effects of control strategy and calibration on hybridization level...

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SAE TECHNICALPAPER SERIES 2006-01-0038

Effects of Control Strategy and Calibrationon Hybridization Level and Fuel Economy

in Fuel Cell Hybrid Electric Vehicle

Kyung-Won Suh and Anna G. StefanopoulouUniversity of Michigan, Ann Arbor

Reprinted From: Applications of Fuel Cells in Vehicles 2006(SP-2006)

2006 SAE World CongressDetroit, Michigan

April 3-6, 2006

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2006-01-0038

Effects of Control Strategy and Calibration on HybridizationLevel and Fuel Economy in Fuel Cell Hybrid Electric Vehicle

Kyung-Won Suh and Anna G. StefanopoulouUniversity of Michigan, Ann Arbor

Copyright © 2006 SAE International

ABSTRACT

Using dynamic causal models for a direct-hydrogen fuelcell and a DC/DC converter we design decentralized andmultivariable controllers regulating the bus voltage andpreventing fuel cell oxygen starvation. Various controllergains are used to span the fuel cell operation from load-following to load-leveling, and hence, determine the re-quired fuel cell-battery sizing (hybridization level) and theassociated trends in the fuel economy.

Our results provide insight on the strategy and calibra-tion of a fuel cell hybrid electric vehicle with no need fora supervisory controller that typically depends on optimalpower split during a specific driving cycle. The proposedcontrollers directly manipulate actuator commands, suchas the DC/DC converter duty cycle, and achieve a desiredpower split. The controllers are demonstrated throughsimulation of a compact sedan using a mild and an ag-gressive driving cycle.

INTRODUCTION

The proton exchange membrane (PEM) fuel cell (FC) sys-tem for use in transportation needs to satisfy stringent re-quirements on transient performance and reliability. Theoverall system should function with a high degree of re-liability under a wide range of conditions. Therefore thepublic success of fuel cell vehicles (FCV) depends on ro-bust fuel cell operation based on system integration andcontrol.

The control of a PEM fuel cell mainly consists of reactantsupply, water/temperature, and power management. Lackof robustness on these control sub-systems can causecross-coupled failures. The fuel cell, running with high re-actant utilization, can often suffer from partial oxidant star-

vation in dynamic load changes even with optimized flowfield design. Insufficient gas flow associated with dynamicload may cause accumulation of excess water, possiblyblocking reactant diffusion. These anomalous operatingconditions can cause not only reversible performance de-crease but irreversible degradation [1].

Hybridization in various electric power configurations withthe fuel cell stack, DC/DC converter and battery, such asthe one shown in Figure 1, offers flexibility in managingthe power demand from the fuel cell [2]. For instance, aload-following fuel cell supplies the majority of power tothe load with a small energy buffer responsible for para-sitic losses or start-up procedures [3]. In a load-levelingfuel cell hybrid system, the battery complements the fuelcell power during transient loading. Hybridization in thefuel cell power system may protect the fuel cell from harm-ful transition and in addition may achieve higher fuel cellefficiency by leveling peak power demand from the FC.

INVERTERFUEL CELLDC / DC

CONVERTER

DC

M

Hydrogen

Air

AUXILIARYLOADS

Battery

Bus

Figure 1: Fuel cell hybrid electric vehicle configuration

The efficiency of fuel cells is generally calculated by theproduced electric energy as the output and heating valueof hydrogen as the input [4]. The cell voltage also can beused as indication of the fuel cell efficiency. However, bat-tery efficiency cannot be calculated directly because thelosses in battery during charging-discharging are varyingwith current. Total vehicle level efficiency can be com-pared through the consumed hydrogen fuel during spe-cific driving cycles.

1


The anticipated benefits of hybridization for fuel cell vehi-cle differ from those for internal combustion engine (ICE)vehicle. Hybridization in ICE vehicle enables the decou-pling of the instantaneous torque and speed demandsfrom the wheels, and in this way, it enforces the optimumengine operation. The fuel cell hybrid electric vehicle, onthe other hand, has high efficiency at wide range of powerlevels so it is not clear if hybridization will increase effi-ciency in any significant manner to justify the increase inweight and complexity associated with the addition of thebatteries. In both cases, regenerative braking helps cap-ture and reuse the energy, improving fuel economy. In-deed [5] shows that a battery-hybrid fuel cell vehicle as-sociated with regenerative braking improves efficiency upto 15 %. The efficiency gain in a fuel cell hybrid vehicledepends on the degree of hybridization [6]. The hybridsystem efficiency can be worse than the stand-alone fuelcell in some driving cycles [3, 7].

