research article adaptive second order sliding mode...

Research ArticleAdaptive Second Order Sliding Mode Control of a Fuel CellHybrid System for Electric Vehicle Applications

Jianxing Liu1 Yue Zhao1 Bo Geng2 and Bing Xiao3

1 Control Science and Engineering Harbin Institute of Technology Harbin 150000 China2Department of Electrical and Computer Engineering University of Texas Austin TX 78712 USA3 College of Engineering Bohai University Jinzhou 121013 China

Correspondence should be addressed to Yue Zhao zhaoyuelj163com

Received 14 June 2014 Accepted 13 July 2014

Academic Editor Ligang Wu

Copyright copy 2015 Jianxing Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We present an adaptive-gain second order sliding mode (SOSM) control applied to a hybrid power system for electric vehicleapplicationsThemain advantage of the adaptive SOSM is that it does not require the upper bound of the uncertaintyThe proposedhybrid system consists of a polymer electrolyte membrane fuel cell (PEMFC) with a unidirectional DCDC converter and a Li-ionbattery stack with a bidirectional DCDC converter where the PEMFC is employed as the primary energy source and the battery isemployed as the second energy source One of the main limitations of the FC is its slow dynamics mainly due to the air-feed systemand fuel-delivery system Fuel starvation phenomenon will occur during fast load demand Therefore the second energy source isrequired to assist the main source to improve system perofrmanceThe proposed energy management system contains two cascadecontrol structures which are used to regulate the fuel cell and battery currents to track the given reference currents and stabilizethe DC bus voltage while satisfying the physical limitations The proposed control strategy is evaluated for two real driving cyclesthat is Urban Dynamometer Driving Schedule (UDDS) and Highway Fuel Economy Driving Schedule (HWFET)

1 Introduction

Polymer electrolyte membrane fuel cells (PEMFCs) haveemerged as the most prominent technology for energizingfuturersquos automotive world They are clean quiet and efficientand have been widely studied in automotive applicationsover the past two decades due to their relatively small sizelight weight and easy manufacturing [1ndash3] Despite theseadvantages there are still major issues concerning costliability and durability to be addressed before they becomea widely used alternative to internal combustion engines

One of the main drawbacks of the FCs is slow dynam-ics dominated by the air-supply system and fuel-deliverysystem As a result the FCs cannot properly respond torapid load changes in vehicle power demand which willcause a high voltage drop in a short time recognized asa fuel-starvation phenomenon [4] Therefore an additionalenergy storage system such as Lithium ion (Li-ion) batteries

is usually used to improve the slow response dynamics of thePEMFC The PEMFC hybrid electric vehicle (HEV) with Li-ion battery storage possesses the advantages of the PEMFCand Li-ion battery stack (large energy and power capacities)The PEMFC provides the main power requirements duringnormal driving condition while the Li-ion battery stackdischarges or stores energy to assist the PEMFC to meetpeak power demand Previous research works have shownthat hybridization of FC vehicles with batteries provides thebenefits of cost and performance as well as fuel economy[5 6]

In order to achieve the optimal operation performanceof the hybrid system suitable model and controller develop-ment efforts are needed [7ndash13] In the hybrid configurationthe DCDC converters adapt the voltage of the fuel cell andthe battery to theDCbus voltageThis allows an active controlof the power sharing between each sourceTherefore a powermanagement strategy is needed to determine this power

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 370424 14 pageshttpdxdoiorg1011552015370424

2 Mathematical Problems in Engineering

sharing while respecting system constraints (eg batterystate of charge (SOC) limits power limits etc) [14ndash16]In [17] a load sharing algorithm using fuzzy logic controlwas studied for a fuel cellsupercapacitor HEV In [18] afuel cellbatterysupercapacitor hybrid bus was studied by afuzzy power management controller with the effectivenessof the fuzzy controller demonstrated by some designed testsRecently energymanagement based onproportional-integral(PI) controllers have been proposed [6 19] Although PI con-trollers are easy to be tuned on-line which provide a practicalsolution to many applications they can not be robust andreliable in the presence of disturbances or uncertainties

Sliding mode technique is known for its insensitivityto external disturbance due to operating conditions highaccuracy and finite time convergence [20ndash24] Sliding modecontrol (SMC)has foundwide applications in various dynam-ical systems such as stochastic systems [25] Markovianjumping systems [26 27] and fuzzy systems [28 29] How-ever the main drawback of SMC is the so-called chatteringphenomenon [30] Adaptive sliding mode has been provento be an efficient solution which does not require thebound of uncertainties [31ndash33]The control gains are adapteddynamically to counteract the uncertaintiesperturbationswhich ensure the sliding mode To the best of the authorsrsquoknowledge it is the first attempt to apply the adaptive SOSMcontrol to the application of HEV In this paper we haveproposed a cascade control strategy for the FC hybrid systemusing an adaptive-gain super twisting algorithm (ASTW)[31] The gains of this algorithm are adapted dynamicallywhich ensures the convergence of the tracking error infinite time without a priori knowledge of the upper boundof uncertainties and perturbations A state based controlalgorithm is proposed to generate the power reference for thefuel cell stack In addition controllers are also designed forthe fuel cell and battery converters to track the given currentreferences and stabilize the DC bus voltage

The rest of the paper is divided as follows the modellingof the FC hybrid system is given in Section 2 Section 3discusses the designs of the power management controlstrategy which generates the reference power for the FCThen the control strategies for the FC and battery convertersusing the proposed algorithm are provided In Section 4simulation results are given for two real driving cycles UDDSand HWFET Finally the major conclusions are presented inSection 5

2 Model of the Hybrid Fuel Cell Power System

Figure 1 shows the schema of the studied hybrid systemfor the vehicle applications The hybrid system is composedof the PEMFC the Li-ion battery FC unidirectional DC-DC converter battery bidirectional DCDC converter andtracking motor

21 Fuel Cell System Modelling In this paper a 30 kW fuelcell composed of 90 cells in series is modeled consideringits dynamics [34] The fuel cell behavior is highly nonlinearand is dependent on several variables such as current density

stack temperature membrane humidity and reactant partialpressures Several assumptions are considered (1) the stacktemperature and humidity in the fuel cell cathode are wellcontrolled (2) the water inside the cathode is only in vaporphase and any extra water in liquid phase is removed fromthe channels (3) the input reactant flows are humidified in aconsistent and rapid way and the high pressure compressedhydrogen is available (4) the anode pressure is well con-trolled to follow the cathode pressure and (5) the currentdynamics of the motor which directly drives the compressoris negligible due to its small time constant as compared to themechanical dynamics [35]

211 Fuel Cell Stack Voltage A single fuel cell operatingvoltage can be modeled as

119881fc = (119864 minus Vact minus Vohm minus Vconc) (1)

where 119864 is the open circuit voltage and Vact Vohm and Vconcpresent the activation loss ohmic loss and concentrationloss respectively

The open circuit voltage 119864 is expressed as

119864 = 1229 minus 085 sdot 10minus3

(119879fc minus 29815)

+ 43085 sdot 10minus5

119879fc [ln (119901H2

) +1

2ln (119901O

2

)]

(2)

where 119879fc is the fuel cell stack temperature and 119901H2

119901O2

arethe partial pressures of hydrogen and oxygen respectively[34]

The activation loss Vact ohmic loss Vohm and concentra-tion loss Vconc are expressed as follows

(1) Vact = V0

+V119886

(1minus119890minus119887

1119894

) is due to the difference betweenthe velocity of the reactions in the anode and cathode[36] where 119894 = 119868st119860 fc is the current density 119868st (A)is the stack current and 119860 fc (cm

2) is the active areaV0

(volts) is the voltage drop at zero current densityand V119886

(volts) and 1198871

are constants that depend on thetemperature and the oxygen partial pressure [37 38]The values of V

0

V119886

and 1198871

can be determined from anonlinear regression of experimental data

(2) Vohm = 119894119877ohm is due to the electrical resistance ofthe electrodes and the resistance to the flow of ionsthrough the electrolyte [36]119877ohm (Ωsdotcm2) representsthe fuel cell internal electrical resistance

