Transcript Presentation

ICHS07 :2nd International Conference on Hydrogen Safety
San Sebastian, Spain - September 11-13. 2007
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IDENTIFICATION AND MONITORING OF
PEM ELECTROLYSER BASED ON
DYNAMICAL MODELLING
Mohamed El Hadi LEBBAL, Stéphane LECŒUCHE
Ecole des Mine de Douai
Département Informatique et Automatique
Laboratory : Informatics and control system
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Presentation outline

Context of the work



PEM electrolyser modelling


Identification using IO data
Monitoring and diagnosis


Electric and thermal models
Parameters estimation


Improvement of the availability of an hydrogen station
Development of tools dedicated to the predictive maintenance
Fault detection and isolation
Conclusions and Perspectives
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Introduction

Supervision of H2 production stations for



On-line monitoring and diagnosis scheme




improving the process quality and availability (competitiveness)
ensuring the environment safety (people, equipment, building…)
Acquire data from sensors, actuators
Compare the process behavior with those of system models
Detect and isolate faults using FDI (Fault Detection and Isolation)
algorithms
In this work, limited to the electrolyser, we propose to



Elaborate a PEM electrolyser dynamical model dedicated to basic
monitoring and diagnosis tasks
Estimate the real model parameters through identification
approach (by using data acquired from the real system)
Build residuals for achieving a first-level diagnosis
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Problem formulation

Detection and isolation of electrolyser faults




Using

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Input/Output measurements u,y
Electrolyser model (giving an estimate of the output)
Fault indicators and decision strategy
fa
fs
fm
Actuators
v
Electrolyser
w
Sensors
y
ŷ
System models
Monitoring
and
diagnosis
fault indicators
u
Actuators faults fa  (v u),
Sensors faults fs  (w y) and
Electrolyser drifts or faults fm (parameters change)
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Electrolyser Modelling

Based on the Functional equation (Electrochemical
conversion)
ΔH = ΔG + T·ΔS
Enthalpy change
Total energy change

Gibbs energy change
Electrical demand
Thermal energy
Heat demand
Electrical and thermal behaviors
I, U
Electrical model
• Cell Current I
• Cell voltage U
T
Thermal model
• Cell temperature T
• Entropy reaction
• Components temperature
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Electrical modelling (1/2)

Electric energy
Cathode (-)
Anode (+)
Reduction  eOxidation  e-
Voltage losses
Hydrogen out
Water in
e-
H+
H2
Oxygen out
Membrane
Electrodes
U: Cell voltage
Vact
H2O
O2
Hydrogen out
Vrev
e-
Vdiff
Vohm
reversible voltage activation voltage Diffusion voltage Ohmic voltage
At equilibrium
thermodynamic
Voltage when
I=0+
Chemical
reaction velocity
Charge
movement near
to electrodes
Transport
phenomena –
Influence of
concentration
change
Electrode
and
Membran
e resistors
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Electrical modelling (2/2)

Voltage expression
Reversible voltage:
Vrev
Activation loss voltage:
Vact
Diffusion loss voltage:
Vdiff
RT  PH 2 PO12/ 2 

 V0 
ln
2 F  aH 2 O 
RT
I

ln( )
2F
I0
RT
I

ln( 1 
)
2 F
I lim
Ohmic loss voltage: Vohm  Rmem I
V0=1.23, R, F, I0, Ilim, Rmem, PH2, PO2, aH2O,  and  : constants

Electrical model U=f(I)
RT  PH 2 PO12/ 2  RT
I
RT
I
 
U  V0 
ln
ln( ) 
ln( 1 
)  Rmem I
2 F  aH 2O  2F
I0
2 F
I lim
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Thermal modelling

Thermal behaviour (Busquet 2004)
d ( T  Ta )
Cp
 ( U  Vth )I  h( T  Ta )
dt
Temperature
variation
Reaction
heat
External
Flow
with Vth=1.48,
Cp, and h: constants,
Ta : Ambient temperature.
Let define x=T-Ta, u=(U-Vth)I and y=T-Ta
h
1
 dx
x
u
 
Cp
Cp
 dt
 y  x
Laplace
transform
1/ h
 y
TL  

 u   Cp


p

1
 h



Basic model of order 1
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Parameters identification

Several model parameters are unknown / difficult to a
priori estimate
RT  PH 2 PO12/ 2  RT
I
RT
I
 
U  V0 
ln
ln( ) 
ln( 1 
)  Rmem I
2 F  aH 2O  2F
I0
2 F
I lim
 T  Ta 
1/ h
 
TL

 ( U  Vth )I   C p

p

1
 h




Identification algorithms
Electrical model parameters (NLS non-linear least squares)
T


