Control of Fuel Cell Power Systems
Anna Stefanopoulou
Department of Mechanical Engineering
University of Michigan
Work funded by
U.S. Army Center of Excellence for Automotive Research (ARC)
and NSF-CMS 0201332 and CMS-0219623
Thanks to
Prof. Huei Peng and Jay Pukrushpan (UMICH)
Scott Bortoff and team (UTRC)
Woong-Chul Yang and Scott Staley (Ford)
Herb Dobbs and Eric Kalio (US-Army NAC)
Powertrain
Control Lab
Historical Perspective
1830, C. F. Schonbein discovered the gas cell
Philosophical Magazine
1839 (Jan) F. C. Schonbein describes the phenomenon
1839 (Feb) W. R. Grove realizes the significance
The gas cell is baptized Fuel Cell
1894, W. Ostwald in the 2nd annual conference
of the German Society of Electrotechnologists
declares that:
“the fuel cell is greater achievement than the
steam engine”
… and predicts
“the Siemens steam generator will end up soon
in the museum”
Powertrain
Control Lab
Fuel Cells
•
Water, electrical energy and heat arise
through the controlled combination of
hydrogen and oxygen.
•
High efficiency, no (locally) harmful
emissions, no moving parts—Long-term
solution??
2H 2  O2  2H 2O  heat
1st FCV - Shell’s Daf 44 (1960)
Powertrain
Control Lab
Fuel Cell Type
Powertrain
Control Lab
Fuel Cell Stack
Polarization Curve
Vcell
MEA
i
I stack  I cell  iAcell
Fuel Cell
Tutorial,
Los Alamos
National Lab
Vstack  n Vcell
Pstack  n Vcell  i  Acell

Powertrain
Control Lab
Fuel Cell Characteristics
Current drawn from
the traction motor
and auxiliaries

Oxygen
Hydrogen
Pressure
Temperature
Humidity
V  V i (t ), p (t ), T (t ), H 2O (t )
Powertrain
Control Lab

Reactant Flow Subsystem
Excess Ratio = Supply/Use
1.2 for Hydrogen
2.0 for Oxygen
Is
t
Provide sufficient reactant flow, fast transient response, minimize auxiliary power consumption
Powertrain
Control Lab
Heat & Temperature Subsystem
Is
t
Fast warm-up, no temperature overshoot, low auxiliary fan and pump power
Powertrain
Control Lab
Water Management Subsystem
Is
t
Maintaining membrane hydrated, balancing water usage/consumption
Powertrain
Control Lab
Power Management Subsystem
Pnet  Pstack  Pauxiliary
Satisfactory vehicle transient response, assist fuel cell system
Powertrain
Control Lab
Overall Control Problem
Powertrain
Control Lab
Literature Review - Model Types
Estimates of time constants for Subsystems
– Electrochemistry O(10-19sec)
– Electrode Membrane RC System O(Unknown)
– Membrane Water Content O(Unknown)
– Hydrogen & Air manifolds O(0.1 sec)
– Flow Control & Supercharge Device O(1 sec)
– Vehicle Dynamics O(100 sec)
– Cell & Stack Temperature O(100sec)
• Multi-Dimensional Fuel Cell Model
[Springer, 91, Nguyen, 93, Amphlett, 95, Dutta 01]
Model: Pressure, Partial Pressure, Temperature, Humidity Effects
Purpose: Design, Sizing
•Dynamic Fuel Cell System Model
[Guzzella, 99, Hauer, 00, Boettner, 01, GCTool]
Model: Temperature, Pressure, Humidity Dynamics
Purpose: Transient Performance, System Efficiency
Powertrain
Control Lab
• Steady-State Fuel Cell System Model
[… many…]
Model: Static Power and Efficiency maps
Purpose: Fuel Consumption, Hybridization
Reactant Supply System
Goal: During fast current demands, providing
sufficient reactant flow to achieve fast transient
response, and reduce auxiliary power consumption
Powertrain
Control Lab
Compressor and Manifolds Model
Compressor
J cp
d cp
dt

