Very Short-Term Electricity Load Demand Forecasting Using
Support Vector Regression
Anthony Setiawan, Irena Koprinska, and Vassilios G. Agelidis
Abstract—In this paper, we present a new approach for very
short term electricity load demand forecasting. In particular,
we apply support vector regression to predict the load demand
every 5 minutes based on historical data from the Australian
electricity operator NEMMCO for 2006-2008. The results show
that support vector regression is a very promising approach,
outperforming backpropagation neural networks, which is the
most popular prediction model used by both industry
forecasters and researchers. However, it is interesting to note
that support vector regression gives similar results to the
simpler linear regression and least means squares models. We
also discuss the performance of four different feature sets with
these prediction models and the application of a correlationbased sub-set feature selection method.
E
I. INTRODUCTION
load forecasting is an important component
for any modern energy management system. Electricity
market operators and participants use load forecasting for
many reasons such as to make unit commitment decisions,
reduce spinning reserve capacity and schedule device
maintenance plan properly to ultimately safeguard system
security and achieve the highest possible reliability of
supply while optimising economic cost. For instance, an
over-prediction of load to meet security requirements could
involve the start up of too many units resulting in an
unnecessary increase in reserve, and hence operating costs,
as market operators must allocate such demand [1-2].
Load forecasting can serve different planning objectives
and assist system operators to meet all critical conditions in
the short, medium and long term. It can be classified into
four types with respect to the future time window of the
forecasting task:
1) Long-term - Typically 1 to 10 years; used to identify
needs for major generation planning and investment, since
large power plants may take a decade to become available
due to the challenging project requirements and the needs to
design, finance and build them;
2) Medium-term - Typically between several months to a
year; used to ensure that security and capacity constraints
LECTRICITY
Anthony Setiawan is with the School of Electrical and Information
Engineering, University of Sydney, NSW 2006, Australia (e-mail:
[email protected]).
Irena Koprinska is with the School of Information Technologies,
University of Sydney, NSW 2006, Australia (phone: +61 2 9351 3764, fax:
+61 2 9351 3838, e-mail: [email protected])
Vassilios Agelidis is with the School of Information and Electrical
Engineering, University of Sydney, NSW 2006, Australia (e-mail:
[email protected]).
are met in the medium term;
3) Short-term (STLF) - A day ahead; used to assist
planning and market participants;
4) Very short-term (VSTLF) - hours and minutes ahead;
used to assist trading and eventually dispatch.
In this paper we focus on VSTLF. In Australia, the
VSTLF plays an important role in the operation of the
national electricity market, as its market operator NEMMCO
must issue every 5 minutes the production schedule of the
generators [3-4]. The 5-minute regional demand forecasting
relates the demand at the beginning of a dispatch interval to
the target at the end [4]. Based on this load forecasting,
generators and network operators are required to notify
NEMMCO of their maximum supply capacity and
availability, and this information is matched against regional
demand forecasts. This then enables the remainder of market
participants to respond to potential supply shortfalls by
increasing their generation or network capacity to meet
expected market demand. All offers to supply (bids) are then
collated so that potential shortfalls of supply against
expected demand can be identified and published.
Participants in the market use this information as the basis
for any re-bids of the capacity they wish to bring to the
market.
In this paper, we deal with the 5-minute VSTLF using
data from 2006, 2007 and 2008 provided by NEMMCO.
Our main objective is to study VSTLF in power system
since there have been only a few published articles [5-12].
We then present an application of support vector regression
(SVR) for 5-minute electricity demand forecasting. SVR has
been successfully used for STLF but has not been reported
in the open technical literature for VSTLF. The performance
of SVR is compared with standard statistical methods such
as linear regression (LR) and least means squares (LMS)
and also with multilayer perceptron trained with the
backpropagation neural network (BPNN) algorithm. The
latter is a very popular model for electricity load forecasting,
predominantly reported in the research literature and it is
also the main method used by industry forecasters. We also
compare several feature sets and study the effect of a
correlation-based feature selector.
