Pacific Gas & Electric (PCG)

PCG»Topics» UCLs, LCLs, UWLs and LWLs for Index 1 and 2 for All Other Voltage Classes

This excerpt taken from the PCG 10-K filed Feb 18, 2005.

UCLs, LCLs, UWLs and LWLs for Index 1 and 2 for All Other Voltage Classes

When data for less than four Transmission Line Circuits with Forced Outages(IMS) are available per year in a Voltage Class for fewer than five years, an exhaustive enumeration of all possible selections with replacement may need to be performed. This is because the number of possible samples for bootstrap resampling will be less than the aforementioned 10,000 resampling frequency used for Voltage Classes containing four or more Transmission Line Circuits with Forced Outages(IMS) for five or more years. For example, if a Voltage Class has only two Transmission Line Circuits per year for five years, the data base will consist of 2*5 = 10 accumulated Forced Outage(IMS) durations assuming both Transmission Line Circuits experience a Forced Outage(IMS) or more per year. Resampling two values from the column of 10 yields only 10**2 = 100 possible means. Thus, bootstrap resampling of 10,000 would over-sample the original data 10,000/100 = 100 times.

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For the general case, let M = the number of accumulated Forced Outage(IMS) durations (or Forced Outage(IMS) frequencies) from the historical data base. If n is the median number of Transmission Line Circuits per year, there are M**n = U possible enumerated means for this Voltage Class. The procedure to determine the appropriate limits for a Voltage Class is to order the column containing U enumerated means from smallest to largest means. Then, the UCL, LCL, UWL, and LWL are determined from this vector as described above (i.e. at the 99.75, 0.25, 97. 5 and 2. 5 percentiles, respectively).