PATHS TO SUSTAINABLE ENERGY_2 potx

In that case, c outis related to the electrons molar flowrate Qt =c in it +bN cell F it where: c i = concentration of the different vanadium ions [mol/l] For a quasi steady state, where t

Energy Storage and Efficient Use of Energy

0 Understanding the Vanadium Redox Flow Batteries

Christian Blanc and Alfred Rufer

Laboratoire d’Electronique Industrielle, Ecole Polytechnique Federale de Lausanne

Switzerland

1 Introduction

Vanadium redox flow batteries (VRB) are large stationary electricity storage systems withmany potential applications in a deregulated and decentralized network Flow batteries (FB)store chemical energy and generate electricity by a redox reaction between vanadium ionsdissolved in the electrolytes FB are essentially comprised of two key elements (Fig 1): thecell stacks, where chemical energy is converted to electricity in a reversible process, and thetanks of electrolytes where energy is stored

Electrode Electrode

Tank Reservoir



 6 6

(b)Fig 1 (a) The schematics of the vanadium redox flow battery (b) View of the differentcomponents composing a VRB stack The surfaces in contact with the catholyte are coloured

in blue and in orange for the anolyte

The most significant feature of the FB is maybe the modularity of their power (kW) and energy(kWh) ratings which are independent of each other In fact, the power is defined by the sizeand number of cells whereas the energetic capacity is set by the amount of electrolyte stored

in the reservoirs Hence, FB can be optimized for either energy and/or power delivery.Over the past 30 years, several redox couples have been investigated (Bartolozzi, 1989): zincbromine, polysulfide bromide, cerium zinc, all vanadium, etc Among them, VRB has the bestchance to be widely adopted, thanks to its very competitive cost, its simplicity and because itcontains no toxic materials

18

In order to enhance the VRB performance, the system behaviour along with its interactionswith the different subsystems, typically between the stack and its auxiliaries (i.e electrolytecirculation and electrolyte state of charge), and the electrical system it is being connected to,have to be understood and appropriately modeled Obviously, modeling a VRB is a stronglymultidisciplinary task based on electrochemistry and fluid mechanics New control strategies,based on the knowledge of the VRB operating principles provided by the model, are proposed

to enhance the overall performance of the battery

2 Electrochemistry of the vanadium redox batteries

Batteries are devices that store chemical energy and generate electricity by areduction-oxidation (redox) reaction: i.e a transformation of matter by electronstransfer VRB differ from conventional batteries in two ways: 1) the reaction occursbetween two electrolytes, rather than between an electrolyte and an electrode, therefore

no electro-deposition or loss in electroactive substances takes place when the battery isrepeatedly cycled 2) The electrolytes are stored in external tanks and circulated through thestack (see Fig 1) The electrochemical reactions occur at the VRB core: the cells These cells

are always composed of a bipolar or end plate - carbon felt - membrane - carbon felt - bipolar or end

plates; they are then piled up to form a stack as illustrated in Fig 1.

In the VRB, two simultaneous reactions occur on both sides of the membrane as illustrated inFig 2 During the discharge, electrons are removed from the anolyte and transferred throughthe external circuit to the catholyte The flow of electrons is reversed during the charge, thereduction is now taking place in the anolyte and the oxidation in the catholyte



 6 6

 6

E

E OXIDATION

REDUCTION 6

E

E REDUCTION

Fig 2 VRB redox reaction during the charge and discharge

The VRB exploits the ability of vanadium to exist in 4 different oxidation states; the vanadium

ions V4+and V5+are in fact vanadium oxide ions (respectively VO2+and VO+2) Thus, theVRB chemical equations become (Sum & Skyllas-Kazacos, 1985; Sum et al., 1985):

2.1 Equilibrium potential

The stack voltage U stack depends on the equilibrium voltage U eqand on the internal losses

U loss; the equilibrium conditions are met when no current is flowing through the stack In

that case, there is no internal loss and U stack equals U eq; otherwise, the internal losses modify

U stack The internal losses1U loss will be discussed in section 3.3 Hence U stackis given by:

U stack(t) =U eq(t ) − U loss(t) [V] (2)

The equilibrium voltage U eq corresponds to the sum of the equilibrium potential E of the

individual cells composing the stack This potential is given by the Nernst equation anddepends on the vanadium species concentrations and on the protons concentrations (Blanc,2009):

where R is the gas constant, T the temperature, F the Faraday constant, c ithe concentration of

the species i and Ethe formal potential If we assume that the product/ratio of the activity

coefficients is equal to 1, the formal potential E, an experimental value often not available,

can be replaced by the standard potential E

2.1.1 Standard potential from the thermodynamics

The standard potential E is an ideal state where the battery is at standard conditions:vanadium species at a concentration of 1 M, all activity coefficients γ i equal to one and

a temperature of 25◦C The standard potential is an important parameter in the Nernstequation because it expresses the reaction potential at standard conditions; the second term

in the Nernst equation is an expression of the deviation from these standard conditions.Together, they determine the equilibrium cell voltage under any conditions

The standard potential E can be found from thermodynamical principles, namely theGibbs free enthalpy ΔG and the conservation of energy, and empirical parameters found

in electrochemical tables We introduce here the standard Gibbs free enthalpy of reaction

ΔGwhich represents the change of free energy that accompanies the formation of 1 M of asubstance from its component elements at their standard states: 25◦C , 100 kPa and 1 M (Vanherle, 2002):

where the standard reaction enthalpyΔH

r is the difference of molar formation enthalpiesbetween the productsΔH

f ,productand the reagentsΔH

and the standard reaction entropyΔS

r is the difference of molar formation entropies between

the products Sf ,product and the reagents Sf ,reagent:

Then, when we introduce the thermodynamical data from Tab 1 into (5), the standard reactionenthalpyΔH

r of the VRB reaction (1) becomes:

and similarly, the standard reaction entropyΔS

r is obtained when these thermodynamicaldata are introduced into (6):

Therefore, we obtain the standard potential Ewhen we introduceΔG(4) with the values

of the standard reaction enthalpy (7) and entropy (8) into the reformulated (9):

The characteristic curve of the equilibrium potential E is illustrated in Fig 3 for a single cell

as a function of the state of charge SoC We can also observe the relation between E, SoC and

the protons and vanadium concentrations

Salt Charge Discharge Electrolyte

+ [mol/l]

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

5 10 15

State of charge [−]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.9

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Cell voltage

Experimental Analytical

(b)Fig 3 (a) Top: Cell voltage versus the state of charge at 25◦ C Bottom: Protons H+andvanadium concentrations (b) Comparison between the Nernst equation (3) and the

experimental data published in (Heintz & Illenberger, 1998) The red bars represent thedifference between the analytical and experimental data

3 Electrochemical model

The main electrochemical relations governing the equilibrium voltage where introduced in theprevious section In order to have an electrochemical model of the VRB, it is now necessary todescribe how the vanadium concentrations vary during the battery operation

3.1 Concentration of vanadium ions

We see clearly from (1) that during the redox reactions, the vanadium ions are transformed

and that some protons H+are either produced or consumed Therefore, the ion concentrationsmust change in the electrolyte to reflect these transformations which depend on how thebattery is operated

