This document summarizes a presentation on developing a dynamic PEM fuel cell model that accounts for temperature. It discusses: 1) The motivation to model fuel cells for power electronics design and the goals of capturing key characteristics simply. 2) The background on fuel cell modeling, including static polarization losses and dynamic effects. 3) How temperature impacts polarization losses and the goal of incorporating its exponential effect on voltage over time into the model. 4) The results of modeling temperature dependency with a linear voltage boost based on output power and an exponential rise time constant, which simulate test data accurately.

1. Dynamic PEM Fuel Cell Model for Power Electronics
Design with Temperature Consideration
Presented March 17th, 2006
by Ken Stanton
for:
Virginia Tech Ph.D. Qualifying Exam
Dr. Jaime De La Ree
Dr. Robert Hendricks
Dr. Doug Nelson

2. Presentation Outline
 Motivation
 Fuel Cell Modeling Background and Goals
 Temperature Dependency Background
 Load Dependent Model Discussion
 Parameters for the Electrical Model
 Simulation Results and Analysis
 Model Improvement Suggestions
 Conclusions

3. Motivation
 With energy costs constantly rising, alternative fuels like
hydrogen are a major focus
 Fuel cells are of great interest
 high efficiency
 minimal moving parts and no combustion
 produce only water vapor as emission (when H2 is fuel)
 To use fuel cell as source, power conditioning must be used
 To design power conditioning circuitry, a system model is
needed for simulation

4.  Goal of modeling the fuel cell is to simulate system
 PSpice is designed to simulate power electronics and electrical
loads
 It does not readily accept chemical or thermodynamic
equations, so we have to transform into electrical components
 Not all inputs to/effects of system are relevant – avoid
complexity and also improve simulation speed
Fuel Cell Modeling Background
DC/
AC
Fuel
Cell
DC/
DC
AC
Load
Vfc
+
vac
+
Vdc
––

5. Fuel Cell Modeling Background
 Complete formulae available for fuel cell parameters
 Electrical models would have to use equation blocks
 Simple electrical models have been developed
 Capture major static and dynamic terminal characteristics
 No extended properties – humidity, temperature, fuel quality
 Thorough PSpice and Simulink fuel cell models exist
 Very precise output
 Cumbersome, too many inputs, slow to simulate
 Time consuming to set up for different fuel cells
 Goal of this work is to incorporate as many terminal
characteristics as possible in the simplest form

6. Fuel Cell Test System
 For this testing, the Ballard Nexa
system was used
 1.2 kW peak output (43A at 28V)
 Pure H2 supplied at constant 7psi
 Ambient O2 supplied by variable
speed compressor
 Fully controlled by on-board digital
system
 Serial data logging connection to PC

7. Fuel Cell Modeling Goals - Static
 Fuel cell output voltage
deviates from ideal (E) due to
polarization losses
 Activation polarization is a
result of slow reaction
kinematics, primarily in cathode
 Vact = A ln(i/i0)
 Ohmic polarization losses are
result of conductors’ resistance
 Vohm = iReff
 Concentration polarization
occurs when reactants are used
up faster than they can diffuse
into cell
 Vconc = -B ln(1 – i/iL)
 V = E – Vact – Vohm – Vconc
(back)
Caisheng Wang et al (2005)

8. Fuel Cell Modeling Goals - Dynamic
 Voltage undershoot and
overshoot due to delay in air
compressor speed change
 Vcomp = 1 - e-t/t1
 Voltage reacts like capacitor
due to charge double-layer
effect
 Vcdl = e-t/t2 - 1
 Vdyn = Vcomp + Vcdl
0
10
20
30
40
50
60
0 2 4 6 8 10 12
t (sec)
0
500
1000
1500
2000
0 2 4 6 8 10 12
t (sec)
vFC(V)
iFC(A)
pFC(W)
Step load: 1.47kW
Parasitic load: 70W
voltage undershoot (2.5V)
due to compressor delay
150W dip
27.2V
300W power
overshoot
43V

9. Dynamic Circuit Model Using Purely
Electrical Circuit Components
 Diode models activation loss
 hact = A ln(i/i0)
 VD = nVT ln(ID/Is)
 Diode internal resistor
represents ohmic loss
 Transistor Q2 turns on in
concentration region
 Capacitor characterizes
charge double layer
 Inductor acts like
compressor coming up to
speed
Yuvarajan et al (APEC 2004)

10. Dynamic Circuit Model Using
Behavior Models
 Parasitic load of controls and
compressor added
 Dynamics simulated with
behavior models containing
time constants
 Fed into voltage controlled
voltage source which will
produce voltage transient
 Static voltage drops handled
mostly by resistances
Lai (SECA Review Meeting 2004)

11. Fuel Cell Modeling Goals
 The original goal was to add effects of temperature on output
 Temperature is not easily isolated nor predicted
 Exponential voltage response observed
 Primary cause is temperature change, but also humidity, hydration, and
other factors are influence
 Goal of this work is to make minor expansion to current model, incorporating
exponential voltage change over time

