The Weibull distribution was used to vary the degradation of each failure mode per time step. This was done to integrate a random number into the degradation calculations and offer a more realistic view of what would happen in a real world system.
Weibull was chosen as the type of distribution to use due to its ability to modulate the degradation rate based upon a shape parameter. Some failure modes that can be experienced in a FC are more severe in the early ‘bedding in’ period, some failure modes have a more linear ‘useful life’ affect, whereas others are more prominent only in the ‘wear out’ period towards the end of life. The Weibull distribution is a good tool to make use of these characteristics by having differing shape parameters as described in section 5.5.
Figure 7.13 shows a comparison between a flat rate of degradation vs a single run of a Weibull integrated degradation under the same operating conditions. Flat rate refers to the constant rate of degradation that, whereas the Weibul degradation line shows how the degradation rate varies based upon the Weibul data input.
0 100 200 300 400 500 600 700 800 900 1000 0 1 2 x 10−4 Time [s] Degradation [V/s] Weibull Degradation Flat Rate Degradation
Figure 7.13: Flat rate degradation vs Weibull distribution degradation
As can be seen in Figure 7.13 the Weibull degradation rate is within the range that is expected if using the flat rate of degradation, however it varies dependent upon the random number that was introduced.
Using the Weibull distribution means that one must repeat simulations a number of times to gain an accurate understanding of the total lifetime of the FC. The simulations were run numerous times until confidence was achieved with the cumulative average lifetime for each simulation run.
The overall running of the combined 1D and Petri-net degradation model is shown in Figure 7.14. For the models to run, the initialisation data detailed in section 5.1.1 are input so that the 1D model knows the specification of the MEA. The time and current profiles are needed
Set initialization
data for 1D
model
Set current
profile for 1D/
Petri-net models
Run models for
one time-step
Start Process
Set time profile
for 1D/Petri-net
models
Is degradation >=
5%?
Write lifetime data to variable
End Simulation
Yes NoStart
Simulation
for the models to know what cycle the FC is running. After this data is input, the simulation process can start.
The degradation model was run until confidence was sought with the cumulative average lifetime. As can be seen in Figure 7.15, the average lifetime varies significantly during the first 40 simulations, then starts to level out, with a minor fluctuation between 60 and 120 simulations. Confidence in the average lifetime is assumed at 151 iterations of the simulation at a lifetime of 1.224 x 105 which is equal to 34 hours of operation. The most significant contributors to the
degradation in this time period were immature platinum agglomeration and H2O2degradation. This was determined by evaluating the contribution of that module versus the others via the real-time value output block of a scope during operation.
The final value ascertained from the degradation simulation performed in this work sits well between the bounds given by the experimental data collected by Borup, et al. [16] in Table 9 of their paper. Their values of 24 hours lifetime due to H2O2 degradation and a lifetime of 50 hours due to H2O2 degradation and pinhole production agree well with the simulated lifetime of 34 hours with H2O2degradation being a significant contributor to the degradation.
0 20 40 60 80 100 120 140 160 1.2239 1.2239 1.2239 1.2239 1.224 1.224 1.224 1.224x 10 5 X: 151 Y: 1.224e+05 Simulation Number Time to Failure [S]
Figure 7.15: Cumulative average lifetime of the cell over 151 simulations
7.4
Conclusions
This chapter has presented the quantitative results of the Petri-Net degradation modelling. The individual results of SSC were presented and showed a strong correlation with experimental results from the literature. It is therefore assumed that degradation due to SSC in the overall Petri-Net model is justified. When the entire Petri-Net model’s modules are run with their interactions, the overall lifetime of a cell under the NEDC based drive cycles was ascertained. Due to using Weibull distributions of the degradation data that included the input of a random
number, numerous iteration of the simulation were run until confidence in an average lifetime was gained. This was assumed to be after 151 cycles and was 1.224 x 105 seconds, which is equal to 34 hours of operation. This falls within the boundaries of the experimentation in the literature, and therefore is considered accurate.
Chapter 8
Conclusions and Future Work
8.1
Introduction
The research carried out has achieved the aims and objectives discussed in section 1.7 of chapter 1:
1. An understanding of current PEMFC degradation phenomena and modelling methods was gained through the use of a literature review and FMEA/FTA.
2. A greater understanding of PEMFC reliability studies was ascertained through an in- depth literature review and analysis of previous work in this area.
3. Based upon the literature review;
i A comprehensive FMEA including 21 failure modes was developed from knowledge gained from the literature review, and is presented as the most comprehensive and up-to-date FMEA currently published. The membrane had 8 main failure modes, the catalyst layer contained 7 failure modes, the GDL had 4 and the BIP had 2 failure modes associated with it.
ii A new FT was developed based upon the failure modes identified in the FMEA, and is also presented as the most up-to-date and specific FT currently in the literature. The quantification of this model used Weibull distributions of degradation data taken from the literature.
4. Interactions and dependencies in a PEMFC were analysed and conclusions presented regarding their effect on reliability analysis.
5. A quantitative degradation model was developed using Petri-net analysis techniques, which predicts fuel cell lifetime under certain operating conditions. 20 failure modules were developed which represented all of the failure modes previously ascertained through the FMEA and FTA research. The product of the work was an estimated lifetime of a cell operating in a certain cycle using Weibull distribution degradation data.
6. The degradation model is validated using an experimental rig that was purpose built, from the ground up. The rig strengthened the confidence in the results of the degrada- tion model by accurately matching the data from previous simulation runs. The rig also offered degradation data to be used in the Petri-net model and filled gaps in the data for degradation of PEMFCs.
The aim of this work was to develop an effective model to predict the lifetime and degrada- tion of a FC in an automotive environment. This has been achieved through the development and presentation of three reliability techniques used to analyse the degradation in a FC system, and the main conclusions are given in 8.2.