For example, when the battery is charged, V2+ and VO+2 are produced and their

concentrations increase; and V3+ and VO2+ are consumed and thus their concentrationsdiminish This process is reversed when the battery is discharged Tab 2 summarizes thedirection of the change for each species

3.1.1 Electron exchange rate

Obviously, the concentration changes are proportional to the reaction rate; and from (1) wealso know that an electron is involved each time a redox reaction occurs Therefore, theconcentration changes are also proportional to the electrical current Thus, the pace of theconcentration variation is set by the electrical current flowing through the cell:

In the case of a stack composed of N cellcells, the electrons travel through the bipolar electrode

to the adjacent cell (Fig 4) Thus, for one electron flowing through the external electrical

circuit, N cell redox reactions have occurred Therefore, the total molar flowrate of electrons

%ND

%ND

OXIDATION REDUCTION

(a)

%LECTROLYTE 4ANK

# CELL (b)

Fig 4 (a) Illustration of the redox reactions required to produce a one electron flow in a 3elements stack during the discharge When the battery is charged, the flow and the reactionsare inverted (b) Illustration of the hydraulic circuit (half cell) where the concentrations areshown

2 By convention, the current is positive during the VRB discharge in order to have a positive power delivered by the battery.

3.1.2 Input, output and average concentrations of vanadium ions

We know now that the vanadium concentrations change within the cells when the battery isoperating Therefore, the concentrations are not uniformly distributed through the electrolytecircuit (Fig 4) Indeed, four concentrations are located in the VRB: the tank concentration

c tank , the concentration at the cell input c in , the concentration inside the cell c cell and the

concentration at the cell output c out

Usually, the size of the reservoir is large compared to the electrolyte flowrate; thus the change

in concentrations due to the flow of used electrolyte is so small that the tank concentrations are considered homogeneous And therefore, the input concentrations c incorrespond exactly

to c tank

The tank concentration c tank reflects the past history of the battery; indeed the change in c tank

is proportional to the quantity of vanadium that has been transformed in the stack: this value

corresponds to the quantity of electrons involves in the reaction Therefore, c tankis defined by

the initial ion concentrations c initial tank

i , the size of the reservoir V tankand the total molar flowrate

− 1 for V2+and V5+ions

The description of the output concentration c out is difficult because it depends on the

electrolyte flowrate Q, the length of the electrolyte circuit and on the current i that the

electrolyte encounters during the cell crossing Since the distribution of the vanadium ionsinside the cell is unknown, we consider that the model has no memory and reacts instantly to

a change in the operating conditions In that case, c outis related to the electrons molar flowrate

Q(t) =c in i(t) +bN cell

F

i(t)

where: c i = concentration of the different vanadium ions [mol/l]

For a quasi steady state, where the current and the flowrate are almost constant, the modelpredicts accurately the output concentrations Unfortunately, it is not able to predict thetransient behaviour when the system encounters extreme conditions such as the combination

of a low flowrate, few active species and sudden current change But when these conditionsare avoided, (17) offers a very good insight of the battery behaviour

We still have to establish the most important concentration: the concentration inside the cell

c cellthat is necessary to solve the Nernst equation (3) Because the ion concentrations are not

uniformly distributed inside the cell, we will make an approximation to determine c cellfrom

the mean value of c in and c out:

c cell i(t) =c in i(t) +c out i(t)

in both electrolytes (Blanc, 2009) The complete ionic equation, illustrated in Fig 5, is useful

to understand how the protons concentration c H+ changes and why the protons cross themembrane to balance the charge

(6/

(

E



6/  / (

6/3/ (3/3/ ( 3/C

6/  3/



(3/D 6/

63/

6

VOLTAGE

(3/B

Fig 5 Illustration of the full ionic equations of the VRB during the charge

Hence, the protons concentration in the catholyte depends on the electrolyte composition andvaries with the state of charge:

where c H+,dischargedis the protons concentration when the electrolyte is completely discharged

3.3 Internal losses

When a net current is flowing through the stack, the equilibrium conditions are not met

anymore and the stack voltage U stackis now given by the difference between the equilibrium

potential U eq and the internal losses U loss These losses are often called overpotentials andrepresent the energy needed to force the redox reaction to proceed at the required rate; a list

of the variables affecting this rate is given in Fig 6

The activationη actand the concentrationη concoverpotentials are electrode phenomena andare respectively associated with the energy required to initiate a charge transfer and caused

by concentration differences between the bulk solution and the electrode surface; in addition,the ohmic η ohm and ionicη ionic losses also alter the stack voltage The ohmic lossesη ohm

occur in the electrodes, the bipolar plates and the collector plates and the ionic lossesη ionic

occur in the electrolytes and the membranes But these overpotentials are seldom found in theliterature and often applicable only to peculiar conditions Therefore, an equivalent resistance

is introduced instead:

U loss(t) =R eq,charge/discharge i(t) [V] (21)

where R eq,charge is the equivalent charge resistance and R eq,discharge corresponds to thedischarge resistance; these values are found experimentally (Skyllas-Kazacos & Menictas,1997) and depends on the electrolyte, electrode materials and stack construction

Electrode Electrode

Tank Reservoir Anolyte

Tank Reservoir Catholyte



 6 6

Electrode variables

Material Surface area Geometry Surface condition

Mass transfer variables

Mode (diffusion, convection, )

Surface concentrations

Solution variables

Bulk concentration of electroactive species Concentration of other species Solvent

Fig 6 Schematic representation of VRB with a list of variables affecting the rate of the redoxreaction (Bard & Faulkner, 2001) Note that only one cell is represented on this figure

3.4 State of charge

The state of charge SoC indicates how much energy is stored in the battery; it varies from 0

(discharged state) to 1 (charged) and is defined by the following relation:

battery is operating The schematic representation of this model is shown in Fig 7

3.6 Efficiencies

Efficiencies are parameters used to assess the performance of storage system Basically,the definition of efficiency is simple, the energy efficiencyη energyis the ratio of the energyfurnished by the battery during the discharge to the energy supplied during the charge:

η energy= P VRB,discharge(t)dt

Nernst potential

Internal losses Tank

concentrations

Vanadium

concentrations

Protons concentration

Σ

+ +/- Ustack

State of charge SoC

E CH+

Istack

Istack

Fig 7 Schematic representation of the electrochemical model

R discharge 0.039Ω initial concentration of vanadium species 1 M

electrolyte flowrate Q 2 l/s

Table 3 The characteristics of the VRB stack

But difficulties quickly arise when different technologies or products are compared becausethe operating mode has a significant impact on the performance: a quick charge producesmore losses than a gentle one The coulombic efficiencyη coulombicis a measure of the ratio of

the charge withdrawn from the system Q discharge during the discharge to the charge Q charge

supplied during the charge:

η coulombic=Q discharge

Q charge = i discharge(t)dt

i charge(t) dt [−] (24)The voltage efficiencyη voltageis defined for a charge and discharge cycle at constant current

