HomeMy WebLinkAbout20160414IPC Attachment 1 to Staff.pdf
1
SUPPORTING DOCUMENTATION
WEATHER NORMALIZATION
2
Table of Contents
I. Weather Normalization Methodology Overview ................................................................................. 3
Overview ...................................................................................................................................... 4
Weather Data ............................................................................................................................... 5
II. Detailed Methodology Description ..................................................................................................... 6
Matching Weather Data With Sales Data .................................................................................... 7
General Discussion ......................................................................................................... 7
Weather Data Sources ..................................................................................................... 7
Actual Weather Data ....................................................................................................... 7
Normal Weather Data ..................................................................................................... 7
Billing Cycle Daily Weights ........................................................................................................ 8
Construction of Weather Actuals .................................................................................... 9
Construction of Weather Normals ............................................................................................... 10
Description of Economic and Price Data ..................................................................................... 11
Description of Regressions .......................................................................................................... 12
General Discussion ......................................................................................................... 12
The Use of Regression Results to Adjust for Abnormal Weather ............................................... 17
3
I. Weather Normalization Methodology Overview
4
Overview
To determine the degree to which actual electricity sales were higher or lower than normal as a result of
actual weather, it is necessary to first quantify the relationship between weather and sales. This
quantification is achieved in the IPCo model through the use of multiple regression1 analysis in which
energy use is statistically estimated as a function of weather and nonweather variables. This relationship
between electricity use and its primary determinants is measured in ten regression equations - two which
describe IPCo's total system residential and commercial sales; two which describe IPCo's Oregon residential
and commercial sales; five which describe irrigation sales for each IPCo operating center; and one which
describes IPCo’s Oregon irrigation sales. The Oregon equations are used in the allocation of the system
adjustments to jurisdictions.
To explain electricity use, the regression equations utilize weather concepts such as heating, cooling and
growing degree days and precipitation, as well as economic and demographic information such as real
electricity prices, real per-capita disposable income, real Gross State Product (GSP), and Producer Price
Indexes (farm). As indicated in the detailed methodology description, the summary statistics demonstrate
that the regressions are accurate in explaining monthly variations in sales. This is particularly true of the
weather variables. Combining data from many months in each regression and estimating over a long time
period allows sufficient variation within the data to incorporate economic variables and more than one
weather concept. The residential and commercial equations quantify use per customer as a function of
weather and nonweather variables while the irrigation equations explain electricity use by operating center.
Once the regression equations have been specified and estimated, it is the coefficients of the weather
variables that are of primary importance to the weather adjustment process. These coefficients measure the
response of sales to changes in those weather variables. For example, the coefficients of the heating degree
day variables in the residential total system equation represent the number of KWh/customer that one
additional heating degree day would cause. By multiplying this coefficient by the difference between the
normal number of heating degree days for a particular month and the number that actually occurred, the
difference between actual and normal KWh/customer is determined. It is important to recognize that the
non-weather variables are used only to estimate the regression equations and that only the coefficients of the
weather variables are used in the actual adjustment. It is also important to note that the primary purpose of
the models is to adjust sales that have already occurred, rather than to estimate future sales. Although the
equations could be utilized as forecasting tools, the focus of these models at the present time is on their
ability to adjust historical sales for abnormal weather, not their ability to forecast.
1A functional relationship between two or more correlated variables that is often empirically determined from
data and is used especially to calculate values of one variable when given values of the others.
5
Weather Data
The weather concepts in the regressions are constructed from temperature and precipitation data from four
weather stations: Boise, Pocatello, Twin Falls, and Ontario. One of the most critical aspects of quantifying
the relationship between electricity use and weather is the correct matching of weather with sales data.
Because the Company's residential, commercial, and irrigation customers are billed in cycles, sales in a
particular month represent consumption that occurred in portions of the current month as well as the
previous two months, depending upon the particular billing cycle being analyzed. Consequently, weather
that occurred during the current month and the previous two months must be considered when examining
sales in the current month. To account for this, and to correctly match weather data with sales data, the
weather variables utilized in the residential, commercial, and irrigation regressions represent weighted sums
of the daily values of those variables over the appropriate time period. Each day's weather measure is
weighted by the number of customers (for a particular month) who experienced that weather.