The paper is organised as follows. Section II discusses the
characteristics of VSTLF and previous research on VSTLF.
Section III presents SVR algorithm and the other prediction
algorithms used for comparison. Section IV introduces the
modelling process including feature sets, evaluation
procedure and performance measures. The results are
presented and discussed in section V before concluding in
Section VI.
II. VERY SHORT TERM ELECTRICITY LOAD FORECAST
A. Characteristics of Electricity Load
Time, random effects and anomalous days are some of the
main factors influencing the VSTLF.
Time: Electricity demand during the day differs from the
demand during the night, and demand during weekdays
differs from the demand during weekends. However, all
these differences have cyclic nature, as the electricity
demand on the same weekday and time but on a different
date is likely to have the same value. Any shift to and from
daylight saving time and the start of school year also
changes the previous load profiles.
Random effects: A power system is continuously
subjected to random disturbances and transient phenomena.
In addition to a large number of very small disturbances,
there are large load variations caused by devices such as
steel mills, synchrotrons and wind tunnels, as their hours of
operation are usually unknown to utility dispatchers. There
are also certain events such as widespread strikers,
shutdown of industrial facilities and special television
programs whose occurrences are not known a priori but
affect the load.
Irregular days: These days include public holidays,
consecutive holidays, and days preceding and following the
holidays, days with extreme weather or sudden weather
change and special event days [14].
B. Previous Work on VSTLF
Table 1 lists the forecasting methods previously used for
STLF and VSTLF. The majority of work has been on STLF.
TABLE 1. SUMMARY OF LOAD FORECASTING TECHNIQUES USED
Method
STLF
VSTLF
Statistical methods
Autoregressive integrated moving average
Autoregressive moving average
General exponential smoothing
Kalman filter
Multiple linear regression
State space
Stochastic time series
Support vector regression
Artificial intelligence - based methods
Artificial neural networks
Expert system
Fuzzy inference
Fuzzy neural system
The most popular prediction models used for VSTLF are
based on neural networks. In [5] a set of BPNN was used
where each network forecasts the load for a particular time
lead and for a certain period of the day. Single BPNNs
showed good accuracy in [9] and [11]. A hierarchical neural
network algorithm was used in [12] for 15-minutes load
forecasting. A combination of several BPNNs was shown to
outperform LR in [7].
In [10] an approach combining fuzzy logic with chaos
theory was applied for 15 minutes ahead forecasting. It uses
data from the previous two weeks to predict the load in the
current week and was shown to compare favourably with a
neural network based approach in terms of accuracy. In [6]
three approaches were compared (fuzzy logic, BPNN and
autoregressive model) and the first two were found to be
more accurate than the third one. A self-organizing fuzzy
neural network was used in [8] and shown to outperform the
standard BPNN and fuzzy neural network.
C. Requirement and Difficulties in VSTLF
A good VSLTF system should fulfil the requirement of
high accuracy and speed. However, there are several
challenges. First, it is not clear how to select the best
prediction algorithm and the best feature set. Good feature
selection is the key to the success of a prediction algorithm.
It is needed to reduce the number of features by selecting the
most informative and discarding the irrelevant features.
Second, overfitting is a common problem in load prediction,
especially for the predominantly used neural network-based
prediction algorithms. It means that the error on the training
data (the historical data used to build the prediction model)
is low but the error on the new data is high. Thirdly, the
neural network algorithms have many parameters that
require manual tuning and greatly influence their
performance.
III. SVR AND OTHER PREDICTION ALGORITHMS
A. Support Vector Regression
SVR is an extension of the support vector machine
(SVM) [19] algorithm for numeric prediction. SVM is a
state-of-the-art machine learning algorithm that is applicable
to classification tasks. Using the training data, it finds the
maximum margin hyperplane between two classes by
applying an optimization method. The decision boundary is
defined by a subset of the training data, called support
vectors. By using a kernel function, nonlinear decision
boundaries can be formed while keeping the computational
complexity low.
