UNIVERSITY OF AMSTERDAM
Anomaly analysis of Short Term Energy
Load Forecast using Artificial Neural
Networks
by
Bastiaan Waanders
10247742
A thesis submitted in partial fulfillment for the Bachelor degree of Information Studies
Supervisor
dhr. dr. M. van Someren m.w.vansomeren@uva.nl
“We need to stop, and admit it: we have a prediction problem. We love to predict things and we aren't very good at it”
Abstract
In this thesis anomalies of short term load forecasts are analyzed for events which might correlate with these anomalies. Short term load forecasts are done using neural networks, with one model for normal days and one for special days. While few concrete events where found to explain anomalies, some information which was found during the search for anomalies could help improving and optimizing the neural network models which could reduce anomalies.
Contents
Abstract ii
1 Introduction 1
2 Background theory 2
2.1 Literature review . . . 2
2.2 Artificial Neural Network . . . 3
3 Data 5 3.1 Historic load data . . . 5
3.2 Historic temperature data . . . 6
3.2.1 Data scarping . . . 6
4 Experiment setup 9 4.1 Gathering data about special days . . . 10
4.2 Neural network settings . . . 11
4.2.1 Input variables . . . 11
4.3 Training and test data . . . 13
4.4 Percentage error and MAPE . . . 13
5 Results 14 6 Anomaly analysis 16 6.1 Anomalies during normal days . . . 16
6.2 Other approaches . . . 18
6.2.1 Sport events . . . 18
6.2.2 Natural disasters . . . 19
6.2.2.1 Storm Dolly . . . 19
6.2.2.2 Earthquakes . . . 20
6.2.3 Results of the anomaly analysis . . . 22
6.3 Anomalies during special days . . . 23
7 Conclusion 24 7.1 Discussion . . . 24
A Appendix 27
Chapter 1
Introduction
Since 1980 the total world energy consumption has grown significantly1. Although there are several initiatives to reduce the growing energy consumption, with the growing electricity consuming technologies it is likely that energy consumption will keep growing. Power plants try to supply the demand of energy, to minimize the waste of electricity which is created from different (green-)energy sources. In order to reduce electricity waste, forecasts of short term load demand are created to predict how much energy will be needed to fullfill demand.
Different models have been created to forecast load demand. While accuracy of those forecast is very good, there are still anomalous values found. One factor to create anomalous forecasts are special days like new year, Christmas and vacations. These days are known anomalies, but there are still anomalies which are unexplained, but could possibly be explained when researched.
This paper describes an implementation of multiple multi-layer feed forward neural networks for short term load forecasts during normal days and special days. After analyzing the results for anomalous values, various Internet resources will be explored to find events that might explain anomalies.
1
Chapter 2
Background theory
This section discusses some background theory about short term load forecasts and neural networks.
2.1
Literature review
Several different techniques have been used for short term load forecast, such as regres-sion analysis (Tso and Yau, 2007), similar days method (Mu et al., 2010) Self Organising Map (Chicco et al., 2001), neural networks (Lee et al., 1992), (Raza et al., 2014), fuzzy Neural network (Kim et al., 2000) or a fuzzy inference method (Wang et al., 2007).
Short term load forecasting using artificial neural networks has been widely researched since 1990 (Peng et al., 1992), (Lee et al., 1992), (Raza et al., 2014), research dif-fers in data sets, input variables and different algorithms to train and test the neural networks (Kisi and Uncuoglu, 2005) (Tso and Yau, 2007).
Well trained neural network models produce accurate forecasts, yet predicting the fore-cast for special days with a neural network trained on data about normal days produces less accurate results (Markou et al., 2008). As Markou et al. discusses in their future work, a separate strategy needs to be incorporated in the model for training and testing the neural network for special days. Based on this previous research two different neural networks are created, this will be further discussed in chapter four.
2.2
Artificial Neural Network
The basic idea of an artificial neural network is to simulate a model which represents the learning momentum of the human brain. This model is used in a variety of domains, such as biology, (computational) neuro-science and artificial intelligence.
As described in the introduction section, there are a variety neural networks and differ-ent training algorithms. In the this paper a Back Propagation multilayer feed-forward network, also know as MLP(Multilayer perceptron)(Svozil et al., 1997), will be used for forecasting load demand.