These unexplored issues highlight the importance ofdefining the achievable performance of a fuel cell powersystem and then the minimum level of hybridization.Therefore we first establish a mathematical model of aPEM fuel cell stack with a compressor driven directly bythe fuel cell power. The electrically connected FC andcompressor allow us to design a realistic air delivery con-troller for regulating the oxygen excess ratio and to cap-ture the FC performance limitation during abrupt changesin the current drawn (load) from the fuel cell. The dynamiccoupling between the voltages and currents among thefuel cell, battery and the traction load is captured by adynamic model of the DC/DC converter as shown in theelectric hybrid configuration of Figure 1. A converter con-troller is then designed to boost and regulate the voltageat the converter output. Good regulation of the voltage atthe converter output is typically achieved by large currentdrawn from the fuel cell and it is typically followed by smallcurrents drawn from the battery. The converter controllercan be tuned to avoid causing abrupt current draw fromthe fuel cell. In this paper, various DC/DC converter con-troller gains result in different levels of power split betweenthe fuel cell and the battery. It is thus possible to assessthe effects of control calibrations on the power split, FCoxygen excess ratio, compressor behavior, and vehicle ef-ficiency.

Apart from exploring the effects of control calibration, wealso clarify the benefits of coordination between the FCand the converter controller. In industry, due to propri-etary concerns the DC/DC converter controller is tradition-ally treated separately from the fuel cell controller, sim-ilarly to what we are presenting in the first sections ofthis paper. In the last section, we introduce coordina-tion between the DC/DC converter controller and the FCcontroller into a combined system controller with optimalgains that emulates an FC load-following power split sce-nario. The centralized control accounts for the limitationsin the fuel cell system and allows us to construct a con-troller for the smallest possible power assist level withoutcompromising the fuel cell operation. The results of fuel

economy and battery sizing with the dynamic model andcontrol in this work provide insight on the necessary hy-bridization of a fuel cell power system without employingcycle-dependent optimization.

FUEL CELL HYBRID VEHICLE MODEL

A complete PEM fuel cell propulsion power system in-cludes several components apart from the fuel cell stackand battery, such as an air delivery system which suppliesoxygen using a compressor or a blower, a hydrogen deliv-ery system using pressurized gas storage or reformer, athermal and water management system that handles tem-perature and humidity, DC/DC converters to condition theoutput voltage and/or current of the stack and finally in-verter/traction motor [2]. Figure 1 shows the configurationof a typical fuel cell power system which is constructedwith fuel cell, DC/DC converter and battery.

This paper presents details of the fuel cell system con-figuration and control that provides system analysis withtransient response characteristics. A complete forward-facing, causal model for a fuel cell hybrid vehicle is desir-able for component evaluation and detailed control simu-lation. The performance can be evaluated for each com-ponent and system in dynamic simulation of the forward-facing model. Interaction among the driver command, ve-hicle dynamics, traction motor load, power converters andpower sources can be highlighted.

VehicleDynamics

MCU/Motor

DC/DCConverter

Fuel CellSystem

Battery

DriverCommand

-

ControlSignals

-PI

Driving Cycle

︷︸︸︷dvcm

Ibt

vbus

Tmvst ωm

speed

Iload

Idc

Inet

Σ

Σ

Figure 2: FC HEV powertrain causality flowchart

Figure 2 depicts the causal flow chart of a fuel cell hy-brid vehicle model in Figure 1. The fuel cell hybrid vehiclemodel in this paper includes not only the forward-facingvehicle and traction motor model but also complete causalmodels for the fuel cell system, the DC/DC converter andthe battery. The fuel cell system model includes reac-tant supply and flow-pressure relations with the input com-mand of air compressor motor. The DC/DC converter ismodeled with the duty cycle as the input. Therefore it ispossible to design controllers and evaluate the feasibilityof fuel cell sub-systems in terms of the dynamic perfor-mance and power losses.

2


Specifically, the air-supply sub-system and its dynamiccontrol is implemented and evaluated. The model cap-tures the dynamic effect of the air supply compressor,which results in major power losses in a direct hydrogenfuel cell system. In this model, regenerative braking isnot included to concentrate on the interaction between theFC, battery and the load. The model for regenerative brak-ing can be added to charge the battery by the current fromthe motor after isolating the fuel cell. Cold start and shut-down are not considered in this paper. For this study, thefuel cell hybrid vehicle characteristics are assumed to bebased on a compact sedan. The values of the parametersare shown in Table 1.

Table 1: Baseline Vehicle CharacteristicsVehicleTotal vehicle mass 1591 kgAerodynamic drag coefficient 0.312Frontal area 2.06 m2

Rolling resistance coefficient 0.02Accessory load (WTM) 500 WFuel cell systemNumber of cells 381Active area 280 cm2

Maximum current 320 ATemperature 80°CMaximum power (stack) 75 kWMaximum power (system) 60 kWCompressor TurbocompressorBattery systemBattery Lead-acidCapacity 18 AhNumber of modules 31Nominal voltage 400 V

MOTOR CONTROL UNIT/MOTOR, VEHICLE MODELIn an FC electric hybrid drive train, the driver control com-mand directly manipulates the torque/power of the tractionmotor. In actual vehicle, the driver command is interpretedas a variable frequency/amplitute command through theDC/AC inverter and AC machine. In this paper, inverter,motor and control unit are modeled as static maps with thedriver torque demand, the speed of the motor ωm and theDC-bus voltage vbus as inputs and the load current Iload

as output. Therefore, the traction power is drawn from thefuel cell and the battery.