12. Temperature Dependency
Background
 Static equations previously shown have variations by
temperature (and more)
     
   
2 2
2
1
2
1 2 3 4
, , ,
0
limit
ln ln
2 2 2
ln ln
where
ln 1
ref H O
act O FC
ohm ohm a ohm membrane ohm c FC ohm
ohm ohm RI FC RT
FC
conc
G S RT
E T T P P
F F F
V T C I
V V V V I R
R R k I k T
IRT
V
zF I
   
       
 
    
 
   
  
 
  
 

13. Thermodynamics
 To predict the temperature of the fuel cell for use in the model,
the heat energy dynamics need to be observed
where
is power of chemical reaction
is electrical output power, V*I
is sensible and latent heat absorbed
is heat
FC FC net
net chem elec sens latent loss
chem
elec
sens latent
loss
dT
M C q
dt
q q q q q
q
q
q
q



   
&
& & & & &
&
&
&
& lost mainly due to air convection (increased by cooling fan)

14. Temperature Dependency - Summary
 Any finite load will induce a reaction in the fuel cell
 The chemical reaction releases energy
 Some of this energy is lost to the outside environment as heat
 Some is translated into electrical energy
 Remaining heat goes into fuel cell stack
 Fuel cell heating causes rise in temperature of stack
 Temperature is also altered by control system on Ballard system
 Changing temperature changes polarization losses
 Therefore, change in load causes change in temperature, which
in turn causes change in polarization voltage losses, and
therefore output voltage

15. Load Dependent Model
 Attempt to find relationship
between output power and
change in output voltage
 convenient for electrical model
 From testing, output voltage
can be 2.5V higher when stack
reaches full-load steady-state
on Ballard system
 This can greatly affect I-V curve
and therefore model accuracy
Stack Voltage Increase (V)
vs. Stack Output Power
with linear regression curve
V = 0.0022*P
0
1
2
3
4
5
0 500 1000 1500Power (W)
V(Volt)
Delta V
Linear (Delta V)
Voltage vs Current
When 2.2V/kW linear heating
relationship applied
27
29
31
33
35
37
39
41
43
45
0 5 10 15 20 25 30 35 40 45 50
Current Supplied (A)
Voltage
V
V + delV

16. Static (Steady-state) Load Conditions
 Output voltage and current
values are fed into multiply to
get power
 Gain factor is applied to
attain relationship between
voltage boost and output
power (2.2V/kW for Ballard)
 Result fed to voltage source
which boosts output voltage
 Note that this model does not
have any dynamic
components in it – purely for
I-V curve


X
+
Current Voltage
Static
Subsystem
Power

17. Dynamic Load Effects
 Output voltage of
stack changes
exponentially when
power demand is
altered
 As such, LaPlace
block added to
implement integral
and time delay of
load dynamics
 Note that all other
dynamics are present
+



X
+
+

+
X
+
Current Voltage
Dynamic
Subsystem
Power

18. Determining Time Constant
 To complete the model, a
time constant is required
 In base e exponential, time
constant equals rise time to
63% of final value
 Dozens of load curves were
recorded
 One major problem is built-in
cooling fan skews power-
temperature relationship
 Time constant is relatively
consistent for different
conditions
 50s chosen as constant

19. Simulation Results
 Plot on left is goal
 Blue curve from Ballard
 Red curve is Ballard + proposed linear gain
 Plot on right is simulation
 Lower curve matches Ballard well* – could use another ‘region’
 Upper curve simply follows linear trend
Voltage vs Current
When 2.2V/kW linear heating
relationship applied
27
29
31
33
35
37
39
41
43
45
0 5 10 15 20 25 30 35 40 45 50
Current Supplied (A)
Voltage
V
V + delV

20. Simulation Results
 Zero to full-load (1.2kW) step
 voltage dip created by the compressor lag
 gradual rise in voltage related to effect of temperature on fuel cell stack
 Simulation matches voltage curve well
 Difference in voltage levels due to age of fuel cell system

21. Simulation Results
 Four load steps show small voltage rises w/ stack loading (and heating)
 When load is removed, voltage falls off smoothly
 Times of load steps are same in simulation and actual test
 Loads: 225W, 360W, 480W, 680W

22. Model Improvement Suggestions
 Voltage “boost” approach shown here works, but is not as
representative as desired
 Perfect temperature model would have:
 Ambient temperature can be entered
 Temperature calculation*
 Temperature reduced by cooling fan*
 Value fed to model components*
 Each altered appropriately by temperature*
 Cold-start limitations added*
 True “thermal” heat energy handling
 Reasons this has not been reached
 Difficulty modeling all of above
 Difficulty with PSpice (* items above)
 May deviate too much from the original goal – to have a simple and fast-to-
simulate fuel cell model

23. Conclusions
 Previous models did not account for temperature transients of stack
 Voltage difference as much as 2.5V for Ballard system ~ 10%
 Implementation of basic temperature effects can be simple
 Create load dependent model
 Dynamics only need one more component than static
 All major fuel cell phenomenon are accounted for
 Power electronics designers can obtain output voltage and current from
this model and use it with confidence

24. Thank You!
Questions?