Fuel cell modeling presentation for my PhD qualifying exam

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?