Plagiarism Declaration
4. Results
4.3. Sensitivity analysis
4.3.3. Sensitivity to power failure mechanism
The base power failure model, as mentioned in previous sections, is based on statistical distributions gained from power supply interruption data collected for the NERC regions over a number of years. This allows for stochastic modeling of North American power supply reliability. The extension is that this is used to represent power supply disruption in the developed world. Comparing developed world power supply to developing world power supply manifests a different mechanism altogether.
Developed world power supply is assumed to have sufficient generation capacity as a result of adequate funding and careful master planning. The failure events were reported as being the result major disruptions, such as fires, extreme weather and vandalism by USADOE (2014). Consequently the failure mechanism results in low frequency, long duration power failure events owing to the severity of the cause. When considering South Africa as a developing country, the failure events are commonly a result of insufficient generation capacity, poor maintenance, minor vandalism, cable theft and overloaded reticulation networks. These power-generation type failures result in higher frequency, shorter duration power failure events (external power trips) compared to the NERC (2014) data. The comparison of these failure mechanisms provides insight into the cost implication of each.
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The lognormal distributions parameters presented in Table 4.3.4, in the case of failure frequency, are used to generate the mean frequency which is used as input to the Poisson process to calculate the time between failure from the average occurrence (as mentioned in 4.3.1). In the case of failure duration, the failure duration is calculated directly from the lognormal cumulative distribution function.
Table 4.3.4: Pump (power) failure lognormal distribution parameters
Parameter Baseline - USA
(NERC, 2014)
SA (Nel, 2009) Mean frequency (failures/annum) 0.104 11.4
Standard deviation (σ) 1.05 0.7
Lognormal mean (μ) 2.92 2.2
Mean duration (hours) 48 1.6
Standard deviation (σ) 1.38 1.54
Lognormal mean (μ) 2.92 -0.61
The result of this variation in power failure mechanism is demonstrated in Figure 4.3.3, Taking into consideration the vast differences in power failure frequency and duration, the solution sets are remarkably similar. The Nel (2009) mechanism produces marginally more expensive options, at the near design criterion reliability level, however the differences are not as substantial as one would assume.
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Figure 4.3.3: Pareto-optimal solution front for varying power failure mechanism 4.3.4. Sensitivity to Load shedding severity
Load shedding, also referred to as planned power outages or rolling blackouts are used as a means of reducing the demand on the electrical grid by switching power off to a specific area or sets of areas in succession. This, aside from placing an economic and social burden on the affected areas, has an effect on the delivery of civil services to the affected areas.
Municipal/service reservoirs supplied with water by pumped systems, and with no backup power generation capacity, will be affected by power outages equally.
The severity of these outages can be measured either in outage time and/or outage frequency.
The City of Cape Town produced a load shedding schedule in 2015, which outlined when load shedding would occur based on the day of the month and the affected zone(s). The zones are delineated by the City of Cape Town and the specific time-of-day allocation per zone was randomly selected. The scaling of the outages was done by increasing the frequency as opposed to increasing the duration of the outage. This is seen to be reasonable as there are many time dependent appliances that are affected by a longer duration outage, such as commercial and domestic refrigerators, battery backup power supplies, etc. The load shedding frequency is classed according to the frequency of power outages, as demonstrated in Table 4.3.5.
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
0.0 2.0 4.0 6.0 8.0 10.0
failure frequency (failures per annum)
Cost ($) Millions
Baseline (NERC 2014) - USA Nel (2009) - SA
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Table 4.3.5: City of Cape Town (2015) load shedding schedule severity Load shedding Severity Level
Parameter Stage 1 Stage 2 Stage 3A Stage 3B
Sensitivity Parameter Low Baseline Not Used High
Outage Frequency (TTF) (hours) 29.5 13.5 8.5 5.5
Outage Duration (hours) 2.5 2.5 2.5 2.5
The time to failure (TTF) was calculated by selecting a zone randomly with population equal to the generic model population (3000 - 5000 stands) and working out the time between power outages. The way that the load shedding schedule has been created ensures that each zone is equally affected by power outages. The acting assumption is that the load shedding stage does not change during the period when load shedding is in effect and that all load shedding events are in addition to the power failures experienced (as described by Nel, 2009).
