The TS-MCS outputs reliability worth indices consisting of Ns data points corresponding to the number of simulations run. This allows for a probabilistic description of these indices. However, the comparisons in this section are mainly on the computed mean of the output data of the indices.
104 Case 1: Effect of CIC model on ECOST
Across all the load points, the evaluated mean ECOST from the TS-MCS is highest using the TIAIC model (Figure 6.4). The TIAIC represents the worst-case average CIC model. The load point ECOSTs obtained using the TVAIC model shows that accounting for the time-variation in cost using business activity level weights results in lower ECOST. This is plausible as significant number of electricity interruptions during the simulation runs might have occurred in season – time intervals with low activity weights. Furthermore, combining both the time-dependencies of CIC with a probabilistic description of CIC results in even lower in ECOST. Very high values in the normalized CIC data can exert a disproportionate effect on the average normalized CIC even if they are few. The probability distributions of the normalized CIC estimates for each sector in this study were significantly right skewed (Table 5.4). Thus sampling from the beta probability distribution of the normalized CIC estimates in the TS-MCS implies that smaller CIC values with higher probability will be picked often. This explains why the mean ECOST based on the TVPIC model is smaller than that of the TVAIC model for load points LP1, LP2, LP5. The feeder’s mean ECOST computed using all three CIC models is depicted in Figure 6.5.
Figure 6.4: Comparison of load point expected interruption cost (ECOST) obtained from the 3 different CIC models described in Table 6.5
LP1 LP2 LP3 LP4 LP5 LP6 LP7
ECOST (Rands/year)
Load points of test feeder
TIAIC model TVAIC model TVPIC model
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Figure 6.5: Comparison of feeder mean ECOST obtained from the 3 different CIC models described in Table 6.5
Effect of different CIC percentile values on evaluated ECOST for an electricity interruption scenario
The effect of choosing different confidence levels to determine the CIC estimate to use for a particular application was considered for a 4 – hour electricity interruption occurring within the weekday time interval 00:06AM to 12:00PM in the October – December season. The computed normalized 4 – hour CIC data from the survey, median of average monthly electricity bill data (Table 6.6) and the business customer designation adopted for the test feeder (Table 6.4) were used to evaluate average feeder ECOSTand risk-based ECOST with the TIAIC, TVAIC and the TVPIC models respectively. Four risk levels were considered for the evaluation of risk-based ECOST viz.
50%, 20%, 10%, and 5% risk. These correspond to the 50th, 80th, 90th percentile and 95th percentile of the beta distribution of the normalized 4 – hour CIC data in the stated season – time interval.
The ECOST computed based on the TIAIC and TVAIC models respectively are almost equal (Figure 6.6) because the time – season window considered in this analysis was the busiest time – season window for the trade, hospitality and manufacturing sectors (i.e. their activity level weights in this time – season window is 1). The activity level weight for ‘other commercial services’ sector was approximately 0.97. With the TVPIC model, the choice of confidence level results in different ECOST (Figure 6.6). This can lead to different decision making. A 5% risk implies a 95% decision
0 500 000 1 000 000 1 500 000 2 000 000 2 500 000 3 000 000 3 500 000
ECOST (Rands/year)
TIAIC model TVAIC model TVPIC model
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making confidence level which accommodates the possibility of extreme CIC values.
ECOST_TVPIC (@50% risk) is significantly lower than ECOST_TIAIC and ECOST_TVAIC because of the heavy right skew of the 4-hour normalized CIC estimates in each sector (Table 5.4) i.e. the 50th percentile value of the beta distribution of the 4 – hour normalized CIC estimates is significantly lower than average value of the estimates.
Figure 6.6: Comparison of average ECOST and risk-based ECOST for the scenario of a 4 - hour full feeder outage occurring between 12:00 - 18:00 in October – December season
Case 2: Effect of alternate supply on ECOST (TVPIC model used)
The switch configuration for this simulation is different from that in case 1; all feeder sections are assumed to have switches. Without considering alternate supply, the feeder mean ECOST reduced by about 41% when compared with its value for the TVPIC model in case 1 – where the feeder was assumed to have no switches. Comparisons of the load point ECOST and ERNC for simulation case 2 shows that including an alternate supply to the feeder reduces the load point ECOST and ERNC considerably (Figures 6.7 and 6.8 respectively). The reduction in ECOST and ERNC is most significant for LP5 and LP6. Overall, the feeder ECOST and the electric utility’s ERNC reduced by approximately 34% respectively (Table 6.8).
0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000
ECOST (Rands/year)
ECOST _TIAIC model ECOST_TVAIC model
ECOST _TVPIC model (@50% risk) ECOST_TVPIC model(@20% risk) ECOST _TVPIC model (@10% risk) ECOST_TVPIC model (@5% risk)
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Figure 6.7: Mean ECOST of test feeder load points when the feeder has an alternate supply and when it does not.
