Fl Pbc Fc Bat Jpc v2

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Nonlinear Control of Fuel Cell and Battery for

Electrical Vehicle with Energy Supervision underSource Limitations

M. Becherif,a, D. Hisselb, M.Y. Ayadc

aIEEE member, University of technology of Belfort-Montbeliard, FEMTO-ST/FCLab, UMRCNRS 6174, 90010 Belfort Cedex, France

bIEEE senior member, University of Franche Comte, FEMTO-ST/FCLab, UMR CNRS6174, 90010 Belfort Cedex, France

cIEEE member, in R&D in Industrial Hybrid Vehicles Applications, France

Abstract

Electrical vehicle propelled by a hybrid source based on of fuel cell (FC) andbatteries is presented. FC does not work properly under transient conditions.The sharp changes in the load power demand can lead to electrochemical andthermal non-uniformities in FC. These non-uniformities increase the degrada-tion rate of FC and reduce its expected life span. To mitigate these detrimentaleffects, a battery bank is used along with FC. This paper deals with the statespace modelling of the hybrid system, and the control of the DC Bus voltage bythe Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). IDA-PBC is a useful technique to control systems assigning a desiredPort-Controlled Hamiltonian (PCH) structure to the closed-loop. In real work-

ing conditions, sources (FC and Batteries) are subject to limitations (Hydrogenfor FC and discharge depth for batteries), these source limitations are takenin account using the Fuzzy Logic (FL) techniques allowing the energy supervi-sion of the electrical vehicle. The battery model and parameter equations aregiven in function of the state of charge and temperature, and are experimentallyvalidated. The global stability proof and simulation results are presented andvalidated by experimentation.

Key words: Passivity-Based Control, Interconnection and Damping, Hybridvehicles, Fuel Cell, Fuzzy Logic.

1. Introduction

Automobiles are one of the major sources of air pollution in urban areas.As air pollution in heavily populated areas becomes unbearable, the search for

Corresponding author. Tel. +33 (0)3 84 58 33 46. Fax +33 (0)3 84 58 33 42Email addresses: [email protected] (M. Becherif),

[email protected] (D. Hissel), [email protected] (M.Y. Ayad)

Preprint submitted to Elsevier August 1, 2011


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cleaner alternatives emerges as an imperative.

In an electric vehicle using a single energy source, the necessary power istransferred from the permanent source, a FC for example, to the load. Thepermanent source must frequently supplies (or absorbs in the case of batteryvehicle) the peaks of power resulting from the accelerations and the braking.This double uses of the permanent source, as energy source and as power source,is strongly penalizing: the losses, volume and the weight are increased and thelifetime of the energy source is reduced [1], [2], [3], [4], [5].

One solution to this problem is the hybridization of the source with a batterythat manages the power peaks. Hence the permanent source can only supply theaverage power which ensures the vehicles energy autonomy. The battery hasthe characteristics of high energy density and relatively low power density (butstill 3 to 5 times higher than the power density of a FC). Energy managementand fuel consumption minimization have been early studied by researchers [6]

and still are an active research area [7], [8], [9], [10] and [11].The battery provides power to the vehicle during periods of peak power

demand such as vehicle acceleration or climbing a mountain. In the studiedapplication, the battery is also considered for braking energy recovery.

Hybrid sources allow dissociating mean power sizing from peak transientpower sizing, the aim being to reduce in volume and weight of the energy supplysource and to ensure a smooth behaviour for the FC for example [12, 13, 14].

To match these aims, the IDA-PBC technique is applied using an open loopcontrol for the FC to regulate the DC bus voltage and a closed loop control forthe battery to control the battery current towards its reference.

In real conditions, sources are subject to limitations, as for example quantityof the embedded hydrogen for FC and the discharge depth of the battery. These

two constrains must be taken to account in the control task to manage energyflows between sources. A Fuzzy Logic technique is used to reach this supervisiontask. FL has as input the State of Charge (SOC) of the battery and the amountof available H2 and gives as output the battery current reference. A negativesign of the battery current provokes the charge of the battery and a positive signa discharge phase. The amount of available H2 is provided by the hydrogen fueltank sensor, and the SOC of the battery is obtained using a lookup table. Thislookup table was obtained experimentally by the characterization of a batterypack available in our Lab. and this characterization takes in account the voltage,temperature, ... to deliver the SOC.

In [15], authors propose an online strategy based on a fuzzy decision system.Fine tuning of the fuzzy system parameters, mainly the membership functions,is made possible using a powerful optimization tool based on a genetic algorithm.

The proposed optimization procedure takes into consideration the minimizationof the hydrogen consumption while satisfying the requested power over a givendriving cycle. The originality of our work, is that the FL supervision ensuresa good behaviour of the system and optimizes the energy flow regarding theremaining H2 and the battery discharge depth; moreover no driving cycle isimposed. Then, an online operation is possible. In [16], authors proposed toapply the fuzzy logic technique to manage the energy for an embedded FC

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system.