(3) Vconc = 119894(1198873

(119894119894max))119887

4 results from the drop in con-centration of the reactants due to the consumption inthe reaction 119887

3

1198874

and 119894max are constants that dependon the temperature and the reactant partial pressures119894max is the current density that generates the abruptvoltage drop

Mathematical Problems in Engineering 3

H2

Air

PEMFC

Battery

FC converterifc

rfc

Vfc

L fc

ufc

ibatt

rbatt

Vbatt

Lbatt

ubatt

S1

S2

S3

Battery converter

Pfc0

Pbatt0

CbusVbus

iload

Pload

DCAC inverterTracking motor

M Differential

+

minus

+

minus

=

sim

Figure 1 Schematic of the fuel cellbattery hybrid power system

212 GasDynamics of119901H2

and119901O2

Thedynamics of119901H2

119901O2

are expressed as follows

119889119901H2

119889119905=

119877H2

119879fc

119881an(119882H

2in minus119882H

2out minus119882H

2react)

119889119901O2

119889119905=

119877O2

119879fc

119881ca(119882O

2in minus119882O

2out minus119882O

2react)

(3)

where119882H2in is themass flow rate of hydrogen gas entering the

anode 119882H2out is the mass flow rate of hydrogen gas leaving

the anode119882H2react is the rate of hydrogen reacted119882O

2in is

the mass flow rate of oxygen entering the cathode119882O2out is

the mass flow rate of oxygen leaving the cathode119882O2react is

the rate of oxygen reacted 119877H2

is the hydrogen gas constant119877O2

is the oxygen gas constant and119881an and119881ca are the anodeand cathode volumes respectively More details are providedin [34]

213Thermal Dynamics Thedynamic temperature model isdescribed by a lumped thermal model [39]

119898st119862119901st119889119879fc119889119905

= sou minus119882119888119862119901c (119879fc minus 119879119888in)

sou = 119868st (minus119879fcΔ119904

4119865+ Vact + 119868st119877ohm)

(4)

where 119898st is the heat mass of the stack 119862119901st

and 119862119901c

arethe specific heat 119882

119888

is the coolant flow rate considered as acontrol variable 119879

119888in is the coolant temperature at the stackinlet and sou is the internal energy source The latter iscalculated as a function of the stack current temperatureelectrical resistance of stack layers 119877ohm Faradayrsquos number119865 and the entropy change Δ119904 The physical parameters wereobtained through extensive experimentation

214 Auxiliary Components The main power consumer ofthe fuel cell system is the air compressor which can consumeup to 30 of the fuel cell power under high load conditions

[40] Therefore the net power from the fuel cell system 119875fcnetcan be calculated as

119875fcnet = 119899119881fc119868fc minus 119875cp minus 119875aux (5)where 119899 is the number of cells and 119875cp and 119875aux are the powerconsumed by the compressor and auxiliary components(such as the cooling pump radiator fan) respectively In thisstudy 119875aux is assumed to be constant and 119875cp is calculated as

119875cp =119862119901

119879atm

120578cm120578cp[(

119901sm119901atm

)

(120574minus1)120574

minus 1]119882cp (6)

where 119901sm is the supply manifold pressure which is equal tothe pressure at the compressor outlet 119901atm is the atmosphericpressure119862

119901

is the specific heat capacity of air 120574 is the ratio ofthe specific hears of air 119879atm is the ambient temperature119882cpis the compressor flow rate and 120578cm and 120578cp are the compres-sor motor efficiency and compressor efficiency respectivelyFigure 2 shows the efficiency curve of the fuel cell system itcan be found that the optimal operating point is near 88 kW

Remark 1 As discussed in [41] the time constants of the gasdynamics and the stack temperature dynamics are estimatedto be the order of magnitude of 10minus1 and 102 respectivelyTherefore the mass storage effects in the channels are notconsidered

22 Fuel Cell Converter Model A classical boost-type unidi-rectional DCDC converter is selected as FC power converterbecause it can be operated in the current control mode ina continuous condition mode [42] It adapts the DC voltagesupplied by the fc to the desired DC bus voltage (420V) Byacting on the switching signal 119906fc it is possible to determinethe load power distribution between FC and battery Theaverage model of the FC converter is expressed as follows

119871 fc119889119894fc119889119905

= 119881fc minus 119903fc119894fc minus 119906fc119881bus (7)

where 119903fc is the total equivalent series resistance in the FCconverter 119906fc = 1minus119863fc and119863fc is the duty ratio of the switch1198781


5 10 15 20 25 30

03

035

04

045

05

PEMFC power (kW)

Syste

m effi

cien

cy

Optimal point

Figure 2 PEMFC efficiency curve

23 Battery Model The Li-ion battery with peak power40 kW and capacity 20Ah is modeled as a voltage source inseries with a resistance [14 43] which is given as

119881batt = 119881oc minus 119903batt119894batt (8)

where the open circuit voltage (119881oc) and the internal resis-tance (119903batt) are both functions of the battery SOC The SOCis defined as the ratio of charge stored in the battery to themaximum charge capacity 119876batt

119889SOC119889119905

= minus119894batt119876batt

(9)

where 119894batt is the battery currentIn order to express 119894batt it is noted that the instantaneous

power delivered by the battery to the load equals 119875batt =

119881batt119894batt Then the rate of change of SOC gives

119889SOC119889119905

= minus

119881oc minus radic1198812

oc minus 4119903batt119875batt

2119903batt119876batt

(10)

The solution (10) is feasible for negative power demandswhich means the battery is in charge mode and maximizesefficiency for positive power demands (discharge mode)

24 Battery Converter Model A simple boost-type bidirec-tional DCDC converter is used to connect the battery tothe high voltage bus enabling the charge and discharge ofthe batteryThe cascade control structure of the bidirectionalconverter is realized through the outer control loop (the DCbus energy loop) and the inner control loop (the batterycurrent loop) The dynamic of the current control loop aredesigned to be much faster than that of the DC bus energyregulation loop

The average model of the battery converter is expressedas follows

119871batt119889119894batt119889119905

= 119881batt minus 119903batt119894batt minus 119906batt119881bus (11)

Table 1 Parameters for the vehicle

Parameters ValueVehicle mass119872 1500 kgRolling resistance 119862

119903

001Drag coefficient 119862

119863

03Frontal area 119860

119891

24m 2

Air density 120588119886

12 kgm 3

Differential ratio 50Differential efficiency 97Wheel radius 029m

where 119903batt is the total equivalent series resistance in thebattery converter 119906batt = 1 minus 119863batt and 119863batt is the duty ratioof the switch 119878

2

The DC link capacitive energy 119910bus is given versus FC

power 119875fc battery power 119875batt and load power 119875load by thefollowing equation

119910bus = 119875fc0 + 119875batt0 minus 119875load (12)

where 119910bus = (12)119862bus1198812

bus 119875fc0 = 119875fcnet minus 119903fc1198942

fc and 119875batt0 =119875batt minus 119903batt119894

2

batt

25 Vehicle Dynamics Modelling The power train is modeledas a point-mass [14]

119872119889V119889119905

= 119865trac + 119865brak minus 119862119903119872119892 cos120572

minus1

2120588119886

119860119891

119862119863

119860119891

V2 minus119872119892 sin120572(13)

where 119865trac is the vehicle traction force 119865brak is the frictionbrake force 119872 is the vehicle mass V is the vehicle velocityand other parameters are defined in Table 1

Then the power required to drive the tracking motor iscalculated as

119875load = 119865tracV(120578119898120578diff)minus sign(119865trac)

(14)

where 120578diff is the efficiency of the differential and 120578119898

is theefficiency of the tracking motor which is a function of motortorque 120591

119898

and its rotation speed 120596119898

that is 120578119898

= 120578(120591119898

120596119898

)In the next section the control strategy of FC and battery

will be presented using super-twisting sliding mode

3 Energy Management System

The energymanagement system implemented is based on thestates based control algorithm and a SOSM control whichgenerate the FC and battery reference currents respectivelyThen the FC and battery current controls are realizedwith SOSM controllers due to its insensitivity to externaldisturbance high accuracy and finite time convergence Inthis paper the EMS are considered and designed based onthe requirements given in Table 2