It is a measure of the ohmic and polarisation losses during the cycling The voltage efficiency

is the ratio of the integral of the stack voltage U stack,dischargeduring the discharge to that of the

voltage U stack,chargeduring the charge:

3.7 Charge and discharge cycles at constant current

The electrochemical model of the vanadium redox battery is compared in this section toexperimental data To determine the performance, a VRB composed of a 19 elements stack andtwo tanks filled with 83 l of electrolytes will be used The total vanadium concentration in eachelectrolyte is 2 M The characteristics of the stack are summarized in Tab 3 and correspond

to an experimental stack built by M Skyllas-Kazacos and co-workers (Skyllas-Kazacos &Menictas, 1997) The electrochemical model is used to assess the stack efficiencies during aseries of charge and discharge cycles at constant currents

Current η energy η voltage η coulombic Current η energy η voltage η coulombic

(Skyllas-Kazacos & Menictas, 1997)

At the beginning of the cycle, the battery state of charge SoC is 2.5% (discharged); the battery

is charged at constant current until a SoC of 97.5% and then discharged until it reached its initial SoC The resulting stack voltages U stack and power P stack are illustrated in Fig 8 andthe efficiencies are summarized in Tab 4 along with experimental data We observe quicklythat the efficiencies decrease as the current increases

15 20 25 30 35

Solution Density Viscosity Vanadium / sulphuric acid

the experimental and simulated energy efficienciesη energyare almost the same, the differencebeing less than 1% In the worst case, cycle 1, the difference is around 8.3%

4 Electrolyte properties

The electrolyte properties are important parameters in the mechanical model; the density

indicates its inertia, or resistance to an accelerating force, and the viscosity describes its fluidity,

it may be thought of as internal friction between the molecules They are both related to theattraction forces between the particles; thus they depend on the electrolyte composition.The VRB electrolytes are composed of vanadium ions dissolved in sulphuric acid; we haveseen previously that their composition changes as the battery is operating (see Fig 3).Therefore, the electrolyte properties must change accordingly to the composition; but forsimplicity reasons, these properties are maintained constant in this work Tab 5 gives thedensity and the viscosity for some vanadium solutions

5 Fluid mechanics applied to the vanadium redox flow batteries

We introduce in this section the mechanical model that determines the power P pumprequired

to flow the electrolytes from the tanks through the stack and back in the tanks (see Fig 1).This model is composed of an analytical part that models the pipes, bends, valves and tanksand a numerical part that describes the more complex stack hydraulic circuit

5.1 Hydraulic circuit model (without the stack)

The analytical hydraulic model describes the pressure dropΔp pipe in the pipes, the valveand the tank; it is based on the extended Bernoulli’s equation that relatesΔp pipeto the fluid

velocity V s , the height z, the head loss h f due to the friction and the minor losses h m:

Δp pipe = − γ



ΔV2

s 2g +Δz+h f+h m



whereγ is the specific weight and g the gravitational acceleration.

The head losses are obtained by dividing the hydraulic circuit into smaller sections where h f ,i

or h m,iare easily determined with the Darcy-Weisbach equation (Munson et al., 1998):

h f ,i=f i L i

D i

V2

s,i 2g, h m,i=k L,i V

2

s,i

geometry Loss coefficient k L,i

from a reservoir into a pipe 0.04 - 0.9

Table 6 Loss coefficients (Munson et al., 1998; Candel, 2001)

where f i is the friction factor, k L,i the loss coefficient given in Tab 6, L i and D iare the lengthand diameter of the conduit

When the flow is laminar, the friction factor f iis derived from the Poiseuille law (28) and for

a turbulent flow, it is obtained from the Colebrook equation (29) (Candel, 2001):

1

whereρ is the density, μ the dynamic viscosity and ν the kinematic viscosity.

5.2 Stack hydraulic model

The stack geometry is too complex to be analytically described (Fig 9), therefore the stackhydraulic model can only be numerically obtained with a finite element method (FEM)

)NPUT OLD

/UTPUT OLD )NPUT

OLD

/UTPUT

OLD

#HANNELS )NPUT

/UTPUT )NPUT

/UTPUT

#ATHOLYT E

!NOLYT E

Fig 9 Hydraulic circuit of a 2 cells stack Note that the frame is not represented and that thecolored segments represented the electrolytes (liquid)

It was assumed that the flow stays laminar in the stack; although the flow might be turbulent

in the manifold at high velocity In this example, the flow stays laminar in the distributionchannels where the major part of the pressure drop Δp stack occurs; therefore, the pressuredrop in the stackΔp stackis proportional to the flowrate:

R is the hydraulic resistance obtained from FEM simulations.

5.3 Mechanical model

Finally, the sum of the pressure drop in the pipesΔp pipeand the pressure drop in the stack

Δp stackdetermines the hydraulic circuit pressure dropΔp system:

The pump power P pump, a determinant variable that influences the battery performance is

related the head rise h psupplied by the pump, to the fluid densityγ and to the flowrate Q;

we can also relate it to the pressure dropΔp (Wilkes, 2005):

The efficiency of the pump η pump is affected by the hydraulic losses in the pump, themechanical losses in the bearings and seals and the volumetric losses due to leakages insidethe pump Althoughη pumpis not constant in reality, it is assume in this work Therefore, the

effective power required by the pump P mechis given by:

P mech=P η pump

Thus, the relations introduced in this section can be combined to form the mechanical model

of the VRB as illustrated in Fig 10 Remember that the VRB needs two pumps to operate

μ

Analytical model

of the pipes, bends, valve and tank Q

Pressure drop & power

Stack hydraulic resistance

~

Δppipes

Fig 10 Flowchart of the VRB mechanical model

6 Multiphysics model and energetic considerations

The combination of the electrochemical model and the mechanical model leads to themultiphysics VRB system model The functions that determine the vanadium concentrations

in the tank c tank and the state of charge SoC have been separated from the electrochemical model in order to be incorporated into a new model named reservoir and electrolyte model A

system control has also been added to supervise the battery operation; this system controls

the flowrate Q and the stack current I stack This multiphysics system model, illustrated inFig 11, is a powerful means to understand the behaviour of the VRB, identify and quantifythe sources of losses in this storage system; thus this multiphysics model is a good means toenhance the overall VRB efficiency

6.1 Power flow

In order to optimize the performance of the VRB, it is important to understand the powerflows within the VRB storage system The power converters represented in Fig 12 are

necessary to adapt the stack voltage U stack to the power source U grid or to the load voltage

U load and to supply the mechanical power required to operate the pumps Since power

Electrochemical stack model

U stack I

C tank

T

Q

Mechanical model ρ

μ

P mech Reservoir &

electrolyte model

SoC

T

VRB control system

I ref / P ref

U stack SoC

E stack

U loss

P stack

P loss Pmech

P stack

stack

I stack

Fig 11 Structured diagram of the multiphysics VRB system model

converters are very efficient, with efficiencies around 98 to 99% (Wensong & Lai, 2008; Burger

& Kranzer, 2009), they are considered, for simplicity, lossless in this work Therefore, they are

two sources of losses: the internal losses that are already included in the stack voltage U stack (2), and the mechanical losses P mech Hence, P mechis provided from the external power sourceduring the charge and from the stack during the discharge By convention, the battery power