In a first step, a dynamic modelling of the overall system is given. Secondly,this system is written in a PCH form where important structural propertiesare exhibited. Then a Passivity-Based Control of the system is presented usingIDA technique. The global stability proof of the equilibrium with the proposedcontrol laws is given. The energy supervision under hydrogen and dischargedepth limitations is presented and solved using FL. Finally, simulation resultsin presence of DC Bus voltage changes and load resistor disturbances, usingMatlab, are presented and validated experimentally using the designed experi-mental setup.

2. FUEL CELLS

The developments leading to an operational FC can be traced back to the

early 1800s with Sir William Grove recognized as the discoverer in 1839. AFC is an energy conversion device that converts the chemical energy of a fueldirectly into electricity. Energy is released whenever a fuel (hydrogen) reactschemically with the oxygen of air. The reaction occurs electrochemically andthe energy is released as a combination of low-voltage DC electrical energy andheat.

Types of fuel cells differ principally by the type of electrolyte they utilize Fig.1. The type of electrolyte, which is a substance that conducts ions, determinesthe operating temperature, which varies widely between types [17, 18, 19, 20, 21].Proton Exchange Membrane (or solid polymer) Fuel Cells (PEMFCs) arepresently the most promising type of FC for automotive use and have been usedin the majority of prototypes built to date.

Figure 1: Different layers of an elementary cell. Source [17]

As the gases are supplied in excess to ensure a good operating of the cell,the non-consumed gases have to leave the FC carrying with them the producedwater [22].

3. Battery

The battery has the characteristics of high energy density and relatively lowpower density (but still times higher than the power density of a FC). The in-

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ternal resistance is the major factor for the limited discharging and charging

current capability. The internal equivalent series resistance has different valuesunder charging and discharging operating conditions. The charging and dis-charging efficiency are nonlinear functions of current and SOC. The battery canbe modelled as an equivalent circuit such as a voltage source and an internalresistor.

Because FC and battery have advantages and disadvantages of their own, itshould be beneficial to have hybrid energy-power sources, in which FC systemsupplies the base energy while battery supplies peak power for fast accelerationand captures the braking energy for regeneration.

3.1. Experimental modelling and identification of the battery

This part presents a model of a Nickel-based battery [24]. The objectiveis to obtain battery model and parameters in function of the temperature andthe state of charge. The test are performed on a nickel cadmium Saft battery(Ccell = 60Ah, Vcell = 1.3V). The internal battery resistance is function ofthe temperature T which represents the electrolyte temperature (and not theambient temperature). Fig. 2 shows the experimental values of the internalbattery resistance versus the temperature and a quadratic interpolation givenby equation (2).

The experimental tests were done under the discharge of the battery at aconstant current. It was noticed that the battery resistance, for the Ni-typebattery, is quite constant in function of the SOC. rB is experimentally obtainedby using the following equation:

rB =eB VB

iB(1)

rB = a1T2 + b1T + c1 (2)

where T is the temperature in C, a1 = 3, 89.107, b1 = 3, 64.105, c1 =

2, 35.103

0 5 10 15 20 25 30 35 40 45 501.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5x 10

3

Temperature C

rB(

)

Experimental rB

Quadratic interpolation of rB

Figure 2: Behaviour of the internal battery resistance as a function of the temperature

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Fig. 3 presents the experimental battery emf versus the SOC. The linear

interpolation of eB is given by equation 3. eB is measured at the cell terminalswith iB = 0.eB = a2SOC + b2 (3)

where a2 = 2, 5.103, b2 = 1, 25

0 10 20 30 40 50 60 70 80

1.25

1.3

1.35

1.4

1.45

SOC

eB

Experimental eB

Linear interpolation of eB

Figure 3: Evolution of the battery emfeB versus the SOC

The battery SOC is obtained using the following equation as given in [24]:

SOC = SOCInit 100

CN

iBdt (4)

with SOCInit is the initial battery SOC, CN is the rated capacity of thebattery.

In the simulation section, the battery is composed of 50 cells connected in

serial and in parallel to obtain an emf around 12 V.

4. Port Controlled Hamiltonian system

PCH systems were introduced by [25] and has since grown to become a largefield of interest in the research of electrical, mechanical and electro-mechanicalsystems. Some of the advantages of expressing systems in PCH form is the factthat they cover a large set of physical systems and capture important structuralproperties.

Consider the nonlinear system given by:

x = f(x) + g(x)u (5)

y = h(x)

where x IRn is the state vector, y IRm is the output vector, f(x), g(x) andh(x) are locally Lipschitz functions and u IRm is the control input.

A PCH form of the system (5) is given by:

x = [J(x) R(x)]H(x) + g(x)uy = g(x)H(x)

(6)

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where J(x) is an nn skew symmetric matrix, R(x) is a nn positive semi-definite symmetric matrix and H is the gradient vector of the energy functionH(x) of the system (5).