Note that FC has a slow dynamic response so that the bat-tery functions to compensate the FCdynamic performance to


Table 2 EMS design requirements

Fuel cell parameters119875fcmin

2 kW119875fcopt 13 kW119875fcmax

30 kW119894fcmin

2A119894fcmax

300A120591fc 025 s119871 fc 2 sdot 10

minus3H119903fc 01ΩFC current dynamic limitation 40AsBattery parameters119875battmin

minus40 kW119875battmax

40 kWSOCmin 30SOCmax 90119871batt 2 sdot 10

minus3H119903batt 01Ω119881lowast

bus 420V

avoid the FC starvation problem [44] supply the overpowerdemand and absorb the regenerative braking power The FCfunctions to supply the power to both the DC bus capacitor119862bus and the battery to be charged when its SOC is low Thecontrol of the whole system is based on the SOCof the battery[6]

(i) when SOC is lower than SOC reference FC is nec-essary to charge the battery through the bidirectionalDCDC converter

(ii) when SOC is higher than its reference value thenthe battery charging current reference is set to zeroand the FC current reference is reduced to zeroFor transient conditions the battery supplies all loadvariations

The main objective of the control is to regulate DC busvoltage Vbus and prevent the FC suffering from fast currentdemand Two SOSM controllers have been proposed forthe unidirectional boost FC converter and the bidirectionalbattery converterThe bidirectional property allows the man-agement of chargedischarge cycles of the battery tank

31 Adaptive-Gain Supertwisting Sliding Mode Control Con-sider a single-input uncertain nonlinear system

= 119891 (119909) + 119892 (119909) 119906 119910 = 119904 (119909 119905) (15)

where 119909 isin 119883 sub R119899 is a state vector 119906 isin 119880 sub R is abounded control input and119891(119909)119892(119909) are sufficiently smoothuncertain functions The control objective is to force thesliding variable 119904(119909 119905) and its time derivative and 119904(119909 119905) tozero in finite time that is 119904(119909 119905) = 119904(119909 119905) = 0

Assumption 2 (See [31]) The relative degree of the system (15)equals one with respect to 119906 and the internal dynamics arestable

Therefore under the Assumption 2 the first time deriva-tive of 119904(119909 119905) can be presented in the following form

119904 =120597119904

120597119905+120597119904

120597119909119891 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120593(119909119905)

+120597119904

120597119909119892 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120574(119909119905)

119906

= 120593 (119909 119905) + 120574 (119909 119905) 119906

(16)

Assumption 3 The time derivative of the function 120593(119909 119905) isbounded |(119909 119905)| le 120575 with an unknown value 120575 forall119909 isin 119883

Assumption 4 There exist positive but unknown constants 120574119898

and 120574119872

such that forall119909 isin 119883 0 lt 119887119898

lt |120574(119909 119905)| lt 119887119872

and| 120574(119909 119905)| le 119861

The following ASTW algorithm is considered [31]

119906 = minus120572|119904|12 sign (119904) + ]

] = minus120573 sign (119904) (17)

where 120572 = 120572(119904 119905) and 120573 = 120573(119904 119905) are the adaptive gains to bedetermined

The system (16) can be rewritten as

119904 = minus120572120574 (119909 119905) |119904|12 sign (119904) + 120596

= minus120573120574 (119909 119905) sign (119904) + (119909 119905) + 120574 (119909 119905) ](18)

where 120596(0) = 0Given that 120573 le 120573

lowast

gt 0 [31] and Assumption 4 it followsthat

1003816100381610038161003816 (119909 119905) +120574 (119909 119905) ]1003816100381610038161003816 le 120575 + 119861int

119905

0

120573119889120591

le 120575 + 119861120573lowast

119905 = 1205751

(19)

for some unknown positive constant 1205751

The control gains 120572 and 120573 are adapted dynamically [31]

=

1205961

radic1205741

2sign (|119904| minus 120583) if 120572 gt 120572

119898

1205781

if 120572 le 120572119898

120573 = 1205761

120572

(20)

where1205961

1205741

120583 1205781

1205761

and 120572119898

are arbitrary positive constants

Remark 5 The practical sliding mode is established in finitetime 119905

119865

that is |119904| le 1205831

| 119904| le 1205832

At the beginning |119904(0)| gt 120583and 120572(0) gt 120572

119898

and the adaptive gains 120572 and 120573 dynamicallyincrease in order to stabilize the system Once the practicalsliding mode is achieved the gains start to decrease

32 FC Reference Power Calculation In this study state basedcontrol algorithm proposed in the work [45] is used tocalculate the FC reference power 119875lowastfc The FC reference poweris determined based on the load power and battery SOCThree levels for the SOC range are considered high (SOC gt

90) normal (60 le SOC le 85) and low (SOC lt 30)Eight states derived from the works of [45ndash47] are given asfollows


SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()

Figure 3 State based control hysteresis

Case 1 SOC is high and 119875load lt 119875fcmin In this case the FC

operates at its minimum power 119875lowastfc = 119875fcmin only supplies

auxiliary components

Case 2 SOC is high and 119875fcminle 119875load le 119875fcmax

In this casethe FC operates with a load following strategy 119875lowastfc = 119875load andthe battery will supply the fast load demand when necessary

Case 3 SOC is high and 119875load ge 119875fcmin In this case the FC is

demanded to generate its maximum power 119875lowastfc = 119875fcmaxand

the battery will provide additional power to assist the FC

Case 4 SOC is normal and 119875load lt 119875fcopt In this case the FCoperates at its optimum power 119875lowastfc = 119875fcopt

Case 5 SOC is normal and 119875fcopt le 119875load le 119875fcmax In this case

the FC operates with a load following strategy which worksthe same as Case 2

Case 6 SOC is normal and 119875load ge 119875fcmax In this case the FC

is demanded to generate its maximum power 119875lowastfc = 119875fcmax it

works the same as Case 3

Case 7 SOC is low and119875load lt 119875fcmax In this case the FCmust

generate the load power plus the battery charging power119875lowastfc =119875fcmax

+ 119875battchar

Case 8 SOC is low and 119875load ge 119875fcmax In this case the FC is

required to generate the maximum power 119875lowastfc = 119875fcmax

The hysteresis control of the battery SOC is shown inFigure 3

33 Control of FC Converter The detailed FC current regu-lation loop is portrayed in Figure 4 From the FC referencepower generated by the states control algorithm and theFC voltage the FC reference current is determined whichis limited to a range [119894fcmin

119894fcmax] In the case of within the

interval the control of FC boost converter ensures currentregulation (with respect to its reference value) In the caseof outside the interval the FC current will be saturated and

the surge current is then provided or absorbed by the batteryMoreover the FC dynamic limitation is also considered usinga low pass filter such that fast current demand is avoidedTheerror between the FC current and its reference is used in aSOSM controller in order to determine the duty cycle of theFC unidirectional converter [48]

The sliding manifold of the FC current control loop isdefined as

1199041

= 119894fcref minus 119894fc (21)

In view of (7) the first time derivative of 1199041

is calculated asfollows

1199041

= 119894fcref minus119881fc minus 119903fc119894fc minus 119906fc119881bus

119871 fc (22)

According to the adaptive SOSM algorithm [31] the FCcurrent controller can be designed as follows

119906fc =119881fc minus 119903fc119894fc minus 119871 fc1205921 (1199041)

119881bus (23)

where 1205921

(1199041

) takes the same structure as (17)

1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)

and the adaptive gains 1205721

and 1205731

are designed accordingto (20) In order to ensure the fast convergence of 119904

1

theparameters have been tuned as follows 120596

1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2

34 Battery Control A cascade control structure is proposedwhich consists of the outer control loop (DC bus energycontrol) and the inner control loop (battery current control)as shown in Figure 5 The DC bus energy regulation lawgenerates the battery reference power 119875lowastbatt This referencevalue is then divided by the measured battery voltage 119881battin order to obtain the battery reference current 119894lowastbatt which islimited by its maximum and minimum current (119894battmax and119894battmin)

