optimization and control of fuel cell electric vehicles (fcev)annastef/fuelcellpdf/linoacc06.pdf2006...

2006 American Control Conference, Minneapolis Workshop “Fuel Cell Power System Modeling and Control”

Optimization and Control of FCEV, Lino Guzzella, ETH Zurich, http://www.imrt.ethz.ch page 1

Optimization and Control of

Fuel Cell Electric Vehicles (FCEV)

Lino Guzzella

ETH Zurich

http://www.imrt.ethz.chAs presented in

The workshop

2006 American Control Conference, Minneapolis

Workshop “Fuel Cell Power System Modeling and Control”



Optimization and Control of Fuel Cell Vehicles (Lino Guzzella, ETH Zurich)

Abstract: Fuel cells are one option for future clean and efficient propulsion systems for

passenger vehicles. In this module first the advantages and drawbacks of such an

approach are discussed on a broader perspective. Then the main components of the

system to be analyzed are introduced and appropriate mathematical descriptions are

presented (“backwards” or “quasi static” formulations). The main goal is to correctly

predict the fuel consumption and system efficiency for test cycles and realistic driving

patterns. Once these models are available, the main approaches for system optimization

are discussed. Several problem areas are mentioned (structural optimization, system

parameter optimization, supervisory control algorithms). Several case studies show how

these tools are applied to optimize the performance of real vehicles.



Remark

• Some additional slides

• Sequence of slides rearranged (slightly)

Please see me for the most recent version.



World Primary Energy Demand

Oil and gas together account for more than 60% of the growth in energy

demand between now and 2030 in the Reference Scenario

Coal

Oil

Gas

Other renewables Nuclear Hydro 0

2 000

4 000

6 000

8 000

10 000

12 000

14 000

16 000

18 000

1970 1980 1990 2000 2010 2020 2030

Mto

e

1971

© OECD/IEA (2006)



OECD Oil Demand Growth by Sector, 1999-2004

In the OECD, the transport sector accounted for almost all the oil demand growth

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Power

generation

Industry Transport Other

mb

/d

© OECD/IEA (2006)



Source: Schäfer & Victor (2000), Transportation Research A, 34(2): 171-205.



0 5000 10000 15000 20000 25000 30000 35000 40000

GDP per capita (dollars)

0

100

200

300

400

500

600

700

800

900

ve

hic

les p

er

1,0

00

pe

op

le

Italy

UKJapan

USA

Germany

France Canada

IsraelKorea

Poland

Malaysia

MexicoBrazil

Russia

Thailand

IndonesiaChina

India

Vehicle Ownership

© OECD/IEA (2006)

The potential for increased vehicle ownership in emerging markets is enormous



Focus on models, methods and tools for the minimization

of the fuel consumption.

Main idea: model-based optimal management of several

energy conversion devices (“supervisory control”).

Many important aspects not presented in this talk (drivability,

cost, etc.)

FCEV are vehicles, i.e., most approaches useful in other

cases (ICEV, HEV, …) as well.

Introduction



Why FCEV?

• Excellent drivability

• Zero pollutant emission (neglecting “well-to-tank”)

• Reasonable energy density (range)

• Excellent tank-to-wheel fuel economy, in particular in

part load conditions



Diesel gasoline

CNG

"hot" Ni/MH Pb

3

2

1

H 2

batterieshydro carbons

kWh/kg

Net energy densities, i.e., including average engine/motor efficiencies



„well-to-tank“

drivinglosses

driving profile

200

100

100 900 1000 1100 12008000

50

primary energysources

on-boardstorage + -H2

propulsion system

vehicle

refineries, …

„vehicle-to-miles“

„tank-to-vehicle“

Focus on “tank-to-miles” (caution!)



