Load Forecasting Eugene Feinberg Applied Math & Statistics Stony Brook University NSF workshop,...
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Transcript of Load Forecasting Eugene Feinberg Applied Math & Statistics Stony Brook University NSF workshop,...
Load Forecasting
Eugene FeinbergApplied Math & StatisticsStony Brook University
NSF workshop, November 3-4, 2003
Importance of Load Forecasting in Deregulated Markets
Purchasing, generation, sales Contracts Load switching Area planning Infrastructure development/capital
expenditure decision making
Types of Forecasting
S h o rt term fo recas ts(o n e h o u r to a w eek )
M ed iu m fo recas ts(a m o n th u p to a year)
Lo n g term fo recas ts(o ver o n e year)
Load Forecasts
Weather Influence
Electric load has an obvious correlation toweather. The most important variables responsible in load changes are: Dry and wet bulb temperature Dew point Humidity Wind Speed / Wind Direction Sky Cover Sunshine
Time factors
In the forecasting model, we should also
consider time factors such as: The day of the week The hour of the day Holidays
Customer Class
Electric utilities usually serve different types of customers such as residential, commercial, and industrial. The following graphs show the load behavior in the above classes by showing the amount of peak load per customer, and the total energy.
Mathematical Methods
Regression models Similar day approach Statistical learning models Neural networks
Our Work
Our research group has developed statistical learning models for long
term forecasting (2-3 years ahead) and
shortterm forecasting (48 hours ahead).
Long Term Forecasting
The focus of this project was to forecast theannual peak demand for distributionsubstations and feeders.
Annual peak load is the value most important
to area planning, since peak load most strongly
impacts capacity requirements.
Model Description
The proposed method models electric powerdemand for close geographic areas, load pocketsduring the summer period. The model takes intoaccount: Weather parameters (temperature, humidity, sky
cover, wind speed, and sunshine). Day of the week and an hour during the day.
Model
A multiplicative model of the following form was developed
L(t)=L(d(t),h(t))f(w(t))+R(t)where: L(d(t),h(t)) is the daily and hourly component
L(t) is the original load f(w(t)) is the weather factor R(t) is the random error
Model Cont:E l e c t r i c l o a d d e p e n d s :
o n t h e c u r r e n t w e a t h e r c o n d i t i o n s w e a t h e r d u r i n g l a s t h o u r s a n d d a y s .
T h e r e g r e s s i o n m o d e l u s e d i s
,
,,0i
titiw Xft
w h e r e X i , t - a r e n o n - l i n e a r f u n c t i o n s o f t h e a p p r o p r i a t e w e a t h e r p a r a m e t e r s .
Computational Results
The performance of proposed method was evaluatedfrom the graphs of the weather normalized load profiles and actual load profiles and from the followingfour statistical characteristics: Scatter plot of the actual load versus the model. Correlation between the actual load and the model. R- square between the actual load and the model. Normalized distance between the actual load and the
model.
Weather Normalized Load Profiles
Weather Normalized Load Profiles
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hours
MW
Sun Mon Tue Wed Thu Fri Sat
Actual Load Profiles
Actual Load Profiles
0
50
100
150
200
250
300
350
400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hours
MW
Sun Mon Tue Wed Thu Fri Sat
Correlation Between the Actual Load and the Model
Correlation between the Actual Load and the Model
0.955
0.96
0.965
0.97
0.975
0.98
0.985
0.99
1 2 3 4 5 6 7 8 9 10
Iteration
Co
rrela
tio
n
R-square Between the ActualLoad and the Model
Regression Output : R2
(defined as the proportion of variance of the response that is predictable from the regressor variables)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10
Iteration
R2
Normalized Distance Betweenthe Actual Load Vs the Model
Normalized Distance between the Actual Load and the Model
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8 9 10
Iteration
Dis
tan
ce
Short Term Forecasting
The focus of the project was to provideload pocket forecasting (up to 48 hoursahead) and transformer ratings.
We adjust the algorithm developed for long
term forecasting to produce results forshort term forecasting.