SVR also produces a decision boundary that can be
expressed in terms of a few support vectors and can be used
with kernel functions to create complex nonlinear decision
boundaries. Similarly to linear regression, SVR tries to find
a function that best fits the training data. In contrast to LR,
SVR defines a tube around the regression line using a userspecified parameter ε where the errors are ignored and it
also tries to maximize the flatness of the line (in addition to
minimizing the error) [17].
SVM and SVR offer several advantages. Similarly to
neural network based algorithms they are capable of forming
complex decision boundaries. However, unlike neural
networks they do not overfit the training data as the decision
boundary depends only on a few training instances. Also,
they have a much smaller number of parameters to optimise.
The main parameters in SVR are ε and C. As mentioned
above, ε defines the error-insensitive tube around the
regression function, and thus controls how well the function
fits the training data [16, 17]. The parameter C controls the
trade off between training error and model complexity; a
11000
10000
9000
8000
7000
6000
03:00
11:10
19:20
Fig. 2 plots the load differences at 5-minute intervals for 2
consecutive days (Monday and Tuesday). It confirms that
there are daily patterns in the electricity demand. These
difference values can be used instead of the actual values or
in addition to them.
3.5%
2.5%
1.5%
0.5%
14:10
15:35
17:00
18:25
19:50
21:15
22:40
15:35
17:00
18:25
19:50
21:15
22:40
12:45
14:10
11:20
09:55
08:30
07:05
05:40
04:15
-1.5%
02:50
-0.5%
01:25
Backpropagation
Neural
Network
(BPNN)
Fig. 1. Daily electricity load at 5-minute intervals, for 1 week (from Monday
to Sunday)
00:00
Least mean
squares
(LMS)
Approximates the relationship between the outcome
and independent variables with a straight line. The
least squares method is used to find the line which
best fits the data. We used the M5's method for
variable selection - starting with all variables at each
step the weakest variable is removed based on its
standardized coefficient until no improvement is
observed in the error estimate.
A modification of LR using least squared regression
functions generated from random subsamples of the
data. The final prediction model is the least squared
regression with the lowest median squared error. We
used sample size=4.
A classical neural network trained with the backpropagation algorithm. We used 1 hidden layer with
the standard heuristic for setting the number of
neurons in it (average of the number of input and
output neurons), sigmoid transfer functions, learning
rate=0.3, momentum=0.2. The training stopped when
a maximum number of epochs was reached (500).
Time
Load Difference [%]
Linear
regression
(LR)
Description and parameters
17:50
02:00
10:10
18:20
02:30
10:40
18:50
TABLE 2. PREDICTION ALGORITHMS USED FOR COMPARISON
Prediction
algorithm
08:40
16:50
01:00
09:10
17:20
01:30
09:40
5000
00:00
08:10
16:20
00:30
B. Other Prediction Algorithms Used for Comparison
The performance of SVR was compared with 3 prediction
algorithms: LR, LMS and BPNN. LR is a standard statistical
method; LMS is a modification of LMS; BPNN is the most
popular algorithm for VSLTF prediction as discussed above.
Table 2 summarizes the algorithms and parameters used. We
used their WEKA's implementations [16].
B. Variable Selection
Variable selection plays a critical role in building a good
forecasting model. It is important to first analyse the data to
ensure all essential variables are included.
Fig. 1 shows a typical daily load graph. As it can be seen,
there is a daily pattern of decreases and increases with two
peaks around 8:00 and 17:00 and 2 lows around 1:00 and
16:00. More specifically, the load is low from 0:00 to 5:00;
it increases from 5:00 to 8:00 and decreases from 8:00 to
17:00 and then gradually decreases till 1:00. The load during
the weekend is lower than the load during the workdays.
Electricity Load [MW]
smaller C increases the number of training errors; a larger C
increases the penalty for training errors and results in a
behavior similar to that of a hard-margin SVM [21].