1
 cp
( Pcm  Pcp )
Supply Manifold
dmsm
 Wcp  Wca ,in
dt
dpsm Ra
WcpTcp,out  Wca ,inTsm 

dt
Vsm
Return Manifold
dprm RaTrm
Wca ,out  Wrm,out 

dt
Vrm
Powertrain
Control Lab
Fuel Cell Stack Model
• Stack Voltage Model
• Cathode Mass Flow Model
• Anode Mass Flow Model
• Membrane Hydration Model
dm O 2
dt
dm N 2
 WO 2 ,in  WO 2 ,out  WO 2 ,react
 WN 2 ,in  WN 2 ,out
dt
dm w ,ca
 Wv ,ca ,in  Wv ,ca ,out  Wv ,gen  Wv ,membr
dt
Powertrain
Control Lab
Stack State Equations
Cathode
dmO2
dt
dmN 2
Electrochemistry
 WO2 ,in  WO2 ,out  WO2 ,react
dt
dmw,ca
 WN 2 ,in  WN 2 ,out
 Wv ,ca ,in  Wv ,ca ,out  Wv , gen  Wv ,membr
dt
Anode
dmH 2
 WH 2 ,in  WH 2 ,out  WH 2 ,react
dt
dmw,an
dt
nI st
4F
nI
W H 2 ,react  M H 2 st
2F
nI
Wv ,gen  M v st
2F
WO2 ,react  M O2
 Wv ,an,in  Wv ,an,out  Wv ,membr
Membrane mass transport
Wv ,membr  f v ( I st , ca , an )
Powertrain
Control Lab
Membrane Hydration Model
Water flow across
membrane from
anode to cathode
= (Electro-osmotic drag) – (Back-diffusion)
Water molar flow rate
through membrane
Current density
Water Concentration


c v, ca  c v, an
i
mol/sec
N v, membr  n d  D w
F
tm
Diffusion coefficient
Electro-osmotic coefficient
Membrane water content
Powertrain
Control Lab
m 
(  an   ca )
2
Voltage Model
(Polarization)
SAE 98C054 and
personal communications
with the authors:
W-C Yang and J.A. Adams
Pressure
V  E  Vact  Vohm  Vconc
 E  V
0
Powertrain
Control Lab
 V 1  e 
 c1i
a

i
 iRohm   i c2
  imax



c3



E (T , pH 2 , pO2 ), Vact (T , pca , pO2 ), Vohm (T , m ), Vconc (T , pO2 )
Stack Voltage Model (Polarization)


V  E  V0  Va 1  e
 c1i


i
 iR ohm   i c 2
i max





c3




pO 2 
 pH2
1
E  1.23  8.5  10  4 ( T  298.15)  4.31  10  5 T ln
 ln

 1.013 2 1.013 
0.12(p ca  p v , sat ) 
 p ca  p v , sat
1
V0  0.28  8.5  10  4 ( T  298.15)  4.31  10  5 T ln
 ln

1.013
2
1.013


2
5
2
4
4
Va  ( 1.62  10 T  1.62  10 )p x  (1.8  10 T  0.17 )p x  ( 5.8  10 T  0.057 )
R ohm 
tm
1
1 

 0.00326 exp 350(
 )
303 T 


4

( 7.16  10 T  0.62)p x  ( 1.45  10  3 T  1.68)
c2  
5
4

 ( 8.66  10 T  0.068)p x  ( 1.6  10 T  0.54)
pO 2
px 
 p v , sat
0.12
0.005139 m
for p x  2 atm
for p x  2 atm
i max  2.2, c1  10, c 3  2
Powertrain
Control Lab
Pukrushpan et al, IMECE 2002
Control Objectives
Net Power
Pnet  PFC  PCM
Oxygen Excess Ratio
O 
2
WO2 ,in
oxygen supplied

oxygen reacted WO2 ,react
pressure
Ist
 w   I st 
 u  Vcm 
Vcm
Powertrain
Control Lab
Power
 Pnet 
z   
 O2 
Optimal Operating Points
Steady-state O2 and Pnet
for different Ist (using model)
Net Power
Pnet  PFC  PCM
Oxygen Excess Ratio
oxygen supplied WO2 ,in ( Vcm )
O2 

oxygen reacted WO2 ,react ( I st )
P 
z   net 
 O2 
Desired
set-point
Powertrain
Control Lab
z
ref
 P ref
net
  ref
 O
 2




