Electrical Load Forecasting Using Machine Learning

Techniques

R. E. Abdel-AalCenter for Applied Physical Sciences

(CAPS)Research Institute, KFUPM

October 2002

Contents

• Introduction to Load Forecasting: Scope, Need, Applications, Problem, and Techniques

• Data-Based Modeling Approach: - Neural Networks: Limitations- Abductive Networks: Advantages

• Proposed Work• Relevant CAPS Experience• Conclusions

Load Forecasting: Scope

• Long-Term (5-20 Years)• Medium Term (1 month-5 Years)• Short-Term (STLF) (1 hour-1 Week)

Daily Peak Load Total Daily Energy Hourly Day Load Curve

• Very Short-Term, Real-Time (RTLF) (Mins-Hrs)

Accurate Short-Term Load Forecasting: Key to Efficient and Secure Operation

• Load Over-estimated: - Reserve units spinned-up unnecessarily

• Load Under-estimated: - Expensive peaking units - Costly emergency power purchases

• Deregulation, competition, and higher loads: - Greater efficiency, lower % forecasting errors

- 1% error costed £10 M annually in 1985- Need faster, more accurate, and more frequent

forecasts

Short-Term Load Forecasting: Applications

• Scheduling Functions: Unit commitment, Hydro-thermal coordination, Short-term maintenance, Fuel allocation, Power interchange and transaction evaluation…

• Network Analysis Functions: Dispatcher power flow, Optimal power flow

• Security and Load Flow Studies: Contingency planning, Load shedding, Security strategies

Short-Term Load Forecasting Problem

Hourly load over a week

Daily peak load over a year

Summer-Peaking Utility

Short-Term Load Forecasting Problem: Factors affecting the load

• Economic, Environmental: (Slow) Population, industrial growth, electricity pricing, …

• Time, Calendar:Daily, weekly, seasonal, holidays, school

year, …

• Weather: (Heating/cooling loads)Temperature, humidity, wind speed, cloud cover, …

• Random Events:Start/stop of large loads, Sports and TV

events, …

Daily Load Curve Forecasting Problem:

• Estimate future load Le(d,h) from knowledge of day type, previous hourly loads, previous temperatures, forecasted temperatures, etc…

Le(d,h) = F [L(d-1,h), L(d-1,h-1), …, L(d-7,h), L(d-7,h-1), …, T(d-1,h), Te(d,h), … ]

• Need to determine optimum inputs and the model relationship

Short-Term Load Forecasting Methods: Conventional Techniques

• Human experts, e.g. using ‘Similar day method’: Slow, unreliable, few experts available.

• Statistical univariate time series analysis: ARMA, ARIMA (Box-Jenkins), Kalman Filtering Ignores important weather factors, computationally intensive, user intervention.

• Statistical multivariate ‘causal’ regression analysis:

Usually linear, difficult to determine correct model relationship, impose own conceptions.

Short-Term Load Forecasting Methods: Artificial Intelligence/Machine Learning Approaches

• Knowledge-Based: e.g. Expert Systems - Accurate knowledge is not always available

- Difficult to extract from human experts and encode into computers

• Data-Based: e.g. Neural Networks - Little or no a priori knowledge of modeled phenomena is necessary

- Utilize abundantly available historical data available at utilities

Short-Term Load Forecasting: Data-based Computational Intelligence Methods

• Can model complex and nonlinear load functions directly from data.• Soft computing- More tolerant to noise, uncertainty,

and missing data.• Faster to develop, easier to update.• Heavy computations required only once, during model synthesis.

Data-based Modeling: Supervised Learning Procedure

Database of solved examples (input-output records) Split into training and evaluation datasets Training, with neural networks: - Start with random weights for the network - Apply training inputs, calculate outputs,

and compare with known outputs - Adjust weights, and iterate to minimize total output

error Evaluation: - See how model performs on the evaluation set Actual use: - Apply successful model to practical setting

The Neural Network (NN) ApproachExample of a day peak forecaster

Inputs:

Weights

Output: Tomorrow’s Peak Load

Independent variables

Dependent variable

Prediction

0.5

43Today’s

Tmax

Tomorrow’s Forecasted

Tmax

48

.6

.5

.8

.2

.1

.3.7

.2

WeightsHidden Layer

0.6

.4

.2

Today’s Peak Load

Limitations of the NN Technique

Ad hoc approach for determining the fixed network structure and the training parameters

Opacity and black-box nature lead to poor explanation capabilities

Significant input variables are not immediately obvious from model

When to stop training to avoid over-learning?