Figure 2.1: A representation of a simple neural network
An MLP consist of different layers: one input layer, one hidden layer and one output layer. Each layer consist of nodes which simulate a neuron or perceptron. All the nodes in each layer are fully connected with the previous and/or next layer. Figure 2.1 represents such an MLP with 3 layers, an input layer with three nodes, a hidden layer with 4 nodes and an output layer with 2 nodes.
The amount of nodes in the input layer are equal to the amount of input variables selected for training and testing the neural network. The selection of the amount of nodes in the hidden layer is done by testing four networks, each with a different amount of nodes in the hidden layer, respectively with five, ten, fifteen and twenty nodes. Twenty hidden nodes resulted in the lowest MAPE score, therefor all MLPs are trained with one hidden layer containing twenty hidden nodes. The output layer of the neural network models during this thesis consists of one node.
Each connection between the different nodes has a weight value. During each iteration of the network the interconnected weights are changed based on the MLP predicted outcome value and the actual outcome value. Any error is back propagated, so weight values can be changed to a weight value which minimizes the error between the predicted value of the MLP and the actual outcome value.
Chapter 3
Data
The data which are used for training and testing the neural network models, are historic data about the hourly load demand of the American state Texas and the temperature of the state Texas. The historic load demand data is gathered from the ERCOT website1. The historic data about the temperature is gathered from the website wunderground2.
3.1
Historic load data
ERCOT stands for Electric Reliability Council of Texas. This non-profit corporation manages approximately 24 million Texas customers which is equivalent to 90% of all of Texas energy consumption. On their website ERCOT has published the hourly load data archives3 which go back until 1995. For unknown reasons the years 2001 and 2002 have not been published. Since 2003 ERCOT archives reports containing the data of eight different areas in Texas, see figure 3.1.
Figure 3.1: the eight different areas report by ERCOT.
1 http://www.ercot.com/ 2 http://www.wunderground.com/ 3 http://www.ercot.com/gridinfo/load/load hist/index.html
The data from the year 2004 until 2013 will be used as training data for the neural networks, and the data of the year 2014 will be used to test the neural network. The load demand is measured in MW, Megawatt, 1 MW equals one million watt. Before the training and the testing of the neural networks the data of the hourly load demand will be normalized within a range of -1 and 1. Normalization reduces the changes for the training data to get stuck in a local minimum (Sola and Sevilla, 1997). Normalization of the data is done by the following formula:
f (LD) = (LD − LDl)(Nh− Nl) (LDh− LDl)
+ Nl
Where LD represents the hourly load demand value, LDlrepresents the lowest measured
load demand value in the data set, LDh represents the highest measured load demand
value in the data set, Nl represents the lowest chosen range value for normalization and
Nh represents the highest chosen range value for normalization.
3.2
Historic temperature data
The website wunderground.com provides information about the current and historic weather conditions and weather forecasts for all over the world. Seventeen different weather stations in the state Texas are selected for gathering the historic weather data. For every area at least two weather stations are selected to provide temperature infor-mation, see figure 3.2.
3.2.1 Data scarping
The data from the weather stations is gathered using a technique called webscraping. Using Python and the python framework scrapy4a webcrawler is made to scrape specific data from a requested HTML page. From every page the following data was gathered:
• The URI for the next day for the same weather station.
• All the available historic data about the temperature per hour, all temperature data reports are in degrees Celsius.
4
Figure 3.2: The places of the selected weather stations in their area.
For certain hours there was no temperature value reported. In this case the arithmetic mean of the temperature was calculated, using the temperature values from the previous hour and the next hour:
t = t(h − 1) + t(h + 1) 2
Where t represents the temperature value and h represents the current hour.
For some of the hourly temperature reports, there are multiple reports per hour. When this is the case the temperature value closest to the next hour is selected as hourly temperature value. Before creating the input variables for the neural network, the data of the weather stations per area are merged together per hour to create a mean value for the temperature. This is done by calculating an arithmetic mean:
¯
x = x1+ x2+ · · · + xn n
Where x represents the temperature value and n represents the total of number of reports per hour.