P VRB and the stack power P stack are positive during the discharge and negative during the

charge; P mech is always positive Thus, P VRBis given by:

In the rest of this section, we will discuss the battery performance under different operating

strategy with a strong focus on the battery power P VRB , the stack power P stack ant the

mechanical power P mech Intuitively, we feel that there should be an optimal control strategythat maximizes the battery performance In these circumstances, the power delivered to thebattery at any operating point is minimized during the charge and the power supplied by thebattery is maximized during the discharge

7 Operation at maximal and minimal flowrates

First, we will discuss the battery operation at maximal and minimal flowrates We must keep

in mind that an efficient control strategy must maximize the power exchanged with the battery

initial concentration of vanadium species 1 M

Table 7 the parameters of the simulation

while minimizing the losses; there is no point to have a battery that consumes more powerthan necessary To illustrate this discussion, we will use a 2.5 kW, 6 kWh VRB in the rest ofthis chapter; its characteristics are summarized in Tab 7

7.1 Maximal flowrate

The simplest control strategy operates the battery at a constant flowrate set to provideenough electroactive species to sustain the chemical reaction under any operating conditions

Therefore, this flowrate Q max is determined by the worst operating conditions: low state of

charge SoC during the discharge and high SoC during the charge at high current in both cases For the battery described in Tab 7, Q maxis around 1.97 l/s: in that case, the mechanical power

P mechis 1720 W In order to assess the performance, an instantaneous battery efficiencyη battery

is defined as follow:

η battery= | P stack |

Clearly, the battery performance is poor as it can be observed in Fig 14 whereη battery is

illustrated as a function of the stack current I stack and the state of charge SoC Indeed,

the battery often consumes more power than necessary; therefore, constantly operating the

battery at Q maxis not a wise strategy Nevertheless, it is possible to improve this efficiency bylimiting the operating range of the battery (smaller current and/or narrower state of charge);

thus the flowrate Q max and the mechanical power P mechare reduced But this also reduces thepower rating and/or the energetic capacity while it increases the cost

7.2 Minimal flowrate

The low efficiency at constant flowrate Q max is due to the large mechanical losses P mech;

therefore, a second control strategy is proposed to minimize P mech In that case, the battery

is operating at a minimal flowrate Q min that is constantly adapted to the actual operating

conditions (SoC and I stack) in order to supply just enough electroactive materials to fuel the

electrochemical reactions Since the vanadium concentrations c V change proportionally to

I stack , there are critical operating points where c V is close to its boundary In some cases,the variations of vanadium concentrations tend toward the limit values (Fig 13) In these

critical regions, the electrolyte flowrate Q must be larger to palliate the scarcity of electroactive

vanadium ions

Hence, the minimal flowrate Q min depends on the required amount of electroactive species,

and in consequence on I stack , and on the input vanadium concentrations c inthat are either

c max

c min

Operating range

Limiting operating conditions

Fig 13 Operating range and limiting operating conditions The arrows represent the

direction of the vanadium concentrations change as a function of the battery operating mode.The critical operating regions are highlighted in red; they represent the regions where the

vanadium concentration c vanadium tends to its limiting concentrations (c max or c min)

being depleted (↓) or augmented (↑ ) Q mincan be derived from (17):

Q min,↓(t) = bN cell i(t)

F(c out,min − c in,↓(t)) [l/s] (37)

Q min,↑(t) = bN cell i(t)

F(c out,max − c in,↑(t)) [l/s] (38)

where c out,min and c out,max are constant minimal and maximal output concentrations The

limiting species depends on the operating mode (charge or discharge); thus Q minis given bythe maximal value of (37) and (38):

Q min,↓(t), Q min,↑(t) [l/s] (39)

Q min is illustrated in Fig 14 for a wide spectrum of operating points; clearly, Q minis larger in

the critical regions that were highlighted in Fig 13 Moreover, Q minis, in comparison, verysmall in the other operating regions; therefore, there must be a large benefit to operate the

battery at Q min

−100

−50 0 50 100

0 0.5

0 0.5 1 0.5 1 1.5 2

charge SoC and current I (b) Minimal flowrate Q min as a function of the stack current I stack and the state of charge SoC.

But a change in the flowrate Q also modifies the vanadium concentrations c cellswithin the

cells according to (18), and in consequence the stack voltage U stack and power P stackaccording

to (2) and (3) This phenomenon is illustrated in Fig 15 where the equilibrium voltage E

at Q max and Q min is shown: an increase of the flowrate has always a beneficial effect on E Furthermore, the equivalent state of charge SoC eq which represents the SoC of the electrolyte within the cells is also illustrated as a function of Q Clearly, SoC eqtends toward the battery

variation of U stack and P stack is expected between the operations at Q min and Q maxas it can be

observed in Fig 16 From the strict point of view of P stack, it is more interesting to operate the

battery at Q max; indeed, more power is delivered during the discharge and less is consumedduring the charge But it will be shown in the next sections that the mechanical power greatly

deteriorates the performance and that the energy efficiency at Q maxis unacceptable

0.8 1 1.2 1.4 1.6 1.8

0 0.02 0.04 0.06 0.08 0.1 0

0.2 0.4 0.6 Discharge, input concentration cin: 1 mol/l

flowrate Q [l/s]

0 0.02 0.04 0.06 0.08 0.1 0.4

0.6 0.8 1 Charge, input concentration cin: 1 mol/l

species

−100

−50 0

50 1000

0.5 1

−400

−200 0 200 400

Current [A]

|Pstack,Qmax

|−|Pstack,Qmin

8 Optimal operating point at constant current

In the previous sections, the advantages and disadvantages of operating the battery at either

Q max and Q min were discussed At Q max , the stack power P stack has the highest possible

value but the mechanical power P mech is also very large and consequently deteriorates the

performance At Q min , P mech is reduced to the minimum, but P stack is negatively affected

Therefore, it should exist an optimal flowrate Q opt somewhere between Q min and Q maxthat

increases P stack while maintaining P mechat a small value

8.1 Optimal flowrate during the discharge

In this section, the battery is controlled by the reference current I stack,re f; therefore there is

only one control variable: the flowrate Q Indeed, the stack power P stack depends on I stack , Q and the state of charge SoC whereas the mechanical power depends on Q and the electrolyte

properties: the densityρ and the viscosity μ that are maintained constant in this work During

the discharge, the optimal operating point is found when the flowrate Q optmaximizes the

power delivered by the stack P stack while minimizing the mechanical power P mech When

these conditions are met together, the power delivered by the battery P VRBis optimized:

In Fig 17, P VRB is represented during the discharge as a function of Q at different states

of charge for a current of 100 A Clearly, an optimal flowrate Q opt exists between Q min and

Q max that maximizes P VRB The shape of the curves can be generalized to other discharge

currents I stack > 0; although in some cases where I stack is low, P VRBmight become negative at

inappropriately high flowrate Q.

