every point in space of the geometry of the system studied, through
the use of a relatively complex spatial mesh (ID, 2D, or 3D). The changes in the characteris­
tic variables of the system (including temperature) are then calculated at each time increment
and at each spatial mesh.

For example, Li [Li et al., 2008] has studied the thermal behavior of 8 Ah cylindrical
Ni-MH batteries (Figure 4.39). The heat flows (in W) generated when charging at different
regimes were determined experimentally (using a calorimeter and a skin thermocouple), then
compared using time-dependent mathematical functions. The heat flow functions generated
are then injected into a 2D finite-element model of the cylindrical cell, characterized by its
geometric, mass, and thermal properties. The simulations show that a heat gradient exists
within the cylindrical cell at the end of the charge, increasing whenever the charging rate is
higher, which is explained by the low heat conductivity in the radial direction.

Chapter 4 · On-board energy storage systems 237

Figure 4.39

(a) Calorimetric determination of heat flow as a function of SOC. (b) 2D simu-
lation of the internal heat gradient in an element based on experimental heat
flow data.
Source: [Li et al, 2008]

b. Coupled Simulation Approach

The use of an electrochemical model with concentrated parameters coupled to a multidimen-
sional thermal model provides an alternative approach to simulating the thermal behavior of a
battery. Among the coupled electrochemical models incorporating the reversible contribution
of heat production at the electrodes, Williford [Williford, 2009] has developed a 2D thermal
model for conventional LiCo02/C technology coupled to a simple static electrical model based
on Ohm's law. Other authors, such as Srinavasan and Wang [Srinivasan and Wang, 2003],
have coupled a 2D electrochemical model to a 2D thermal model for LiMn204/C technology.
A comparative study of the various thermal models, where temperature generation is either
local (nonisothermal) or average (isothermal) over the entire volume of the system, has shown
that an approach based on local heat flow generation is the most precise. Both approaches are
equivalent for low current regimes, but the discrepancies are non-negligible for higher regimes.

The following example illustrates the work of E. Prada on nD thermal modeling of cells/
modules/packs using finite-element analysis and coupling a 0D electrochemical model at the
scale of the individual mesh. The geometrical structure of the element considered is finely
meshed based on the desired precision and knowledge of internal geometry. Each cell is char-
acterized by its physical properties (thermal conductivity, mass capacity, electrical resistance),
which vary with the nature of the meshed domain: cell envelope, active material, electronics, air,
and so on. Thus, at the pack level, different properties can be assigned to each element of the
pack if one of them is degraded or failing. The limit conditions of each battery element exposed
to a fluid are defined in terms of its conduction or convection, depending on the fluid, character-
ized by a temperature and a coefficient of convective exchange. The initial conditions (uniform if
the system is at equilibrium) are also defined in terms of temperature and current, given that the

238 Hybrid vehicles

same current profile, i(t), is applied to each mesh starting at time 0. An axisymmetric 2D thermal
model has been developed for a 2.3 Ah Li-ion LiFeP04/carbon cylindrical cell (Α123 Systems),
coupled at the mesh scale to the 0D electrothermal model described in 4.2.7. LB. At each time
step, the internal state (SOC, temperature) of each mesh is recalculated as a function of the input
current, SOC, and temperature of the previous step. The SOC, voltage, and heat flow are given at
the output. As the system cycles, a radial SOC and temperature gradient is established within the
elements as well as a longitudinal gradient, depending on the heat elimination properties at the
extremities of the element compared to the core. This model has been experimentally confirmed
by comparison with temperature measurements of the skin of the element and by measurements
of internal temperatures made by the Laboratory of the Reactivity and Chemistry of Solids and
the Université Technologique de Compiègne using this cell technology [Forgez et al, 2010].
Figure 4.40 shows the simulation of a continuous discharge at 2C, 30 °C, with cooling by mild
air convection (the heat exchange coefficient is fixed at 12 W/m2/K).

Figure 4.40

Axisymmetric 2D simulation of heat gradients in a 2.3 Ah LFP/C cell during
continuous discharge at 2C and 30 °C: temperature map and longitudinal tem-
perature profiles in the core and on the skin of the cell.
Source: [Prada et al, 2010c]

The skin temperature is relatively uniform along the cell, in agreement with measure-
ments taken using a heat camera; the ends of the cell, however, provide greater insulation
because of the air space they contain. The core-skin gradient remains limited in this case to
less than 1 degree. The influence of cooling is noticeable at rapid discharge at 6C, typically
corresponding to a power pulse in a hybrid vehicle. Based on Figure 4.41, the higher the
forced air convection (increase of the convection coefficient from 5 to 50 W/m2/K), the lower
the skin temperature and the higher the internal gradient, exceeding 10 degrees in this case.

Chapter 4 · On-board energy storage systems 239

Figure 4.41
Temperature change of the skin and core in a cell simulation using a 2D thermal
model coupled to an electrochemical model of a 2.3 Ah Li-ion LFP/C cell during
continuous discharge at 6C and 24 °C with air convection.
Source: [Prada et al, 2010c]

Given the difficulty of obtaining a temperature measurement of the core of a storage cell,
these simulations suggest that cooling strategies must rely on multidimensional models to
avoid under- or overestimating the risk of uncontrolled internal aging.

4.2.7.2 Modeling Supercapacitors

The behavior of supercapacitors is frequently modeled by electrical analogy. Aside from the
purely descriptive black-box approach, "grey-box" models, which attempt to represent the
physical phenomena involved, have also been used.

A. Electrical Model of an Ideal Supercapacitor

If we treat a supercapacitor as two capacitors and various resistors in series, the first represent-
ing the two electrodes, the second representing the resistance of the electrolyte and the internal
resistance of the electrodes, we obtain an equivalent electric circuit of the black box type:

where (4.33)
and (4.34)

240 Hybrid vehicles
However, the impedance diagram for the model of the ideal supercapacitor is not repre-

sentative of the diagram of an actual supercapacitor (Figure 4.4.2). In the Nyquist representa-
tion (the inverse of the imaginary part as a function of the real part of complex impedance),
we observe a bend in the capacitance line, especially at high frequencies, which reflects the
size distribution of pores inside the electrodes.

Figure 4.42
Impedance diagrams of (a) an ideal and (b) a real supercapacitor.
Source: [Lassègues, 2001]
B. Electrical Models of a Porous Electrode
Because pores have dimension, shape, and highly variable access paths, their surface is
only gradually accessible to electrolyte ions. The porous electrode is often modeled using
an equivalent electric circuit known as a "transmission line," consisting of a distribution of
RC loops reflecting the variation in resistance and capacitance as a function of pore depth
(Figure 4.43). The associated impedance diagram, in the Nyquist representation, reflects the
porous nature of the electrode with a straight line with a 45° slope at high frequencies.

Figure 4.43
Model of a porous electrode: equivalent circuit of the "transmission line" type
with four loops and the corresponding impedance diagram.