We used WEKA’s SVR implementation which is based
on a sequential optimization algorithm [16] with the
following parameters, which were set empirically:
polynomial kernel, ε =0.001 and C=1.
SVR is yet to be tested for VSTLF. It has been found very
efficient and accurate for STLF and shown to outperform
autoregressive and BPNN algorithms [14]. The winners of
the 2001 EUNITE (European Network on Intelligent
Technologies) competition on electricity load forecasting
also used SVR for STLF [15].
-2.5%
IV. MODELLING
2.5%
1.5%
0.5%
12:45
11:20
09:55
08:30
07:05
05:40
04:15
02:50
-1.5%
01:25
-0.5%
00:00
A. Historical Data
We have obtained data for the electricity load in NSW in
2006, 2007 and 2008. To predict the load for August 2008,
we used the data from August 2006 and 2007 as training
data, as discussed in the following sections.
3.5%
Load Difference [%]
As stated already, we aim to predict the electricity load
every 5 minutes for August 2008 based on the historical data
for the period of 2006 and 2007 in the NSW region of
Australia. In this section we describe the data, the extracted
features for use with the prediction algorithms, the
evaluation procedure and performance measures.
Time
-2.5%
Time
Fig. 2. Load difference at 5-minute intervals for 2 consecutive days:
Monday (above) and Tuesday (below)
Fig. 3 shows that there are seasonal differences in the
electricity load in NSW. As expected, the loads for spring,
summer and autumn are similar, while the load for winter is
different and significantly higher. However, it has been
shown that the weather (e.g. temperature) does not influence
the accuracy of VSTLF [13] as it changes slowly within a 5minute forecasting time window.
Feature
set 2
(15
features)
Xt,...,Xt-4
XXt+1,...,XXt-4
As in feature set 1.
time interval of
the predicted load
4 binary variables, each representing
one of the time intervals:
v1: 6:00-9:00
v2: 9:00-17:00
v3: 17:00-20:00
v4: 20:00-6:00
Feature
set 3
Xt,...,Xt-4
XXt+1,...,XXt-4
(15
features)
day of the week
for Xt+1
Fig. 3. Seasonal electricity patterns - daily electricity load at 5-minute
intervals for a week for each season
C. Feature Selection
Based on the results from the previous section, four feature
sets were selected. They are summarised in Table 3.
To predict the load Xt+1at time t+1, feature set 1 uses the
previous 5 loads from the same day Xt,…,Xt-4, the load at
the same time and weekday the previous week XXt+1 and
also the previous 5 loads XXt,…,XXt-4. Thus, feature set 1
takes into account the load similarity in the previous 25
minutes and the weekly load pattern.
Feature sets 2, 3 and 4 are supersets of feature set 1.
Feature set 2 also takes into account the daily load pattern by
encoding 4 daily intervals based on the pattern from Fig.1.
Feature set 3 tries to exploit more the weekly load pattern by
adding a feature that encodes the weekday (Monday,
Tuesday, etc) for the forecast day. Feature set 4 tries to take
advantage of the daily pattern by adding features based on
more fine grained information about the time for which the
forecast is made. It also adds the 5-minute load differences
for the features from set 1.
TABLE 3. FEATURE SETS USEDTO PREDICT THE LOAD Xt+1
Predicting Xt+1
Description
based on
Feature
Actual load on the forecast day at
Xt,...,Xt-4
set 1
times t,…, t-4
(11
XXt+1,...,XXt-4
Actual load on the same weekday the
features)
previous week at times t+1,..,t-4.
Example: The load for any Monday
10:30 will be predicted using the load
on the same day at 10:25, 10:20,
10:15, 10:10, 10:05 and the load on
Monday the previous week at 10:30,
10:25, 10:20, 10:15, 10:10 and 10:15.
Example: Predicting the load at 10:30
Monday based on the 11 features from
feature set 1 and also using 4 variables
representing the time interval for
10:30 (i.e. their values will be 0, 1, 0,
0).