Data values of the temperature is normalized before training and testing the neural networks. Using the following formula:
f (T ) = (T − Tl)(Nh− Nl) (Th− Tl)
+ Nl
Where T represents the temperature value, Tl represents the lowest measured
tempera-ture value in the data set, Th represents the highest measured temperature value in the
data set, Nlrepresents the lowest chosen range value for normalization and Nhrepresents
Chapter 4
Experiment setup
The forecast of the short term load demand is done using neural networks. Figure 4.1 shows the behaviour of the load demand during a special day and two normal days. The behaviour of the load demand on a special day is distinctly different then during a normal day, which supports the idea of (Markou et al., 2008) for creating a separate strategy for special days. On the basis of this information, two separate neural networks will be trained and tested for each area. Data set one will include all the data about the normal days and data set two will include all the data about the special days.
4.1
Gathering data about special days
Data about vacation days and other special events are gathered from several Internet searches. Texas does not have any regulated vacations such as Easter-vacation, spring break or Christmas vacation. The following days are selected as special day’s.
January
• 1 - New Years day
• 19 - Confederate Heroes Day • 3rd Monday - Martin Luther
King Jr. Day
February
• 3rd Monday - Presidents’ Day March
• 2 - Texas Independence Day • 31 - Cesar Chavez Day April
• Good Friday • Easter Sunday • 21 - San Jacinto Day May
• Last Monday - Memorial Day June
• 19 - Emancipation Day In Texas July
• 4 - Independence Day August
• 27 - Lyndon Baines Johnson Day
September
• 1st Monday - Labor Day October • 31th Halloween November • 11 - Veteran’s Day • 4th Thursday - Thanksgiving Day December • 24 - Christmas Eve • 25 - Christmas day • 26 - day after Christmas
For some of the selected days, the special days occur on a different data varying each year. This has been taken into account when selecting the dates for the special days.
4.2
Neural network settings
The neural networks are programmed in Python version 2.7.61 using the FANN libary2
and its bindings for Python. The additional settings of the neural networks are the following:
• Number of layers: 3, 1 input layer, 1 hidden layer, 1 output layer • Number of nodes in input layer: 6 for ANN 1, 7 for ANN 2 • Number of hidden nodes in hidden layer: 20
• Number of nodes in output layer: 1 • Learning rate: 0.7
• Maximum epochs: 1000 • Desired error: 0.0001 4.2.1 Input variables
The features for the input variables are based on several other research papers. Table 4.1 shows the input variables for normal days, NNM 1. Table 4.2 shows the input variables for a special day, NNM 2.
Table 4.1: Features for NNM 1
Feature Notation Load demand Ld(w, d, h − 1) Load demand Ld(w, d − 1, h) Load demand Ld(w − 1, d, h) Temperature T(w, d, h − 1) Temperature T(w, d, h − 2) Temperature T(w, d, h − 3) 1 https://www.python.org/ 2 http://leenissen.dk/fann/wp/
Table 4.2: Features for NNM 2
Feature Notation Load demand Ld(w, d, h − 1) Load demand Ld(w, d − 1, h) Load demand Ld(w − 1, d, h) Load demand Ld(y − 1, h) Temperature T(w, d, h − 1) Temperature T(w, d, h − 2) Temperature T(w, d, h − 3)
Where y represents the year, w represents the week, d represents the day h represents the hour. Ld represents the load demand and T represents temperature.
The following load demand features are chosen since they are most likely to give a to give accurate indication of the load demand for the predicted hour. For special days also the load demand value of the same hour on the same day a year prior is included, this is done to give the model more information about the load demand on special days. The weather features are chosen since the three hours prior to a predicted hour are the hours which have the most influence on the energy use of people during the predicted hour. If you wanted to predict the load demand for the 2nd of January for 14:00-15:00, the values for the input variables are as displayed in table 4.3
Table 4.3: Input values for 02-01-2014 14:00-15:00
Feature Value Ld(w, d, h − 1) 10526.294164999972 Ld(w, d − 1, h) 8562.753469000018 Ld(w − 1, d, h) 9069.610280000003 T(w, d, h − 1) 11.4 T(w, d, h − 2) 11.2 T(w, d, h − 3) 9.15
4.3
Training and test data
Both neural network models will be trained and tested using the same historical data, the training data will be the years 2004-2013 and the test data will be the year 2014. NNM1 will be trained and tested on data set 1, containing the normal days. NNM2 will be trained and tested on data set 2, containing the specials days.