The IPCo service area contains regions with different weather patterns. To incorporate these different
weather patterns in the system regressions, the weather variables were constructed using weighted weather
data from the Boise, Twin Falls, Pocatello, and Ontario weather stations. For example, the heating degree
day variable used for each month in the system residential equation is a weighted sum of the heating degree
days of Boise, Twin Falls, Pocatello, and Ontario with the weights based on the number of customers in
IPCo's five operating centers represented by those cities. By constructing the weather variables in such a
way, the model has the capability of incorporating the diversity of weather in the Company's service area.
6
II. Detailed Methodology Description
7
Matching Weather Data With Sales Data
General Discussion
In general, the weather concepts used in the weather adjustment model are matched with sales as follows:
1) For those categories representing customers billed by calendar month, calendar month heating and
cooling degree actuals and normals are collected from the National Oceanic and Atmospheric
Administration (NOAA).
2) For those categories representing billing cycle customers, (System Residential, Oregon
Residential, System Commercial, Oregon Commercial, Irrigation by Operating Center, and
Oregon Irrigation), monthly weather concepts are generated by aggregating daily data over the
appropriate days of the billing month. Weather concepts calculated in this manner include heating
degree days, cooling degree days, growing degree days, and precipitation. Each of these weather
concepts are calculated for four service area weather stations: Boise, Pocatello, Twin Falls, and
Ontario.
Weather Data Sources
The following weather data is used directly in the weather adjustment or in the construction of the monthly
billing month weather variables (the source of data is the NOAA):
Actual Weather Data
Ontario: Monthly Heating and Cooling Degree Days from 1961 Forward
Twin Falls: Monthly Heating and Cooling Degree Days from 1964 Forward
Boise: Daily Maximum Temperature, Minimum Temperature, and Precipitation - 1961 Forward
Pocatello: Daily Maximum Temperature, Minimum Temperature, and Precipitation - 1961 Forward
Twin Falls: Daily Maximum Temperature, Minimum Temperature, and Precipitation - 1964 Forward
Ontario: Daily Maximum Temperature, Minimum Temperature, and Precipitation - 1961 Forward
Normal Weather Data
Ontario: Monthly Heating and Cooling Degree Day Normals (Median)
Twin Falls: Monthly Heating and Cooling Degree Day Normals (Median)
The degree day concepts used in the weather adjustment are defined as follows:
Heating Degree Days = Maximum[0,65-((Maximum+Minimum Temperatures)/2)]
Cooling Degree Days = Maximum[0,((Maximum+Minimum Temperatures)/2)-65]
Growing Degree Days = Maximum[0,((Maximum+Minimum Temperatures)/2)-50]
8
Billing Cycle Daily Weights
The cyclic billing of IPCo residential, commercial, and irrigation customers has two primary implications
for the matching of weather and sales data. First, sales in a particular month represent consumption that
occurred in that month and the previous two months. Thus, a weather variable which will be used to help
explain that month's sales must reflect the appropriate period over which consumption occurred.
Second, the impact of a particular day's weather over this period is different for different days. The weather
on a day for which consumption of all 21 cycles will be recorded for a particular sales month is far more
important to that sales month than the weather on a day for which consumption of only 1 cycle will be
recorded. Consequently, when constructing monthly weather concepts from daily data, each day's weather
must be weighted according to its importance to the billing month.
Figure 1 below demonstrates how consumption of the 21 cycles is spread over each billing month. The
diagram shows the number of cycles consuming electricity for each day of the billing month based on
Company meter reading dates. The month May 2009 is used here for illustrative purposes. The first day of
the first cycle of this billing month is March 31 - for that day, only the first cycle's consumption will be
recorded as May sales. On April 1, cycle 2 begins and so the consumption of two cycles on that day will
contribute to May sales. On April 28, the consumption of all 21 cycles will be recorded as May sales. Those
days with a higher number of cycles are more important in constructing weather measures to explain
weather-related consumption in the May sales month than those with a smaller number of cycles.