ˆ  arg min G(ˆ)T y  g (ˆ, r ) where ˆ   1 1 1 1 Rˆmem 
ˆ
ˆ ˆ
 ˆ I 0  I lim





Thermal model parameters (linear system properties)
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Electrical model parameters identification

Non linear least square method

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Measurements coming from a 100Nl/h PEM electrolyser
 H2 production 100 [Nl/h] , experiments at (1 atm, T=318 K)
Parameter values :

 =0.452; I0 =0.1310-3;  =0.04; Ilim =120; and Rmem =3.210-3
Real and identified electrical model
Average relative error : 0.32%.
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Thermal model parameters identification

Step identification
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Estimation static gain and response time of linear system
Identified parameters values
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at Ta=298°K, Cp=68544 and h=10.71
0.1
0.7
Real
Model
0.6
0.08
0.06
0.04
0.02
0.4
Error
x=(T-Ta) (K)
0.5
0.3
0
-0.02
-0.04
0.2
-0.06
0.1
-0.08
0
0
1
2
3
4
5
Time (s)
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7
8
9
10
4
x 10
Real and identified thermal model
for U=1.74 and I=24
-0.1
0
2
4
6
Time (s)
8
10
4
x 10
Average relative error : 0.0045.
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Online monitoring and diagnosis

Ik
Model based Monitoring and diagnosis
Real system
fa
Actuator
fm
Electrolyser
f
s
Sensors
Uk
Tk
Using electrical model
Û k
Using thermal model
T̂k
R1
Monitoring
and diagnosis
R2
Rj
Electrolyser modelling
RTk  PH 2 PO12/ 2  RTk
I
RT
I
 
Û k  V0 
ln
ln( k )  k ln( 1  k )  Rmem I k
2 F  aH 2O  2F
I0
2 F
I lim
T̂k  a( Tk 1  Ta )  b( U k 1  Vth )I k 1  Ta

High-level Residuals generation
R1  U  Û  0
R2  Tk  T̂k  0
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Drift or fault detection and isolation

Definition (off-line) of a signature table
Aij=1  Residual i sensitive to fault j


A  ( Aij )
Aij=0  Residual i insensitive to fault j
Example of basic table
Electrolyser
is healthy
Thermal part
is faulty
Electrical
part is faulty
Sensors or
actuators are faulty
R1(U,I,T,, , I0
Ilim ,Rmem)
0
0
1
1
R2(U,I,T, a, b)
0
1
0
1

Online detection
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

Update of the vector of residuals B
For each residual i : if Ri> Threshold then Bi=1; else Bi=0.
Decision according to the signature table :
if B=Aj  fault j is isolated
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Experiments (1/2)

Healthy case vs Actuator fault
An offset on the actuator current occurs

Current actuator value is deviated
by a fault equal to 0.3 A
Healthy case
-4
-4
-4
Healthy system
x 10
x 10
0.5
10
-4
Fault on current actuator
x 10
x 10
1
0.5
0.5
0
R2 residual
0
R1 residual
0
R2 residual
R1 residual
5
0
-0.5
-0.5
-0.5
-5
0
2
4
6
Time (s)
0 
Signature B   
0 
8
10
4
x 10
0
2
4
6
8
Time (s)
1
Signature B   
1
10
4
x 10
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Experiments (2/2)
Electrolyser faults
Membrane resistor
deviation equals to 10%
h thermal parameter deviated
by a value equals to (10)
-4
x 10
-4
Fault on overall thermal admittance h
-4
x 10
x 10
-4
Fault on membrane resistor Rmem
x 10
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
0
0.6
0.4
R1 residual
6
R2 residual
R1 residual
8
0.2
4
0
-0.2
2
R2 residual

-0.4
0
0
2
4
6
Time (s)
0 
Signature B   
 1
8
-2
10
4
x 10
-2
0
2
4
6
Time (s)
8
10
4
x 10
 1
Signature B   
0 
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Conclusions


This work is a first attempt to supervise on-line an
PEM electrolyser and need to be improved
The main difficulties are


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It is necessary to combine different modelling
approaches



the variety of physical phenomena to be modelled
the highly non linear behaviors
analytical analysis of the process
parameters estimation through experimental modelling
Fault detection and isolation

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Residuals designed according the electrical or thermal behavior
 Detection performance bounded by the quality of the modelling
Several residuals need to be defined in order to isolate faulty
components
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The next steps

Improve the modelling by using a multi-modelling
representation

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Improve the monitoring approach by:

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
different discrete states, different functioning points
Adaptive thresholding for fault detection defined according the
variance of the parameter estimations
Analysis of fault detectors (residuals) sensitivity for several
parameters.
Introduce the prediction of faults that could lead to
risks


based on the trend analysis of the residuals and not only on their
signatures
requirement of a dynamical decision space
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