4.4
Percentage error and MAPE
The accuracy of for a predicted hour is measured by calculating the percentage error:
P E(t) = ALDt− F LDt ALDt
Where ALDt represents the actual load demand value at time t and FLDt represents the forecasted load demand value at time t. t represents the hour.
The overall performance of the neural network is measured using the mean absolute percentage error. MAPE is widely used for calculating error percentages for time series data sets in statistics. A lower MAPE score represents a better score then a higher MAPE score, actual zero means there is a perfect fit for the neural network model.
M AP E = 1 N N X t=1 ALDt−F LDt ALDt
Where ALDt represents the actual load demand value at time t and FLDt represents the forecasted load demand value at time t, t represents the hour and N represent the total amount of predicted entities.
Chapter 5
Results
After training the different neural networks, the data of the year 2014 is used to test the different neural networks for the different areas and the two different conditions. For every tested network the following information is reported. The anomaly threshold will be discussed in chapter six.
1. The amount of entities tested
2. The lowest percentage error in %
3. The highest percentage error in %
4. Amount of entities above threshold
5. MAPE score in %
6. Threshold value for anomalies
Table 5.1 shows the results of the tested neural networks. Due possible SCADA or report errors the total reports hours on the load demand differ for each area.
T a ble 5.1 T est results of neural net w orks Area 1 2 3 4 5 6 Coast normal da ys 8286 0,0000313916925755657 14,8115537111765 170 2,57327360984764 7,72075261238294 East normal da ys 8151 0,000293662237600404 45,2524688886715 332 4,1200684617605 12,3617219748993 F ar W est normal da ys 8278 0,000368430469813367 13,680592623256 554 2,23910804714139 6,71813570650106 W est normal da ys 8274 0,000320499023552704 25,1970171193021 200 2,68490315588624 8,05568308176094 North normal da ys 8265 0,0000876565209984733 17,2829083153316 338 1,91825462786865 5,75546024903234 North Cen tral normal da ys 8292 0,000358009729893194 24,2935825870638 393 4,76648670496478 14,3011848115672 South normal da ys 8281 0,00076983316387374 20,0060615697846 283 3,421739460396 10,266458141862 South Cen tral normal da ys 8275 0,00178338446554533 27,7409913533651 226 4,772812917068 14,3201692852566 Coast sp ecial d a ys 396 0,00252597030352709 10,9877527743697 8 2,3611016585561 7,10123739332823 East sp ecial da ys 395 0,0238388914247029 30,3754392649879 12 3,8020547333919 11,4351138555061 F ar W est sp ecial da ys 398 0,0031317771599078 15,5658111601264 33 2,34613316017008 7,0561284464561 W est sp ecial da ys 394 0,000840388078069101 11,1876080781381 7 2,64514087676729 7,9556145453917 North sp ecial da ys 398 0,000478944124235643 12,6803338217042 17 1,73001620359864 5,20312178110019 North Cen tral sp ecial da ys 398 0,00780933323650362 22,503335659178 28 4,99560837262016 15, 0245753070742 South sp ecial da ys 398 0,0171492504745514 15,3903059277665 10 3,13672845275526 9,43388859594403 South Cen tral sp ec ial da ys 397 0,0141038155624455 14,7621990668315 3 4,65614958449671 14,0037226139787
Chapter 6
Anomaly analysis
An anomaly is a value which varies from the expected behaviour. While anomalous values differ for every field of expertise, within the field of forecasting load demand an unpredicted increase or decrease in energy could be considered an anomaly. A value of the actual load demand is considered an anomalous value when the percentage error of the difference between the actual value and predicted value is above a certain threshold. The threshold is equal to three times the standard deviation of the percentage error of test data. T = 3 ∗ sd sd = v u u t 1 N − 1 N X i=1 (xi− x)2.
