DECLARATION 2- PUBLICATIONS
6.4 Results and discussion
6.4.3 Reliability and cost analysis
In the Chapters three to five, it was shown that the CDF, PDF and hazard rate are important in modelling the technical life of components; so that the impact of strategies on costs can be evaluated. Time horizons considered for cost models must be based on the CDF and PDF because of the following reasons: the CDF gives a projection of the life span or the probability of having a life span of at most x, whereas the PDF indicates the chance of a unit failing at the age of x. These
functions play an important role in mitigating the risk in the process of energy supply. The CDFs, PDFs and plots of costs were generated using parameters that were derived by the MLE, listed in Table 6-3. The detailed analysis and discussion is provided in Section 6.4.3.1.
6.4.3.1 Survival probabilities and hazard rates
Figures 6-5 and 6-6 are hazard rates for the distribution transformers and transmission transformers, respectively. The hazard rate, h (t), is the probability that a component that has survived up to a given time will fail. It represents the risk associated with the component. For the distribution transformers, the h (t) at time zero is 0.023 and it decreases asymptotically. For the transmission transformers, the h (t) increases gradually from zero at t = 0 and it takes about 25 years to reach the value of its distribution counterparts at time zero. This shows that the risk of failure for the distribution transformers under the run-to-failure strategy is very high.
Figure 6-5: Hazard rates (distribution transformers)
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0
0.005 0.01 0.015 0.02
0.025 Hazard rate(distribution) for =0.5257
Technical life, t [hr.]
Magnitude
Figure 6-6: Hazard rates (transmission transformers)
Figures 6-7 and 6-8 display the PDFs for the distribution and transmission transformers, respectively. The PDF for the distribution is very low, ranging from 0 to 4 x 10-3 within a year;
whereas that for the transmission is relatively high, ranging from 0 to 0.035 within 70 years.
Figure 6-7: PDF (distribution)
0 10 20 30 40 50 60 70
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0.45 Hazard rate for =3.43
Technical life, t [yr.]
Magnitude
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
0 0.5 1 1.5 2 2.5 3 3.5
4x 10-3 PDF (distribution) for =0.5257
Probability density
Technical life,t[hr.]
A critical examination of the distribution asset history showed that the poor asset performance was partly caused by the run-to-failure strategy and partly by poor pre-installation planning. For example, failure analysis showed that 50% of causes of failure were related to improper earth impedance, fuse rating and surge diverter rating. On the other hand, the situation for the transmission transformers was different as they went through a thorough planning phase prior to the installation stage.
Figure 6-8: PDF (transmission)
Figure 6-9 portrays the CDF for the distribution transformers, which rises from 0 to 1 in about 1.2 years. Figure 6-10 is the CDF for the transmission transformers. It rises from 0 to 1 in about 70 years (actually, 67years).
0 10 20 30 40 50 60 70
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
0.04 PDF (transmission) for =3.43
Probability density
Technical life, t[yr.]
Figure 6-9: CDF (distribution transformers)
Figure 6-10: CDF (transmission transformers)
The CDF shows the ultimate lifespan that each of the two asset groups can attain, which is very poor for the distribution assets that are managed on the run-to-failure strategy.
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 CDF for distribution transformers for =0.5257
Cumulative density
Technical life, t[hr.]
0 10 20 30 40 50 60 70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 CDF (transmission) for =3.43
Cumulative density
Technical life, t[yr.]
The next section concludes the presentation and analysis of results, but focusing on the impact of the strategies on maintenance costs.
6.4.3.2 Simulation and modelling of costs
Figure 6-11 compares costs for distribution and transmission transformers under the run-to- failure regime and planned preventive maintenance, respectively. Point A on Figure 6-11 is a point in time when planned costs equal unplanned costs for the distribution transformers, which happens just at about a month of operation. This point corresponds to point B for the transmission transformers, which occurs at about 30 years of age.
Figure 6-11: Comparison of costs: (a) distribution and (b) transmission transformers In terms of AM, points A and B are decision criteria for either refurbishment or other end-of- lifecycle strategies so as to ensure that downtime costs do not exceed planned maintenance costs. It
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-500 0 500 1000
1500 (a) Maintenance cost (distribution) for =0.5257
Technical life, t [yr.]
Cost, US$ Planned costs
Unplanned costs Total cost
0 10 20 30 40 50 60 70
0 0.5 1 1.5 2 2.5
3x 104 (b) Maintenance costs (transmission) for =3.43
technical life, t [yr.]
Cost, US$
Planned costs Unplanned costs Total cost A
B
can be seen that point A (Figure 6-11) is reached too early in the distribution items (that are run-to- failure) to make the strategy sustainable. The frequency of failure means that high operating costs are incurred in an effort to rectify the problems.
Point B represents 44.8% of the lifespan of the transmission transformers. It can be inferred that the refurbishment can be timed at, say, 42-44% of the lifespan, that is, 28 to 30 years of age.
Thus the model presented can be a useful tool for the life cycle management planning by power utilities.
Comparison of costs in Figure 6-11 shows that costs incurred on the distribution transformers per year account for 5.2% of costs incurred in a 30-year period of their transmission counterparts.
Therefore, although the run-to-failure strategy is viewed to provide quick wins in the short term, it is too expensive and unsustainable in the long run. This result is similar to what another researcher indicated by stating that the run-to-failure strategy is not the least cost option for aging infrastructure assets, as most utilities think, because it leads to high customer interruption costs [13]. It has been possible to see this (holistic picture) because of the systems approach that was applied in this chapter. This result is similar to what [25] showed by stating that industries tend to lose out when they focus on short term gains at the expense of long term sustainability.