The motor torque Tm generated following the driver com-mand forms the traction force of the vehicle. The vehi-cle speed is the output of first order vehicle dynamics as-sociated with its mass and other parameters through thetraction force. In driving cycle simulation, the driver com-mand is the output from a proportional-integral (PI) con-troller that is designed for tracking the speed of a givencycle.

FUEL CELL SYSTEM MODEL The fuel cell systemmodel in this paper captures dynamic performance inpower including effects of parasitic losses. The modelalso predicts oxygen starvation from the dynamics of itsair supply system. The performance variables for the FCpower system are (i) the stack voltage vst which directlyinfluences the stack power Pfc = vstIst when the currentIst is drawn from the stack, and (ii) the oxygen excess ra-tio λ

O2in the cathode that indicates the level of oxygen

supply to the stack. The FC system configuration is de-picted in Figure 3.

Hydrogen Tank

CompressorMotor

M

Hum

idifie

ran

dT

em

peratire

Con

troller

Hydrogen PressureControl

Fuel Cell Stack

Hydrogen

Air & Water

Air

Air FlowControl

Supply Manifold

Air

vcm

patm

patm

Wcp

Wca,in

pca

psm Wca,out

vst

Ist

Figure 3: Fuel cell reactant supply system

Stack voltage is calculated as the product of the number ofcells and average cell voltage vst = nvfc. The combinedeffect of thermodynamics, kinetics, and ohmic resistancedetermines the output average cell voltage

vfc = E − vact − vohm − vconc (1)

where E is the open circuit voltage, vact is the activationloss, vohm is the ohmic loss, and vconc is the concentrationloss. The detailed equation of the FC voltage, also knownas the polarization characteristic, can be found in [8].

The FC voltage has rich dynamic behavior due to its de-pendance on dynamically varying stack variables such ascurrent density ifc = Ist/Afc, oxygen and hydrogen par-tial pressures p

O2and p

H2, and cathode pressure pca. De-

pending on the current drawn from the fuel cell and the airsupply to the fuel cell, the stack voltage varies between220 V and 350 V.

The total current drawn from the fuel cell stack, Ist is de-fined by the net current Inet which is the current from theFC to the DC/DC converter (in Figure 2), and augmentedby the current load drawn from all of the auxiliaries andparticularly from the compressor motor, Icm,

Ist = Inet + Icm. (2)

Here it is considered that the compressor motor con-tributes the largest percent of losses [9]. In this paper, thecompressor power Pcm, or current Icm is supplied directlyfrom the fuel cell instead of a secondary battery, establish-ing a power-autonomous fuel cell system that provides netcurrent Inet.

3


We assume a compressed hydrogen supply as shown inFigure 3, which simplifies the control of anode reactantflow. We also assume that the anode pressure is regu-lated to follow the cathode pressure. Controlled anodepressure can be achieved either with anode recirculationor a dead-ended anode outlet. The cooler and humidifierare neglected for this work because their power require-ments are much smaller than that of the compressor [10].

The dynamic behavior of the variables associated with theair flow control, namely, oxygen pressure p

O2, total cath-

ode pressure pca, and oxygen excess ratio in the cathodeλ

O2can be found in [8]. The flow dynamics of the oxygen

and hydrogen reactants are governed by pressure dynam-ics through flow channels, manifolds and orifices.

Mass continuity of the oxygen and nitrogen inside thecathode volume and the ideal gas law yield

dpO2

dt=

R̄Tst

MO2

Vca

(W

O2,in − W

O2,out − W

O2,rct

), (3)

dpN2

dt=

R̄Tst

MN2

Vca

(W

N2,in − W

N2,out

)(4)

where Vca is the lumped volume of cathode, R̄ is the uni-versal gas constant, and M

O2and M

N2are the molar

mass of oxygen and nitrogen, respectively.

The compressor motor state is associated with the ro-tational dynamics of the motor through thermodynamicequations. A lumped rotational inertia is used to describethe compressor rotational speed ωcp

dωcp

dt=

1

Jcp

(τcm − τcp) (5)

where τcm is the compressor motor torque definedthrough the supplied power in (8) and τcp is the loadtorque of the compressor calculated through nonlinearmaps supplied by the manufacturer (function of pressureratio, flow, and compressor speed).

The rate of change of air pressure in the supply manifoldthat connects the compressor with the fuel cell (shown inFigure 3) depends on the compressor flow into the supplymanifold Wcp(ωcp, psm, patm), the flow out of the supplymanifold into the cathode Wca,in and the compressor flowtemperature Tcp

dpsm

dt=

R̄Tcp

Ma,atmVsm

(Wcp − Wca,in) (6)

where Vsm is the supply manifold volume and Ma,atm isthe molar mass of atmospheric air.

The supply manifold model describes the mass flow ratefrom the compressor to the outlet mass flow. A linear flow-pressure condition Wca,in = kca,in(psm − pca) is parame-terized experimentally after assuming small pressure dif-ference between the supply manifold pressure psm andthe cathode pressure pca which is the sum of oxygen, ni-trogen and vapor partial pressures pca = p

O2+ p

N2+ psat

where psat is the vapor saturation pressure. The totalflow rate at the cathode exit Wca,out(pca, patm) is calibratedwith the nozzle flow equation because the pressure differ-ence between the cathode and the ambient pressure islarge in pressurized stacks.