6.1
Anomalies during normal days
For the ten anomalies with the highest percentage error in each state a search is done on the Internet for articles or events that might correlate with the time and date of the event. Different sources where queried to find information:
• http://www.newspapers.com/ • http://www.google.com/ • http://news.google.com
• http://www.brownsvilleherald.com/
• http://www.expressnews.com/archive/search/ • http://www.houstonchronicle.com/archive/search/
Queries on the different website contained words such as; Texas, the areas name or a name of city within the area. Also search parameters were limited to the day before and a day after the anomalous day.
For only two of the anomalous hours, events were found that could explain a sudden increase or decrease in load demand.
East area:
• 27-05-2014 23:00:00: This was an election day (Ramsey, 2014). It is possible there was more energy consumption due to special election broadcasts, offices and big convention centres that might have had longer opening hours on this day.
West area:
• 10-05-2014 05:00/06:00: This was also an election day, maybe certain public build-ings opened earlier for voting (Cascos, 2014).
To get a better understanding of when the anomalies occur, figures 1 until 8 in the appendix show information about the anomalies on what day and what time they occur. Analyzing these graphs reveals interesting facts about the anomalies. For most of the areas in Texas, anomalies seem to occur on weekdays during morning hours, mostly around the hours of 06:00 until 07:00 and in some cases also from 07:00-08:00 and 08:00-09:00. A possible explanation could be the weather; Texas has had extreme weather conditions during the last couple of years, ranging from extreme drought (Henry, 2014) to extreme cold weather (Wilonsky, 2014). This extreme weather can effect the energy load demand in different ways, power grids are exposed to the extreme conditions which can cause complete outrages or local problems. Another effect could be that during morning hours people start going to work and load demand could increase since heathers are turn up due to extreme colds or ventilators are turned on due to extreme draught and heat.
Although during all days of the week anomalies occur, anomalies on Mondays seem the happen more frequent then on other days. A possible explanation for this could be due to the selected features for the neural network model, one of the chosen load demand
features represents the load demand of 24 hours prior to a predicted hour, for Mondays this means including a load demand value of a Sunday, a weekend day. The load demand seems to differ on week and weekend days, including a value of a weekend day to forecast a week day could explain why there are more anomalies found on Mondays then during the other week days.
6.2
Other approaches
Searching the Internet for events or news which could explain the anomalies did not result in a lot of concrete results. Therefor other events were considered which might explain some of the anomalies.
6.2.1 Sport events
Sport is enormous in the United States, Texas is no exception on that. During national sport events people from all over the state are watching their television during the game, and when sport events occur in Texas, an enormous stadium is used full of lights and electricity, which all together can cause high energy consumption.
Five different sports teams are selected: two baseball teams(MLB), the Houston Astros and the Texas Rangers. Three basketball teams(NBA), the San Antonio Spurs, the Dallas Mavericks and the Houston Rockets. The data about the game schedules is gathered from the ESPN website1. Table 6.1 shows the results of the hours of the game and if those hours correlated with an anomalous hour. Respectively the hour when a game starts and the two following hours after that are considered as game played hours.
Table 6.1: Percentage of games played during an anomaly
Team Games during anomaly hours, in %
Houston Astros (MLB) 4.4
Texas Rangers (MLB) 6.9
Dallas Mavericks (NBA) 6.7
Houston Rockets (NBA) 4.4
San Antonio Spurs (NBA) 3.8
Table 6.1 shows that sport games rarely correlate with anomalies, based on the results displayed in table 6.1, it can be concluded that sport games do not likely to increase load demand.
1
6.2.2 Natural disasters
Since multiple news sources reported on the extreme weather conditions in Texas also natural disasters such as earthquakes and tsunami’s are compared to anomalies. The results are discussed below.
6.2.2.1 Storm Dolly
On September 3th 2014 the tropical storm Dolly arrived at the coast of Mexico. The storm went more north and the remains of Dolly arrived at the Southern coast of Texas around the 5th of September2. Figure 6.1 shows the load demand from the 2nd of September until the 7th of September.
Figure 6.1: Load demand prior and post of Storm Dolly.
On September the 5th there are only two anomalies. The days prior to the storm do show multiple anomalies, these anomalies could be caused by people preparing themselves for the storm. Although it is very well possible there is no direct connection too the upcoming storm and the anomalies prior to it.