The error between the battery current and its referenceis used in another SOSM controller in order to determinethe duty cycle of the battery bidirectional converter On theone hand the battery is in the discharge mode when thesystem demands power from the battery and the duty cycleof the battery converter increases in order to supply power tomaintain the DC bus voltage On the other hand the batteryis in the charge mode when there is excess power in thesystem and the duty cycle of the battery converter decreasesand thus the battery voltage increasesTherefore the batteryconverter is controlled for DC bus energy regulation and isswitching between the charge and discharge modes [46]

341 External Control Loop For the DC bus energy regula-tion a SOSMC is employed with the error between the bus


SOC

Pload

Design

FC reference power

States basedcontrol algorithm

1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus

FC converter control law

ASTW control+

minus

requirements

Figure 4 Control law of FC current

Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt

Battery converter control lawDC energy control law

1

2Cbus(middot)

2

1

2Cbus(middot)

2

ASTW controlASTW control

Figure 5 Control law of battery current

0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET

Figure 6 Standard driving cycles (UDDS and HWFET)

energy and its reference as input The sliding manifold of theouter loop is defined as

1199042

= 119910lowast

bus minus 119910bus (25)

where 119910lowastbus = 05119862bus(119881lowast

bus)2 and 119910bus = 05119862bus119881

2

busIn view of (12) the first time derivative of 119904

2

is calculatedas follows

1199042

= minus119875fc0 minus 119875batt + 119903batt1198942

batt + 119875load (26)

Then the battery power reference is obtained as

119875lowast

batt = 1205922 (1199042) minus 119875fc0 + 119903batt1198942

batt + 119875load (27)

where 1205922

(1199042

) is the adaptive SOSM controller with the samestructure of (20) and (24)

The battery reference current is obtained as follows

119894lowast

batt =119875lowast

batt119881batt

(28)

342 Inner Control Loop The inner loop contains a SOSMcurrent controller which generates the duty cycle of thebattery bidirectional converter The sliding manifold of theinner loop is defined as

1199043

= 119894lowast

batt minus 119894batt (29)



s3

= 119894lowast

batt minus119881batt minus 119903batt119894batt minus 119906batt119881bus

119871batt (30)

The battery current controller 119906batt is designed using theadaptive SOSM algorithm

119906batt =119881batt minus 119903batt119894batt minus 119871batt1205923 (1199043)

119881bus (31)

where 1205923

(1199043



SOC

Power management controller

ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat

Figure 7 Hybrid system configuration

0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET

Figure 8 FC and battery powers under UDDS and HWFET driving cycles

Remark 6 Due to the cascade control structure and theconstant switching frequency 120596

119878

of the power electronic thecutoff frequency of the inner loop 120596

119868

is ten times higher thanthat of the outer loop 120596O and less than 120596

119878

that is 120596119874

≪ 120596119868

≪

120596119878

In order to have an effective cascade control system it isessential that the inner loop responds much faster than theouter loop

4 Simulation Results and Discussion

The proposed hybrid system and control strategies havebeen implemented in MATLABSimulink and tested for

the standard drive cycles that is the Urban DynamometerDriving Schedule (UDDS) and Highway Fuel EconomyDriving Schedule (HWFET) The UDDS and HWFET wereused to represent typical driving conditions of light dutyvehicles in the city and highway driving conditions respec-tively In this paper the driving cycle implemented in theFC-Battery hybrid system is obtained from the simulationpackage Advanced Vehicle Vehicle Simulator (ADVISOR)[49] Specific characteristics of the UDDS are shown inTable 3 The speed and mechanical power required by theelectrical vehicle is shown in Figure 6The implementation ofthe proposed EMS in the FC-battery hybrid system is shownin Figure 7


0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET

Figure 9 FC power tracking and its error under UDDS and HWFET driving cycles

The multirate simulation of the proposed FC-batteryhybrid system has been carried out Multirate approachrealizes the achievement of realistic simulation results bytaking into account some implementation issues

(1) the control evaluation rate 1198912

is less than the sim-ulation rate 119891

1

(ie the integration was carried outaccording to the Euler method)

(2) the power elements switch rate 1198913

is less than thecontrol evaluation rate 119891

2

due to switching loss

Theparameters of the PEMFC system andmultirate approachused in this study are shown in Tables 4 and 5 Parametersassociated with the FC converter control and battery con-verter control are given in Table 2

Table 3 Driving cycle specific characteristics [50]

Driving cycle UDDS HWFETDuration 1369 s 765 sDistance 1207 km 1645 kmMaximum speed 567mph 5990mphAverage speed 1958mph 4828mphAverage accelerate 050ms2 019ms2

Average decelerate minus058ms2 minus022ms2

The tests are performed under the same initial conditionsthe initial battery SOC = 05 the initial FC voltage 119881fc =

350V and the initial FC temperature 119879fc = 35315K The


0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET

Figure 10 Battery SOC under UDDS and HWFET driving cycles

0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)

Figure 11 DC bus voltage performance under UDDS and HWFET driving cycles


0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET

Figure 12 Duty cycles of the FC and battery converters under UDDS and HWFET driving cycles

0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET

Figure 13 Hydrogen consumption under UDDS and HWFET driving cycles

simulation results under UDDS and HWFET driving cyclesare shown Figures 8ndash13

It is shown from Figure 8 that both the fuel cell andbattery output powers are in their allowable operationalranges In addition the FC power works often at its optimalpower which increases the the efficiency The rate of changeof the FC power is significantly alleviated using the statebased control Figure 9 presents the performance of theproposed ASTW controller for regulating the FC power to itsreference value Figures 9(b) and 9(d) prove the effectivenessof the controller Figure 10 shows that the battery SOC aresuccessfully sustained between SOCmin = 03 and SOCmax =09 under both driving cycles

TheDCbus voltage performance is comparedwith awell-tuned linear Proportional-Integral (PI) controller as shownin Figure 11TheproposedASTWcontroller stabilized theDCbus voltage at the reference value 119881lowastbus = 420V which actsin the outer control loop while PI control results in higherfluctuation around the desired value and higher voltageovershoot compared with the adaptive ASTW control Fasterconvergence can also be observed from the enlarged viewSome overshoots of the DC bus voltage can be observedfrom Figure 11 this is because the power demands changerapidly at the DC bus during the driving process Figure 12gives the duty cycles of the FC unidirectional converter andbattery bidirectional converter which are generated from the


Table 4 PEMFC system parameters

Symbol Parameter Value119899 Number of cells in stack 381119877 Universal gas constant 8314 J(mol K)119879fc Temperature of the fuel cell 35315 K119865 Faraday constant 96485Cmol119901atm Atmospheric pressure 101325 times 10

5 Pa119879atm Atmospheric temperature 29815 K119881ca Cathode volume 001m3

119881an Anode volume 0005m3

119909O2 atm Oxygen mass fraction 023119872119886

Air molar mass 289644 times 10minus3 kgmol

119872O2 Oxygen molar mass 32 times 10minus3 kgmol

119872N2 Nitrogen molar mass 28 times 10minus3 kgmol

120574 Ratio of specific heats of air 14119862119901

Specific heat capacity of air 1004 J(kgK)120578cp Compressor efficiency 80120578cm Motor mechanical efficiency 98

Table 5 Parameters for the multirate simulation

Symbol Parameter Value1198911

Simulation rate 10 kHz1198912

Sampling rate 2 kHz1198913

Chopping frequency 1 kHz

FC current control loop and the battery current control looprespectively Both of the current control loop are based onthe proposed ASTW algorithm which act in the inner loopFigure 13 shows the hydrogen consumption underUDDS andHWFET driving cycles

5 Conclusions

This paper investigated the power management control fora FC hybrid system using a Li-ion battery stack as a sec-ondary storage element A hysteresis controller is proposedto determine the power reference for the fuel cell stack Theadaptive STW control is employed for the fuel cell converterto track the given power commandwhile satisfying the powerlimitations A cascade control structure is also designedfor the battery converter where the battery current controlacts as the inner loop and the DC bus regulation acts asthe outer loop which aims to stabilize the DC bus voltageBoth of the control loops are based on the adaptive STWalgorithm Finallymultirate simulations are carried out in theMatlabSimulink environment over two driving cycles UDDSand HWFET The simulations results have shown that theproposed approach is effective and feasible