The rate of oxygen consumption WO2

,rct = MO2

nIst

4Fin (3)

depends on the stack current Ist and the Faraday numberF . The oxygen excess ratio

λO2

=W

O2,in

WO2

,rct

(7)

is typically regulated at λrefO2

= 2 to reduce the formationof stagnant vapor and nitrogen films in the electrochemicalreaction area. Values of λ

O2lower than 1 indicate oxygen

starvation and have serious consequences for stack life.

The compressor motor torque τcm = Pcm/ωcp depends onthe power

Pcm = vcm(vcm − kvωcp)/Rcm (8)

provided by the compressor motor, which is calculated us-ing the compressor motor voltage input vcm and its rota-tional speed ωcp assuming an ideal DC motor.

To calculate the current consumed by the compressor, weassume again that the compressor motor has an idealpower transformer and supplies the necessary power Pcm

in (8) by drawing a current Icm at the stack bus voltagevst,

Icm = Pcm/vst (9)

where vst is given by the polarization curve in [8]. Thus thecompressor motor current, that adds to the current drawnby the DC/DC converter from the fuel cell, is implementedso that Pcm is simply drawn from the stack through a com-pressor motor control unit instantaneously.

DC/DC CONVERTER MODEL The DC/DC convertertransforms the DC fuel cell stack power to the outputvoltage-current requirements of the external power de-vices that connect to the FC system. Here we consider aDC/DC converter (shown in Figure 4) boosting stack volt-age to the 400 V DC-bus (vbus).

The input voltage vst and current Inet of the converter arethe FC output voltage and the net FC current. The outputvoltage vbus depends on the output current Idc and theduty cycle d of the solid state switch in the circuit. Theinductance of the input inductor Lin and the capacitanceof the output capacitor Cout are shown in Figure 4.

An average nonlinear dynamic model can be used to ap-proximate the boost converter switching dynamics

Lin

dInet

dt= vst − (1 − d)vbus,

Cout

dvbus

dt= (1 − d)Inet − Idc (10)

4


D Cvst

Inet Idc

d

Lin

Cout Zload

vbus

Figure 4: DC/DC boost converter

with inputs Idc and vst and outputs, the bus voltage vbus

and the current from the fuel cell Inet.

BATTERY MODEL The battery current is determinedby an internal resistance model. The battery open cir-cuit voltage vo and the internal resistance Rint are staticfunctions of the battery state of charge (SOC) as shownin Figure 5 (a) and temperature T . The internal resis-tance of the battery also changes with sign of the cur-rent, or charging/discharging as shown in Figure 5 (b).Assuming the battery is placed in parallel with the DC/DCconverter, as shown in Figure 1, the terminal voltage ofeach battery module is determined by the DC-DC con-verter (vbt = vbus/31) and the battery current is then

Ibt =vo(SOC, T ) − vbt

Rint(SOC, sign(Ibt), T ). (11)

Here we assume that the battery temperature is main-tained constant with an external cooling circuit. The bat-tery parameters are based on ADVISOR model [11].

0 0.2 0.4 0.6 0.8 1

12

12.5

13

State of charge

Bat

tery

op

en c

ircu

it v

olt

age

v o (

V)

(a) Battery open circuit voltage vo

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

State of charge

Inte

rnal

Res

ista

nce

Rin

t (Ω

)

dischargecharge

(b) Internal resistance Rint

vbt−� �

�Σ

+� 1

Rint

/vo ��

�−

kbt

s

Ibt �SOC

(c) Block diagram

Figure 5: Battery model

The SOC is calculated from the battery current and thecapacity of the battery (1/kbt)

dSOC

dt= −kbtIbt. (12)

Figure 5 (c) shows the block diagram of the battery modeland the relationship between the battery parameters, Rint

and vo, and the state of charge.

To insure proper shut down and start-up power from thebattery, the battery should remain half charged. The SOCof each of the 31 battery modules is indeed maintainedat 0.6 as shown later by regulating the bus voltage at400 V. Note that at SOC=0.6 a battery module has opencircuit voltage of 12.9 V (Figure 5 (a)), thus 31 modulesat SOC=0.6 can be connected in parallel with the 400 Vbus.

CONTROL OF FC HYBRID POWER

In most cases, the fuel cell with its compressor and com-pressor controller is viewed as one sub-system and theconverter with its controller as another. Two different con-trol objectives, oxygen excess ratio regulation in the fuelcell and bus voltage (or battery SOC) regulation in theDC/DC converter are pursued by two controllers. The twocontrollers are calibrated separately and small correctionsare performed after the two sub-systems are connected.This control strategy is called decentralized and is tradi-tionally followed in industry due to proprietary concernsbetween the FC and the DC/DC converter manufactur-ers. The calibration is called sequential, because onecontroller is tuned and then the other is re-tuned for a rea-sonable tradeoff between the two objectives.