0 500 1000 1500 2000 2500

Fig 17 Optimal flowrate Q opt as a function of the flowrate Q and the state of charge SoC Note that when SoC is low, Q opt is equal to the minimal flowrate Q, and the discharge

current is equal to 100 A

8.2 Optimal flowrate during the charge

At constant current I stack,re f , the quantity of electrons e − stored in the electrolyte does not

depend on the stack power P stack but solely on the stack current I stack; therefore, there is no

reason to have a high P stack Hence, the optimal flowrate Q optduring the charge is found

when the sum of P stack and P mechis simultaneously minimal This condition is expressed bythe following relation3:

other charge currents I stack <0

2500 3000 3500 4000 4500

SoC = 0.5 SoC = 0.7 SoC = 0.9 SoC = 0.95 SoC = 0.955 SoC = 0.96 SoC = 0.965 SoC = 0.97 SoC = 0.975 Minimal Power

Fig 18 Optimal flowrate Q opt as a function of the flowrate Q and the state of charge SoC Note that when SoC is high, Q opt is equal to the minimal flowrate Q, and that the charge current I stackis equal to -100 A

8.3 Charge and discharge cycles

It is always difficult to assess the performance of a battery because it often depends on theoperating conditions In this section, a series of charge and discharge at constant current is

performed at minimal flowrate Q min , at maximal flowrate Q max and at optimal flowrate Q opt

in order to assess the performance of this new control strategy

The voltage η voltage and energy η energy efficiencies are summarized in Tab 8 and 9; thecoulombic efficiencyη coulombicis in all cases equal to 100% because the model does not takeinto account any side reactions such as oxygen or hydrogen evolution nor any cross mixing ofthe electrolyte

Bothη voltageandη energydecrease when the current increase; this is mainly due to the internal

losses U losses that are proportional to the current I stack , although the flowrates Q min and

Q optincreases to supply enough electroactive species The highest voltage efficiencies occur

3 A close look at this relation reveals that it is the same as (40), but (41) is more intuitive for the charge.

Current η voltage,Qmax η voltage,Qmin η voltage,Qopt

Table 8 Stack voltage efficiencyη voltage at constant maximal flowrate Q max, at minimal

flowrate Q min and at optimal flowrate Q opt

Current Time η energy,Qmax η energy,Qmin η energy,Qopt

Table 9 Overall VRB energy efficienciesη energy at constant maximal flowrate Q max, at

minimal flowrate Q min and at optimal flowrate Q opt

at Q max because of its positive effect on the stack voltage U stack highlighted in section 7.2;

consequently, the worst voltage efficiencies occur at Q min Moreover, the voltage efficiencies

at Q opt are very close to the maximal efficiencies obtained at Q max In fact, the stack voltages

U stack,Qmax and U stack,Qoptare very close as it can be observed in Fig 19

Obviously, operating the battery at Q maxis a problematic strategy asη energy,Qmaxis very small

or even negative: at small currents, the battery does not deliver any power to the load but

consumes more power to operate the pumps than the stack is furnishing When P mech is

minimized, the energy efficiencies already become interesting at Q min, but they are increased

by a further 10% when the battery is operating at Q opt

In order to compare the model with experimental data, the stack characteristics were defined

to match the stack presented in section 3.7 The experimental results of M Skyllas-Kazacosand al are summarized in Tab 4 (Skyllas-Kazacos & Menictas, 1997); note that they donot take into account the mechanical power required to operate the pumps and that the

flowrate was constant (2 l/s which correspond to Q max) The losses in coulombic efficiency

η coulombiccan be caused by side reactions or cross mixing of electrolyte through the membranewhich are not taken into account in the model; butη coulombicimproves as the battery becomesconditioned In that case, the energy efficiencyη energy,Qoptat optimal flowrate is very close tothe maximal electrochemical energy efficiency Finally, a very good concordance is observed

between the voltage efficiencies at Q maxand the experimental results

9 Optimal operating point at constant power

In practice, the battery must often deliver a certain amount of power to the load: the battery

is controlled by a reference power P re f In that case, a second control variable is available

in supplement of the flowrate Q: the stack current I stack The optimal operating point is

the couple Q opt and I opt that maximizes the amount of charge that are stored within theelectrolyte during the charge and minimizes the amount of charge that are consumed during

the discharge These conditions can be related to I stack:

during the charge: max(| I stack |) [A]

Again, an optimal operating point exists in between the maximal Q max and minimal Q min

flowrates as it can be observed in Fig 20 where operating points are represented for different

battery power P VRB during the discharge at a SoC equal to 0.5 At the optimal flowrate Q opt,

the battery delivers the same power P VRBbut consumes less active vanadium ions; therefore,

the battery will operate longer and deliver more power Q opt increases with P VRB until itreaches a plateau due to the transition between the laminar and the turbulent regime

Battery power PVRB SoC = 0.5

current Istack [A]

Fig 20 Battery power P VRB as a function of the discharge current I stackand the electrolyte

flowrate Q at a state of charge SoC equal to 0.5 The optimal operating points occurs when the current I stack is minimal for a given battery power P VRB

In fact, I stackincreases above the optimal flowrate to compensate the higher mechanical loss:

the stack must deliver more power Below Q opt , I stackincreases this time to compensate the

lower stack voltage U stackdue to the lower concentrations of active species The shape of the

curves can be generalized for other states of charge SoC.

The optimal operating points during the charge are illustrated in Fig 21 where the battery

power P VRB is shown as a function of the current I stack and the flowrate Q at a state of charge

of 0.5 The optimal operating point maximizes the current| I stack |delivered to the stack in

order to store the maximum amount of electroactive species at a given power P VRB,re f; again,

the optimal flowrate Q opt increases with the battery power P VRBuntil it reaches the plateaudue to the flow regime transition

Fig 21 Battery power P VRB as a function of the charge current I stackand the electrolyte

flowrate Q at a state of charge SoC equal to 0.5 The optimal operating points occurs when

the current| I stack | is maximal for a given battery power P VRB

Interestingly, we observe in Fig 21 that the stack current I stack changes its sign at high

flowrate Q; in these unacceptable conditions, the stack is discharged while the battery is being

charged During the charge, the stack current| I stack |decreases above the optimal flowrate

Q opt to compensate the higher mechanical loss P mech; in consequence, less power is available

to charge the stack (see (42)) Below the optimal flowrate Q opt, the stack current| I stack |also

decreases because the stack voltage U stack increases due the change in electroactive species

concentrations within the cells c cell ; note that the mechanical power P mechis also reduced

below Q opt Furthermore, the shape of the curves in Fig 21 might be generalized to other

states of charge SoC.