As in feature set 1
4 binary variables, each representing
the weekday
v1: Mon, Tue, Wed
v2: Thu, Fri
v3: Sat
v4: Sun
Example: Predicting the load at 10:30
Monday based on the 11 features from
feature set 1 and also using 4 variables
representing the weekday for Monday
(i.e. their values will be 1, 0, 0, 0).
As in feature set 1
Feature
set 4
Xt,...,Xt-4
XXt+1,...,XXt-4
(22
features)
hour of Xt+1
Value: integer from 1 to 24
hour half for Xt+1
Value: 0 for first half and 1 for the
second half)
DiffX1,...,DiffX4
DiffX1 = Xt-Xt-1, DiffX2=Xt-1-Xt-2, etc.
DiffXX1=XXt+1-Xt, DiffXX2=Xt-Xt-1, etc.
DiffXX1,...,DiffXX5
Example: Predicting the load for
10:35 Monday based on the 11
features from feature set 1 and also
using a variable for the hour (value =
10), hour half (value = 1) and 4 load
differences for the prediction day and
5 load differences from Monday the
previous week.
D. Evaluation Procedure
The quality of each prediction algorithm was evaluated in
two ways: using cross validation and by testing the
prediction algorithm on new data.
We firstly used 10-fold cross validation on the data set
from August 2006 and August 2007 (17,856 instances). 10fold cross validation is the standard procedure used in
machine learning [17]. The main idea is to use independent
testing set for performance evaluation rather than the
training data. This allows obtaining a more reliable estimate
of the prediction performance. In 10-fold cross validation,
the dataset is divided into 10 subsets of approximately equal
size. Ten experiments are conducted: each time k-1 subsets
are put together to form the training set which is used to
build the model. The remaining test set is used to test the
model calculating the performance measure (e.g. a mean
absolute error). In each of the 10 runs, a different test set is
used. The overall performance measure for the model is
calculated as the average across the 10 runs.
We also evaluated the quality of the models on new data,
i.e. the data from August 2006 and 2007 was used to build
the models and then they were tested on the data from
August 2008.
E. Performance Measures
We used the following performance measures:
1) Mean absolute error (MAE):
MAE =
1
∑ L _ actuali − L _ forecasti
n i =1
n
where L_actuali and L_forecasti are the actual and
forecasted electricity loads, respectively, at the 5-minute
interval i and n is the total number loads that are being
predicted.
2) Relative absolute error (RAE) – It measures the
performance of the prediction model used, relative to a very
simple predictor, the ZeroR algorithm. ZeroR predicts the
mean value in the training data and is used as a baseline.
3) Mean absolute performance error (MAPE), an
extension of MAE defined as
MAPE =
1
L _ actuali − L _ forecasti
∑
n i =1
L _ actuali
n
4) KPI - a performance improvement indicator which can
be used to compare the MAPE performance of the predictor
relative to no prediction (MAPEnaive):
KPI =
MAPE naive − MAPE
MAPE naive
MAPE naive =
1 n L _ actuali −1 − L _ actuali
∑
n i =1
L _ actuali
An acceptable target for KPI would be 20%.
All results in Section V are presented in % using these
performance measures.
V. RESULTS AND DISCUSSION
A. Performance Evaluation Using Cross Validation
Table 4 summarises the performance of the four prediction
algorithms using the four feature sets and 10-fold cross
validation as an evaluation method. Three of the algorithms
(LR, LMS and SVR) performed similarly obtaining the best
MAE (MAE=0.41%, i.e. 41 MW). BPNN was slightly
worse with MAE=0.51-0.53%. LR was the fastest to build
the model, followed by LMS, BPNN and SVR. In particular,
it took approximately two hours to build SVR using a
computer with a 2 GHz processor and 1.49 GB of RAM. In
[20] SVR was found to be faster than BPNN but this may be
due to the different stopping criterion used by BPNN and
the smaller amount of training data.
