Business Forecasting:
Experiments and Case Studies
Dr. Yukun Bao
School of Management, HUST
Case 3: Load Forecasting
Dr. Yukun Bao
School of Management, HUST
Contents
1. Problem Statement
2. Modeling tasks
3. Data Analysis
4. Experimental Results
5. Summary
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1. Problem Statement

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1. Problem Statement

Load Forecasting



Predict the future electric demand based on historical
load, climate factors, seasonal factors, social activities,
and other possible factors.
Typical applications

Short-term: from one hour to one week ahead forecasts

Medium-term: a week to a year ahead

Long-term: Longer than a year
Forecasts for different time horizons are important for
different operations within a utility company
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1. Problem Statement

Benefits of accurate forecasting of Load demand



Utilities/ System Operators/Generators/ Power
Marketers/ other participants in electric generation,
transmission, distribution, and markets
automatic generation control, safe and reliable
operation, and resource dispatch
Energy transaction in deregulated and competitive
electricity markets

infrastructure development

…
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1. Problem Statement

Goal of this case study


Data


Primary experimental study in day-ahead load forecast
(Short-term Load forecasting)
Hourly load and temperature data from North-American electric
utility
Forecasting Methods ( by Matlab/R)

Support Vector Regression

Artificial Neural Network

ARIMA

ES

MA
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2. Modeling Tasks



Step1: Data Analysis (SPSS/Matlab)

Preprocess

Visualize and Analysis
Step2: Constructing Model

Input features selection

Parameters Optimization
Step3: Experimental Results and Analysis

Run Model

Results and comparison
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3. Data Analysis (1)

Testing period:


Training period:


January in 1991
The previous three months hourly data
Preprocess:

Zero values

[0,1]
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3. Data Analysis (1)-Descriptive

Descriptive Statistics
SPSS:
N
Minimu Maximu
Range
m
m
Std.
Mean
Deviation
Variance
Skewness
Statisti
c
Load
Kurtosis
Std.
Statistic Statistic Statistic
Statistic
Statistic
Statistic Statistic
2904 3285.00 1350.00 4635.00 2623.7999 616.25958 379775.8
Error
Std.
Statistic
Error
.180
.045
-.417
.091
-.854
.045
.928
.091
76
Temperature
2904
Valid N
2904
54.00
12.00
66.00
42.9490
9.33553
87.152
(listwise)
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3. Data Analysis (1)-ScatterPlot

In SPSS: GraphsLegacy DialogsScatter/Dot…Simple Scatter
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3. Data Analysis (2)
Hourly load from 01,
May,1990 --- 05,
July,1990


3500
3000
load demands have
multiple seasonal
patterns including the
daily and weekly
periodicity.
load level in the
weekend days and
holidays is lower than
that in working days
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2500
Load Value

2000
1500
1000
0
500
1000
1500
Hour
Fig.3 Hourly load from 01, May,1990 to 05, July,1990
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3. Data Analysis (3)
Average hourly load
during 24 hours



varies from hour to
hour
working days except
Friday have similar
shapes and similar
magnitude
weekend days <
working days
2600
2400
Load Value

2800
2200
2000
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
1800
1600
1400
2
4
6
8
10
12
14
Hour
16
18
20
22
24
Fig.4 Hourly load during a day
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3. Data Analysis (4)

Temperature v.s. Load Demand

nonlinear relationship
5000
4500
4000
Load
3500
3000
2500
2000
1500
1000
10
20
30
40
50
60
Temperature
70
80
90
100
Fig.5 Correlation between the load and temperature.
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3. Data Analysis (4)

Temperature v.s. Load Demand
Only for training and testing period

Correlations
Load
Load
Pearson Correlation
Temperature
1
Sig. (2-tailed)
N
Temperature
Pearson Correlation
-.574**
.000
2904
2904
-.574**
1
Sig. (2-tailed)
.000
N
2904
2904
**. Correlation is significant at the 0.01 level (2-tailed).
Fig.5 Correlation between the load and temperature.
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3. Data Analysis (5)

Input features for SVR/ANN



hourly load values of the previous 12 hours, and similar hours in
the previous one week
Temperature variables for time point that the load was included,
plus the forecasted temperature for the forecasting hour.
daily and hourly calendar indicators
 L ( t  1), L ( t  2 ), ..., L ( t  1 2 ), L ( t  2 4 ), L ( t  4 8), ..., L ( t  1 6 8),



In p u t ( t )   T ( t ), T ( t  1), T ( t  2 ), ..., T ( t  1 2 ), T ( t  2 4 ), T ( t  4 8), ..., T ( t  1 6 8 ), 
 D I ( t ), H I ( t )



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4. Experiments

Forecasting Methods ( by Matlab/R)

Support Vector Regression

Artificial Neural Network

ARIMA

ES

MA

Input features: all the above features

Parameter optimization: Grid search, PSO
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4. Experiments

Evaluation measures
Metrics
M APE
Formula
M APE 
1
M A SE 
1
y t  i  yˆ t  i
i 1
yt i
N
y t  i  yˆ t  i

N
M A SE
N

N
i 1
1
t 1
 100
t

y j  y j 1
j2
N
d
DS
DS 
N 1
 1, if
di  
 0,
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i
i2
 100
 yt i
 y t  i  1   y t  i  yˆ t  i  1   0
otherw ise
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4. Experiments

Results
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MAPE(%)
MASE
DS(%)
SVR_GS
6.95
0.77
89.23
SVR_PSO
7.01
0.79
90.19
NN
8.55
0.86
85.15
ARIMA
9.24
0.95
76.91
ES
10.11
1.792
61.24
MA
13.62
2.42
45.09
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4500
4. Experiments
Actual
Forecast
Error
4000
3500
3000
Results
Load

2500
2000
1500
1000
4500
4000
-500
0
100
200
300ESForecast
400
500
set
Hour
600
700
original
data
ESForecast set forecast
8
3500
3000
Demand
Demand
0
4000
3500
2500
3000
2500
2000
1500
500
MAForecast set original data
MAForecast set forecast
4500
2000
0
100
200
300
400
Time
500
600
700
800
1500
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0
100
200
300
400
Time
Business Forecasting: Experiments and Case Studies
500
600
700
800
20
Summary


Electricity load forecasting is an important issue to
operate the power system reliably and economically. In
this case study, support vector regression (SVR) is applied
for short-term load forecasting. Characteristics of the
hourly loads are firstly analyzed to select the input
features. Then forecasting results of SVR with two
parameter optimization methods are compared with
several benchmark forecasting models.
Further topics: features selection method, separated
modeling for each day and special days.
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