Number of Cycles Recording Sales for May Sales Month
(number of cycles)
figure 1
0
3
6
9
12
15
18
21
Ma
r
3
0
Ap
r
0
1
Ap
r
0
3
Ap
r
0
5
Ap
r
0
7
Ap
r
0
9
Ap
r
1
1
Ap
r
1
3
Ap
r
1
5
Ap
r
1
7
Ap
r
1
9
Ap
r
2
1
Ap
r
2
3
Ap
r
2
5
Ap
r
2
7
Ap
r
2
9
Ma
y
0
1
Ma
y
0
3
Ma
y
0
5
Ma
y
0
7
Ma
y
0
9
Ma
y
1
1
Ma
y
1
3
Ma
y
1
5
Ma
y
1
7
Ma
y
1
9
Ma
y
2
1
Ma
y
2
3
Ma
y
2
5
Ma
y
2
7
9
To construct a weather measure representative of every billing month while accounting for these differences
in each day's influence, each day within the month is assigned a weight measuring the number of cycles of
that day. For example, on a day where 15 cycles are recording sales for a particular month, the weight is
15/21. Note that all 21 cycles are consuming electricity every day. The only thing that varies is the month in
which that consumption will be recorded. Thus, if 15 of the 21 cycles will be recorded in one month, the
other 6 will be recorded in another month. The assignment of weights to each day in this manner assumes an
equal number of customers in each cycle.
Construction of Weather Actuals
With weights assigned to each day on the basis of a number of cycles, billing month weather variables are
calculated by summing the weighted weather measure over every day in the billing month. For example, to
calculate billing month heating degree days, daily heating degree days are weighted and summed over every
day of the billing month. The same procedure is followed for cooling degree days, growing degree days, and
precipitation. The following variables are constructed in this manner for each of four weather stations:
Boise, Pocatello, Twin Falls, and Ontario and from 1961 to present (or where data permits).
Billing-Adjusted Heating Degree Days - Base 65
Billing-Adjusted Cooling Degree Days - Base 65
Billing-Adjusted Growing Degree Days - Base 50
Billing-Adjusted Precipitation
The billing-adjusted weather concepts for Ontario are used in the Oregon-specific regressions. The billing-
adjusted growing degree day and precipitation weather concepts are used in the operating center and
Oregon-specific irrigation regressions. The system weather variables used in the system residential and
commercial regressions require one more step described below.
With these billing-adjusted weather concepts constructed for each of the four cities, it is now possible to
construct aggregate service area measures for use in the system regressions. These aggregate service area
measures are weighted averages of the billing-adjusted measures for the four cities. For example, the
residential heating degree day variable used in the system residential regression is a weighted average of the
heating degree days of Boise, Twin Falls, Pocatello, and Ontario with the weights based on the number of
residential customers in IPCo's five operating centers represented by those cities. Similarly, the residential
system cooling degree day variable is constructed as a weighted sum of the cooling degree days of the four
cities using the same weights. The system commercial degree day variables used in the regression are
calculated in the same way but the weights used in that calculation are based upon commercial customers in
the five operating centers.
Following is a list of the weather data actuals used in the residential, commercial, and irrigation weather
adjustment regressions calculated as described above:
System Residential Heating and Cooling Degree Days
System Commercial Heating and Cooling Degree Days
Irrigation Growing Degree Days and Precipitation by City for each Operating Center
Oregon Residential Heating and Cooling Degree Days
Oregon Commercial Heating and Cooling Degree Days
Oregon Irrigation Growing Degree Days and Precipitation
10
Following is a list of the calendar month weather data actuals:
Twin Falls Heating and Cooling Degree Days
Construction of Weather Normals
For those customers billed on a calendar month basis, calendar month normals for heating and cooling
degree days are calculated over the years 1986 to 2015 (most recent 30 years). The median values are
calculated and used to represent a “normal” number of heating and cooling degree days. The median figures
have a 50/50 chance of occurrence and are not adversely influenced by a few extreme weather events.
For billing cycle customers, normal weather concepts are calculated as follows:
1) For each city, normal weather concepts are calculated by first calculating the median weather
concept over the period 1986 to 2015. That is, for each city, the 30 values for January's heating
degree days are used to determine the median, as are February's values, and so forth. This provides
12 normals for each city and for each weather concept. The normal billing-adjusted weather
concepts calculated for Ontario, together with the billing-adjusted actuals for Ontario are used in the
Oregon-specific weather adjustment models.
2) With the normal billing-adjusted weather concepts calculated for each of the four cities, it is now
possible to construct aggregate normal weather concepts representing the entire service area.
These aggregate service area normals are weighted averages of the billing-adjusted normals for
the four cities. For example, the residential system heating degree day normal is a weighted
average of the billing-adjusted heating degree day normals for Boise, Pocatello, Twin Falls, and
Ontario. The system normal weather concepts are calculated in precisely the same manner as the
system actuals. The operating center weights used for the system residential variables are
residential customers and those used for the system commercial variables are commercial
customers. Note that a normal weather concept for January (or any other month) of one year may
differ from the normal for January of another year if the operating center weights change from
year to year.