H =

H

x1(x)

H

x2(x)

H

xn(x)

T(7)

g(x) is a full-rank left annihilator of g(x), that is g(x)g(x) = 0.PCH systems, with H(x) non-negative, are passive1 systems. A recent and

very interesting approach to solve these problems is the IDA-PBC method,which is a general way of stabilizing a large class of physical systems, see [26, 27].

IDA-PBC approach consists on identifying the natural energy function of thesystem called H(x), then rewrite the nonlinear system (5) versus the gradientof the energy function.

5. Hybrid DC Source using Fuel Cell as Main Source

5.1. Structure of the hybrid source

As shown in Fig. 4, the studied system comprises a DC link supplied bya FC and a non reversible DC-DC Boost converter which maintains the DCvoltage VDC to its reference and desired value Vd [28], and a battery storagedevice which is connected to the DC link through a current reversible DC-DCconverter. The function of FC is to supply the mean power to the load, whereasthe storage device is used as a power source: it supplies peak loads requiredduring acceleration and braking.

5.2. Dynamic modellingThe proposed hybrid structure is given by Fig. 5. It is composed by a FC as a

main source, a FC DC-DC Boost converter, a DC Bus, a battery, a bidirectionalcurrent battery DC-DC converter and a RL load. The load corresponds to aDC motor. The breaking phases are not simulated because our experimentalsetup has a passive (RL) load. Hence, the simulated breaking phases cannot bevalidated experimentally. Consequently, the DC motor emf can be neglected.The load inductance models the dynamic changes in the load. Consider inthe sequel: VFC, iFC, eB , iB , Vs as the FC voltage and current, battery emfand current, and the boost output voltage, respectively. rB , Cs, CDC, LDCand LB are the internal battery resistance, the boost capacitance, the DC buscapacitance and inductance and the inductance of the DC buck-boost converter,

respectively.

1A passive system is one where the stored energy cannot exceed the energy supplied to itfrom its environment, the difference being dissipated.

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DC Bus

LoadPEM

FC

FC

Air, O2

H2

LDC

CDC

B

VFC VDC

iB

PBC

VdBi

Energy supervision under source

limitations using Fuzzy Logic

SOCQuantityof H2

Figure 4: Hybrid sources structure controlled by PBC and optimized by FL

5.2.1. PEMFC model (Static model) [17]

The characteristic FC voltage as a function of the FC current magnitude ispresented in Fig. 6. Here, only a static model of the FC stack is considered,as the dynamic of the current (and thus voltage) remains relatively low versus

the battery current. The obtained curve is composed of three main regionscorresponding to three preeminent phenomena: the electrochemical activationphenomena (region 1), a linear part (region 2) where the voltage drop is due toelectronic and ionic internal resistances and the last region where the diffusionkinetics of gases through the electrodes becomes the limiting factor (region 3).This last zone is characterized by a brutal voltage fall.

Vst = EA.log

ist + in

io

Rm (ist + in) + B.log

1

ist + iniLim

(8)

Vst = f(ist), where E is the reversible voltage of the FC, ist is the deliveredcurrent, io is the exchange current, A is the slope of the Tafel line, iLim is the

limiting current, B is the constant in the mass transfer, in is the internal currentand Rm is the membrane and contact equivalent resistance.The FC parameters are:

Fuel Cell parameters

P[W] E[V] io[A] Rm[m] A[V] B[V] iLim[A] in[A]500 27.1 6.54 45 1.35 1.19 100 0.23

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VL

LBiB

TB

TB

DC BusLDCLFCiFC

VFCTFC

CDC

CS

VS

iDC

PEMFC

VDC

iL

Load

LL

RL

rB

eBBattery VB

Figure 5: Hybrid sources electrical model

iFC

VFC

E0

E

region1

region2 region3

Figure 6: Static FC characteristic.

5.2.2. PEMFC + FC Boost converter model

dVs

dt=

1

Cs[(1 uFC) iFC iDC] (9)

diFC

dt=

1

LFC[ (1 uFC) VS + VFC] (10)

If uFC = 1 TFC is closed.

5.2.3. DC Bus model

dVDC

dt=

1

CDC[iDC iL + (1 uB) iB ] (11)

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diDC

dt=

1

LDC[VS VDC] (12)

If uB = 1 TB is closed, and TB (open).