CONTROL OF THE AIR SUPPLY SUB-SYSTEM InPEM fuel cells fed by compressed high-purity hydrogen,dynamic performance in the range of 0.1-1 second mainlydepends on the air supply sub-system [9]. Excludingstart-up and shut down periods, the transient responseassociated with controlling air and avoiding oxygen star-vation is a key factor in hybrid vehicle design. To concen-trate on control of the air supply, the humidity and tem-perature of the fuel cell stack is assumed to be controlledperfectly by dedicated hardware and controller.

The control objective of regulating the oxygen excess ra-tio λ

O2can be achieved by a combination of feedback

and feedforward algorithms that automatically defines thecompressor motor voltage input vcm. Since the oxygenexcess ratio λ

O2is not directly measured, we control λ

O2

indirectly by measuring the compressor air flow rate Wcp

and the demanded load current Ist. Figure 6 shows thefeedback and feedforward controllers which are designedto regulate the oxygen excess ratio in an autonomous fuelcell power system.

CMLoad

H 2 Tank

AirCompressor

MSetpoint

MapFeedbackController

FeedforwardController

λO2

Ist

vst

vcm

vffcm

vfbcm

Inet

Inet

Icm

Wcp

W refcp

eW

−+

++

Figure 6: Schematic of fuel cell with air flow control usingcompressor

5


A feedforward controller is essential for oxygen excess ra-tio regulation because the compressor air flow is far fromthe cathode inlet and there is only an indirect measure-ment of λ

O2. Feedforward control can accurately regulate

λO2

to its desired value at steady-state if all the model pa-rameters are known. Specifically, feedforward control toair compressor voltage vff

cm can be applied based on thenet current to the load, Inet, i.e. the compressor motorvoltage is vff

cm = f(Inet) [12].

To improve steady-state λO2

regulation despite modelingerrors or device aging, the feedforward controller vff

cm canbe combined with a feedback controller based on the com-pressor flow measurement Wcp (shown in Figure 6). Thesetpoint map in Figure 6 defines the demanded air flowrate W ref

cp for the flow rate measurement position basedon the stack current measurement [13], the desired oxy-gen excess ratio λref

O2

and the atmospheric humidity ratiowatm

W refcp (Ist, λ

refO2

) = (1 + watm)1

xO2

λrefO2

MO2

nIst

4F. (13)

A proportional and integral (PI) controller can be appliedto the difference of Wcp and W ref

cp . Finally the compressorcontrol command can be written as

vcm(t) = vffcm(t) + vfb

cm(t)

= f(Inet) + KP

(W ref

cp (Ist(t)) − Wcp(t))

+KI

∫ t

0

(W ref

cp (Ist(τ)) − Wcp(τ))dτ. (14)

Regulating air flow based on the flow rate measurementat the supply manifold inlet has a potential limitation be-cause the actual air flow at the cathode inlet is not thesame as that at the compressor outlet. The volume ofsupply manifold including humidifier and heat exchangerafter the flow meter causes significant lag or delay on reg-ulating oxygen excess ratio inside the stack [8, 14]. On theother hand, using a large compressor control effort mayovercome the limitation above at the risk of causing insta-bilities when the compressor draws current directly fromthe stack [12, 15]. To address these limitations, the loadcurrent to the fuel cell stack should be shaped (filtered) tomatch the dynamic performance of the air sub-systems.

POWER CONVERTER CONTROL In the DC/DC con-verter model described in Figure 4 and (10), the only con-trol input is the duty cycle of the DC/DC converter. Theduty cycle, the actual control command to the DC/DC con-verter, is controlled in order to achieve the following objec-tives: (a) protect the fuel cell system from abnormal loadincluding transient (b) maintain state of charge of the bat-tery (c) maintain the DC-bus voltage vbus (d) regulate thecurrent (from both the fuel cell and battery) to the opti-mized values if supervisory control demand exists. A con-trol strategy for splitting power between the fuel cell andthe battery is implemented based on controlling the duty

cycle of the DC/DC converter. In our case, the fuel cell isaugmented with the DC/DC boost converter, matching thevoltage of the DC-bus, vbus to the desired value vref

bus . Bychanging the duty cycle, the net current of the fuel cell andthe voltage of the battery which is equal to the bus voltagecan be regulated, but not independently from each other.

Figure 7 shows the controller design for a DC/DC con-verter. Dual loop control (voltage/current control) can beimplemented for the DC/DC boost converter [16]. Bothcurrent of the fuel cell, Inet and voltage of the bus, vbus

are controlled by the feedback controller. Regulating vbus

to a vrefbus is equivalent to regulating Ibt to zero due to the

integration achieved naturally through the battery state ofcharge (see Figure 5). The regulation at zero battery cur-rent ensures that the battery serves as a power assist de-vice without an explicit supervisory controller.

vref

bus

� �Σ-

� Cv� �

Σ-

� CI�d DC/DC

Converter

�

�

vbus

Inet

�

�

vst Idc

�

Figure 7: DC/DC boost converter control

In this control scheme, the outer loop controller Cv is com-posed of a proportional-integral (PI) controller for zerosteady-state error in DC-bus voltage vref

bus . Then the out-put from Cv can be the virtual reference of Inet, whichbecomes the current drawn from the fuel cell when theconverter connects to the fuel cell. A proportional con-troller (P) is used for the net fuel cell current controllerCI . Both P and PI controllers for Cv and CI , respec-tively, can be tuned sequentially using classical controltechniques. The Cv and CI controllers can also be tunedusing single-input, single-output classical proportional, in-tegral and derivative (PID) control tuning techniques forregulating vbus. Indeed, adding a proportional feedbackCI around the Inet measurement is equivalent to a deriva-tive controller around vbus which is needed to dampen thetypically under-damped DC/DC converter dynamics [17].