FbFl

Fr

vaerodynamic

friction

rolling frictioninertial forces

Energy Losses Vehicles



200

40

80

20

100 900 1000 1100 1200

v km/h

t s800

4 Wiederholungen

0-40

60

100

120

Test Cycles (“to compare apples with apples”)

Many other cycles in use (FUDS, Japan, proprietary, …)

Real driving patterns more “aggressive” than MVEG-95

four repetitions



E Af cw 19'000 + m cr 840 + m 11 kJ /100km

0.5

0

mass

aero rolling

Af cw = 0.7 m2 , cr = 0.012, m = 1'500 kg

Full-size car

Mechanical Energy (MVEG-95, no recuperation)

Sensitivities (MVEG-95, no recuperation)



t0 100

770 m

Pmax

Drivability

Problem!

Full-size car: average power MVEG-95 7 kW

maximum power MVEG-95 34 kW

power to reach 100 km/h in 10 s 115 kW

Af cw = 0.7 m2 , cr = 0.012, m = 1'500 kg

Acceleration time from standstill to 100 km/h



Part-Load Problem

Input

Output

idling input

0

part-load

output

part-load

input

full-load

output

full-load input



cooling system

I

U

hydrogentank (200 bar)

H2

pump

air

air & water

humidifier

motoredsupercharger

u2

PC

u1

fc

fc

u4u3

FC Stack/System

fc =Pfc

PH2

, =Pfc Paux

PH2



Efficiency (experimental data test bench)



Efficiency (experimental data road tests)

FC stack (electrochemical) efficiency

FC system efficiency



A Second Electric Power Source

• FC too expensive to be sized for drivability specs.

• Part-load problem a second reason why FC must not

be chosen to cover full power range.

• FC are not reversible energy converters (recuperation).

A second power source with high power density (kW/kg)

must be included (probably …). Supercaps could be a

good option, other alternatives possible.

This additional element renders the optimization problem

much more interesting!



Estimate the braking power dissipated in standard brakes

when decelerating a sport car (mass approximately 1’500 kg)

in 3 s from 100 km/h (60 mph, 30 m/s) to standstill.

Just for fun …

Neglect all other friction forces (aero, rolling, …), assume

constant braking force.

E =1

2m v2

=1

21500 302

= 675 kJKinetic energy

E / t = 675 / 3 kW = 225 kW (300HP)Braking power



Potential of Recuperation (MVEG-95)

=0.0rec

mrec50 100 150 200 250 kg

0.8

0.9

1

1.1 =0.2rec

=0.4rec

=0.6rec =0.8rec

=1.0rec

E( , m ) rec rec

MVEG-95E

Af cw = 0.7 m2 , cr = 0.012, m = 1'500 kg

Full-size car



Pathways to Better Fuel Economy

“Local Methods”

• Produce the required mechanical energy at the best

possible system operating point

• Recuperate the mechanical energy of the vehicle

when braking

• Avoid unnecessary losses by shutting down the system

when the power demand is below a threshold (zero)

“Global Methods”

• Optimally manage the contents of all available energy

reservoirs using information on the driving profile and

the actual and the future traffic conditions



Heuristic and Causal Approaches

1 Total energy control (“Hamiltonian approach”)

2 Electric assist and equivalence factors (ECMS)

3 Duty cycling



Example 1 – Problem Setting

“Energy-based control”

v

h

U

μ



Example 1 – Key Idea

• Keep the total reversible energy constant

• Replace irreversible energy losses by the FC

Ev

EU



Example 2 – Equivalence Factors (FCEV with “large batteries”)

In simple settings (driving cycles with no elevation changes)

equivalence factors are constants

SOC

fuel cell

bus

DC/DC

to EMH2-tank

battery




Most of the time

the FC system

operates in the

region



Example 3 – Duty Cycling

Optimal trade off

of bad operating

point versus

losses while

charging &

discharging SC

Constant operation at

Duty cycle between

vUμ

Assume FCEV

with supercaps



Systematic and Noncausal Approaches

1 Dynamic Programming (“backward”)

2 Minimum Principle (“forward”)



Modeling Paradigms

“Forward,” physics-based, causal, …

“Backward,” inverted causality, …

Mathematical models only way to cope with complexity



Driving cycle fixed a priori (speed and

elevation as functions of either time or

vehicle position)