5.2.4. Battery + Battery DC-DC converter model

VB = eB rBiB (13)

diB

dt=

1

LB[ (1 uB) VDC + VB ] (14)

5.2.5. RL Load model

diL

dt = 1LL[RLiL + VL] (15)

VL = VDC (16)

the overall model of the hybrid system can be written in a state space modelby choosing the following state space vector:

x =

x1, x2, x3, x4, x5, x6T

=

VS, iFC, VDC, iDC, iB , iLT

The control is a vector function of the FC and Battery control laws (dutyratios of the boost and the buck-boost converters)

=

FC, BT

=

(1 uFC), (1 uB)T

(17)

oru =

uFC, uB

T(18)

The 6th order overall state space model is then :

x1 =1

Cs[FCx2 x4]

x2 =1

LFC[FCx1 + VFC]

x3 =1

CDC[x4 x6 + Bx5]

x4 =1

LDC[x1 x3] (19)

x5 =1

LB[eB rBx5 Bx3]

x6 =1

LL[RLx6 + x3]

y = x3

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with VFC = VFC(x2) given by (8). In the sequel, VFC will be considered as

a measured disturbance, and from physical consideration, it comes that VFC [0, Vd[.

5.2.6. Equilibrium:

The equilibrium vector is:

x =

x1, x2, x3, x4, x5, x6T

=

Vd,V2d

RLVFC, Vd,

VdRL

, iB ,VdRL

T(20)

Where Vd is the desired DC Bus voltage. An implicit purpose of the proposedstructure Fig. 5 is to use the battery as a power source supplying the transientpeak power. The equilibrium value of the battery current will be given by thesupervision task by the FL control and is discussed in section 8, hence x5 = i

B.

The following equations obtained at the equilibrium will be used in the closedloop dynamic and the stability proof.

FCx2 x4 = 0

FCx1 + VFC = 0

x4 x6 + Bx5 = 0 (21)

x1 x3 = 0

eB rBx5 Bx3 = 0

RLx6 + x3 = 0

=

FC, BT =

VFCVd

, eBVd

T (22)

or

u =

uFC, uBT

=

1 VFCVd

, 1 eBVd

T(23)

The natural energy function of the system is

H =1

2xTQx (24)

where Q = diag{Cs; LFC; CDC; LDC; LB ; LL} is a diagonal matrix.

6. Problem Formulation

The purpose is the control of the load voltage and consequently the DC Busvoltage by the mean of the control of the two DC-DC converters. The loadis unknown and the load resistor is subject of changes. The second aim is tomaintain a constant mean energy delivered by the FC, without a significantpower peak, as the transient power is supplied by the battery. A third purposeconsists on recovering energy through the charge of the battery. Finally, energysupervision under source limitations should be incorporated in the control task.

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7. Port-Controlled Hamiltonian representation of the system

In the sequel, a closed loop PCH representation is given.The desired closed loop energy function is:

Hd =1

2xTQx (25)

where x = x x is the new state space defining the error between the statex and its equilibrium value x. The state space equation can be written with thenew error variables (where (21) has been used):

x1 =1

Cs[FCx2 x4 + FCx2 x4]

x2 = 1LFC

[FCx1 + VFC FCx1]

x3 =1

CDC[x4 x6 + Bx5 + x4 x6 + Bx5]

x4 =1

LDC[x1 x3] (26)

x5 =1

LB[eB rBx5 Bx3 rBx5 Bx3]

x6 =1

LL[RLx6 + x3]

y = x3

The representation (26) in function of the gradient of the desired energy (25)is given by (27).

x = [J(FC, B) R]Hd + Ai(x, ) (27)

with

Hd =

Csx1, LFCx2, CDCx3, LDCx4, LBx5, LLx6T

Ai(x, ) =

x2Cs

[FC FC]x1LFC

[FC FC]x5CDC

[B B ]

0x3LB

[B B ]

0

(28)

J(FC, B) = JT(FC, B) is a skew symmetric matrix defining the in-

terconnection between the state space and R = RT 0 is symmetric positivesemi definite matrix defining the Damping of the system.

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J(FC, B) R =

0 FCCsLFC

0 1CsLDC

0 0FCCsLFC

0 0 0 0 0

0 0 0 1CDCLDC

BCCDLB

1CDCLL

1CsLDC

0 1CDCLDC

0 0 0

0 0 BCDCLB

0 rBL2B

0

0 0 1CDCLL

0 0 RLL2L

(29)

The following control laws are proposed:

uFC = uFC

uB = uB rx5(30)

where r is a positive design parameter.

Proposition 1. The origin of the closed loop PCH system (27), with the controllaws (30) and (23) with the radially unbounded energy function (25), is globallyasymptotically stable.

Proof. The closed loop dynamic of the PCH system (27) with the laws (30) and(23) with the radially unbounded energy function (25) is:

x = [J(FC, B) R]Hd + Q (31)

where R = diag{0;0;0;0; rB+rVdL2B

; RLL2L

} = RT 0 and

Q =

0 0 0 0 0 00 0 0 0 0 00 0 0 0 r x5

CCDLB0

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

Hd = AHd (32)

The derivative of the desired energy function (25) along the trajectory of

(31) is:Hd = H

Td

x = HTd (R A)Hd (33)

According to the theorem stated by author in [27], (33) is non positive if [RA]is non negative. The eigenvalues of [RA] are {0;0;0;0; rB

L2B

; RLL2L

} and are non

negative. Consequently,

Hd = HTd

x = HTd (R A)Hd 0 (34)

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The asymptotic stability proof is deduced from the derivative analysis of Hd

and the invariance principle of the LaSalle theorem [29] with Hd(x) =

Hd(x) = 02.