11
Description of Economic and Price Data
Price Terms: Each price term is an average price, calculated as the ratio of revenue to sales. In the
cases of the Oregon price terms, the revenue or sales for the appropriate jurisdiction are
used. A 12-month moving total of revenue and sales are used to dampen seasonal
fluctuations and mitigate the multicollinearity between variables. Real price terms are
calculated from these nominal price variables using the following deflators:
Residential System - Personal Consumption Deflator
Residential Oregon - Personal Consumption Deflator
Commercial System - Gross Domestic Product (GDP) Deflator
Commercial Oregon - GDP Deflator
Irrigation by Operating Center - GDP Deflator
Irrigation Oregon - GDP Deflator
Electric
Space Heat
Saturation: IPCo residential survey data is used when available. Prior to 1977, saturation data is
derived using the last data point, the 1970 census, and the ratio of electric space heating
customers to total residential customers.
Central Air
Conditioning
Saturation: Similar to Electric Space Heat Saturation
Total
Employment: As provided by Moody’s Analytics
Gross
State
Product: As provided by Moody’s Analytics
Real per Capita
Disposable
Income: As provided by Moody’s Analytics
Producer
Price Index -7
Farm Products: As provided by Moody’s Analytics
12
Description of Regressions
General Discussion
Total System Residential Model:
A model of electricity sales using monthly observations was estimated for the system residential class over
the period January 2002 to December 2015. First order autocorrelation was detected and corrected.
The dependent variable in the total system residential model is system residential use-per-customer. The
pattern of electricity use is described by the combination of weather and non-weather factors discussed
below.
Degree Days
The weather variables utilized by the system weather adjustment model are constructed as weighted
averages of degree day variables from four service area weather stations: Boise, Twin Falls, Pocatello, and
Ontario. That is, the heating degree day variables (Base 65) are an average of heating degree days from the
four weather stations, each weighted by the number of customers in the operating center associated with that
weather station. The same weighting mechanism was used to construct the cooling degree day variable
(Base 65).
Price
The price term represents the residential average price of electricity. The personal consumption deflator
deflates the nominal price term.
Trends
Linear trends are used to pick up the effects of unmeasured and immeasurable factors which change over
time and influence energy consumption.
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as number of daylight hours, school vacations,
holidays, etc. These variables contributed to the explanatory power of the model. These variables could also
help account for other weather-related variables, such as cloud cover and wind speed, which the Company
was not able to account for at this time but which may exhibit definite monthly patterns.
Oregon Residential Model:
A model describing residential electricity sales per customer for the Oregon portion of the Company's
service area was estimated over the period January 2002 to December 2015. First order autocorrelation was
detected and corrected.
The dependent variable in the Oregon residential model is Oregon residential use-per-customer. The pattern
of electricity use is described by the combination of weather and non-weather factors discussed below.
13
Degree Days
The weather variables used for the Oregon specification are heating and cooling degree days (Base 65) for
Ontario, Oregon.
Price
The price term represents the residential average price of electricity. The price term is constructed from
Oregon-specific revenue and sales data.
Trends
Linear trends are used to pick up the effects of unmeasured and immeasurable factors which change over
time and influence energy consumption.
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as number of daylight hours, school vacations,
holidays, etc. These variables contributed to the explanatory power of the model. These variables could also
help account for other weather-related variables, such as cloud cover and wind speed, which the Company
was not able to account for at this time but which may exhibit definite monthly patterns.
Total System Commercial Model:
The total system commercial model was estimated over the period January 2002 to December 2015 and is
structurally similar to the system residential model.
The dependent variable in the total system commercial model is system commercial use-per-customer. The
pattern of electricity use is described by the combination of weather and non-weather factors discussed
below.
Degree Days
The weather variables utilized by the system weather adjustment model are constructed as weighted
averages of degree day variables from four service area weather stations: Boise, Twin Falls, Pocatello, and
Ontario. That is, the heating degree day variables (Base 65) are an average of heating degree days from the
four weather stations, each weighted by the number of customers in the operating center associated with that
weather station. The same weighting mechanism was used to construct the cooling degree day variable
(Base 65).
Price
The price term represents the commercial average price of electricity.
Trends
Linear trends are used to pick up the effects of unmeasured and immeasurable factors which change over
time and influence energy consumption.