FC system described by a quasistatic

model (“map”)

(speed, torque)

(voltage, current)

Only one reversible energy reservoir

in the vehicle (battery or SC)


200

40

80

20

100 900 1000 1100 1200

v km/h

t s800

4 Wiederholungen

0-40

60

100

120

vUμ

FC (n,T )

FC (U, I )



Example 1 – Control Signal

Define “power-split factor” u(k) that describes how much power

is provided by the FC and by the SC

PFC (k) = u(k) P0 (k), PSC (k) = (1 u(k)) P0 (k)

where the power Po(k) required to drive the cycle is defined by

the vehicle parameters and the cycle

P0 (k) = v(k) m g sin( (k))+ cr( ) + ca v2 (k)+ m a(k)[ ]

Here k is the time interval (the cycle is discretized), (k) the

slope of the cycle, cr and ca the rolling and the aerodynamic

coefficients, respectively, m the mass and a (k) the acceleration

of the vehicle.



q(k) =1

Q0

ISC (l) hl=1

k

Example 1 – Criterion

Minimize the fuel consumption (h is the time interval)

J(k) = PFC (l)h

FC (l)l=1

k

while maintaining a desired state of charge (SOC) q of the

battery or SC (all times, at the end, …)



Example 1 – DP Main Tool

J (i)k+1

J (1)k+1

J (a)k+1

q (i)k

u (j)k

u (1)k

u (b)k

q (i)k+1

1 k k+1

q (a )k k+1

q (1)k q (1)k+1

zj

z b

z1

n

m

q

UN

q (a)



O N an bm

N = number of time steps

n = number of “state variables” (SOC, …)

a = number of grid points of the s.v.

m= number of “control variables” (u, …)

b = number of grid points of the c.v.

Example 1 – Numerical Cost

Good news! Few reversible reservoirs (SC, battery, …), but

long cycles are OK.



0 200 400 600 800 1000400

450

500

550

600

650

700

0 200 400 600 800 10000

10

20

30

40

50

60

70

0 200 400 600 800 1000-3000

-2000

-1000

0

1000

2000

0 200 400 600 800 1000-3

-2

-1

0

1

2

3x 10

4



optimal

heuristic heuristic

optimal

Results A B



optimal

heuristic

optimal

heuristic

Results A B



Feedback Solution (“Cost to Go”)

A

B




Vehicle

Control (no braking assumed)

Objective function

“forward” model!

i.e., work at wheels, assumption FC system constant efficiency



Resulting Hamiltonian

Affine in the control!

Costate

Minimum Principle

Example 2 – Optimal Control Problem



Resulting optimal control law

Singular arc

yields constant speed!

Example 2 – Result



Example 2 – Main Insight

Two motors:

• One to sustain the desired speed; optimized for

efficiency.

• One to provide the desired drivability (acceleration);

optimized for torque.

• Of course during accelerations both motors are

used in parallel mode.

• When coasting both motors are shut down; complete

separation from wheels (minimize friction).

This is a general principle!



30 km/h (20 mph)

5385 km/le (12666 mpge)



FCEV offer many interesting opportunities for heuristic and

systematic (model-based) optimizations.

Structures, system parameters and control algorithms are the

three most important obvious areas of optimization. Substantial

improvements can be reached with such an approach.

The optimization method (nonlinear programming, dynamic

programming, optimal control, etc.) depends on the problem.

Optimization of supervisory control schemes and power train

structure/parameters and vehicle parameters not independent.

Such an multi-level optimization is much more difficult to solve.

Summary



For an extensive list of references see:http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-51643759-0

optimization and control of fuel cell electric vehicles (fcev)annastef/fuelcellpdf/linoacc06.pdf2006...

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