We choose to apply a model-based linear quadratic reg-ulator approach after transforming the Cv and CI con-trollers to state feedback as follows. The controlled dutycycle d is

d(s) = −KDvInet(s) − KPvvbus(s) −KIv

svbus(s) (15)

and formulated as state feedback when an integrator isadded for the vbus regulation objective. The optimal statefeedback gains KDv, KPv and KIv can be selected froma linear quadratic regulator design. With known gains,the two equivalent controllers, Cv and CI , are separatedCv(s) = KPv

KDv+ KIv

KDvsand CI(s) = KDv.

If there is a pre-defined current command from the super-visory control or fuel cell system itself, the current loop (in-ner loop), CI control can be used without the outer loop

6


Cv. The demanded current can be drawn from the fuelcell as fast as the control bandwidth of the inner loop al-lows. The supervisory command may decide the fuel cellcurrent for optimal efficiency in terms of energy manage-ment or dynamic FC limitations such as oxygen starva-tion. Many FC manufacturers bundle their FC with a fuelcell controller unit that broadcasts the maximum FC cur-rent that is safe to draw from the FC. This signal can thenbe used with the inner loop controller CI , eliminating theCv controller. Nonlinear logic such as a slew rate limiter,saturation or filter can be added to shape the current de-manded from the fuel cell stack. However, current con-trol can lead to conservative operation of the fuel cell orexcessive battery use. Due to the complexity and uncer-tainty in the fuel cell system, control of battery current haslower priority most times. Thus it is necessary to imple-ment high fidelity logic that can handle the fuel cell andbattery performance with extensive optimization.

The outer loop through the selection of Cv gains mainlyhandles the bus voltage regulation if there exists no super-visory control command. We define the DC/DC converterloop time constant τ

DCas the time needed to regulate vbus

within 63 % of vrefbus after a load disturbance Idc. This time

constant also defines how fast Inet is drawn from the FCand should be tuned to match the dynamic performanceof the fuel cell system. The Cv calibration allows us tomodify the fuel cell current request based on its impact onoxygen starvation or other dynamic limitations. The dualloop controller in (15) shows that the dual loop can man-age the fuel cell system and battery performance in hybridpower and achieve different power split levels dependingdirectly on the controller Cv gains and the achieved closedloop time constant τ

DC.

DISCUSSION OF SIMULATION RESULTS

The simulation results from the causal model for thefuel cell hybrid powertrain show the impact of differentsub-system control designs on the hybrid design. Twodifferent control calibration emulating load-following andload-leveling scenarios were designed to demonstrate thecharacteristic of the fuel cell operation. Both controlstrategies use decentralized control to show the effectof controller design on the performance of oxygen sup-ply and power split. Simulation comparison is performedfirst using the FTP (Federal Test Procedure) driving cy-cle, which emulates an urban route as shown in Figure 8.Battery and FC sizes are fixed in the simulation analysisto concentrate on the effect of the control strategy (effectof Cv calibration).

Figure 9 shows the simulation results for a portion of theFTP driving cycle with two different power control calibra-tions. First a controller calibration, that results in a load-leveling FC hybrid, is considered which uses limited FCpower and relies on transient power from the battery. Thepower split is achieved by the DC/DC converter control in(15) with low bandwidth (τ

DC=2 s) in the voltage loop. The

other strategy shown is a load-following FC, which uses

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Figure 8: Vehicle speed on the FTP cycle

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icle

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tery

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Figure 9: Power split in the FTP driving cycle with respectto control calibration

the FC power to the maximum whenever needed. Thecontrol calibration was performed by changing the band-width of the DC/DC converter response, i.e., fast responseof the DC/DC converter for load-following FC operation(τ

DC=0.6 s).

During cycle simulation, the operating characteristics ofthe FC hybrid vehicle depend on the control calibration.Although both the load-leveling and load-following FC hy-brid show limited FC net power below 36 kW, maximumpower from the battery differs from 17 kW (load-leveling)to 7.5 kW (load-following). As can be seen in Figure 9,battery power is mostly used as transient power assist inload-leveling FC hybrid.

The changes in control calibration have limited effect onthe fuel cell in the case of FTP driving cycle (mild powerdemand), leading to FC usage up to current density of0.43–0.53 A/cm2 as can be seen in Figure 10 (a) and (b).Even though load-following operation of FC shows higherpower use in FC (0.53 A/cm2), the histogram distribution(in the bar graph) shows similar overall characteristics. Inboth cases, the FC operates in the region of system effi-ciency over 45 %.