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Al-Durra S Yurkovich and Y Guezennec ldquoStudy of non-linear control schemes for an automotive traction PEM fuel cellsystemrdquo International Journal of Hydrogen Energy vol 35 no20 pp 11291ndash11307 2010

[2] D Feroldi M Serra and J Riera ldquoDesign and analysis of fuel-cell hybrid systems oriented to automotive applicationsrdquo IEEETransactions on Vehicular Technology vol 58 no 9 pp 4720ndash4729 2009

[3] T Raminosoa B Blunier D Fodorean andAMiraoui ldquoDesignand optimization of a switched reluctancemotor driving a com-pressor for a PEM fuel-cell system for automotive applicationsrdquoIEEE Transactions on Industrial Electronics vol 57 no 9 pp2988ndash2997 2010

[4] P Thounthong S Rael and B Davat ldquoEnergy management offuel cellbatterysupercapacitor hybrid power source for vehicleapplicationsrdquo Journal of Power Sources vol 193 no 1 pp 376ndash385 2009

[5] T Kojima T Ishizu T Horiba and M Yoshikawa ldquoDevelop-ment of lithium-ion battery for fuel cell hybrid electric vehicleapplicationrdquo Journal of Power Sources vol 189 no 1 pp 859ndash863 2009

[6] P Thounthong S Rael and B Davat ldquoControl algorithm offuel cell and batteries for distributed generation systemrdquo IEEETransactions on Energy Conversion vol 23 no 1 pp 148ndash1552008

[7] J E Dawes N S Hanspal O A Family and A Turan ldquoThree-dimensional CFDmodelling of PEM fuel cells an investigationinto the effects of water floodingrdquoChemical Engineering Sciencevol 64 no 12 pp 2781ndash2794 2009

[8] R J Talj D Hissel R Ortega M Becherif and M HilairetldquoExperimental validation of a PEM fuel-cell reduced-ordermodel and a moto-compressor higher order sliding-modecontrolrdquo IEEE Transactions on Industrial Electronics vol 57 no6 pp 1906ndash1913 2010

[9] S V Puranik A Keyhani and F Khorrami ldquoNeural networkmodeling of proton exchange membrane fuel cellrdquo IEEE Trans-actions on Energy Conversion vol 25 no 2 pp 474ndash483 2010

[10] S Yin G Wang and X Yang ldquoRobust PLS approach for KPI-related prediction and diagnosis against outliers and missingdatardquo International Journal of Systems Science vol 45 no 7 pp1375ndash1382 2014

[11] S Yin G Wang and H R Karimi ldquoData-driven design ofrobust fault detection system for wind turbinesrdquo Mechatronicsvol 24 no 4 pp 298ndash306 2014

[12] S Yin X Yang and H R Karimi ldquoData-driven adaptiveobserver for fault diagnosisrdquo Mathematical Problems in Engi-neering vol 2012 Article ID 832836 21 pages 2012

[13] S Yin X Li H Gao and O Kaynak ldquoData-based techniquesfocused on modern industry an overviewrdquo IEEE Transactionson Industrial Electronics 2014

[14] C Lin H Peng J W Grizzle and J Kang ldquoPower managementstrategy for a parallel hybrid electric truckrdquo IEEE Transactionson Control Systems Technology vol 11 no 6 pp 839ndash849 2003

[15] B Geng J K Mills and D Sun ldquoEnergy management controlof microturbine-powered plug-in hybrid electric vehicles usingthe telemetry equivalent consumption minimization strategyrdquoIEEE Transactions on Vehicular Technology vol 60 no 9 pp4238ndash4248 2011


[16] BGeng J KMills andD Sun ldquoTwo-stage energymanagementcontrol of fuel cell plug-in hybrid electric vehicles consideringfuel cell longevityrdquo IEEE Transactions on Vehicular Technologyvol 61 no 2 pp 498ndash508 2012

[17] M C KisacikogluMUzunoglu andM S Alam ldquoLoad sharingusing fuzzy logic control in a fuel cellultracapacitor hybridvehiclerdquo International Journal of Hydrogen Energy vol 34 no3 pp 1497ndash1507 2009

[18] D Gao Z Jin and Q Lu ldquoEnergy management strategy basedon fuzzy logic for a fuel cell hybrid busrdquo Journal of PowerSources vol 185 no 1 pp 311ndash317 2008

[19] Z Amjadi and S S Williamson ldquoPower-electronics-basedsolutions for plug-in hybrid electric vehicle energy storageand management systemsrdquo IEEE Transactions on IndustrialElectronics vol 57 no 2 pp 608ndash616 2010

[20] J Liu S Laghrouche and M Wack ldquoAdaptive-gain second-order sliding mode observer design for switching power con-vertersrdquo Control Engineering Practice vol 30 pp 124ndash131 2014

[21] J Liu S Laghrouche and M Wack ldquoObserver-based higherorder sliding mode control of power factor in three-phaseACDC converter for hybrid electric vehicle applicationsrdquoInternational Journal of Control vol 87 no 6 pp 1117ndash1130 2014

[22] LWangH Zhang andX Liu ldquoSlidingmode variable structureIO feedback linearization design for the speed control ofPMSM with load torque observerrdquo International Journal ofInnovative Computing Information and Control vol 9 no 8 pp3485ndash3496 2013

[23] B Xiao QHu andGMa ldquoAdaptive slidingmode backsteppingcontrol for attitude tracking of flexible spacecraft under inputsaturation and singularityrdquo Proceedings of the Institution ofMechanical Engineers G Journal of Aerospace Engineering vol224 no 2 pp 199ndash214 2010

[24] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[25] L Wu W X Zheng and H Gao ldquoDissipativity-based slidingmode control of switched stochastic systemsrdquo IEEE Transac-tions on Automatic Control vol 58 no 3 pp 785ndash791 2013

[26] L Wu X Su and P Shi ldquoSliding mode control with bounded1198712

gain performance of Markovian jump singular time-delaysystemsrdquo Automatica vol 48 no 8 pp 1929ndash1933 2012

[27] L Wu P Shi and H Gao ldquoState estimation and sliding-mode control of Markovian jump singular systemsrdquo IEEETransactions on Automatic Control vol 55 no 5 pp 1213ndash12192010

[28] MR Soltanpour B ZolfaghariM Soltani andMHKhoobanldquoFuzzy sliding mode control design for a class of nonlin-ear systems with structured and unstructured uncertaintiesrdquoInternational Journal of Innovative Computing Information andControl vol 9 no 7 pp 2713ndash2726 2013

[29] B Wang P Shi and H R Karimi ldquoFuzzy sliding mode controldesign for a class of disturbed systemsrdquo Journal of the FranklinInstitute vol 351 no 7 pp 3593ndash3609 2014

[30] G Bartolini A Ferrara and E a Usai ldquoOn multi-inputchattering-free second-order sliding mode controlrdquo IEEETransactions on Automatic control vol 45 no 9 pp 1711ndash17172000

[31] Y Shtessel M Taleb and F Plestan ldquoA novel adaptive-gainsupertwisting sliding mode controller methodology and appli-cationrdquo Automatica vol 48 no 5 pp 759ndash769 2012

[32] F Plestan Y Shtessel V Bregeault and A Poznyak ldquoNewmethodologies for adaptive slidingmode controlrdquo InternationalJournal of Control vol 83 no 9 pp 1907ndash1919 2010

[33] V I Utkin and A S Poznyak ldquoAdaptive sliding mode controlwith application to super-twist algorithm equivalent controlmethodrdquo Automatica vol 49 no 1 pp 39ndash47 2013

[34] J Pukrushpan A Stefanopoulou and H Peng Control of FuelCell Power Systems Principles Modeling Analysis and FeedbackDesign Springer New York NY USA 2004

[35] S M Rakhtala A R Noei R Ghaderi and E Usai ldquoDesign offinite-time high-order sliding mode state observer a practicalinsight to PEM fuel cell systemrdquo Journal of Process Control vol24 no 1 pp 203ndash224 2014