6.2.2.2 Earthquakes
In the year 2014 there have been 46 registered earthquakes in the state of Texas. Data about the earthquakes is gathered from the website earthquake.usgs.gov 3. Figure 6.2 shows a visual representation of all the earthquakes.
Figure 6.2: Earthquakes in Texas in 2014
From the 46 earthquakes two happened in areas where the load demand is not measured by ERCOT. Eleven earthquakes happened in the Northern area, 26 happened in the North Central area, four happened in the area of Far West, two in the Southern area, one in east and one in west.
During most earthquakes there was no anomaly found when predicting the load demand. In most cases the difference between the actual load demand and the predicted load demand was lower then 2%. For two earthquakes there were anomalies found during and after the earthquakes. One of the earthquakes happened on June 28 2014 in the far-west area, see figure 6.3, and the other earthquake happened on November 30 2014 in the area north central, see figure 6.4.
During seven other earthquakes, the load demand was lower then the predicted load demand and the percentage error was 5% or higher. During the following three to five hours, load demand was lower still then predicted, while the percentage error was still lower then the threshold. After three to five hours, depending on the earthquake, the difference between the predicted load demand and the actual load demand returned back to a percentage error lower then 2%.
3
Figure 6.3: Load demand during the day of the earthquake
Figure 6.4: Load demand during the day of the earthquake
The difference between the actual load demand and the predicted load demand could be caused by the earthquakes, earthquakes could have damaged a major infrastructure, damaged power grids or disabled multiple buildings or factories from their energy re-sources. In the hours after the earthquakes, emergency professionals perform damage control and/or repair the damage. This could explain why in the following three to five
hours the percentage error returns to 2% or lower. During all the other earthquakes the difference between the predicted load and actual was lower then 2%, so these were not noted as a significant correlation.
Earthquakes differ in their influence on the load demand. Two earthquakes correlate with anomalies. For seven earthquakes there was a bigger difference between predicted load demand and the actual load demand, likely caused by some power outrage. For the other earthquakes no anomalies were found and the difference between the actual load demand and predicted load demand was within a 1% percentage error. Earthquakes can cause anomalies but this depends on the impact on power grids and other energy delivery systems.
6.2.3 Results of the anomaly analysis
Table 6.2 shows the results of the different searches for anomalies and the percentage of anomalies which remains unexplained. While some possible explanations have been found there remains a large amount of anomlies unexplained.
Table 6.2
Anomalies explained in percentage
Area Total of anomalies Possible explanations Percentage unexplained
Coast 170 16 90.6 % East 332 1 99.7% Far West 554 7 98.7% West 200 1 99.5% North 338 0 100% North Central 393 60 84.7% South 283 11 96.11% South Central 226 0 100%
6.3
Anomalies during special days
Searching online for events during anomalies on special days did not result in any corre-lating events which could explain the anomalies. Figure 9 until 16 show the distribution of the anomalies on special days. Analyzing the distribution of the anomalies shows that a lot of the anomalies happen on Mondays. This could be caused be the earlier discussed factor of including a load demand of 24 hours prior to the predicted hour. There are again anomalies found on weekdays in the morning hours, these could be explained by extreme weather conditions also discussed earlier for the normal days.
Although results for special days are relatively good, training a neural network model with data about different special days might not result in a useful solution. The be-haviour of load demand on selected special days differs from each other as can be seen in figure 6.5. There are big differences between special days, therefor anomalies could be caused by a wrong forecast for a special day since the trained model does not fit the behaviour of the load demand during the special day.
Chapter 7
Conclusion
Separately training and testing normal and special days results in well trained neural networks for special days with varying MAPE scores between 1.7% and 4.9% and MAPE scores between 1.9% and 4.7% for neural networks trained for forecasting normal days, although still a lot of hourly entities can be considered to be anomalies.
Analyzing anomalies via online searches did not result in any concrete events which could explain the anomalous behaviour, only in two cases a possible explanation was found. While searching for anomalies online a lot of information was found about the extreme weather conditions in Texas, this could be a possible explanation for the reoccurring anomalies between 07:00 and 09:00 on week days, this will be further discussed in the next section. Comparing other reoccurring events with anomalies, such as sports games and natural disasters, shows to be of minor influence on the load demand.
