Dr. Yukun BaoSchool of Management, HUST

Business Forecasting: Experiments and Case Studies

                          

Dr. Yukun BaoSchool of Management, HUST

Case 3: Load Forecasting

April 21, 2023 Business Forecasting: Experiments and Case Studies

3

Contents

1. Problem Statement

2. Modeling tasks

3. Data Analysis

4. Experimental Results

5. Summary

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1. Problem Statement

Business Forecasting: Experiments and Case Studies

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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

Business Forecasting: Experiments and Case Studies

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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 …

Business Forecasting: Experiments and Case Studies

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1. Problem Statement

Goal of this case study Primary experimental study in day-ahead load

forecast (Short-term Load forecasting) Data

Hourly load and temperature data from North-American electric utility

Forecasting Methods ( by Matlab/R) Support Vector Regression Artificial Neural Network ARIMA ES MA

Business Forecasting: Experiments and Case Studies

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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

Business Forecasting: Experiments and Case Studies

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3. Data Analysis (1)

Testing period: January in 1991

Training period: The previous three months hourly data

Preprocess: Zero values [0,1]

Business Forecasting: Experiments and Case Studies

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3. Data Analysis (1)-Descriptive

SPSS:

Business Forecasting: Experiments and Case Studies

Descriptive Statistics

N Range

Minimu

m

Maximu

m Mean

Std.

Deviation Variance Skewness Kurtosis

Statisti

c Statistic Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

Load 2904 3285.0

0

1350.00 4635.00 2623.7999 616.25958 379775.8

76

.180 .045 -.417 .091

Temperature 2904 54.00 12.00 66.00 42.9490 9.33553 87.152 -.854 .045 .928 .091

Valid N

(listwise)

2904

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3. Data Analysis (1)-ScatterPlot

In SPSS: GraphsLegacy DialogsScatter/Dot…Simple Scatter

Business Forecasting: Experiments and Case Studies

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3. Data Analysis (2)

Hourly load from 01, May,1990 --- 05, July,1990 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

Business Forecasting: Experiments and Case Studies

0 500 1000 1500

1000

1500

2000

2500

3000

3500

Hour

Load

Val

ue

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

Business Forecasting: Experiments and Case Studies

2 4 6 8 10 12 14 16 18 20 22 241400

1600

1800

2000

2200

2400

2600

2800

Hour

Load

Val

ue

SundayMonday

Tuesday

Wednesday

Thursday

FridaySaturday

Fig.4 Hourly load during a day

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3. Data Analysis (4)

Temperature v.s. Load Demand nonlinear relationship

Business Forecasting: Experiments and Case Studies

10 20 30 40 50 60 70 80 90 1001000

1500

2000

2500

3000

3500

4000

4500

5000

Temperature

Load

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

Business Forecasting: Experiments and Case Studies

Fig.5 Correlation between the load and temperature.

Correlations

Load Temperature

Load Pearson Correlation 1 -.574**

Sig. (2-tailed) .000

N 2904 2904

Temperature Pearson Correlation -.574** 1

Sig. (2-tailed) .000

N 2904 2904

**. Correlation is significant at the 0.01 level (2-tailed).

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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

Business Forecasting: Experiments and Case Studies

( 1), ( 2),..., ( 12), ( 24), ( 48),..., ( 168),

( ) ( ), ( 1), ( 2),..., ( 12), ( 24), ( 48),..., ( 168),

( ), ( )

L t L t L t L t L t L t

Input t T t T t T t T t T t T t T t

DI t HI 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

Business Forecasting: Experiments and Case Studies

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4. Experiments

Evaluation measures

Business Forecasting: Experiments and Case Studies

Metrics Formula

1

11

2

2

1 1

ˆ1100

ˆ11

1

1001

ˆ1, 0

0,

Nt i t i

i t i

Nt i t it

ij j

j

N

ii

t i t i t i t ii

y yMAPE MAPE

N y

y yMASE MASE

Ny y

t

dDS DS

N

if y y y yd

otherwise

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4. Experiments

Results

Business Forecasting: Experiments and Case Studies

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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4. Experiments

Results

Business Forecasting: Experiments and Case Studies

0 100 200 300 400 500 600 700 800-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Hour

Load

Actual

Forecast

Error

0 100 200 300 400 500 600 700 8001500

2000

2500

3000

3500

4000

4500

Time

Dem

and

MAForecast set original data

MAForecast set forecast

0 100 200 300 400 500 600 700 8001500

2000

2500

3000

3500

4000

4500

Time

Dem

and

ESForecast set original data

ESForecast set forecast

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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.

Business Forecasting: Experiments and Case Studies