14
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as number of daylight hours, school vacations,
holidays, etc. These variables contributed to the explanatory power of the model. These variables could also
help account for other weather-related variables, such as cloud cover and wind speed, which the Company
was not able to account for at this time but which may exhibit definite monthly patterns.
Economic
Total employment for the Boise Metropolitan Statistical Area (MSA) was used as an independent or
explanatory variable in the system commercial model.
Oregon Commercial Model:
A model describing commercial electricity sales per customer for the Oregon portion of the Company's
service area was estimated over the period January 2002 to December 2015. First order autocorrelation was
detected and corrected.
The specification is structurally similar to and provides results consistent with the commercial total system
specification. The price term is constructed from Oregon specific revenue and sales data.
The dependent variable in the Oregon commercial model is Oregon commercial use-per-customer. The
pattern of electricity use is described by the combination of weather and non-weather factors discussed
below.
Degree Days
The weather variables used in the Oregon commercial specification were heating and cooling degree days
(Base 65) adjusted for billing cycles for Ontario, Oregon.
Price
The price term represents the commercial average price of electricity. The price term is constructed from
Oregon-specific revenue and sales data.
Trends
Linear trends are used to pick up the effects of unmeasured and immeasurable factors which change over
time and influence energy consumption.
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as number of daylight hours, school vacations,
holidays, etc. These variables contributed to the explanatory power of the model. These variables could also
help account for other weather-related variables, such as cloud cover and wind speed, which the Company
was not able to account for at this time but which may exhibit definite monthly patterns.
15
Operating Center Irrigation Models:
A basic model of electricity sales using monthly observations was estimated for irrigation sales for each
IPCo operating center over the months April/May 2002 through September 2015 (May 2002 through
September 2015 was used in the Payette Operating Center model). First order autocorrelation was detected
and corrected. Operating center irrigation sales are considered a function of growing degree days,
precipitation, maximum number of active irrigation customers connected, real electricity prices, and the
producer price index for farm products. This pattern of electricity use is described by the combination of
weather and non-weather factors discussed below.
Degree Days and Precipitation
The weather variables utilized by the system irrigation weather adjustment model are constructed as
weighted averages of degree day variables from four service area weather stations: Boise, Twin Falls,
Pocatello, and Ontario. That is, the growing degree day variable (cooling degree days Base 50) is an average
of growing degree days from the four weather stations, each weighted by the share of total system irrigation
pumping horsepower connected in the division associated with that weather station. The precipitation
variable was constructed and weighted in the same manner. A second precipitation variable was used to
measure the impact of pre-growing season precipitation on the early months of the growing season (May
and June). This variable is zero for all months except May and June of each year where it is the total of the
weighted precipitation for the two previous months. For example, the pre-growing season precipitation for
May 2009 is the total of the weighted precipitation for March and April 2009. This variable was used
because of the fact that precipitation prior to the growing season is partially retained by the soil. This may
minimize the need for irrigation water applications in the early months of the growing season. The opposite
would also be true. Small amounts of pre-growing season precipitation cause decreased amounts of retained
moisture in the soil which may increase early growing season irrigation applications.
Price
The price term represents the system irrigation annual average price of electricity. The gross domestic
product (GDP) deflator was used to deflate the nominal price term.
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as the stage of the growing cycle that the crops
are in at various times during the year, harvest patterns, etc. The linear trend is used to pick up the effects of
unmeasured and immeasurable factors which change over time and influence energy consumption.
Economic Variables
The producer price index for farm products term was used to help explain the impact on electricity sales of
prices received by agricultural customers.
Oregon Irrigation Model:
A model describing irrigation electricity sales for the Oregon portion of the Company's service area was
estimated over the period May 2002 through September 2015. First order autocorrelation was detected and
corrected. The specification is structurally similar to and provides results consistent with the Payette
Operating Center model described above. The dependent variable in the Oregon irrigation model is Oregon
16
irrigation sales. The pattern of electricity use is described by the combination of weather and non-weather
factors discussed below.
Degree Days and Precipitation
The weather variables used in the Oregon irrigation specification were growing degree days (cooling degree
days Base 50) and precipitation adjusted for billing cycles for Ontario, Oregon. The degree days and
precipitation variables were constructed using Ontario, Oregon historical weather data. A second
precipitation variable was used to measure the impact of pre-growing season precipitation on the early
months of the growing season (May and June) and was constructed as described in the Operating Center
Irrigation Models above.