[36] J Larminie A Dicks and M S McDonald Fuel Cell SystemsExplained vol 2 Wiley Chichester UK 2003

[37] K Kordesch and G Simader Fuel Cell and Their ApplicationsWiley 2006

[38] J C Amphlett R M Baumert R F Mann B A Peppley P RRoberge and T J Harris ldquoPerformancemodeling of the BallardMark IV solid polymer electrolyte fuel cell II Empirical modeldevelopmentrdquo Journal of the Electrochemical Society vol 142 no1 pp 9ndash15 1995

[39] S-Y Choe J-W Ahn J-G Lee and S-H Baek ldquoDynamicsimulator for a PEM fuel cell system with a PWM DCDCconverterrdquo IEEE Transactions on Energy Conversion vol 23 no2 pp 669ndash680 2008

[40] A Vahidi A Stefanopoulou and H Peng ldquoCurrent manage-ment in a hybrid fuel cell power system a model-predictivecontrol approachrdquo IEEE Transactions on Control Systems Tech-nology vol 14 no 6 pp 1047ndash1057 2006

[41] E A Muller A G Stefanopoulou and L Guzzella ldquoOptimalpower control of hybrid fuel cell systems for an acceleratedsystem warm-uprdquo IEEE Transactions on Control Systems Tech-nology vol 15 no 2 pp 290ndash305 2007

[42] P Thounthong S Rael and B Davat ldquoTest of a PEM fuel cellwith low voltage static converterrdquo Journal of Power Sources vol153 no 1 pp 145ndash150 2006

[43] S J Moura H K Fathy D S Callaway and J L Stein ldquoAstochastic optimal control approach for power management inplug-in hybrid electric vehiclesrdquo IEEE Transactions on ControlSystems Technology vol 19 no 3 pp 545ndash555 2011

[44] J T Pukrushpan A G Stefanopoulou and H Peng ldquoControlof fuel cell breathingrdquo IEEE Control Systems Magazine vol 24no 2 pp 30ndash46 2004

[45] L M Fernandez P Garcia C A Garcia J P Torreglosaand F Jurado ldquoComparison of control schemes for a fuel cellhybrid tramway integrating two dcdc convertersrdquo InternationalJournal of Hydrogen Energy vol 35 no 11 pp 5731ndash5744 2010

[46] P Garcia L M Fernandez C A Garcia and F Jurado ldquoEnergymanagement system of fuel-cell-battery hybrid tramwayrdquo IEEETransactions on Industrial Electronics vol 57 no 12 pp 4013ndash4023 2010

[47] S Njoya Motapon L Dessaint and K Al-Haddad ldquoA com-parative study of energy management schemes for a fuel-cellhybrid emergency power system ofmore-electric aircraftrdquo IEEETransactions on Industrial Electronics vol 61 no 3 pp 1320ndash1334 2014

[48] P Garcıa J P Torreglosa L M Fernandez and F JuradoldquoViability study of a FC-battery-SC tramway controlled by


equivalent consumption minimization strategyrdquo InternationalJournal of Hydrogen Energy vol 37 no 11 pp 9368ndash9382 2012

[49] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[50] United States Environmental Protection Agency ldquoDynamome-ter drive schedulesrdquo 2008 httpwwwepagovnvfeltestingdynamometerhtm

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


sharing while respecting system constraints (eg batterystate of charge (SOC) limits power limits etc) [14ndash16]In [17] a load sharing algorithm using fuzzy logic controlwas studied for a fuel cellsupercapacitor HEV In [18] afuel cellbatterysupercapacitor hybrid bus was studied by afuzzy power management controller with the effectivenessof the fuzzy controller demonstrated by some designed testsRecently energymanagement based onproportional-integral(PI) controllers have been proposed [6 19] Although PI con-trollers are easy to be tuned on-line which provide a practicalsolution to many applications they can not be robust andreliable in the presence of disturbances or uncertainties

Sliding mode technique is known for its insensitivityto external disturbance due to operating conditions highaccuracy and finite time convergence [20ndash24] Sliding modecontrol (SMC)has foundwide applications in various dynam-ical systems such as stochastic systems [25] Markovianjumping systems [26 27] and fuzzy systems [28 29] How-ever the main drawback of SMC is the so-called chatteringphenomenon [30] Adaptive sliding mode has been provento be an efficient solution which does not require thebound of uncertainties [31ndash33]The control gains are adapteddynamically to counteract the uncertaintiesperturbationswhich ensure the sliding mode To the best of the authorsrsquoknowledge it is the first attempt to apply the adaptive SOSMcontrol to the application of HEV In this paper we haveproposed a cascade control strategy for the FC hybrid systemusing an adaptive-gain super twisting algorithm (ASTW)[31] The gains of this algorithm are adapted dynamicallywhich ensures the convergence of the tracking error infinite time without a priori knowledge of the upper boundof uncertainties and perturbations A state based controlalgorithm is proposed to generate the power reference for thefuel cell stack In addition controllers are also designed forthe fuel cell and battery converters to track the given currentreferences and stabilize the DC bus voltage

The rest of the paper is divided as follows the modellingof the FC hybrid system is given in Section 2 Section 3discusses the designs of the power management controlstrategy which generates the reference power for the FCThen the control strategies for the FC and battery convertersusing the proposed algorithm are provided In Section 4simulation results are given for two real driving cycles UDDSand HWFET Finally the major conclusions are presented inSection 5

2 Model of the Hybrid Fuel Cell Power System

Figure 1 shows the schema of the studied hybrid systemfor the vehicle applications The hybrid system is composedof the PEMFC the Li-ion battery FC unidirectional DC-DC converter battery bidirectional DCDC converter andtracking motor

21 Fuel Cell System Modelling In this paper a 30 kW fuelcell composed of 90 cells in series is modeled consideringits dynamics [34] The fuel cell behavior is highly nonlinearand is dependent on several variables such as current density

stack temperature membrane humidity and reactant partialpressures Several assumptions are considered (1) the stacktemperature and humidity in the fuel cell cathode are wellcontrolled (2) the water inside the cathode is only in vaporphase and any extra water in liquid phase is removed fromthe channels (3) the input reactant flows are humidified in aconsistent and rapid way and the high pressure compressedhydrogen is available (4) the anode pressure is well con-trolled to follow the cathode pressure and (5) the currentdynamics of the motor which directly drives the compressoris negligible due to its small time constant as compared to themechanical dynamics [35]

211 Fuel Cell Stack Voltage A single fuel cell operatingvoltage can be modeled as

119881fc = (119864 minus Vact minus Vohm minus Vconc) (1)

where 119864 is the open circuit voltage and Vact Vohm and Vconcpresent the activation loss ohmic loss and concentrationloss respectively

The open circuit voltage 119864 is expressed as

119864 = 1229 minus 085 sdot 10minus3

(119879fc minus 29815)

+ 43085 sdot 10minus5

119879fc [ln (119901H2

) +1

2ln (119901O

2

)]

(2)

where 119879fc is the fuel cell stack temperature and 119901H2

119901O2

arethe partial pressures of hydrogen and oxygen respectively[34]

The activation loss Vact ohmic loss Vohm and concentra-tion loss Vconc are expressed as follows

(1) Vact = V0

+V119886

(1minus119890minus119887

1119894

) is due to the difference betweenthe velocity of the reactions in the anode and cathode[36] where 119894 = 119868st119860 fc is the current density 119868st (A)is the stack current and 119860 fc (cm

2) is the active areaV0

(volts) is the voltage drop at zero current densityand V119886

(volts) and 1198871

are constants that depend on thetemperature and the oxygen partial pressure [37 38]The values of V

0

V119886

and 1198871

can be determined from anonlinear regression of experimental data

(2) Vohm = 119894119877ohm is due to the electrical resistance ofthe electrodes and the resistance to the flow of ionsthrough the electrolyte [36]119877ohm (Ωsdotcm2) representsthe fuel cell internal electrical resistance

(3) Vconc = 119894(1198873

(119894119894max))119887

4 results from the drop in con-centration of the reactants due to the consumption inthe reaction 119887

