20150818AVU to Staff 77.doc

AVISTA CORPORATION
RESPONSE TO REQUEST FOR INFORMATION

JURISDICTION: IDAHO DATE PREPARED: 08/12/2015
CASE NO.: AVU-E-15-05/AVU-G-15-01 WITNESS: Tara Knox
REQUESTER: IPUC RESPONDER: Tara Knox/Curt Puckett (DNV GL)
TYPE: Production Request DEPARTMENT: State & Federal Regulation
REQUEST NO.: Staff - 077 TELEPHONE: [phone]

REQUEST:

Equation 2 on page 21 of the Electric Load Research Study presented in Ms. Knox' workpapers is an expression for standard deviation as a power function of a variable, x. Please answer the following:
a. For each class and strata, what values of σ0 and γ were used?
b. Was this standard deviation estimate used only for planning, or was it also used as part of the analysis? If used in the analysis, please explain how it was used.
c. Would it have been possible to estimate standard deviation from actual data (e.g. the previous load study)? If so, why was this estimate of standard deviation not used?
d. Please provide summary statistics (sample size, mean, and sample standard deviation) for the data used to estimate system load factor and class load factor, coincident peak, and non-coincident peak for each of classes listed in Table 11 (page 14).

RESPONSE:

Sigma naught and gamma are used in the secondary equation to describe the expected standard deviation of the typical heteroscedastic relationship between the demand variable (s) of interest and the explanatory variable, typically annual use. As discussed in the response to Staff Production Request No. 76, this relationship is used to guide the sample design by establishing strata cut points that place a near equal amount of the overall standard deviation in each stratum. This allows the MBSS design to allocate the same number of sample points to each stratum, i.e., a balanced sample design. Since sigma naught is a constant it is effectively ignored during the sample and we simply work with the gamma parameter. In previous work, we have found gamma to be a positive number between 0.5 and 1.0 with a gamma of 0.8 being a good general “rule of thumb.” Gamma simply tells us how much to emphasize the larger customers in the current design. To develop the sample design we simply sort the population of customers of interest by the planned stratification variable, e.g., annual use. Next, the annual use is raised to the gamma power. Next, a cumulative sum is created and divided into an appropriate number of strata. The number of stratum used is determined by how much spread there is from the smallest stratification variable and the largest. Typically, h=5 strata are normally sufficient to capture the desired variability. Of course, on occasion the sample design elects certain very large points with 100% certainty. A typical MBSS sample design will have more customers from the population (Nh) in the lower stratum and fewer customers in the upper stratum. Since the theory uses the same sample size in each stratum (nh), the sampling fraction (nh/Nh) increases as we go from the lower stratum to the higher stratum, resulting in a similar decrease in the case weights (Nh / nh) applied to each representative sample point.

The calculated standard deviation is used to simply guide the sample design, i.e., creates the stratum cut points, and is not used in the actual analysis of the resulting load data.

No, at the design phase of this project there was no current load data available for creating estimates of the standard deviation or error ratio for the planning phase. Avista relied on the experience of their statistical design consultant, i.e., DNV GL, to develop reasonable assumptions that would provide appropriate stratification and sample size estimates for use in this project. The error ratio assumption which governs the sample size calculation was documented in Table 11 and the gamma assumption was set at 0.8. The current load study results could certainly be used to plan the next study.

The requested statistics, i.e., sample size, mean, and standard deviation, for the various statistics requested, i.e., coincident peak, class peak, and non-coincident peak are provided in the following tables. Error ratios are also provided (more information on the error ratio can be found in the AEIC Load Research Manual, p 4-21). Statistics are provided separately for each peak since the calculations are performed for each hour of the 12-month study period.
Table 1 – Sample Statistics for Selected Peaks: Residential, General Service, Large General Service (Idaho)

Table 2 – Sample Statistics for Selected Peaks: Extra Large General Service, Pumping, Lighting, Extra Large General Service-CP (Idaho)

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