9.1 Charge and discharge cycles

A new series of charge and discharge cycles at constant power was performed to determine

the energy efficiencies at minimal flowrate Q min and at the optimal operating point: I optand

Q opt This optimal point is constantly determined as a function of the actual conditions Theenergy efficiencies are given in Tab 10 The energy efficiency at optimal flowrateη energy,Qoptisincreased by 10% at maximal power when compared to battery operations at minimal flowrate

Q min

10 Epilogue

Today, the electricity industries are facing new challenges as the market is being liberalizedand deregulated in many countries Unquestionably, electricity storage will play, in thenear future, a major role in the fast developing distributed generations network as it has

Power η energy,Qmin η energy,Qopt

Table 10 Overall VRB energy efficienciesη energyfor a charge and discharge cycle at constant

power at either optimal flowrate Q opt and minimal flowrate Q min

many advantages to offer: management of the supply and demand of electricity, powerquality, integration of renewable sources, improvement of the level of use of the transportand distribution network, etc Over the years, many storage technologies have beeninvestigated and developed, some have reached the demonstrator level and only a fewhave become commercially available The pumped hydro facilities have been successfullystoring electricity for more than a century; but today, appropriate locations are seldom found.Electrochemical storage is also an effective means to accumulate electrical energy; among theemerging technologies, the flow batteries are excellent candidates for large stationary storageapplications where the vanadium redox flow battery (VRB) distinguishes itself thanks to itscompetitive cost and simplicity

But a successful electricity storage technology must combine at least three characteristics tohave a chance to be widely accepted by the electrical industry: low cost, high reliability andgood efficiency A lot of works have already been done to improve the electrochemistry of theVRB and to reduce its overall manufacturing cost With the multiphysics model proposed inthis chapter, we are able to address primarily the battery performance and indirectly its cost;indeed, a good efficiency enhances the profitability and consequently reduces the operatingcost

This ambitious model encompasses the domains of electricity, electrochemistry and fluidmechanics, it describes the principles and relations that govern the behaviour of the VRBunder any set of operating conditions Furthermore, this multiphysics model is a powerfulmeans to identify and quantify the sources of losses within the VRB storage system; indeed,

we are now able to understand how the VRB operates and to propose strategies of control andoperation for a greater effectiveness of the overall storage system

Another important feature of this multiphysics model is to facilitate the integration of the VRBinto the electrical networks Indeed, power converters, whose properties and characteristicsare known and efficient, are required in practice to interface the VRB with the network;the overall performance might improve if their control strategy takes into account the VRBcharacteristics

Burger, B & Kranzer, D (2009) Extreme high efficiency pvpower converters, EPE 2009

-Barcelona

Candel, S (2001) Mcanique des Fluides.

Heintz, A & Illenberger, C (1998) Thermodynamics of vanadium redox flow batteries

-electrochemical and calorimetric investigations, Ber Bunsenges Phys Chem 102 Kausar, N (2002) Studies of V(IV) and V(V) species in vanadium cell electrolyte, PhD thesis,

UNSW, Australia

Mousa, A (2003) Chemical and electrochemical studies of V(III) and V(II) solutions in sulfuric

acid solution for vanadium battery applications, PhD thesis, UNSW, Australia Munson, B., Young, D & Okiishi, T (1998) Fundamentals of Fluid Mechanics, third edn.

Oriji, G., Katayama, Y & Miura, T (2004) Investitgation on V(IV)/V(V) species in a vanadium

redox flow battery, Electrochimica Acta 49.

Skyllas-Kazacos, M & Menictas, C (1997) The vanadium redox battery for emergency

back-up applications, Intelec 97

Sum, E., Rychcik, M & Skyllas-Kazacos, M (1985) Investigation of the V(V)/V(VI) system

for use in the positive half-cell of a redox battery, Journal of Power Sources 16.

Sum, E & Skyllas-Kazacos, M (1985) A study of the V(II)/V(III) redox couple for redox flow

cell applications, Journal of Power Sources 15.

Van herle, J (2002) Electrochemical Technology, Fuel Cells and Batteries, postgrade course.

Wen, Y., Zhang, H., Qian, P., Zhao, P., Zhou, H & Yi, B (2006) Investigation on the electrode

process of concentrated V(IV)/V(V) species in a vanadium redox flow battery, Acta

Physico-Chimica Sinica 22.

Wensong, Y & Lai, J.-S (2008) Ultra high efficiency bidirectional dc-dc converter with

multi-frequency pulse width modulation, IEEE Applied Power Electronics Conference

and Exposition, APEC 2008

Wilkes, J (2005) Fluid mechanics for chemical engineers.

Desing of Multiphase Boost Converter for Hybrid Fuel Cell/Battery Power Sources

Sun, wind and oceans are all being harnessed to provide stable and reliable energy That energy is converted for immediate use or for storage in supercapacitors, chemical energy sources or as a derived chemicals (Hydrogen is produced, for instance)

Next link in the alternative energy chain is efficient use New supercapacitors are being developed and there are many different battery types already available on the market, each with its own unique application that optimizes efficiency of chemical conversion and number of charge/discharge cycles with minimum of capacity loss

Fuel cells are being used to efficiently reclaim energy stored in Hydrogen The process has been well known for decades and is being used in power generation industry in high power systems As the technology advanced, lower power applications were found – chemical industry was a big benefactor: most of the exhaust gasses could be reclaimed and have Hydrogen extracted in a simple, cost effective manner, ensuring a free energy supply once initial investment in fuel cells and regenerators has been made

Development of new materials helped further reduce costs and increase efficiency, and even low power fuel cells are now widely available Even though there are still many new and exciting ongoing developments, the technology is now considered mature and ready for prime time Fuel cells have a good history in many applications (chemical industry, power generation, transportation) and is considered a serious contender in many other industries

In some of these industries fuel cells will gain faster acceptance than in others Material handling industry is among those where benefits of fuel cells can be easily documented and increased cost of initial implementation justified A fuel cell based system that replaces standard forklift battery pack has many advantages, such as: fast refueling, longer run time between refueling, longer life of the energy source and low maintenance requirements

In a typical electric vehicle fuel cells are augmented by an energy storage element, such as a supercapacitor, flywheel or battery Such hybrid system makes some of the fuel cell deficiencies (high output impedance, for example) transparent to the final user The typical systems used in industrial vehicles use battery as the energy storage component

A critical part of such fuel cell system is the load regulator Its main role is to enable controlled current draw from the fuel cell It also needs to maintain the auxiliary batteries in

a fully charged state and to regulate load current

This thesis illustrates work on overcoming major challenges of fuel cell load regulator design and offers an illustration in the form of a practical realization of a 5kW unit with application in industrial electric vehicles

2 Fuel cell systems

A fuel cell is an electrochemical power source that converts chemical fuel into electrical energy The electricity is generated via reactions between the fuel and an oxidant (so called reactants) in the presence of an electrolyte The reactants flow into the cell, and the reaction products flow out of it, while the electrolyte remains within it The electrolyte is a substance specifically designed so ions can pass through it, but the electrons cannot

Unlike conventional electrochemical batteries, fuel cells consume reactant from an external source, and it must be replenished, as long as the reactant is available the power can be generated, there are no other restrictions on the fuel cell “capacity” By contrast, batteries store electrical energy chemically and have limited capacity.Hydrogen based fuel cells are the most common They use Hydrogen as the fuel and Oxygen as the oxidant Oxygen is most commonly used from air Many other combinations of fuels and oxidants are possible, but they are not widely utilized

2.1 Principle of fuel cell operation

The core of a fuel cell consists of a membrane electrode assembly, which is placed between two flow-field plates The assembly consists of two electrodes, the anode and cathode, separated by

a Proton Exchange Membrane (PEM) The block diagram of a fuel cell is shown in Figure 1