Figure 6.8: Mean ERNC of test feeder load points when the feeder has an alternate supply and when it does not.
Table 6.8: Improvement in test feeder reliability worth indices gained by including alternate supply No alternate supply Alternate supply Percentage reduction
ERNC (Rands/year) 8 911.20 5 899.55 34%
ECOST (Rands/year) 57 2644.82 37 8428.88 34%
0 20 000 40 000 60 000 80 000 100 000 120 000
LP1 LP2 LP3 LP4 LP5 LP6 LP7
ECOST (Rands/year)
Load points of test feeder
No alternate supply Alternate supply
0 500 1 000 1 500 2 000 2 500
LP1 LP2 LP3 LP4 LP5 LP6 LP7
ERNC (Rands/year)
Load points of test feeder
No alternate supply Alternate supply
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Case 3: Optimal location of switches (TVPIC model used)
For the feeder of figure 6.2, there are 26 = 64 possible switch configurations, thus an exhaustive search routine was used for the determining the optimal of placement of 3 switches that minimizes the feeder ECOST. The routine is outlined below:
1. Index switch configurations with positive integers, i = 0, 1, 2, …,63.
2. For each switch configuration i, obtain a corresponding 1 x 6 binary vector Si indicating the presence or absence of a switch on feeder line sections L1, L3, L5, L6, L7, L9, L11.
3. For each Si satisfying sum(Si) ≤ 3, evaluate the corresponding mean feeder ECOST using the TS-MCS algorithm in section 6.5.
4. Determine the switch configuration with the minimum mean feeder ECOST.
For the case where there is no alternate supply, the optimal locations of the 3 switches that the electric utility can afford to install are feeder line sections L1, L3, L7 (Figure 6.2). The feeder’s mean ECOST and ERNC for this case are approximately R 603 649.67 and R 9615.26 respectively.
For the case where there is an alternate supply, the optimal locations of the 3 switches are line sections L3, L5, L11. The feeder’s ECOST and ERNC for this case are approximately R 444 863.38 and R 6917.84 respectively. The presence of an alternate source of supply results in a reduction of the feeder’s mean ECOST and ERNC. A comparison of the load points’ ECOST and ERNC with optimal placement of the 3 switches, with switches on all feeder main sections and with no switch at all is depicted in Figures 6.9 and 6.10 respectively for the scenario without alternate supply.
Optimal placement of the 3 switches which the budget-constrained electric utility in this case study can afford achieves similar reduction in the load points’ mean ECOST and ERNC as placement of switches on all feeder sections.
The ECOST at LP7 is approximately equal across all three scenarios. It is at the farthest end of the feeder, thus the placement of switches on the feeder only causes marginal improvement in its reliability. The ECOST of LP4 is quite similar to that of LP5 and LP6 (Figure 6.9), but its ERNC is smaller than those of the duo (Figure 6.10). This is because of the business customer mix at the load points (Table 6.4). LP4 has only trade and ‘other commercial services’ sectors that have high CICs (Table 5.4), but low average monthly electricity bills (Table 6.6).
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Figure 6.9: Comparison of the load points’ ECOST with optimal placement of the 3 switches, with switches on all feeder main sections and with no switch at all for the scenario without alternate supply.
Figure 6.10: Comparison of the load points’ mean expected revenue not collected (ERNC) with optimal placement of the 3 switches, with switches on all feeder main sections and with no switch at all for the scenario without alternate supply.
Summary
In this chapter, a case study distribution system (Feeder 2 of bus 6 of the RBTS ) was adopted to demonstrate the practical application of the CIC data analyzed in the previous chapter in power system reliability planning. The reliability parameters of the test feeder components, as well as CIC and load models developed in this study were used in a time-sequential Monte-Carlo
LP1 LP2 LP3 LP4 LP5 LP6 LP7
ECOST (Rands/year)
LP1 LP2 LP3 LP4 LP5 LP6 LP7
ERNC (Rands/year)
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simulation framework to evaluate reliability worth indices for the test feeder under different scenarios. The results obtained show that a probabilistic description of CIC is more robust and effective for power system decision making. Also, a constrained optimization problem of optimal switch placement was solved to demonstrate that electric utilities can still make optimal and effective decisions even under budget constraint using reliability worth indices. The next chapter discusses the investigative procedures and results of an exploratory macroeconomic analysis done to assess the potential economy-wide cost of a hypothetical nation-wide blackout which may be precipitated by a sporadic event.
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7 Economy-Wide Cost of Electricity Interruptions: An Exploratory Case Study
This chapter discusses the application of publicly available macroeconomic data and a suitable economy-wide model to assess the economic cost of a potential nation-wide blackout in South Africa. The chapter ends with a summary of key findings from the macroeconomic analysis.