8. Fuzzy logic for the source limitations

In order to increase the FC lifespan and to minimize the use of H2, one candecide to use the battery as the primary (or unique) source, if this latter is fullycharged and to solicit the battery in the peak transient. Hence, the batterysupplies the transient peak power to the load:

If the battery is discharged, it can not provide this power, in this case twopossibilities are available:

1. If the Hydrogen tank is full, the FC can be used to recharge thebattery. Hence, iB should be negative.

2. If the Hydrogen tank is in a critical level, the battery is not used,neither charged and nor discharged. Hence, iB = 0

If the battery in not discharged. Hence, if the Hydrogen tank decreasesbelow 50%, the battery should start helping the FC by supplying a smallquantity of energy (small positive value for iB). If the Hydrogen tankstarts dangerously to decline, the battery should increases its percentageof supplied energy (big positive value for iB).

iB values are in the admissible range depending on the used battery charac-teristics.

The available H2 in the fuel tank is measured by the mean of an hydrogentank sensor.As mentioned before, the control relies on linguistic rules, coming from a

human expertise, thus fuzzy logic control is here chosen. Fig. 7 illustrates thechosen membership functions for the two inputs, the available H2 and the SOCof the battery. Z, Half and Full stand for Zero (the source is completely empty),50% available and the source is full, respectively. The amount of the availableenergy is given in per unit between 0 (empty) and 1 (full). Three membershipfunctions are enough to describe the state of the inputs (the two linguisticvariables are the remaining H2 and SOC). For each input, three linguistic valuesare considered (Zero, Half and Full), the FL allows to identify the percentageof belonging to each set. Hence, for each functioning point, inputs range in theset [0, 1].

Fig. 8 shows the chosen membership functions for the battery current refer-ence where NB, N, Z, P, PB stand for Negative Big, Negative, Zero, Positive andPositive Big, respectively. The chosen battery has a maximum current of 5A.

2it can be easily founded that Hd(x) = 0 (x3 = x5 = x6 = 0)

using(21)

x4 = x1 = x2 = 0

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0 1

Z Half Full1

0

SOC

0 1

Z Half Full1

0

H2

Figure 7: Membership functions for the H2 and SOC FL inputs.

Consequently, the battery reference current is in the set [5, 5]A where -5A cor-

responds to a deep discharge of the battery and if Hydrogen is available a rapidrecharge of the battery is needed (negative big value of the battery current). IfiB is in the range N, the battery is recharged with a small negative current. IfiB is Zero, the battery is not used. When iB is positive, the battery is providingpower to the load to help the FC. If iB is Positive Big, this corresponds to afast discharge of the battery to help the FC in a transient peak power or whenthe Hydrogen tank dangerously decreasing to zero. Authors have chosen fivemembership functions to obtain the following scenario:

1. NB: Fast battery recharge;

2. N: Slow battery recharge;

3. Z: The battery is not used (neither discharged, nor recharged);

4. P: Slow battery discharge;

5. PB: Fast battery discharge.

-5 0 5

NB N Z P PB1

0

Bi

Figure 8: Membership functions for the iB output of the FL.

Table 1 presents the different rules to obtain the battery current referenceaccording to the values ofH2 and SOC. One can noticed that when H2 and SOCare full, this case corresponds to the startup of the vehicle when the availablehydrogen and the battery are charged. In this case, iB is positive allowing thebattery to help FC with the startup phase.

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Table 1: Rules for the Fuzzy Logic supervisionP

PPPPPPP

H2SOC Z Half Full

Z Z P PBHalf N Z PFull NB N P

9. Simulations

Two different situations are tested and simulated in order to exhibit thebenefit of the proposed supervision under different source limitations.

1. situation 1: The battery is half charged (SOC = 50%) and the hydrogen

tank is full2. situation 2: The battery is completely charged and the hydrogen tank

is half filled (H2 = 50%)

9.1. Situation 1:

0 1 2 3 4 5 620

0

20

40

60

t(s)

Vd

&VDC

(V)

0 1 2 3 4 5 62

0

2

4

6

t(s)

iL(A)

Figure 9: (a) DC Bus voltage and its reference.(b) Load current.

0 1 2 3 4 5 616

18

20

22

24

t(s)

VFC

(V)

0 1 2 3 4 5 60

5

10

15

t(s)

iFC

(A)

Figure 10: (a) FC voltage. (b) FC current.