Local Minima may prevent reaching optimum solution

Self-Organizing Abductive Networks

-Network of polynomial functional elements- not simple neurons

-No fixed a priori model structure. Evolves with training

-Network size, element types, connectivity, inputs used, and coefficients are all determined automatically

-Automatic stopping criteria, with simple control on complexity

-Analytical input-output relationships

“Double” Element:

y = w0+ w1 x1 + w2 x2 + w3 x12 + w4 x22

+ w5 x1 x2 + w6 x13 + w7 x23

Advantages of Abductive Networks

More automated model synthesis Automatic selection of effective inputs Automatic stopping criteria giving good

generalization Faster model development Reduced user intervention Simple control on model complexity Analytical expressions. Better explanation facilities.

Easier comparison with regression/empirical models. Models are easier to export to other applications

Abductive Networks at CAPS Modeling/forecasting electric energy consumption Modeling/forecasting meteorological data Modeling of petrochemical processes Oil and gas reservoir characterization Medical diagnostics Identification/Determination of radioisotopes and

peak fitting in nuclear spectroscopy Online monitoring of vibrations on vacuum

pumps. Direct estimation of noisy sinusoids

Proposed Work

Apply abductive networks data-based modeling to the important areas of:

Electrical load modeling and forecasting at power utilities of the kingdom.

Hourly air temperature forecasts that may be required.

Benefits to Client

Transparent and accurate forecasters for economic and reliable operation

Comparison with existing models Improve understanding of daily, weakly, and

seasonal load variations Determine social, economic, and weather

factors influencing load Introduce the use of modern computational

intelligence techniques Train junior engineers in load forecasting

Outline of Work

1. Identify application area2. Determine relevant input variables3. Select data sets for model development 4. Data preprocessing:

Scan for outliers and missing data, trend adjustment, normalization, transformations, …

5. Model development6. Model evaluation and analysis7. Model integration into client setup8. Assess performance, compare with present

practices.

Examples of relevant modeling and forecasting applications at CAPS

Monthly electrical energy consumption in the Eastern Province

Daily maximum temperatures at Dhahran

Hourly electrical load forecasting using data from the USA

Modeling the Monthly Electrical Energy Consumption in the Eastern Province

Domestic Electrical Energy Consumption was modeled in terms of six exogenous parameters

6-year data: (5 years for training, 1 year forecasted for

evaluation) Derived analytical model relationships from

simplified models

Monthly Electrical Energy Consumption:The data set

Six Inputs: Month Index (m): m=1,2,…,72 Monthly average of the global solar radiation (S) Population (P) Gross domestic product per capita (G) Monthly average of the daily mean air temperature

(T) Monthly average of the daily mean relative humidity

(H)

One Output: Monthly Domestic Electrical Energy Consumption (E)

Monthly Electrical Energy Consumption: The Model

Automatically selects the most relevant inputs as:

m, H, and T

Ignores remaining inputs

Gives an overall analytical model relationship

SPG

Monthly Electrical Energy Consumption: Model Performance

MAPE Error over Evaluation year: 5.6%

Previous regression model gave MAPE = 9.2%.

Training

Evaluation

Aug 1987

Modeling the Maximum Daily Air Temperature (TX)

TX was modeled in terms of average temperatures (TA) for the previous three days:

TX (d+1) = F [TA (d-2), TA (d-1), TA (d)]

1987 year data for training, 1988 data for evaluation.

Derived analytical model relationships.

Maximum Daily Air Temperature (TX): The Model

TX(d+1) = 5.243 + 0.272 TA (d-2) – 0.589 TA (d-1) + 1.339 TA (d)

Maximum Daily Air Temperature (TX):Model Performance

Evaluation on 1988 data: MAE = 2.1 °C

Hourly electrical load forecasting Using Abductive Networks

Hourly load and temperature data for 6 years (1985-1990) from Puget Power, Seattle, USA*

5-year data (1985-89) for model training and 1990 data for evaluation.

Developed 24 dedicated models that forecast tomorrow’s hourly load curve for any day of the year.

______________________________________________* Courtesy Professor M. A. El-Sharkawi, University

of Washington, Seattle, USA.

