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Weather sensitive profiles are used to model energy using piece-wise linear regression of weather variables: temperature only (spring and fall), or temperature and relative humidity (summer only), or temperature and wind speed (winter only). Each weather sensitive profile is a Least Square Error regression based on historical hourly load data for a particular customer class, season and day type (e.g., RESVA, fall, Saturday, etc.) Each customer class will have a unique set of hourly weather sensitive profiles. A set of hourly profiles created for a four season, three day type customer class would consist of 288 sets of profiles (4*3*24).

Equation Development

A weather sensitive profile is calculated for each hour (1-24) from data in hour-ending format and is composed of one to three line segments, based on optimal temperature break points. The temperature breakpoints were determined to optimize the goodness of fit of the resulting regression equations. The temperature breakpoints (T-min, T-max) define the beginning and end of each line segment. Each hour within a weather sensitive profile will be comprised of 1 to 3 sets of equations, depending on the season and day type.

The basic equation for a line is: Y = mX + b

Where

Y is the dependent or response variable, m is the slope of the line X is the independent or predictor variable, and b is the intercept or constant.

The full equation for estimating customer load from multiple weather variables is

LOAD(c)(h)(t) = (m1)(X1) + (m2)(X2) + b

Where

(c) = Customer class
(h) = Hour specified (1-24)
(t) = Temperature range
m1 = temperature variable from the weather sensitive profile
X1 = temperature in degrees Fahrenheit from a weather station source
m2 = the auxiliary weather variable from the weather sensitive profile, either relative humidity (summer only) or wind speed (winter only). In the spring and fall this variable will be zero.
X2 = the auxiliary weather variable from the weather station, either percent relative humidity (summer only) or wind speed in miles per hour (winter only)
b = a constant

Note that the weather data for X1 and X2 will be from a weather forecast when the supplier is scheduling load and will be based on actual weather for settlement. (Also, please be aware that the constant coefficient should not be confused with base, or constant load. It is simply a coefficient in the regression equation and will vary widely within a class set of equations.)

Detailed Examples

For purposes of this example, we will use a hypothetical profile for a hypothetical customer class that we will designate as “Good Customers” or the GC class, as designated in column A. Secondly, we must determine the appropriate season and day type shown in column B. These tables are very wide and will appear below broken into three sections, one for each line segment.

PART 1 – LOW TEMPERATURES (first line segment)

Good Customer (GC) Profile
Spring Season Three Day Type (Weekday, Saturday, Sunday)
Weather sensitive profile

 

Retail
Account (A)
Season
Day Type (B)
Hour
(C)
T min
(D)
T max
(E)
Constant
(F)
Temp
(G)
RH
(H)
Wind
(I)
GC Spring
Weekday
1 0 53 2.83237414 -0.03855615
GC Spring
Weekday
2 0 55 2.62655319 -0.03577579
GC Spring
Weekday
3 0 55 2.57581797 -0.03563571
GC Spring
Weekday
4 0 55 2.68780948 -0.03805798
GC Spring
Weekday
5 0 55 2.69383037 -0.03785989
GC Spring
Weekday
6 0 55 2.89170182 -0.04066103
GC Spring
Weekday
7 0 54 2.95914394 -0.03870797
GC Spring
Weekday
8 0 55 3.1226878 -0.03622407

 

Note: T-min (col. D) and T-max (col. E) define the temperature ranges for this line segment. Note that over hours 1-8, T-max varies between 53 and 55 degrees F. Determining the appropriate temperature range for an hour is the next step in selecting the correct line segment.

Temperature ranges for the mid-range are shown in PART 2 in cols. J-K and the high ranges are shown in PART 3 in cols. P-Q.

