Electrical Load Forecasting Using Machine Learning Techniques R. E. Abdel-Aal Center for Applied...
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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.