A comparison across the feature sets shows that there was
no difference in accuracy. Thus, the additional features such
as the time of the day and week, when used with the
classifiers we studied, did not improve the prediction
accuracy. Feature set 1 is the smallest (11 features) while
feature set 4 is the biggest (22 features). Naturally, the
bigger the feature set, the longer the training time (this is not
reflected in Table 4 for LR and LMS as these algorithms
perform additional sub-set feature selection as mentioned in
Table 2). All prediction models improved over the baseline
(ZeroR) as indicated by RAE.
TABLE 4. 10-FOLD CROSS VALIDATION PERFORMANCE USING DATA FROM
AUGUST 2006 AND 2007
LR
LMS
BPNN
SVR
Feature set 1
Time [seconds]
1.13
123.88
132.31
7712.42
MAE [%]
0.41
0.41
0.51
0.41
RAE [%]
4.32
4.33
5.33
4.32
Feature set 2
Time [seconds]
1.05
240.39
105.99
7717.06
MAE [%]
0.41
0.41
0.51
0.41
RAE [%]
4.31
4.32
5.33
4.30
Feature set 3
Time (seconds)
0.45
109.72
410.14
7724.2
MAE [%]
0.41
0.41
0.53
0.41
RAE [%]
4.32
4.33
5.54
4.32
Feature set 4
Time (seconds)
1.09
266.86
455.61
7854.66
MAE [%]
0.41
0.41
0.43
0.41
RAE [%]
4.32
4.33
4.53
4.32
B. Performance Evaluation on New Data
Table 5 shows the accuracy when the models were used to
predict new data (i.e. they were trained on data for August
2006-2007 and used to predict the load for August 2008).
TABLE 5. PERFORMANCE IN PREDICTING THE LOAD FOR AUGUST 2008
USING DATA FROM AUGUST 2006 AND 2007
LR
LMS
BPNN
SVR
Feature set 1
MAPE [%]
0.31
0.32
0.41
0.31
MAPEnaive [%]
0.58
0.58
0.58
0.58
KPI [%]
46.11
44.52
30.06
46.16
Feature set 2
MAPE [%]
0.45
0.39
0.77
0.43
MAPEnaive [%]
0.58
0.58
0.58
0.58
KPI [%]
22.58
32.40
-31.99
26.05
MAPE [%]
0.31
0.32
0.73
0.31
MAPE [%]
0.58
0.58
0.58
0.58
KPI [%]
46.01
44.95
-25.72
45.95
Feature set 3
Feature set 4
MAPE [%]
0.31
0.31
0.40
0.31
MAPEnaive [%]
0.58
0.58
0.58
0.58
KPI [%]
46.03
46.36
31.20
46.14
11000
10000
9000
8000
7000
6000
5000
5000
6000
7000
8000
9000
10000
11000
12000
9000
10000
11000
12000
9000
10000
11000
12000
10000
11000
12000
Xt
12000
11000
10000
Xt+1
13500
12000
Xt+1
The results are consistent with the cross-validation results
in Table 4. SVR, LR and LMS perform best obtaining the
lowest MAPE. In particular, the best performing algorithms
are: on feature set 1 - LR and SVM, MAPE=0.31%; on
feature set 2: LMS, MAPE=0.39%; on feature set 3 – LR
and SVR, MAPE=0.31%; on feature set 4: LR, LMS and
SVR, MAPE=0.31%. Thus, the best result is MAPE=0.31%
achieved by LR, LMS and SVR using one or more feature
sets. BPNN is slightly worse; its MAPE is between 0.4%
using feature set 4 and 0.77% with feature set 2.
A MAPE of 0.3-0.4% is a very good result. Fig. 4 shows
the actual and predicted values for MAPE=0.33%. The
prediction model is SVR with feature set 1 for the 7th of
August 2008. As it can be seen, there is almost no difference
between the two graphs.