 


PART 2 MID-RANGE TEMPERATURES (2nd line segment) (w/ cols. D .. I compressed)

Good Customer (GC) Profile
Spring Season Three Day Type (Weekday, Saturday, Sunday)
Weather sensitive profile

 

Retail
Account (A)
Season
Day Type (B)
Hour
(C)
T min
(J)
T max
(K)
Constant
(L)
Temp
(M)
RH
(N)
Wind
(O)
GC Spring
Weekday
1 53 65 -0.9403846 0.02971833
GC Spring
Weekday
2 55 64 -0.69035015 0.0243002
GC Spring
Weekday
3 55 64 -2.55560285 0.05395406
GC Spring
Weekday
4 55 64 -0.79614852 0.02511204
GC Spring
Weekday
5 55 64 -0.42639302 0.01936894
GC Spring
Weekday
6 55 64 -0.67059797 0.02453588
GC Spring
Weekday
7 54 64 0.36228872 0.00926277
GC Spring
Weekday
8 55 63 1.43000172 -0.00544019

 


PART 3 HIGH TEMPERATURES (3rd line segment) (w/ cols. D .. O compressed)

Good Customer (GC) Profile
Spring Season Three Day Type (Weekday, Saturday, Sunday)
Weather sensitive profile

Retail
Account (A)
Season
Day Type (B)
Hour
(C)
T min
(P)
T max
(Q)
Constant
(R)
Temp
(S)
RH
(T)
Wind
(U)
P_Min
(V)
P_Max
(W)
GC Spring
Weekday
1 65 110 -3.5665 0.068 0.6175 2.8064
GC Spring
Weekday
2 64 110 -2.8514 0.057 0.6175 2.8064
GC Spring
Weekday
3 64 110 -2.5836 0.052 0.6175 2.8064
GC Spring
Weekday
4 64 110 -3.3044 0.062 0.6175 2.8064
GC Spring
Weekday
5 64 110 -2.9656 0.058 0.6175 2.8064
GC Spring
Weekday
6 64 110 -3.1672 0.062 0.6175 2.8064
GC Spring
Weekday
7 64 110 -2.2709 0.05 0.6175 2.8064
GC Spring
Weekday
8 63 110 -2.0649 0.049 0.6175 2.8064

 

For this hypothetical illustration, we will continue to forecast load for the GC class, on a Spring Weekday, for the hour ending 8 a.m. The forecast from your subscription weather service is calling for a temperature of 69 degrees F, relative humidity of 14% and wind speed of 5 MPH. We have indexed the correct row based on columns A, B, and C. After testing T-min <69< T-max, it is determined that the line segment for high temperatures, line segment 3, is appropriate (with a range of 63<Temp<110).

Good Customer (GC) Profile
Spring Season Three Day Type (Weekday, Saturday, Sunday)
Weather sensitive profile

Retail
Account (A)
Season
Day Type (B)
Hour
(C)
T min
(P)
T max
(Q)
Constant
(R)
Temp
(S)
RH
(T)
Wind
(U)
P_Min
(V)
P_Max
(W)
GC Spring
Weekday
8 63 110 -2.0649 0.049 0.6175 2.8064

Applying these coefficients to the temperature data produces an average kW load per customer. Since the season is Spring, there are no coefficients for relative humidity (RH) or for wind.

LOAD (hour8)= -2.0649 + (0.049)(69) + (0.14)(0) + (5)(0)

LOAD (hour8)= -2.0649 + 3.381

LOAD (hour8)= 1.3161 kW

The regression software has also provided a range of acceptable values for the resulting answer (as shown in cols. V-W) to prevent unusually extreme temperatures from producing extreme results. The lower range for an acceptable answer is 0.6175 kW in this case, and the upper range is 2.8064 kW. Since 1.3161 is well within [P_Min<LOAD <P_Max] it is an acceptable answer.

Programming should include this test:

If Load<p_min then LOAD=P_min
Else
If Load>p_max then LOAD=P_max

Expand this average kW per customer number to your total customer class population by applying a scalar developed to reflect your number of customers in that class on that date, their usage factors, and the class loss factors.

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