Simulation comparison is also performed on a portion ofthe US06 driving cycle which represents driving with hard-

7


0 0.2 0.4 0.6 0.8 1Current Density (A/cm2)

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Figure 10: System efficiency (-x-), FC response (· · ·) anddistribution (bar) for the FTP cycle

acceleration and high power demands as shown in Fig-ure 11. Figure 12 shows the simulation comparison withtwo different power control calibrations during the portionof the US06 cycle. During aggressive demands in propul-sion power, the operating characteristics of the FC de-pend on the control strategy. The load-leveling FC hybridshows limited FC power up to 40 kW and uses batterypower up to 30 kW. The load-following FC tuning uses FCpower to satisfy approximately the maximum transient ve-hicle power demand of 50 kW.

In both cases, accurate air-supply and power-assist en-sure regulation of oxygen supply in safe regimes as can

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Figure 11: Vehicle speed on a portion of the US06 cycle

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icle

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Figure 12: Power split in a portion of US06 driving cyclewith respect to control calibration

be seen in Figure 13 (a) and Figure 14 (a). The oxy-gen excess ratio λ

O2is well regulated around the desired

setpoint (λrefO2

= 2) without large excursion, which couldcause oxygen starvation. The regulation is achieved de-spite the large currents drawn from the fuel cell, 0.7 A/cm2

and 1 A/cm2 for the load-leveling and load-following cali-brations as shown in Figure 13 (b) and Figure 14 (b). Asthe power demand of the traction motor changes, deficitpower from fuel cell is naturally covered by the battery fora short while. Battery current is not used when powerfrom the fuel cell follows the motor load. The changes inSOC of the load-leveling system are larger than that ofload-following system, but battery usage for power-assistis minimal in both cases as intended.

It is observed that the hydrogen fuel economy is almostinvariant to the control tuning, being 66–67 MPGE (milesper gallon equivalent to the energy stored in one gallon ofgasoline) on the FTP cycle and 44 MPGE on the US06cycle as can be seen in Figure 15. As it is shown in Fig-ures 10, 13 (b) and 14 (b), aggressive fuel cell use, whichmight lower the fuel cell efficiency during a load-followingFC calibration, is only effective for a short period. Thusthe hydrogen fuel consumption shows no difference over-all with respect to control calibrations. However, the re-sults in battery usage ΔSOC (0.51 % in load-following vs.up to 5 % in load-leveling for US06) and maximum power(15 vs. 30 kW) suggest that it is feasible to accommodatea smaller size battery, saving weight and volume in load-following FC. Thus, FC transient power response and notefficiency is the key consideration in sizing the battery ina hybrid FC vehicle.

As can be seen in λO2

and the battery current profile inFigure 14, minimizing battery power with load-followingcalibration is followed by larger deviation in oxygen ex-cess ratio than that with load-leveling calibration. Highbandwidth in regulating vbus to vref

bus results in abrupt Inet

variation and thus drop in λO2. It is more clear in Figure 16

8


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(a) FC current, oxygen excess ratio, battery current and SOC


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Figure 13: Fuel cell and battery operating characteris-tics of hybrid vehicles for a portion of the US06 cycle -load-leveling FC

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Figure 14: Fuel cell and battery operating characteris-tics of hybrid vehicles for a portion of the US06 cycle -load-following FC

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

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Figure 15: Battery usage and fuel economy with respectto controller calibration and the cycle

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Figure 16: Battery usage and oxygen excess ratio withrespect to controller calibration and the cycle

9


that there is a tradeoff between the two performance vari-ables, namely, the battery SOC and oxygen excess ratio.The oxygen excess ratio regulation degrades when theSOC variations are reduced. Therefore, decision in con-troller tuning and battery sizing should be done under thespecification for maximum allowable oxygen excess ratiodeviation.

In the controller tuning, actuator limits should be alsobe taken into account. Specifically, in a high-pressureFC system with an air supply compressor, the dynamicbehavior of the compressor imposes additional limita-tions through its surge and choke characteristics. Surgecauses large variations in flow and choke is an upper limitto the compressor air flow. In a fuel cell system there isa potential for both compressor surge and choke duringan abrupt decrease and increase, respectively, in the ap-plied compressor voltage command vcm. Figure 17 showsthe compressor transient response with load-following FCon a portion of the US06 cycle. As can be seen in theFigure 17, the transient responses are mostly within theregion of safe compressor operation, not falling into thesurge region (left solid line) or choke region (right solidline). A more sophisticated control for surge prevention bymanipulating current load can be found in [18].

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Figure 17: Compressor transient response(blue line) onstatic compressor map(x) with load-following FC power

Another significant compressor consideration arises fromits parasitic loss and its effects on the FC system effi-ciency at low loads. Lowering the minimum air flow ratein the compressor helps in achieving high efficiency in lowpower ranges [19]. The minimum air flow rate in the com-pressor can be as low as 5 g/s (the air flow at the maxi-mum power is 95 g/s) with the controller described in thispaper. Also note here that the fuel cell model in this workis not turned off anytime during simulation because 500 Wof accessary load is always applied independently of thevehicle speed. The simulation result shows that the FCefficiency is always over 40 % mainly because of low min-imum air flow rate explained above (see all histograms ofdriving cycle simulations).