9000
8000
7000
12500
Electricity Load [MV]
6000
5000
5000
11500
6000
7000
8000
Xt-1
10500
9500
12000
11000
8500
Xt+1
10000
23:45
22:30
21:15
20:00
18:45
17:30
16:15
15:00
13:45
12:30
11:15
8:45
10:00
7:30
6:15
5:00
3:45
2:30
1:15
0:00
7500
8000
7000
Time
Actual
9000
6000
5000
5000
Predicted
Fig. 4. Actual versus predicted load using SVR and feature set 1 for 7
August 2008
7000
8000
XXt+1
12000
11000
10000
Xt+1
A comparison across the feature sets shows that feature
sets 1, 3 and 4 perform similarly while feature set 2 is
slightly worse. Recall that feature set 1 is the smallest and
the remaining feature sets are supersets of it. Thus, adding
additional features do not seem to improve performance.
In terms of the KPI, the 20% target is met by all models
for feature set 1 and 4, by LMS for feature set 2 and by all
models except BPNN for feature set 3. Even though BPNN
with feature set 1 and 4 meets the target, its performance is
14-16% lower than the other algorithms.
To summarize, feature set 1 in combination with SVR, LR
and LMS produces the best results and significantly
outperforms BPNN. The KPI accuracy results of the three
models are 25-26% higher than the KPI target.
The good performance of LR and LSM indicates that
there is a linear relationship between the independent
variables (features used for prediction) and the dependent
variable (the load that we are predicting). Fig. 5 shows
scatter plots of Xt, Xt-1, XXt+1 and XXt versus the dependent
variable Xt+1 confirming the strong linear relationships.
6000
9000
8000
7000
6000
5000
5000
6000
7000
8000
9000
XXt
Fig. 5. Scatter plots of predicted load (Xt+1) and historical load data Xt, Xt-1,
XXt+1 and XXt
We also investigated if the number of features in the best
performing feature set (set 1) can be further reduced without
deteriorating the prediction accuracy. We applied a simple,
fast and efficient method for feature sub-set selection, called
correlation-based feature selection (CFS) [18]. It searches
for the “best” sub-set of features where “best” is defined by
a heuristic which takes into consideration 2 criteria: 1) how
good the individual features are at predicting the outcome
and 2) how much the individual features correlate with each
other. Good feature subsets contain features that are highly
correlated with the outcome and uncorrelated with each
other.
To evaluate CFS, we used the data for 2006 and 2007.
Table 6 shows the selected features using CFS. As it can be
seen, 1 or 2 features were selected for each month, which is
a drastic feature reduction from the original 11 features. The
most important features for predicting the load Xt+1 are Xt,
XXt+1, XXt and XXt-1, with Xt (the load 5 minutes before)
being always selected. There seem also to be a seasonal
pattern that requires further investigation. Table 7
summarizes the performance of the prediction algorithms
using the selected features and 10-fold cross validation as an
evaluation procedure. A comparison with Table 4 shows that
the accuracy results are worse - there is an increase in MAE
of 0.14% for LR and LMS, 0.27% for BPNN and 0.12% for
SVR. However, the time to build the prediction models is
reduced, especially for BPNN and SVR.
TABLE 6. SELECTED VARIABLES BY CFS APPLIED TO FEATURE SET 1
Month
Xt
XXt+1
XXt
XXt-1
February
March
April
May
June
July
August
September
October
November
December
TABLE 7. 10-FOLD CROSS VALIDATION PERFORMANCE USING THE FEATURES
SELECTED BY CFS
LR
LMS
BPNN
SVR
Time [seconds]
0.59
74.5
17.6
0.97
MAE [%]
0.55
0.55
0.78
0.52
RAE [%]
5.79
5.77
8.26
5.51
ACKNOWLEDGMENT
We would like to thank NEMMCO for providing the data
and all the information needed to conduct the research.
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VI. CONCLUSION
We presented a new approach for the 5-minute electricity
load demand forecasting using SVR. The results showed
that SVR is a very promising prediction model, outperforming the BPNN prediction algorithms which is widely
used by both industry forecasters and researchers. However,
we found that simpler models such as LR and LNS produced
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We investigated the performance of four feature sets based
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