0 1 2 3 4 5 611.3

11.4

11.5

11.6

11.7

t(s)

VB

(V)

0 1 2 3 4 5 65

0

5

10

t(s)

i B(A

)

Figure 11: (a) Battery voltage. (b) Battery cur-rent.

0 1 2 3 4 5 60.4

0.6

0.8

t(s)

uFC

0 1 2 3 4 5 60.65

0.7

0.75

t(s)

uB

0 1 2 3 4 5 610

15

t(s)

RL

()

Figure 12: (a) FC Boost control. (b) Battery DC-DC converter control. (c) Load resistance change.

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0 1 2 3 4 5 6100

50

0

50

100

150

200

250

t(s)

Power(W)

PB

PFC

PL

Battery recharge

Battery discharge

Figure 13: FC power, battery power and loadpower.

0 1 2 3 4 5 6

0.6

0.8

1

t(s)AvailableH2

(%)

0 1 2 3 4 5 60.4

0.6

0.8

t(s)

SOC(%)

0 1 2 3 4 5 610

0

10

t(s)

iBref

&iB(A)

Figure 14: H2 level, SOC of the battery, batterycurrent and its reference.

In Fig. 9, the DC Bus voltage Vd is tracking its variable reference VDC. The

load current iL is also subject to load variation.Fig. 10 presents the FC voltage and current VFC&iFC. A smooth behaviour

of the FC voltage and current is observed. As in situation 1 the battery is notcompletely charged, the FC current is bigger in order to recharge the battery.Hence, it can be seen in Fig. 11 the battery current is negative at the start-ing corresponding to the recharging phase of the battery. Once the batteryrecharged and the hydrogen fuel tank decreases, the battery starts to supplythe load.

Fig. 12 presents the FC Boost control signal uFC, the battery convertercontrol signal uB and the changes in the load resistance RL.

Fig. 13 illustrates the benefit of this supervision technique where it can beseen that when the battery is not charged, the FC (under the condition that the

hydrogen fuel tank is full) recharges the battery in addition to feed the load.When the battery is recharged and the hydrogen level decreases, the battery ishelping to supply the load.

Fig. 14 illustrates the available amounts of H2 (top) and SOC (middle)and the calculated iB by the FL and the real iB (bottom). It can be seen thataccording to the remaining H2 and the remaining battery SOC, the membershipfunctions calculate the optimal battery reference iB in order to manage thesource limitations. The PBC has then the charge to track the battery reference,that is done quite well (no overshoot and no steady state error are observed).

9.2. Situation 2:

Fig. 15 shows the response of the system to the DC Bus voltage reference

changes Vd&VDC and the load current iL. Good tracking performances areobtained.Fig. 16 presents the FC voltage and current VFC&iFC. A smooth behaviour

of the FC voltage and current is observed regarding the changes in the DC Busvoltage reference. The battery supplies the transient power.

In this situation the hydrogen fuel tank is not full, then the FL supervisiondecides to use the battery (which was initially charged). Consequently, the FC

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0 1 2 3 4 5 620

0

20

40

60

t(s)

Vd

&VD

C(V)

0 1 2 3 4 5 62

0

2

4

6

t(s)

iL(A)

Figure 15: (a) DC Bus voltage and its reference.(b) Load current.

0 1 2 3 4 5 616

18

20

22

24

t(s)

VFC

(V)

0 1 2 3 4 5 60

5

10

15

t(s)

iFC

(A)

Figure 16: (a) FC voltage. (b) FC current.

0 1 2 3 4 5 611

11.5

12

12.5

t(s)

V

B(V)

0 1 2 3 4 5 65

0

5

10

t(s)

i B(A)

Figure 17: (a) Battery voltage. (b) Battery cur-rent.

0 1 2 3 4 5 6

0.4

0.6

0.8

t(s)

uFC

0 1 2 3 4 5 60.65

0.7

0.75

t(s)

uB

0 1 2 3 4 5 610

15

t(s)

RL

()

Figure 18: (a) FC Boost control. (b) Battery DC-DC converter control. (c) Load resistance change.

current is low (comparing to the situation 1) and the battery current is alwayspositive (discharging) as it can be seen in Fig. 17.

Fig. 18 presents the FC Boost controller uFC, the battery bidirectionalconverter controller uB and the changes in the load resistance RL. uFC and uBare in the set [0, 1].

It can be seen from Fig. 19 that the battery is supplying a large amountof energy to compensate the lack of hydrogen. Fig. 20 illustrates the availableamounts of H2 and SOC and in the bottom the calculated iB by the FL andthe real iB . It can be seen from this last Fig. that according to the remainingH2 fuel level and the remaining battery SOC, the defined membership functionscalculate the optimal battery reference iB in order to manage the source lim-itations. The PBC has then the charge to track the battery reference, that isdone quite well (no overshoot and no steady state error are observed).