The Data Set

Available Data: 24 daily hourly loads (L1,L2,…,L24), MW 24 daily hourly temperatures (T1,T2,…,T24), °FGenerated Data: Tmax and Tmin from hourly temperatures Used actual Tmax and Tmin for next day as

forecasted values ETmax and ETmin. Classified the forecasted day as:

Working day, Saturday, Sunday, or Holiday. Represented as 4 binary inputs.

Load at Hour 12 for 1985-90: Actual Data

0

500

1000

1500

2000

2500

3000

3500

4000

45001 91

181

271

361

451

541

631

721

811

901

991

1081

1171

1261

1351

1441

1531

1621

1711

1801

1891

1981

2071

2161

Day

Lo

ad

, M

W

Average Annual Upward Trend: 3.6%

1985 1989Training: 1821 Records 1990

Evaluation:364 Records

Load at Hour 12, 1985-90: Processed Data

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1 91 181 271 361 451 541 631 721 811 901 991 1081 1171 1261 1351 1441 1531 1621 1711 1801 1891 1981 2071 2161

Day

Lo

ad

, M

W

Trend Removed by normalizing to 1989 mean

Hourly Load Forecasters

LoadForecasterfor Hour h

24L(i), Hourly Loads

on day (d-1)2Tmin,

Tmaxon day (d-

1) 2Tmine, Tmaxe

Estimated for day d4Day type code

for day d

Total : 32 inputs

1

Le(d,h)

Forecasted Loadat hour h, day d

LoadForecasterfor Hour h

24 off

Examples of Hourly Load Forecasters:Hour 1 (Midnight) Model Structure:

Out of the 32 inputs, only 3 load inputs are selected No temperature inputs No day-type inputs 1-layer nonlinear model

X1 = -4.52 + 0.00303 L3 X2 = -4.66 + 0.00295 L20 X3 = -5.61 + 0.00315 L24

Y = 0.125 X1 + 0.868 X3 – 0.115 X1 X2 + 0.0506 X1 X3 + 0.0582 X2 X3

LE1 = 1600 + 312 Y

Hour 1 (Midnight)Model Performance:

1990 Hour 1 Load Forecsating

y = 1.008x - 26.701R = 0.998

1000

1500

2000

2500

3000

3500

1000 1500 2000 2500 3000 3500

Actual, MW

Fo

rec

as

ted

, MW

1990 Hour 1 Load Forecasting

0

500

1000

1500

2000

2500

3000

3500

1 31 61 91 121 151 181 211 241 271 301 331 361

Day

Lo

ad

, M

W

Actual

Forecasted

MAPE = 1.14%

Examples of Hourly Load Forecasters:Hour 12 (Midday) Model Structure:

More complex, 4-layers Only 4 load inputs, including same hour on previous day Only Sunday day-type input Forecasted temperature inputs

Hour 12 (Midday)Model Performance:

1990 Hour 12 Load Forecasting

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1 31 61 91 121 151 181 211 241 271 301 331 361

Day

Lo

ad

, M

W

Actual

ForecastedMAPE = 2.41%

1990 Hour 12 Load Forecsating

y = 0.969x + 82.366

R2 = 0.959

1500

2000

2500

3000

3500

4000

4500

1500 2000 2500 3000 3500 4000 4500

Actual, MW

Fo

reca

ste

d,

MW

Forecasting Error Statistics Over the 1990 Evaluation Year:

Overall MAPE = 2.67 %, with the following distribution:

MAPE% of forecasted

hours

1 % 29 %

3 % 68 %

6 % 9 %

Overall MPE = - 0.16 %, mainly due to error in estimating growth for the forecasting year

Examples of Day Load Curve Forecasts

Wednesday 8 August 1990 (Working Day)

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Load

, MW

Actual

Forecasted

MAPE = 1.73 %

Monday 3 September 1990 (Holiday: Labor Day)

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Load

, MW

Actual

Forecasted

MAPE = 3.48 %

Saturday 11 August 1990

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Load

, MW

Actual

Forecasted

MAPE = 2.30 %

Sunday 12 August 1990

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Load

, MW

Actual

Forecasted

MAPE = 1.97 %

Conclusions Apply abductive networks machine learning to

load modeling and forecasting.

Many advantages over neural networks, e.g. faster modeling and better explanations.

CAPS have used the technique in many areas, including energy, load, and meteorological forecasting.

Benefits include greater forecasting accuracy (reduced operating cost, improved security) and better insight into the load function.