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Highlights from
Electricity Load and Price Forecasting Webinar Case Study

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Electricity Load and Price Forecasting Webinar Case Study

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10 Sep 2010 (Updated )

Slides and MATLABĀ® code for the day-ahead system load and price forecasting case study.

Electricity Load Forecasting using Neural Networks

Electricity Load Forecasting using Neural Networks

This example demonstrates building and validating a short term electricity load forecasting model with MATLAB. The models take into account multiple sources of information including temperatures and holidays in constructing a day-ahead load forecaster. This script uses Neural Networks. A similar script "LoadScriptTrees" uses Bagged Regression Trees.

Contents

Import Weather & Load Data

The data set used is a table of historical hourly loads and temperature observations from the New England ISO for the years 2004 to 2008. The weather information includes the dry bulb temperature and the dew point. This data set is imported from an Access database using the auto-generated function fetchDBLoadData.

If using the MATLAB Central File Exchange script, load the MAT-files from the Data folder and skip to line 74.

data = fetchDBLoadData('2004-01-01', '2008-12-31');
addpath ..\Util

Import list of holidays

A list of New England holidays that span the historical date range is imported from an Excel spreadsheet

[num, text] = xlsread('..\Data\Holidays.xls');
holidays = text(2:end,1);

Generate Predictor Matrix

The function genPredictors generates the predictor variables used as inputs for the model. For short-term forecasting these include

  • Dry bulb temperature
  • Dew point
  • Hour of day
  • Day of the week
  • A flag indicating if it is a holiday/weekend
  • Previous day's average load
  • Load from the same hour the previous day
  • Load from the same hour and same day from the previous week

If the goal is medium-term or long-term load forecasting, only the inputs hour of day, day of week, time of year and holidays can be used deterministically. The weather/load information would need to be specified as an average or a distribution

% Select forecast horizon
term = 'short';

[X, dates, labels] = genPredictors(data, term, holidays);

Split the dataset to create a Training and Test set

The dataset is divided into two sets, a training set which includes data from 2004 to 2007 and a test set with data from 2008. The training set is used for building the model (estimating its parameters). The test set is used only for forecasting to test the performance of the model on out-of-sample data.

% Create training set
trainInd = data.NumDate < datenum('2008-01-01');
trainX = X(trainInd,:);
trainY = data.SYSLoad(trainInd);

% Create test set and save for later
testInd = data.NumDate >= datenum('2008-01-01');
testX = X(testInd,:);
testY = data.SYSLoad(testInd);
testDates = dates(testInd);

save Data\testSet testDates testX testY
clear X data trainInd testInd term holidays dates ans num text

Build the Load Forecasting Model

The next few cells builds a Neural Network regression model for day-ahead load forecasting given the training data. This model is then used on the test data to validate its accuracy.

Initialize and Train Network

Initialize a default network of two layers with 20 neurons. Use the "mean absolute error" (MAE) performance metric. Then, train the network with the default Levenburg-Marquardt algorithm. For efficiency a pre-trained network is loaded unless a retrain is specifically enforced.

reTrain = false;
if reTrain || ~exist('Models\NNModel.mat', 'file')
    net = newfit(trainX', trainY', 20);
    net.performFcn = 'mae';
    net = train(net, trainX', trainY');
    save Models\NNModel.mat net
else
    load Models\NNModel.mat
end

Forecast using Neural Network Model

Once the model is built, perform a forecast on the independent test set.

load Data\testSet
forecastLoad = sim(net, testX')';

Compare Forecast Load and Actual Load

Create a plot to compare the actual load and the predicted load as well as compute the forecast error. In addition to the visualization, quantify the performance of the forecaster using metrics such as mean absolute error (MAE), mean absolute percent error (MAPE) and daily peak forecast error.

err = testY-forecastLoad;
fitPlot(testDates, [testY forecastLoad], err);

errpct = abs(err)./testY*100;

fL = reshape(forecastLoad, 24, length(forecastLoad)/24)';
tY = reshape(testY, 24, length(testY)/24)';
peakerrpct = abs(max(tY,[],2) - max(fL,[],2))./max(tY,[],2) * 100;

MAE = mean(abs(err));
MAPE = mean(errpct(~isinf(errpct)));

fprintf('Mean Absolute Percent Error (MAPE): %0.2f%% \nMean Absolute Error (MAE): %0.2f MWh\nDaily Peak MAPE: %0.2f%%\n',...
    MAPE, MAE, mean(peakerrpct))
Mean Absolute Percent Error (MAPE): 1.61% 
Mean Absolute Error (MAE): 243.18 MWh
Daily Peak MAPE: 1.63%

Examine Distribution of Errors

In addition to reporting scalar error metrics such as MAE and MAPE, the plot of the distribution of the error and absolute error can help build intuition around the performance of the forecaster

figure;
subplot(3,1,1); hist(err,100); title('Error distribution');
subplot(3,1,2); hist(abs(err),100); title('Absolute error distribution');
line([MAE MAE], ylim); legend('Errors', 'MAE');
subplot(3,1,3); hist(errpct,100); title('Absolute percent error distribution');
line([MAPE MAPE], ylim); legend('Errors', 'MAPE');

Group Analysis of Errors

To get further insight into the performance of the forecaster, we can visualize the percent forecast errors by hour of day, day of week and month of the year

[yr, mo, da, hr] = datevec(testDates);

% By Hour
clf;
boxplot(errpct, hr+1);
xlabel('Hour'); ylabel('Percent Error Statistics');
title('Breakdown of forecast error statistics by hour');

% By Weekday
figure
boxplot(errpct, weekday(floor(testDates)), 'labels', {'Sun','Mon','Tue','Wed','Thu','Fri','Sat'});
ylabel('Percent Error Statistics');
title('Breakdown of forecast error statistics by weekday');

% By Month
figure
boxplot(errpct, datestr(testDates,'mmm'));
ylabel('Percent Error Statistics');
title('Breakdown of forecast error statistics by month');

Generate Weekly Charts

Create a comparison of forecast and actual load for every week in the test set.

generateCharts = true;
if generateCharts
    step = 168*2;
    for i = 0:step:length(testDates)-step
        clf;
        fitPlot(testDates(i+1:i+step), [testY(i+1:i+step) forecastLoad(i+1:i+step)], err(i+1:i+step));
        title(sprintf('MAPE: %0.2f%%', mean(errpct(i+1:i+step))));
        snapnow

    end
end

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