10. Experimental results

Fig. 21, 22 and 23 are an illustration of the experimental test benches builtby authors by using basic commercial elements. The used components are:Ballard Nexa 1.2 kW FC (Fig. 22) connected to the DC bus via the DC-DCBoost (designed and built by authors, see 23), battery connected to the DC Bus

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0 1 2 3 4 5 650

0

50

100

150

200

t(s)

Power(W)

PB

PFC

PL

Figure 19: FC power, battery power and loadpower.

0 1 2 3 4 5 6

0.35

0.4

0.45

t(s)AvailableH2

(%)

0 1 2 3 4 5 6

0.7

0.8

0.9

t(s)

SOC(%)

0 1 2 3 4 5 610

0

10

t(s)

iBref

&iB(A)

Figure 20: H2 level, SOC of the battery, batterycurrent and its reference.

through a current bidirectional DC-DC buck-boost converter (Fig. 21), the load

is constituted by a variable resistor in parallel with the DC bus capacitance.

Figure 21: Battery, load and DC-DCbuck-boost setup. Figure 22: Ballard Nexa FC. Figure 23: Global experimental setup.

The FC boost and the battery DC-DC current bidirectional converter arecontrolled by means of a real time dSpace DS1104 board. The considered bat-tery delivers a voltage of 12V. The desired DC bus reference Vd is online changedusing Matlab-ControlDesk, the operating scenario consists on the control of theFC boost and the battery DC-DC buck-boost to meet, at the DC bus, thedesired voltage Vd. In order to exhibit, during the few seconds of the exper-imentation duration, the ability of dealing with the tank (H2 and electricity)limitation, scroll input buttons are implemented in the ControlDesk to emulatea variation of the hydrogen level tank and the battery SOC3. Fig. 24 presentsthe experimental results.

The experimental test consists first in the regulation problem of the DCbus voltage VDC toward its reference Vd and the battery current iB toward itsreference iBref which is defined using the FL technique. A change in the DC bus

3It is evident that during the short considered experimentation duration, the level of thehydrogen fuel tank or the battery SOC can not be affected.

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voltage reference is applied directly from the ControlDesk and consists on a step

change from 42V, to 41V and then to 43V as it can be seen in the Fig. 24(a).One can see that the tracking of these two variables towards their referencesare very good until 19 seconds. At approximatively 19 seconds, the hydrogenlevel starts decreasing, this variation of the hydrogen fuel level is emulated byadjusting the scroll input button. When the hydrogen level is becoming critical,around 20% at 25 seconds, the FL rules compute the new battery referencewhich is approximatively multiplied by two as it can be seen from Fig. 24(d) and (j). The battery current tracking is very good without overshoot andno steady state error. Thus, the battery provides a large amount of energyto overcome the lack of hydrogen and the FC supplied energy decreased as itshown in the power flows Fig. 25. At approximatively 32 seconds, the batterySOC scroll input button is decreased (Fig. 24(h)) emulating a decreasing in thestate of charge of the battery due to its contribution in feeding the load during

the previous seconds. Fig. 24(j) shows that FL rules computes the new batterycurrent reference. If this battery SOC decreasing happened when the hydrogenfuel tank is full, the new battery current reference can be negative allowing therecharge of the battery using the FC. But as the hydrogen fuel is also around40%, the new battery current reference slightly decreased managing then theoverall sources (hydrogen fuel and battery SOC). One can see from Fig. 25that the amount of the supplied battery energy decreases and the amount ofthe supplied FC energy increased with the same ratio in order that the FC plusthe battery energies match at each time the requested load energy. One maynotice also that at approximatively 8 seconds, the transient power peak due tothe step change in the DC bus reference is provided by the battery allowing asmooth behaviour on the FC energy shape.

11. Conclusion

A dynamic modelling of a hybrid source system composed of a FC and abattery sources is presented.PCH structure of the overall system is given. Theproblem of the DC bus voltage control is solved using simple linear controllersbased on the IDA-PBC approach. These controllers need the measurementof two variables only (the FC voltage VFC and the battery current iB). Theproposed structure allows supplying and absorbing the power peaks by usingbattery which also allows recovering energy. Global Stability proof is giveninsuring the convergence of the state space vectors towards their desired equi-librium values. The other contribution of this paper consists on the supervisionof the energy flow under source limitations using the fuzzy logic technique. This

supervision allows to calculate in real time the reference of the battery currentallowing to decide from which source the load will be supplied (or with whichusage ratio of each of the sources). The energy supervision needs the measure-ment of the hydrogen fuel tank level and the state of charge of the battery iscalculated upon the measurement of the battery current and temperature. TheFL energy supervision aims to calculate the optimal equilibrium value of thebattery current (according to the chosen rules). Hence, the incorporation of the

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0 10 20 30 4040

42

44

(a)

Vdc

(V)

Vd(V)

0 10 20 30 400.5

1

1.5

(b)

iL(V)

0 10 20 30 4012

12.1

12.2

(c)

