# Electricity Price Forecasting with Neural Networks

This example demonstrates building and validating a short term electricity price forecasting model with MATLAB using Neural Networks. The models take into account multiple sources of information including fuel prices, temperatures and holidays in constructing a day-ahead price forecaster.

## Contents

- Import Weather, Load and Price Data
- Import list of holidays
- Generate Predictor Matrix
- Split the dataset to create a Training and Test set
- Build the Price Forecasting Model
- Initialize and Train Network
- Forecast using Neural Network Model
- Compare Forecast Price and Actual Price
- Examine Distribution of Errors
- Group Analysis of Errors
- Generate Weekly Charts

## Import Weather, Load and Price Data

The data set used is a table of historical hourly loads, prices 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 *fetchDBPriceData*.

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

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

## 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
- System load
- 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
- Previous day's average price
- Price from the same hour the previous day
- Price from the same hour and same day from the previous week
- Previous day's natural gas price
- Previous week's average natural gas price

If the goal is medium-term or long-term price forecasting, only the inputs hour of day, day of week, time of year and holidays can be used deterministically. The weather/price 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.

% Interpolate missing values ind = data.ElecPrice==0; data.ElecPrice(ind) = interp1(find(~ind), data.ElecPrice(~ind), find(ind)); % Create training set trainInd = data.NumDate < datenum('2008-01-01'); trainX = X(trainInd,:); trainY = data.ElecPrice(trainInd); % Create test set and save for later testInd = data.NumDate >= datenum('2008-01-01'); testX = X(testInd,:); testY = data.ElecPrice(testInd); testDates = dates(testInd); save Data\testSet testDates testX testY clear X data trainInd testInd term holidays dates ans num text

## Build the Price Forecasting Model

The next few cells builds a Neural Network regression model for day-ahead price 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
forecastPrice = sim(net, testX')';
```

## Compare Forecast Price and Actual Price

Create a plot to compare the actual price and the predicted price 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-forecastPrice; fitPlot(testDates, [testY forecastPrice], err); errpct = abs(err)./testY*100; fL = reshape(forecastPrice, 24, length(forecastPrice)/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): 6.57% Mean Absolute Error (MAE): 5.21 MWh Daily Peak MAPE: 5.61%

## 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 price 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) forecastPrice(i+1:i+step)], err(i+1:i+step)); title(sprintf('MAPE: %0.2f%%', mean(errpct(i+1:i+step)))); snapnow end end