3

1198874

and 119894max are constants that dependon the temperature and the reactant partial pressures119894max is the current density that generates the abruptvoltage drop


H2

Air

PEMFC

Battery

FC converterifc

rfc

Vfc

L fc

ufc

ibatt

rbatt

Vbatt

Lbatt

ubatt

S1

S2

S3

Battery converter

Pfc0

Pbatt0

CbusVbus

iload

Pload


M Differential

+

minus

+

minus

=

sim



and119901O2


119901O2


119889119901H2

119889119905=

119877H2

119879fc

119881an(119882H

2in minus119882H

2out minus119882H

2react)

119889119901O2

119889119905=

119877O2

119879fc

119881ca(119882O

2in minus119882O

2out minus119882O

2react)

(3)




2in is







119898st119862119901st119889119879fc119889119905


sou = 119868st (minus119879fcΔ119904

4119865+ Vact + 119868st119877ohm)

(4)


and 119862119901c


119888






119875cp =119862119901

119879atm

120578cm120578cp[(

119901sm119901atm

)

(120574minus1)120574

minus 1]119882cp (6)


119901




119871 fc119889119894fc119889119905




5 10 15 20 25 30

03

035

04

045

05

PEMFC power (kW)

Syste

m effi

cien

cy

Optimal point





119889SOC119889119905


(9)




119889SOC119889119905

= minus



2119903batt119876batt

(10)




119871batt119889119894batt119889119905




119903


119863


119891

24m 2


12 kgm 3



2




where 119910bus = (12)119862bus1198812



2

batt


119872119889V119889119905


minus1

2120588119886

119860119891

119862119863

119860119891

V2 minus119872119892 sin120572(13)




(14)



119898


that is 120578119898

= 120578(120591119898

120596119898










30 kW119894fcmin

2A119894fcmax

300A120591fc 025 s119871 fc 2 sdot 10





bus 420V






= 119891 (119909) + 119892 (119909) 119906 119910 = 119904 (119909 119905) (15)




119904 =120597119904

120597119905+120597119904

120597119909119891 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120593(119909119905)

+120597119904

120597119909119892 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120574(119909119905)

119906

= 120593 (119909 119905) + 120574 (119909 119905) 119906

(16)



and 120574119872


lt |120574(119909 119905)| lt 119887119872

and| 120574(119909 119905)| le 119861


119906 = minus120572|119904|12 sign (119904) + ]

] = minus120573 sign (119904) (17)



119904 = minus120572120574 (119909 119905) |119904|12 sign (119904) + 120596

= minus120573120574 (119909 119905) sign (119904) + (119909 119905) + 120574 (119909 119905) ](18)


lowast


1003816100381610038161003816 (119909 119905) +120574 (119909 119905) ]1003816100381610038161003816 le 120575 + 119861int

119905

0

120573119889120591

le 120575 + 119861120573lowast

119905 = 1205751

(19)



=

1205961

radic1205741

2sign (|119904| minus 120583) if 120572 gt 120572

119898

1205781

if 120572 le 120572119898

120573 = 1205761

120572

(20)

where1205961

1205741

120583 1205781

1205761

and 120572119898



119865

that is |119904| le 1205831

| 119904| le 1205832


119898





SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()


















+ 119875battchar









1199041

= 119894fcref minus 119894fc (21)



1199041


119871 fc (22)



119881bus (23)

where 1205921

(1199041


1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)


and 1205731


1


1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2





SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










H2

Air

PEMFC

Battery

FC converterifc

rfc

Vfc

L fc

ufc

ibatt

rbatt

Vbatt

Lbatt

ubatt

S1

S2

S3

Battery converter

Pfc0

Pbatt0

CbusVbus

iload

Pload


M Differential

+

minus

+

minus

=

sim



and119901O2


119901O2


119889119901H2

119889119905=

119877H2

119879fc

119881an(119882H

2in minus119882H

2out minus119882H

2react)

119889119901O2

119889119905=

119877O2

119879fc

119881ca(119882O

2in minus119882O

2out minus119882O

2react)

(3)




2in is







119898st119862119901st119889119879fc119889119905


sou = 119868st (minus119879fcΔ119904

4119865+ Vact + 119868st119877ohm)

(4)


and 119862119901c


119888






119875cp =119862119901

119879atm

120578cm120578cp[(

119901sm119901atm

)

(120574minus1)120574

minus 1]119882cp (6)


119901




119871 fc119889119894fc119889119905




5 10 15 20 25 30

03

035

04

045

05

PEMFC power (kW)

Syste

m effi

cien

cy

Optimal point





119889SOC119889119905


(9)




119889SOC119889119905

= minus



2119903batt119876batt

(10)




119871batt119889119894batt119889119905




119903


119863


119891

24m 2


12 kgm 3



2




where 119910bus = (12)119862bus1198812



2

batt


119872119889V119889119905


minus1

2120588119886

119860119891

119862119863

119860119891

V2 minus119872119892 sin120572(13)




(14)



119898


that is 120578119898

= 120578(120591119898

120596119898










30 kW119894fcmin

2A119894fcmax

300A120591fc 025 s119871 fc 2 sdot 10





bus 420V






= 119891 (119909) + 119892 (119909) 119906 119910 = 119904 (119909 119905) (15)




119904 =120597119904

120597119905+120597119904

120597119909119891 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120593(119909119905)

+120597119904

120597119909119892 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120574(119909119905)

119906

= 120593 (119909 119905) + 120574 (119909 119905) 119906

(16)



and 120574119872


lt |120574(119909 119905)| lt 119887119872

and| 120574(119909 119905)| le 119861


119906 = minus120572|119904|12 sign (119904) + ]

] = minus120573 sign (119904) (17)



119904 = minus120572120574 (119909 119905) |119904|12 sign (119904) + 120596

= minus120573120574 (119909 119905) sign (119904) + (119909 119905) + 120574 (119909 119905) ](18)


lowast


1003816100381610038161003816 (119909 119905) +120574 (119909 119905) ]1003816100381610038161003816 le 120575 + 119861int

119905

0

120573119889120591

le 120575 + 119861120573lowast

119905 = 1205751

(19)



=

1205961

radic1205741

2sign (|119904| minus 120583) if 120572 gt 120572

119898

1205781

if 120572 le 120572119898

120573 = 1205761

120572

(20)

where1205961

1205741

120583 1205781

1205761

and 120572119898



119865

that is |119904| le 1205831

| 119904| le 1205832


119898





SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()


















+ 119875battchar









1199041

= 119894fcref minus 119894fc (21)



1199041


119871 fc (22)



119881bus (23)

where 1205921

(1199041


1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)


and 1205731


1


1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2





SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










5 10 15 20 25 30

03

035

04

045

05

PEMFC power (kW)

Syste

m effi

cien

cy

Optimal point





119889SOC119889119905


(9)




119889SOC119889119905

= minus



2119903batt119876batt

(10)




119871batt119889119894batt119889119905




119903


119863


119891

24m 2


12 kgm 3



2




where 119910bus = (12)119862bus1198812



2

batt


119872119889V119889119905


minus1

2120588119886

119860119891

119862119863

119860119891

V2 minus119872119892 sin120572(13)




(14)



119898


that is 120578119898

= 120578(120591119898

120596119898










30 kW119894fcmin

2A119894fcmax

300A120591fc 025 s119871 fc 2 sdot 10





bus 420V






= 119891 (119909) + 119892 (119909) 119906 119910 = 119904 (119909 119905) (15)




119904 =120597119904

120597119905+120597119904

120597119909119891 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120593(119909119905)

+120597119904

120597119909119892 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120574(119909119905)

119906

= 120593 (119909 119905) + 120574 (119909 119905) 119906

(16)



and 120574119872


lt |120574(119909 119905)| lt 119887119872

and| 120574(119909 119905)| le 119861


119906 = minus120572|119904|12 sign (119904) + ]

] = minus120573 sign (119904) (17)



119904 = minus120572120574 (119909 119905) |119904|12 sign (119904) + 120596

= minus120573120574 (119909 119905) sign (119904) + (119909 119905) + 120574 (119909 119905) ](18)


lowast


1003816100381610038161003816 (119909 119905) +120574 (119909 119905) ]1003816100381610038161003816 le 120575 + 119861int