The effect that the implementation of load shedding has on the cost of designing a bulk supply system is demonstrated in Figure 4.3.4:
Figure 4.3.4: Pareto-optimal solution fronts for varying load shedding severity
0.00 0.01 0.10 1.00 10.00 100.00 1,000.00
0.0 2.0 4.0 6.0 8.0 10.0
failure frequency (failures per annum)
Cost ($) Millions
Baseline (Stage 2) High (Stage 3B) Low (Stage 1) Nel (2009) - SA Base
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As can be seen from Figure 4.3.4, the load shedding severity has a significant impact on the cost of bulk water supply system at an equal failure frequency level. The cost offset between different load shedding stages is seen to be constant throughout the failure frequency range.
Between low and base (Stage 1 and Stage 2), the offset is approximately $400k, while the offset between base and high (Stage 2 and Stage 3B), is approximately $1.2m - $1.5m.
Comparing the results to the existing South African reliability model as defined by Nel (2009), gives an indication of the additional cost to the water authority should they choose to develop a bulk water supply system exhibiting design criterion failure frequency. At base- level load shedding (Stage 2), also under consideration of design criterion failure frequency, the difference is slightly more pronounced At a failure frequency lower than 1 failure every 10 years, the different results from different stages of load shedding begin to converge to the minimum failure frequency of approximately 0.01 failures per annum. It is proposed to be likely that at this failure frequency level the random power failures with substantially lower frequency, but higher duration (Nel, 2009) are more likely to result in failure compared to the lower duration, load shedding outages. This results in convergence to the minimum failure frequency as exhibited by the Nel (2009), South African model. This is, however, only observed in the low failure frequency zone (0.08 – 0.01 failure per annum).
The most significant observations are obtained when comparing the baseline, Nel (2009) model to the high-level, stage 3B load shedding results. The extra cost of a desired design criterion solution is approximately $2.2m or an equivalent 38% increase in cost. These results are summarised in Table 4.3.6.
Table 4.3.6: Load shedding cost and parameter sizing implication by severity level System Average Nel (2009) Stage 1 Stage 2 Stage 3B
Sensitivity Parameter Baseline Low Base High
Pump Power (kW) 93 98 105 142
Modal Pipe Size (m) 0.36 0.36 0.43 0.48
Supply Ratio (/SPD) 1.08 1.17 1.27 1.78
Reservoir Capacity (h SPD) 13.23 15.5 15.5 11.6
Reservoir Failure Duration (h) 10.7 3.76 3.84 1.45
Design Criterion Cost ($m) 5.5 5.9 6.4 7.7
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From the above Table, the influence of load shedding can be quantifiably compared. It can be seen that the efficient means of producing an optimally efficient set of solutions under high-level load shedding is to drastically increase supply. This, following on from prior observations would be in response to the decreased refill time between load shedding events and power failures. Another relevant observation is the reservoir failure duration, the time between when the reservoir empties, to when it receives a net inflow. It can be seen, in this instance, that the increased supply results in shorter reservoir failure duration.
Another, more concerning, observation is the consequence should a system be designed and constructed optimally as per the proposed method, to perform at design criterion failure frequency level and be subject to the implementation of load-shedding, not considered during design. In this case, the failure frequency under low-level load shedding increases by a factor of 10, to 1 failure per year. Under base-level load shedding, failure frequency increases by a factor of 100, from 1 failure every 10 years to 10 failures per annum. Under high-level load shedding, complete system failure occurs. It is proposed that this is not seen more prominently in South Africa, under 2015 load shedding conditions, as the implementation of load-shedding is not continuous and the existing bulk water systems are not designed optimally, implying the possibility of excess reservoir capacity and/or supply.. There are also times when load shedding is suspended completely. In addition, the occurrence of high-level (Stage 3B) load shedding is infrequent. However, should Stage 2 or Stage 3A/B load shedding be implemented in a continuous manner, without implementation of additional backup generation, it is likely that potable water service levels will decrease. The exact effect of this decrease will be dependent on the demanding population and system.