Gelfi et al, ACC 2003
Transient Interactions
w
u
G z1w
G
 z2 w
 Pnet 
 O   z
 2
G z1u 
G z2u 
Cancelation Controller
c
K 
Gz 2 w
Gz 2u
(Ist)=w
Gz1w
Gz1u
Kc
Gz2 w
(Vcm)=u
Powertrain
Control Lab
S
(Pnet)=z1
Gz 2 u
S
O2)=z2
Performance Tradeoff

J   z T Qz z  uT Ru  qT Qq q dt
0
Powertrain
Control Lab
Voltage should be used in the feedback
Varigonda et al, AICHE 2003
Performance Tradeoff (cont.)
Closed Loop Bode Plots for
Different Control Gains
Power transients faster than 10 rad/s cause severe
compromise to the FC Stack life due to O2 starvation
Powertrain
Control Lab
Nonlinear Simulation Results
Powertrain
Control Lab
Transients and Coordination with Power Electronics
Powertrain
Control Lab
Outline
• Overview --- How FC work?
• Modeling of Fuel Cell System
• Control of Oxygen Reactant
• Control of Fuel Processor for Hydrogen Reactant
• Experimental Setup
Powertrain
Control Lab
Problem—Hydrogen Supply
On-board storage (“direct”)
•
•
•
Cryogenic (liquid) hydrogen
Liquifying hydrogen is expensive and storing this
extremely cold fuel on a vehicle is difficult.
Pressurized (gaseous) hydrogen
Requires significant energy for compression,
stringent safety precautions and bulky,
heavy and expensive storage tanks.
Metal hydride or Carbon nanofiber storage
New technology
far from commercial development.
Adams et al., “The Development of Ford's P2000
Fuel Cell Vehicle,” SAE 2000-01-1061
Onboard fuel processors (“reformer”)
Convert hydrocarbon fuel, such as methanol or gasoline, to a H2 rich
gas.
Powertrain
Control Lab
Hydrogen-on-Demand
Direct H2
Electrolyser
Fuel Processor
Solar
Regenerative
Powertrain
Control Lab
Source: Nature 414, 2001
On-Board Reforming
• Advantage: Widely Available, Inexpensive, Consumer Acceptance, Fuel
Flexibility
• Liquid Fuels From Petroleum and/or Other Sources (e.g, Ethanol)
• Natural gas
– Large potential reserves, distributed worldwide
• H2 From Catalytic Partial OXidation (CPOX)
– Partial Oxidation: CH4 + 0.5O2 + Heat = CO +2 H2 (at 700o )
– Total Oxidation: CH4 + 2O2 + Heat = CO2 +2 H2O
– Water-Gas Shift: CO + H2O = CO2 + H2
 Autothermal point balances heat input/output
 0.25-0.5 % (2500-5000 ppm) of CO remains in the feed
 Unacceptable performance if CO% is 0.001% (10ppm)
• Preferential Oxidation (PrOX) is needed!!
– Precise Control of O2 feed for the CO oxidation
 Any extra O2 will react with H2 (loss of fuel)
Powertrain
Control Lab
From Direct Hydrogen to Hydrogen-on-Demand
When direct (stored) hydrogen is not available....
the Fuel Processor Control System becomes critical for
efficiency, responsiveness and reliability.
Air
Water
Water
Fuel
Vaporizer/
Desulfurizer
Reformer
High-Temp
WGS
Fuel Processor
Powertrain
Control Lab
Water
Low-Temp
WGS
Air
PROX
Hydrogen-rich
gas
From Direct Hydrogen to Reformate Hydrogen
H2 generation from Catalytic Partial OXidation (CPOX)
Partial Oxidation: CH4 + 0.5O2 + Heat = CO +2 H2 (at
700o )
Total Oxidation: CH4 + 2O2 + Heat = CO2 +2 H2O
Powertrain
Control Lab
Goals:
Coordinate fuel (methane) and air flow to achieve
-- high conversion of H2 (regulate CPOX Temperature)
-- maximize H2 utilization
Integrated FPS+FCS+CBrn
Burn the excess H2 (Catalytic burner)
use the heat for
(i) heating (or vaporizing) the fuel
(ii) recover power throughTC
Highly coupled system with non-minimum
phase response  very slow start-up
Powertrain
Control Lab
Varigonda et al, AIChE 2003
Baseline Controller
Ist
ublo
uvlv
Tcpox
Tcpox
VH2
Powertrain
Control Lab
VH2
Multivariable Controller
Ist
ublo
uvlv
Tcpox
VH2
Tcpox
VH2
Powertrain
Control Lab
Pukrushpan et al, ACC 2003
Analysis of MIMO Controller
 ublo  C11 C12  Tcpox 