CENTRALIZED CONTROL

In fuel cell hybrid power systems, the performance vari-ables, oxygen excess ratio and battery SOC, are definedthrough the interaction between the fuel cell system andDC/DC converter. Controller bandwidth of the DC/DCconverter mainly determines SOC by vbus regulation andλ

O2through controlling current from the FC, Inet. Another

control design that takes into account directly the tradeoffbetween small excursions in λ

O2and SOC is called multi-

variable control and it results in a centralized controller asshown in Figure 18.

Fuel CellSystem

DC/DC &Battery

Measurement

FCController

DC/DCController

StateEstimator

λO2

vcm

dΣ

Σ

Iload

Ibt

Ist

...

vst

Inet

Figure 18: Centralized control architecture in fuel cell hy-brid vehicle

We apply a model-based linear quadratic regulator ap-proach for the whole FC-DC/DC-battery hybrid system.This coordinated control preserves the control authorityon oxygen regulation and power distribution in the sameway as decentralized control, and in addition introducesinteraction between the FC and the converter controllers.The bandwidths achieved in the two decentralized con-trollers (vcm-Wcp and d-vbus loops) are preserved with thecentralized controller. The resulting optimal control pro-duces additional command to d through the estimated de-viation in λ

O2. Moreover, the vcm command is now shaped

through its effects to current drawn from the battery Ibt.

Note here that the centralized controller penalizes devia-tions of the battery current Ibt instead of vbus in order tominimize SOC deviation. As can be seen from the decen-tralized load-following FC hybrid scheme (in Figure 14),reduced Ibt helps minimizing SOC indirectly. The infor-mation that is required for the centralized controller iscollected by the state estimator designed from the vari-ous existing measurements, namely, the stack current Ist,the stack voltage vst and the supply manifold pressurepsm [17].

This communication and coordination help obtain accu-rate control in air delivery and improve transient FC per-formance. Communication between the FC controller andDC/DC controller yield optimized performance in coordi-nated control, resulting in minimal battery usage. Fig-

10


ure 19 shows the simulation result of the centralized con-trol for the portion of the US06 cycle. As can be seen inthe figure, the maximum current from the battery is limitedto 30 A (or 12 kW power), compared with the 15 kW max-imum power obtained from the load-following decentral-ized control in Figure 14. The variation in SOC is 0.39 %,which is lower than the 0.51 % achieved through the load-following decentralized control in Figure 15.

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Figure 19: Fuel cell and battery operating characteristicsof hybrid vehicles for a portion of the US06 cycle - central-ized control

CONCLUSION

In this paper we consider a compact sedan fuel cell elec-tric hybrid with a compressor driven 75 kW proton ex-change membrane fuel cell, a boost DC/DC converter anda battery, and assess the effect of different control cali-brations and strategies in the power split, the vehicle ef-ficiency, the battery utilization and the FC oxygen star-vation. A forward-facing (causal) model is used and theassessment is performed for two different driving cycleswith mild (FTP) and aggressive (US06) accelerations.

The overall controller automates two processes. First, itadjusts the FC air flow through a compressor motor com-mand to minimize oxygen starvation periods. Second, itregulates the bus voltage through the duty cycle of theboost converter. The FC compressor controller is novelbecause its calibration balances the benefits from the in-stantaneous flow increase and its drawbacks from the in-crease in the FC load (parasitic losses). Once the FC con-troller is tuned, a DC/DC converter controller is designedto transform the unregulated FC voltage to regulated busvoltage.

Different gains in the converter controller achieve differenttransient responses in the bus voltage regulation. Fastvoltage regulation corresponds to a load-following FC cal-ibration with high FC utilization and low battery utilization(50 kW in FC power versus 15 kW in battery power forthe aggressive cycle). Slow voltage regulation results in aload-leveling FC calibration that does not exhibit any sig-nificant benefits when compared to the load-following cal-ibration. The control calibration has minimal effect on fueleconomy primarily because typical driving cycles can beaccomplished by a well controlled FC with efficiencies upto 45 %. A smaller battery size (15 kW versus 30 kW) canreduce the vehicle weight and volume without adverselyaffecting the FC performance (efficiency, oxygen excessratio) or requiring operation close to the compressor surgeand choke limits.

The control design in this work deals with actual currentand voltage instead of power unlike many other papers,respecting their causal relationship. Also the designedcontrol system does not require inner loop controllers thatrealize the power split command from a supervisory con-troller since the designed controllers manipulate directlyphysical actuators setting in the FC stack system and theDC/DC converter. Therefore applying and re-tuning ourcontrol methodology to various hardware configurationscan be done directly without cycle dependent optimiza-tion.

ACKNOWLEDGMENTS

This work is funded by NSF 0201332 and the Automo-tive Research Center (ARC) under U.S. Army contractDAAE07-98-3-0022.

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effects of control strategy and calibration on hybridization level...

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