7.1
Discussion
Finding the best combination of input variables was not one of the objectives of this paper therefor a very basic selection of input variables was chosen to train and test the neural networks. Although these input variables produced good forecast results, testing different selections of input variables could further improve forecasts of the neural network models. During the online search a lot of news articles were found about the extreme weather conditions; meaning that including more information about the weather conditions as neural network input variables could result in a better trained neural network. Also anomalies seem to occur more on Mondays, this could be caused by the fact that a value of 24 hours prior of the predicted hour is included on Mondays this is a value from Sunday a weekend day.
The selection of special days could be extended, for example days such as valentine day, days during the Easter activities and one or two days before new year could be classified as special days.
The temperature information from the website wunderground was not always consistent sometimes there was no reported value of the temperature. Also the exact coordinates of the measuring points were unknown. It is possible that a selected measuring point was not a good representation of the temperature for the whole area.
Using neural networks for forecasting short term load demand returns good results, none of the networks preformed exactly similar to the another. Although this is a known factor of neural networks, it was interesting to see how much difference there can be in neural networks trained with the same information.
The lack of knowledge of the author about the daily life of Texas causes certain problems. Since news articles and events were selected manually to be possible causes for anomalies, a lack of knowledge about what is normal and what is abnormal in Texas, could influence the decision about an event or news article to be relevant for an anomaly.
7.2
Future work
Finding explanations for anomalies for a complete state or partial areas of a state deems to be very difficult. Future research could include testing more input variables, to optimize the model to predict the hourly load demand. Including more input variables about weather conditions as described in the discussion could improve the trained model. Also including data about week and weekend days might improve the neural network model. Although separating normal and special days in two different data sets and separately trained neural network models result in well trained networks it might not be the ideal conditions to create a prediction model. Since there two prediction models created, research could be done to test if normal days and special days could be trained within one neural network model, for example adding a feature which represent a normal day and a special, noted as an 0 or 1. The same could be done for week and weekend days. Improving the models for short term load forecast could help in finding more information about anomalies or make it even more difficult to find information about anomalous values. Because more factors which influence load demand are included in the model this might result in less anomalies or at least anomalies which could be explained better after research is done to find a possible event for the anomalous value. Although a better model could also make it even more difficult to explain anomalous values, since
searching sources might result in even less information which might explain anomalous values.
Creating a list of information sources which report more accurately about events which influence energy consumption could help in the search for explanations why there are differences in the actual load demand and the predicted load demand.
Using more advanced methods (Chandola et al., 2009) for selecting anomalies could reduce the amount of anomalies and could improve results of online searches when trying to find information about anomalies.
Appendix A
Appendix
Figure A.1: Graph of the total amount of anomalies on a day at the same time, for the Coast area.
Figure A.2: Graph of the total amount of anomalies on a day at the same time, for the Eastern area.
Figure A.3: Graph of the total amount of anomalies on a day at the same time, for the Western area.
Figure A.4: Graph of the total amount of anomalies on a day at the same time, for the Far West area.
Figure A.5: Graph of the total amount of anomalies on a day at the same time, for the Northern area.
Figure A.6: Graph of the total amount of anomalies on a day at the same time, for the North Central area.
Figure A.7: Graph of the total amount of anomalies on a day at the same time, for the Southern area.
Figure A.8: Graph of the total amount of anomalies on a day at the same time, for the South Central area.
Figure A.9: Graph of the total amount of anomalies on a day at the same time, for the South Central area on special days.
Figure A.10: Graph of the total amount of anomalies on a day at the same time, for the Southern area on special days.
Figure A.11: Graph of the total amount of anomalies on a day at the same time, for the North Central area on special days.
Figure A.12: Graph of the total amount of anomalies on a day at the same time, for the Northern area on special days.
Figure A.13: Graph of the total amount of anomalies on a day at the same time, for the Coast area on special days.
Figure A.14: Graph of the total amount of anomalies on a day at the same time, for the East area on special days.
Figure A.15: Graph of the total amount of anomalies on a day at the same time, for the Far West area on special days.
Figure A.16: Graph of the total amount of anomalies on a day at the same time, for the West area on special days.
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