VB(V)

0 10 20 30 400

1

2

3

(d)

iB(V)

0 10 20 30 4038.8

39

39.2

(e)

VFC

(V)

0 10 20 30 400.4

0.6

0.8

(f)

iFC

(V)

0 10 20 30 400

0.5

1

(g)

Remaining H2

0 10 20 30 400.8

0.9

1

(h)

SOC

0 10 20 30 401

0

1

t(s)

(i)

uB

uFC

0 10 20 30 400

2

4

t(s)

(j)

iB(A)

iBref

(A)

Figure 24: Experimental results. (a) DC Bus voltage and its reference, (b) load current, (c)battery voltage, (d) battery current, (e) FC voltage, (f) FC current, (g) remaining hydrogenlevel in percentage, (h) battery SOC in percentage, (i) battery DC-DC converter and the FCBoost converter controls, (j) battery current and it reference

FL technique didnt affect the stability of the whole system, since the batterycurrent reference is always a bounded value.An encouraging simulation resultshas been obtained exhibiting also the robustness of the proposed controllers to-wards load resistor variations. A low power experimental setup has been builtby authors.The designed system is online controlled using Matlab dSpace andthe hydrogen fuel tank level and the battery SOC have been online emulatedusing ControlDesk. The realized test scenario validates the control objectives.Itis experimentally shown that the proposed controllers react to the sources limi-

tation and manage the energy flows between the two sources in order to matchat each time the requested load power demand. In addition, the same simplecontrollers allows the recharge of the battery if the SOC is critical and the hy-drogen fuel level is full. These encouraging experimental results are validatingthe overall theoretical contribution.

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0 10 20 30 400

10

20

30

40

50

60

t(s)

Powers(W)

FC PowerBattery Power

Load Power

Figure 25: Experimental battery, FC and load powers.

References

[1] Becherif M., Passivity-based control of hybrid sources: Fuel cell and Battery, 11th

IFAC Symposium on Control in Transportation Systems (CTS06), Netherlands,2006.

[2] Hilairet M., Bethoux O., Azib T., and Talj R., Interconnection and dampingassignment passivity-based control of a fuel cell system, IEEE InternationalSymposium on Industrial Electronics (ISIE), pp. 219 - 224, Italy, 2010.

[3] Kolavennu P., Telotte J.C., and Palanki S., Analysis of battery backup and

switching controller for a fuel-cell powered automobile, International Journal ofHydrogen Energy, vol. 34(1), pp. 380-387, January 2009.

[4] Kim Y.B., and Kang S.J., Time delay control for fuel cells with bidirectionalDC/DC converter and battery, International Journal of Hydrogen Energy, vol.35(16), pp. 8792-8803, August 2010.

[5] Andreasen S.J., Ashworth L., Remon I.N.M, and Kr S.K., Directly connectedseries coupled HTPEM fuel cell stacks to a Li-ion battery DC bus for a fuel cellelectrical vehicle, International Journal of Hydrogen Energy, vol. 33(23), pp.7137-7145, December 2008.

[6] Gilbert E.G., Vehicle cruise: Improved fuel economy by periodic control, Auto-matica, pp. 159-166, vol. 12(2), 1976.

[7] Halpin, S.M.; Ashcraft, S.R.: Design considerations for single-phase uninterrupt-ible power supply using double-layer capacitors as the energy storage element,IEEE-IAS, San Diego, vol.4, pp.23962403, 1996.

[8] Kim M.J., and Peng H., Power management and design optimization of fuelcell/battery hybrid vehicles, Journal of Power Sources, pp. 819-832, vol. 165(2),2007.

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[24] Boulon L., Hissel D., and Pera M.C., Multi-Physics Modelling and Energy Man-agement of a Battery Supercondensator Electric Vehicle Taking Into Account theOperating Temperature Conditions. ELECTRIMACS, Quebec, Canada, 2008.

[25] Van der Schaft A.J., and Maschke B., On the hamiltonian formulation of non-holonomic mechanical systems, Reports on Mathematical Physics, pp. 225233,vol. 34(2), 1994.

[26] Ortega R., Van der Schaft A.J., Maschke B., and Escobar G., Interconnectionand damping assignment passivitybased control of portcontrolled hamiltoniansystems, Automatica, pp. 585596, vol. 38(4), 2002.

[27] Becherif M., and Mendes E., Stability and robustness of Disturbed-Port Con-trolled Hamiltonian system with Dissipation, 16th IFAC World Congress, Prague,2005.

[28] Mangold M., Buck A., and Hanke-Rauschenbach R., Passivity based control ofa distributed PEM fuel cell model, Journal of Process Control, vol. 20(3), pp.292-313, March 2010.

[29] Lasalle J.P., Stability theory for ordinary differential equations, Journal of Dif-ferential Equations, vol. 4, no. 1, pp. 57-65, 1968.

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