Fig 1 Fuel cell block diagram

The two electrodes are coated with thin layer of Platinum that acts as a catalyst At the anode, the catalyst oxidizes the fuel (Hydrogen), turning it into a positively charged ion and

a negatively charged electron The membrane (PEM) is designed so that ions can pass

through it, but the electrons cannot The freed electrons travel through a wire creating the electrical current The ions travel through the electrolyte to the cathode Once reaching the cathode, the ions are reunited with the electrons and the two react with a third chemical, usually oxygen, to create water and heat

A typical fuel cell produces a voltage of 0.6 - 0.7V at full rated load Voltage decreases as current increases, due to several factors:

• Activation loss (activation polarization)

• Ohmic Polarization (voltage drop due to resistance of the cell components and interconnects)

• Gas transport loss (depletion of reactants at catalyst sites under high loads, causing rapid loss of voltage)

A typical fuel cell load curve is shown in Figure 2

Fig 2 A typical fuel cell load curve

To deliver the desired amount of energy, the fuel cells can be combined in series and parallel circuits Such a design is called a fuel cell stack

A few different fuel stacks are shown in Figure 3

Fig 3 Examples of fuel cell stacks

2.2 Fuel cell systems

As discussed in the Introduction, the thesis will concentrate on fuel cell applications for industrial off road vehicles Electric forklifts (Figure 4) are especially interesting due to the problems with existing battery packs

Fig 4 Electric forklift

A fuel cell based system that replaces standard forklift battery pack has many advantages, such as: fast refueling, longer run time between refueling, longer life of the energy source and low maintenance requirements

In a typical electric vehicle fuel cells are augmented by an energy storage element, such as supercapacitor, flywheel or battery Such hybrid system makes some of the fuel cell deficiencies (the most important one being high output impedance) transparent to the final user

Hybrid systems with a small lead acid battery have many advantages in material handling applications The most significant two are: (1) battery provides peak current handling capabilities and (2) it ensures reserve power to drive the vehicle to refueling station should hydrogen tank be completely depleted

Block diagram of a hybrid fuel cell system using auxiliary Sealed Lead-Acid (SLA) battery is shown in Figure 5

LOAD

F/C CONTROL

DC-DC CONVERTER

Fuel cell is used as a main energy source, controlled by a dedicated electronics (F/C Control) that controls main aspects of fuel cell operation – Hydrogen flow and pressure,

monitors output voltage and current and sets operating parameters of a fuel cell regulator

The load regulator processes raw power from the fuel cell, converting it into levels suitable

for the load, while keeping auxiliary battery charged and providing adequate protections of the fuel cell, load and self-protection against overvoltage, overtemperature and overload

Auxiliary battery is a small (70Ah) Sealed lead-Acid battery with the main purpose to

provide peak power when demanded by the load Typical peak loads are during vehicle’s rapid acceleration and lifting heavy loads If the Hydrogen tank goes empty, the battery also provides backup power sufficient to drive the vehicle to the refueling station Finally, the

system’s load comprises forklift’s traction motor, hydraulic pumps, lift motors and various

communication and control electronics: new generations of forklifts bear very little resemblance to the noisy and slow vehicles of the past – typical rider vehicle (Class I or Class II) in a larger fleet has a sophisticated joystick controls, very informative displays, radio communication equipment, GPS and tracking devices, and the total power draw is not negligible

2.3 Specification requirements

There are two main factors influencing every design: electrical specifications and application based details Electrical specifications are straightforward and require little explanation For our particular design, a fuel cell regulator, electrical specifications are fairly simple:

• Maximum power: 5,5kW

• Input voltage range: 24-36V

• Output voltage range: 36-60V

• Maximum output current: 150A

Specification parameters related to this particular application add more clarity regarding expected performance of the final product The parameters are not always clearly defined by numbers and physical values – most common examples are “small size”, “low cost”, etc Regardless of their ambiguity or lack of definition, they are still valuable information that is specific to the application and affects the design process

In this case application specific requirements are summarized as:

• Continuously variable control with automatic crossover:

• Input current controlled in the range 0-220A

• Low input current ripple: <1% of output current, measured with 0-10kHz bandwidth (critical for longevity of the fuel cell)

• High efficiency: 94% min at 2kW and 96% above 2.5kW

• Protection against reverse current (which may cause temperature rise and hazardous pressure build up)

• Ability to sustain peak load currents of up to 800A for short period of time (1-5 seconds)

• Operating ambient temperature -30 to +60°C

• Low physical profile (load regulator needs to fit into a predefined space)

• Low cost

3 Multiphase boost converters

Boost converter belongs to the family of basic power conversion topologies (the other two being buck and buck-boos derivative) Boost converters are probably the most versatile

power converters today They cover power range from fraction of a Watt (for example raising a single cell battery voltage to a 3.3 or 5V logic levels in portable equipment) to tens

of kW (alternative energy sources and distributed power) Extremely popular and almost exclusively used in Power Factor Correction (PFC) applications, they are being manufactured in millions of units

Unlike buck converter, boost topology is somewhat more difficult to control, due to the Right Half Plane (RHP) Zero in the control transfer function RHP Zero sets practical limits

on the control loop bandwidth but

Another comparative disadvantage is no inherent short circuit protection: if the output terminals are shorted there is nothing (other than circuit parasitic) to limit or interrupt short circuit current

Over time, designers have learned how to deal with the two major drawbacks mentioned above and today there are very few restrictions for practical use of this topology

The boost converter is well understood and successfully used in the multitude of applications

It is typically used when output voltage needs to be higher than the input voltage

Introduction of multiphase topologies has expanded field of practicality for the converters

by offering many advantages that will be discussed below The simplest way of describing a multistage converter is to see it as consisting of several power stages (converter “phases”) with inputs and outputs connected in parallel and drive signals shifted to ensure uniform distribution over a switching period – this techniques is also known as “interleaving” and the term will be used throughout this work

Input inductance of the boost converter helps control current ripple and has positive effects

on reducing electromagnetic emissions However, the size of the inductor is proportional to the inductance and the square of the peak current and for high power applications its size is considerable

For high power converters operating from relatively low input voltages, inductor current can be limiting factor due to the fairly large size and lack of space or even availability of adequate core sizes

One way to reduce the inductor’s size would be running the converter at high frequency Unfortunately, for high power converters, practical considerations such as core’s eddy current losses, switching losses in the power switch and rectifier and electromagnetic emissions severely limit the maximum switching frequency

Output capacitor in the boost converter is subjected to large variations of the current through them Capacitors’ peak-to-peak current is equal to the sum of the input inductor peak current and load current Consequently, the RMS value of the capacitor current is high resulting in high stress, heating and reduced life and overall reliability of the unit

One way to deal with the problems is by designing multiphase, interleaved power stages In

a typical interleaved converter several power stages are connected in parallel and driven with signals shifted by 360°/(number of phases) Effective switching frequency is, thus, increased proportionally to the number of phases with several important benefits:

- For the same value of inductance (compared to an equivalent single-phase boost), current ripple is significantly reduced, helping reduce size of the inductor;

- For the same ripple current, individual inductors can have lower inductance, again reducing their size;

- Reduced ripple current helps relieve stress on the output filter capacitors and increased effective switching frequency makes capacitors running closer to their optimum (most

of the aluminum electrolytic capacitors have increased RMS current rating as frequency increases)

3.1 Single-phase boost converter

This is the standard boost converter Simplified schematic of the power train is shown in Figure 6

D1

+Vout

-Vout

Lin +Vin

Cout SW1

-Vin

Fig 6 Boost converter schematic

This is the basic and most commonly used variation, typical for low power converters as well as medium to high power PFC designs The reason for its popularity is obvious – simplicity with low parts count makes this an inexpensive and reliable solution Additionally, the topology has typically high conversion efficiency thanks to its simplicity and principle of operation: in normal operation, at any moment within a switching cycle current flows through only one semiconductor part (it alternates between the switch and the rectifier) This is can be seen in Figure 7 that shows main waveforms

Iin(pp)

Icout

I

ON OFF SW1

Fig 7 Boost converter input current and output capacitor waveforms

Basics of the boost converter operation are well known and easily accessible so they will be omitted from this work

Specific requirements of the application which can be described in simplest terms as “low voltage- high current”, dictate that special attention is paid to the current loading of components As seen in Figure 6, there are only four components employed by the basic topology, two semiconductor switches, inductor and capacitor Naturally, there will be a lot more parts in the final design, but properly defining critical parameters for the four components will make a selection process for the rest pretty straightforward

Semiconductor switches, shown in the schematics (Figure 6) as MOSFET and a diode are

less critical of the four indicated components Modern semiconductor have high current

density in miniature packaging and major constraint is not their current handling capacity –

rather it is power dissipation that small package can conduct to the ambient Starting with

power loss budget, derived from desired efficiency, it will be fairly easy to make proper

selection of the component type and quantity

Unlike semiconductors, where achieving adequate design margins is not a difficult process,

inductors and capacitors present a bigger challenge Even though material science has

brought new materials, inductors and capacitors have seen slower progress

Relationship between power dissipation and saturation characteristics is still a limiting

factor for an inductor design, directly affecting its size and operating temperature

Electrolytic capacitors are still the best part for controlling output voltage ripple, but their

life is severely limited by temperature rise due to high ripple currents.In order to make

proper selection of adequate parts, the work will concentrate on defining input inductor and

output capacitor current ripple and defining a method for their optimization

3.1.1 Input current ripple

For a single phase boost converter input current (Iin) is same as the input inductor current

(ILin) All input variables and component designations in the following equations are

referenced to Figure 6, and δ is operating duty cycle of the active switch, defined as turn-on

time (Ton) divided by switching period (T)

Rising slope of the inductor current is given as

in Lin in

V k L

out in

V

the final equation for the inductor ripple current is derived as

(1 ) out Lin

in

V T I

L

3.1.2Output capacitor RMS current

Most commonly used method for calculating RMS values of typical power converter

waveforms is by splitting it into piecewise segments and then adding squared RMS values

of each individual segment That is the method that will be used for multiphase converters

The method certainly works for single phase converters as well, but there is a more elegant

alternative: we can resort to a Kirchoff’s Law’s equivalent for RMS currents and calculate

output capacitor current by considering all RMS currents inside a boost converter:

The average input current for an ideal, lossless converter can be calculated by starting with a

premise that input power equals the output power:

Substituting equations (5) and (10) into (9), we are getting the closed form equation for the

output capacitor RMS current as follows:

As δ is always less than one, the right hand side of the equation can be neglected with only a

small negative effect on overall accuracy Practical illustration of this simplification is that

the AC ripple component is neglected, i.e considered negligible when compared to the

average value of the input inductor current, which is a meaningful and common practice in

everyday engineering This simplification will pay large dividends when multiple phases

are analyzed, as the complete closed form equations would otherwise be difficult to manage

and understand Also the practical measurements will show that, in an optimized

multiphase converter, the ripple is indeed very small when compared to the average input

current The identical simplification will be used for deriving RMS capacitor current

equations for multiphase converters It should be noted, though, that this simplification will

result in capacitor ripple current being zero at specific values for duty cycle In reality, the ripple current will never reach zero but the actual value will be equal to the neglected factor

in the above equation

Simplified Eq (11) is then:

3.2 Two-phase interleaved boost converter

By adding another power stage, connecting inputs and outputs in parallel and shifting drive signals by 180° a two phase interleaved boost converter is created Principle schematics is shown in Figure 8

SW2

+Vout

-Vout +Vin

-Vin

Fig 8 Two phase boost converter

For a two-phase interleaved boost converter, two distinct modes of operation can be analyzed One is for duty cycles lower than 0.5 (50%) and the other one for duty cycles above 0.5 At exactly 0.5 the converter benefits from ripple cancellation and input current ripple is zero, while output capacitor ripple is at minimum (although not exactly zero, as explained in 3.2) The two modes of operation are illustrated in Figures 9 and 10

The input current ripple, ΔIin will be analyzed for the two cases, δ<0.5 and δ>0.5

- δ<0.5

Input current and input inductor current waveforms for a duty cycle below 0.5 are shown in Figure 9 For the sake of clarity, designations for ripple currents and duty cycles are removed from the graphs, as they are similar to the single stage boost diagrams

The duration of the rising slope of the input current equals the rising time of an individual inductor’s current, i.e δT The input current ripple's rising slope in this interval is a difference of the rising current slope of one inductor and falling slope of the other one:

OFF ON

OFF ON

Phase 2 switch Phase 1 switch

Output capacitor current (Ico)

Iin (phase 2)

Iin (phase 1) Input current (Iin)

Input current (Iin)

Fig 11 Two-phase boost converter - input current waveforms, δ<0.5

V T I

Fig 12 Two-phase boost converter - input current waveforms, δ>0.5

The duration of the input current rising slope in this case equals T/2-(1-δ)T, or (δ-1/2)T The slope equals:

Similar process will be followed in analyzing current ripple in the output filter capacitor

Output capacitor current waveform for δ<0.5 is shown in Fig 13

By neglecting the input inductor ripple, the waveform gets the rectangular shape This approximation (discussed in 3.2) is acceptable as it helps get results which are easier to understand and interpret Loss of accuracy is negligible when compared to tolerances and required design margins Positive amplitude of the waveform equals (IinAVG-Iout) and negative amplitude is (Iout-IinAVG/2) The signal is negative during time that equals

δT and positive during time (1/2-δ)T RMS current is then calculated starting with:

Output capacitor in the boost converter is subjected to large variations of the current through them Capacitors’ peak -to- peak current is equal to the sum of the input inductor peak current... voltages, inductor current can be limiting factor due to the fairly large size and lack of space or even availability of adequate core sizes

One way to reduce the inductor’s size would... Ability to sustain peak load currents of up to 800A for short period of time (1-5 seconds)

• Operating ambient temperature -30 to +60°C

• Low physical profile (load regulator needs to