Price
The price term represents the system irrigation annual average price of electricity. The gross domestic
product (GDP) deflator was used to deflate the nominal price term.
Monthly Binaries
Monthly binary variables were included in the regression to account for factors which vary from month to
month but which are relatively constant over the years, such as the stage of the growing cycle that the crops
are in at various times during the year, harvest patterns, etc. The linear trend is used to pick up the effects of
unmeasured and immeasurable factors which change over time and influence energy consumption.
Economic Variables
The producer price index for farm products term was used to help explain the impact on electricity sales of
prices received by agricultural customers.
17
The Use of Regression Results to Adjust for Abnormal Weather
The method by which the preceding regression results are used to weather normalize monthly sales is the
same method used by the Electric Power Research Institute as described in Weather Normalization of
Electricity Sales.2 That description is paraphrased below:
Any model that can be used for weather normalizing monthly sales can be written in the general form:
where Sm is electricity sales per customer for month m;
wm is a vector of weather measures related to electricity sales
in month m;
xm is a vector of non-weather variables related to electricity
sales in month m; and
f is a function of observed explanatory variables wm and xm.
Given a model of this kind, weather normalization of electricity sales proceeds as follows. Predicted sales
per customer for month m under actual weather conditions mAw is
Predicted sales per customer for month m under normal weather conditions mNw is
where mNw is a measure of normal weather in month m. Consequently, the predicted adjustment in sales that
is required to reflect non-normal weather conditions is
where Cm is the number of customers billed in month m. This adjustment, Am, is applied to the actual sales
for the month of m to obtain "weather normalized sales." If predicted sales under normal weather exceeds
predicted sales under actual weather, then the adjustment is positive and weather normalized sales are
greater than actual sales. If predicted sales under normal weather is less than predicted sales under actual
weather, then the adjustment is negative and weather normalized sales are less than actual sales.
2Electric Power Research Institute, Weather Normalization of Electricity Sales, (June 1983), EA-3143,
Research Project 1922-1.
m m mS = f (w , x ) ,
. )x ,w( f = S mAmAm
m
N mN mS = f (w , x ) ,
m m
N
m
A mA = (S - S ) x C ,
18
This procedure for normalizing sales has two implications regarding the construction and evaluation of
weather normalization models. The first implication is that the primary purpose of the models is for
adjusting previous sales, rather than forecasting future sales. That is, the models are used to adjust sales that
have already occurred, with the adjustment being the portion of those sales that were due to abnormal
weather. While the models could also perhaps be used to predict sales that would occur in the future, either
under normal or predicted actual weather, that is not their primary function. This means that in constructing
and evaluating the models, their ability to accurately adjust past sales for abnormal weather is the focus, not
their ability to forecast accurately into the future.
The second implication, which follows the first, is that variables that might affect sales, but do not affect the
weather adjustment of sales, are not essential to the model. For example, consider a linear model with two
variables:
where wm is a weather variable, and
xm is a non-weather variable.
With this model, estimated sales under actual weather is
and under normal weather is
Consequently, the adjustment in sales that is required to reflect non-normal weather is:
m m mS = w + x ,
m
A mA mS = w + x ,
m
N
mN mS = w + x .
m m
N
m
A
m mN m mA m mA = (S - S ) x C = (w + x ) - (w + x ) x C
= (w - w ) x CmNmAm
= (w - w ) x C .mN mA m
19
The value of the variable xm and the value of its coefficient are irrelevant in weather normalizing sales data;
only the weather variable and its coefficient enter the adjustment procedure. This implies that, in estimation,
non-weather variables that enter linearly are important to include only if their inclusion affects the estimated
coefficients of weather variables. Non-weather variables that enter linearly and whose inclusion does not
affect the coefficients of weather variables are not important to weather normalization.
The procedure by which the Company's residential, commercial, and irrigation weather adjustment is
allocated to specific jurisdictions and schedules is as follows:
The Oregon and system adjustments are calculated by the methodology described above except
irrigation adjustments are not multiplied by the number of customers billed.
The Oregon adjustments are subtracted from the system adjustments to obtain the adjustment for
Idaho.
Each jurisdiction's adjustment is then apportioned to the following schedules:
Residential - all the adjustment is applied to Schedule 1
Commercial - adjustment is apportioned to Schedules 7 and 9S (secondary) on the basis of sales
Irrigation - all the adjustment is applied to Schedule 24S (secondary)