Past Outage History

One of the key insights provided by this analysis flows from our specification of a rich structure for past outage history. By using two components of past outage history, log duration and number of occurrences, we show that past outage history is not a uni-dimensional concept, but instead illustrate that different components of outage history have contrasting effects on WTP. These contrasting effects derive from the significant and opposite signs for the number of past outages during the preceding 12 months (num out) and the log of combined duration of such outages in hours (out past). This implies that an increase in historic outage frequency, ceteris paribus, decreases a household's WTP to avoid further interruptions. This could be indicative of a learning-to-cope, or preparedness effect induced by frequent outage events. In stark contrast, however, estimated WTP increases with the combined duration of recent interruptions. Evidently, one or more longer blackouts in the recent past stir up decidedly unpleasant memories in affected respondents and seem to induce substantially higher costs than they generate learning gains.

These results may explain the contradicting findings in the existing outage cost literature on the role of outage history on cost estimates for a specified future interruption. Specifically, Doane, Hartman et al. (1988b) find that households that traditionally experience a larger number of outages have a decreased WTP to avoid additional blackouts, while Doane et al. (1988a) and Beenstock et al. (1998) reach the exact opposite conclusion. This apparent discrepancy could be a result of different average length of past outages in each of these cases. None of these studies incorporate measures of historic outage duration in their estimation models.

Figure 3.2. WTP for a One-Hour Outage: Past Duration vs. Past Events. The iso-WTP lines show that WTP to avoid this particular outage is the same for households that have experienced one long outage or several shorter interruptions. Alternatively, WTP is lower if a given past duration is distributed over several outage occurrences. This may be indicative of two countervailing forces: a cost-awareness factor versus a learning-to-cope effect.

Figure 3.2. WTP for a One-Hour Outage: Past Duration vs. Past Events. The iso-WTP lines show that WTP to avoid this particular outage is the same for households that have experienced one long outage or several shorter interruptions. Alternatively, WTP is lower if a given past duration is distributed over several outage occurrences. This may be indicative of two countervailing forces: a cost-awareness factor versus a learning-to-cope effect.

Figure 3.2 illustrates these offsetting effects. The surface plane of figure 3.2 connects simulated cost estimates for a hypothesized evening outage of one-hour duration at different combinations of number and duration of past interruptions. In each case, cost estimates were first generated for each respondent and then averaged over households. For example, a prototypical household that experienced one 20-hour outage in the past would be willing to pay approximately $22 to avoid the stipulated interruption (point A). If the com bined duration of 20 hours is distributed over, say, 10 individual events, WTP decreases to approximately $16 (point B). The darker lines crossing the cost surface represent iso-WTP curves for several dollar amounts. For instance, a WTP value of $15 could be reached with one 6-hour interruption (point C), ten outages with a combined duration of 16 hours (point D) or any of the frequency / duration pairs along the line C-D.

Figure 3.3. Outage Costs by Scenario Duration and Past Duration. The WTP to avoid future outages of a given duration increases with the combined duration of past outages. This effect is relatively stronger for longer hypothetical future outages.

Figure 3.3 shows the importance of capturing historic duration effects when analyzing the value of electric reliability to residential customers from a different perspective. The figure depicts cost estimates associated with a new unannounced future outage as a function of combined duration of past interruptions. For ease of interpretation, cost estimates for one, four, and 12-hour duration are highlighted through cross-section planes. For example, a four-hour evening interruption causes costs of approximately $7 to a household that has not experienced any blackouts over the preceding 12 months (point A). In contrast, WTP to avoid a four-hour outage is about five times higher for a household with a combined past duration of 20 hours (point B). Comparing the vertical height of the cross-sections at any historic duration value, one can also note that combined past duration affects WTP estimates relatively more for longer proposed interruptions.

The recognition of these interactive effects of frequency and duration of past blackouts may offer additional guidance to utilities in identifying residential neighborhoods with relatively high sensitivity to power interruptions. Clearly, a sole focus on the number of past outage events in this context may lead to sub-optimal allocation of reliability efforts.

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