119905

0

120573119889120591

le 120575 + 119861120573lowast

119905 = 1205751

(19)



=

1205961

radic1205741

2sign (|119904| minus 120583) if 120572 gt 120572

119898

1205781

if 120572 le 120572119898

120573 = 1205761

120572

(20)

where1205961

1205741

120583 1205781

1205761

and 120572119898



119865

that is |119904| le 1205831

| 119904| le 1205832


119898





SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()


















+ 119875battchar









1199041

= 119894fcref minus 119894fc (21)



1199041


119871 fc (22)



119881bus (23)

where 1205921

(1199041


1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)


and 1205731


1


1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2





SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













30 kW119894fcmin

2A119894fcmax

300A120591fc 025 s119871 fc 2 sdot 10





bus 420V






= 119891 (119909) + 119892 (119909) 119906 119910 = 119904 (119909 119905) (15)




119904 =120597119904

120597119905+120597119904

120597119909119891 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120593(119909119905)

+120597119904

120597119909119892 (119909)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

120574(119909119905)

119906

= 120593 (119909 119905) + 120574 (119909 119905) 119906

(16)



and 120574119872


lt |120574(119909 119905)| lt 119887119872

and| 120574(119909 119905)| le 119861


119906 = minus120572|119904|12 sign (119904) + ]

] = minus120573 sign (119904) (17)



119904 = minus120572120574 (119909 119905) |119904|12 sign (119904) + 120596

= minus120573120574 (119909 119905) sign (119904) + (119909 119905) + 120574 (119909 119905) ](18)


lowast


1003816100381610038161003816 (119909 119905) +120574 (119909 119905) ]1003816100381610038161003816 le 120575 + 119861int

119905

0

120573119889120591

le 120575 + 119861120573lowast

119905 = 1205751

(19)



=

1205961

radic1205741

2sign (|119904| minus 120583) if 120572 gt 120572

119898

1205781

if 120572 le 120572119898

120573 = 1205761

120572

(20)

where1205961

1205741

120583 1205781

1205761

and 120572119898



119865

that is |119904| le 1205831

| 119904| le 1205832


119898





SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()


















+ 119875battchar









1199041

= 119894fcref minus 119894fc (21)



1199041


119871 fc (22)



119881bus (23)

where 1205921

(1199041


1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)


and 1205731


1


1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2





SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SOC normal

SOC low40 60

SOC ()

SOC high

SOC normal85 90

SOC ()


















+ 119875battchar









1199041

= 119894fcref minus 119894fc (21)



1199041


119871 fc (22)



119881bus (23)

where 1205921

(1199041


1205921

(1199041

) = 12059211

(1199041

) + 12059212

(1199041

)

12059211

(1199041

) = minus1205731

sign (1199041

)

12059212

(1199041

) = minus1205721

100381610038161003816100381611990411003816100381610038161003816

12 sign (1199041

)

(24)


and 1205731


1


1

= 150 1205741

= 251205831

= 01 1205781

= 25 1205721119898

= 001 and 1205761

= 2





SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SOC

Pload

Design

FC reference power


1

120591fcs + 1

Plowastfc

times

divide

Vfc

ifc

ilowastfcufc

Vbus


ASTW control+

minus

requirements


Vlowastbus

times

divideVbus

Pload

ybus

ylowastbus

Pfc0

Vbatt

ibatt

ilowastbatt

Plowastbatt+

minus

+

+

minus+

minus

Vbus

ubatt


1

2Cbus(middot)

2

1

2Cbus(middot)

2



0 200 400 600 800 1000 1200 14000

10

20

30

Time (s)

Spee

d (m

s)

0 200 400 600 800 1000 1200 1400minus40

minus20

0

20

40

Time (s)

Load

pow

er (k

W)

(a) UDDS

0 100 200 300 400 500 600 700 800minus10

0

10

20

30

Time (s)

Spee

d (m

s)

0 100 200 300 400 500 600 700 800minus50

0

50

Time (s)

Load

pow

er (k

W)

(b) HWFET



1199042

= 119910lowast



bus)2 and 119910bus = 05119862bus119881

2


2


1199042


batt + 119875load (26)


119875lowast


batt + 119875load (27)

where 1205922

(1199042



119894lowast

batt =119875lowast

batt119881batt

(28)


1199043

= 119894lowast




s3

= 119894lowast


119871batt (30)



119881bus (31)

where 1205923

(1199043



SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SOC


ufc

Hydrogen

Fuel cell converter

Battery converter

SOC

Battery

Hydrogen

SOC

Time

Fuel cell

[SOC]

Driving cycles

DC bus

Clock

[Vbus]

[ubat]

[Vbat]

Vbus

ubat

Vbat

ibat [ibat]ibat

Vbat

Vbus

Vfc

Vbat

Pbatt

[SOC]

[Vbat]

Pload

[ibat]

Pbatt

ifc

iL

ubat

ufc

ifc

iL

ibat

Vbat

Vbus

[Vbus][Vbus]

[Vbus]

VbusVbus

Vbus

Vfc

[Vbus]

Vfc

ifc

ifc

ifc

iL

Vfc

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

[Vfc]

[iL]

[ifc]

[ibat]

[Vbat]

ubatt

[ubat]

[ufc]

ufc

[ifc]

[Vfc]

[ufc]

[iL]

[ifc]

[Vfc]

Pfc

[Pd]Pd

Pfc

[ifc]

[Pd] Pd

ibat


0 200 400 600 800 1000 1200minus40

minus30

minus20

minus10

0

10

20

30

Time (s)

PfcPbatt

Pfc

andP

batt

(kW

)

(a) UDDS

0 100 200 300 400 500 600 700Time (s)

minus40

minus30

minus20

minus10

10

20

30

PfcPbatt

Pfc

andP

batt

(kW

)

0

(b) HWFET



119878


119868


119878

that is 120596119874

≪ 120596119868

≪

120596119878






0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 1000 12000

05

1

15

2

25

3

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(a) UDDS

0 200 400 600 800 1000 1200minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(b) UDDS

0 100 200 300 400 500 600 7000

05

1

15

2

25

Time (s)

FC p

ower

trac

king

(kW

)

Pfc

Plowastfc

times104

(c) HWFET

0 100 200 300 400 500 600 700minus3

minus2

minus1

0

1

2

3

Time (s)

FC p

ower

trac

king

erro

r (kW

)

Error

(d) HWFET





1




2









0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 1000 1200048

05

052

054

056

058

06

062

064

Time (s)

Batte

ry S

OC

SOC

(a) UDDS

0 100 200 300 400 500 600 700038

04

042

044

046

048

05

052

Time (s)

Batte

ry S

OC

SOC

(b) HWFET


0 200 400 600 800 1000 1200

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

19998 200 20002 200044195

420

4205

(a) ASTW (UDDS)

0 200 400 600 800 1000 1200410

415

420

425

430

435

440

445

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005415

420

425

(b) PI (UDDS)

0 100 200 300 400 500 600 700

418

420

422

424

426

428

430

Time (s)

Bus v

olta

ge (V

)

199

98 200

200

02

200

04

200

06

4195

420

4205

Vbus

(c) ASTW (HWFET)

0 100 200 300 400 500 600 700410

415

420

425

430

435

440

445

450

Time (s)

Bus v

olta

ge (V

)

199 1995 200 2005 201417418419420421

Vbus

(d) PI (HWFET)



0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 1000 12000

005

01

015

02

025

03

035

04

045

05

Time (s)

Dut

y cy

cles

DfcDbatt

(a) UDDS

0 100 200 300 400 500 600 7000

01

02

03

04

05

06

Time (s)

Dut

y cy

cles

DfcDbatt

(b) HWFET


0 200 400 600 800 1000 12000

002

004

006

008

01

012

014

016

018

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(a) UDD

0 100 200 300 400 500 600 7000

002

004

006

008

01

012

014

Time (s)

Hyd

roge

n co

nsum

ptio

n (k

g)

Hydrogen

(b) HWFET






















5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























5 Conclusions




References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article adaptive second order sliding mode...

Documents