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# Opening the Black Box

A new approach to utility asset management.

a spare will have additional incremental value in one area if it can mitigate the consequences of transformer failure elsewhere. This means one can’t simply add up the expected value of spares at each location to determine the overall expected value of locating spare transformers at every location. For example, if a transformer at location X fails, but transformers in nearby locations A, B, and C can handle the additional loads, then the value of a spare transformer at X will be reduced if there are already spares located at A, B, and C.

For the RTO analysis, step-down transformers were grouped into geographic areas. For example, the “Northern Group” consisted of transformers at 18 separate substations. To mitigate failure risk, the RTO had located one spare transformer at each of the substations.

The value of locating a first spare at each location was then calculated. The analysis showed that locating a spare at “Lovell” ** ^{12}** had a net expected value of $29.5 million,

**larger than the incremental values at any other location. Moreover, the analysis showed that, because siting a first spare at Lovell also provided additional risk mitigation benefits in the event of transformer failures at other locations, the overall expected net benefit of siting the first spare at Lovell was $32.8 million.**

^{13}Next, the analysis determined the optimal location of siting a second spare, given that the first spare was already sited at Lovell. This analysis showed that siting a second spare at “Elgin” had an expected value of $27.4 million. The process continued, each time calculating the incremental expected value provided by the next spare, given the spares that had been sited. In total, the analysis showed that there was no incremental benefit to siting more than seven spares in the entire group, as shown in Figure 8. Moreover, the analysis determined that locating a second spare at Elgin had greater value than siting a first spare at many other locations in the Northern Group. Thus, rather than using 18 spares, one at each location, the analysis freed up 11 spares, which the RTO then relocated. In fact, approximately two weeks after the RTO relocated one of the redundant spares to a location in a different transformer group, as recommended by a subsequent analysis, the existing transformer at that substation failed. Because of the location recommendation, the RTO was able to restore service far more quickly and minimize the consequences of the transformer’s failure.

#### Endnotes:

1. The hazard rate, *h*(*t*), measures the probability that an asset will fail shortly after time *t, *given that it’s survived until time *t*. The hazard rate can be found empirically by estimating the survivor rate, * S(t), *which is the probability that an asset survives until at least time *t. *Mathematically, for some small interval Δ *t *that begins at time *t,* the probability of failure during this small interval of time * = h(t) *Δ*t* , where h(t) = [dS(t)/dt ]/S(t).

2. At the optimal retirement age, the expected present value marginal cost from higher risk equals