u valve   C21 C22   V
 H2 
VH2
C12 term is important
Closed-loop step response
Powertrain
Control Lab
Closed-loop frequency response
Multivariable Controller  Coordination
Ist
ublo
uval
Tcpox
Powertrain
Control Lab
VH2
Analysis of the FPS+FC Interaction
…
The current command
affects hydrogen…
The error in hydrogen
is detected by the
controller through
the C22 (typically
a PI controller).
The fuel valve tries to
compensate for the
detected hydrogen
error
… and causes a
disturbance to the Tcpox
through the P12 plant
interaction
Powertrain
Control Lab
S
C11
S
C22
Ist
Tcpox
ublo
uvalve
S
S
S
VH2
Analysis of the FPS+FC Interaction (cont.)
… and causes a
disturbance to the Tcpox
through the P12 plant
interaction
The Tcpox pertrubation
Is detected by the
PI controller in C11
…
S
That energizes the
blower signal which
eventually rejects the
P12 disturbance.
… for faster response,
S
one can use a direct
command to the blower
signal based on the fuel
valve excursion. This is
accomplished by the C12 term!!
Powertrain
Control Lab
C11
S
ubl
Ist
Tcpox
S
C12
C22
uvlv
S
VH2
Adding Measurements from FPS  Robustness+Performance
Ist
ublo
uval
Tcpox
Powertrain
Control Lab
Pprox
...
Pa
VH2
Outline
• Overview --- How it works?
• Modeling of Fuel Cell
• Control of Oxygen Reactant
• Control of Fuel Processor for Hydrogen Reactant
• Experimental Setup
Powertrain
Control Lab
Estimation of Hydrogen Starvation
Question:
Can we use the Fuel Cell Voltage to predict
the hydrogen and oxygen content during
typical flow, pressure, current transients?
Answer: is between the
ODE and the PDE world
Attempt:
Powertrain
Control Lab
Fuel Cell Control Test Station
Designed by The Schatz Energy Research Center (SERC)
Humboldt State University, Arcata, CA
1082 WE Lay Auto Lab
Powertrain
Control Lab
PEM Fuel Cell (2.4 kW)
Air
Hydrogen
Water
Current
Powertrain
Control Lab
Fuel Cell Control Test Station
Hydrogen Sensor
Thermal
Management
Data-Acquisition
with LabView
Mass Air
Controllers
Hydrogen
Storage and
Pressure
Regulation
Controllable
Load
1082 WE Lay Auto Lab
Powertrain
Control Lab
Summary
• Control of Fuel Cells
-- Stringent tradeoffs between net power response and oxygen supply
-- Estimation of hydrogen utilization with conventional sensors
• Control of Fuel Processor (Hydrogen reformer)
-- Multivariable Control of Natural Gas and Air Flow
Thanks to
-- Scott Bortoff and Shubro Ghosh (UTRC and UTC-FC)
-- W-C Yang and Scott Staley (Ford SRL and Th!nk)
-- Charles Chamberlin, Peter Lehman (SERC)
Powertrain
Control Lab
Sponsors: NSF and ARC (TACOM)
Thanks!!!
Graduate Students
Jay Pukrushpan
Ardalan Vahidi
UnderGraduate St.
Marietsa Edje
Dave Nay
Visiting Students
Sylvain Gelfi
Denise McKay
Thanks to Professor Peng
Powertrain
Control Lab