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An Efficient Hour-Ahead Electrical Load Forecasting Method
Based on Innovative Features
Amir Rafati 1, Mahmood Joorabian1,*, Elaheh Mashhour1
1 Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz,
Iran
* Corresponding author: mjoorabian@scu.ac.ir, Tel/Fax: +98-6133336642
Abstract
Deregulation of electric power market and aggregation of renewable resources raise the need
for new hour-ahead load forecasting models. This paper proposes a new hybrid data-driven
method for hour-ahead electrical load forecasting based on innovative features that represents
the nonlinear and dynamic characteristics of electrical load. These features predict hourly load
changes and improve the accuracy and performance of STLF. These innovative features first
construct the pool of features along with historical load variables. Then, a feature selection
method is used for choosing most relevant features and finally, a multi-layer perceptron neural
network is employed as a forecasting engine—due to its advantages such as self-organization,
fault tolerance and ease of integration in existing technologies. The efficiency of the proposed
model is evaluated through various comparative experiments and compared with benchmark
models using the three years’ real energy market data from New England ISO by four
evaluation criteria. The results demonstrate the superiority of proposed method in forecasting
performance for the period of analysis including 12 test months as well as special days.
Keywords: Hour-ahead load forecasting, Feature selection, Neural networks, Deregulated
energy system.
Nomenclature
xjLoad data GOA Grasshopper Optimization
Algorithm
xiNormalized load data HLC Hourly Load Change
x
Normalized forecasted load ISO Independent System Operator
x D-normDe-normalized Forecasted load LM Levenberg-Marquardt
algorithm
xminMinimum value of load data MAE Mean Absolute Error
xmaxMaximum value of load data MAPE Mean Absolute Percentage
Error
LD,H Load at current hour of forecast day MDMAPE Maximum Daily Mean
Absolute Percentage Error
ACAuto-correlationMLP Multi-Layer Perceptron
ANNArtificial Neural Networks MSE Mean Squared Error
BPNNBackpropagation Neural Network PSO Particle Swarm Optimization
DAMEDaily Absolute Maximum Error RF RreliefF
DLCDaily Load ChangeRF+NN RReliefF with multi-layer
perceptron neural network
DTFDemand Tracking FeatureSTLF Short Term Load Forecasting
FSFeature SelectionSVM Support Vector Machine
GA Genetic Algorithm SVR Support Vector Regression
1. Introduction
Short-term Load forecasting(STLF), for predicting one hour to one-week electrical loads, has
always been important for management, security, planning and operation of power systems
[1,2]. As for the utilities, electrical load forecasting has important role in unit commitment,
power dispatch, maintenance scheduling and operational decisions such as voltage control, load
switching, power interchange, etc. [3]. A conservative estimate proposed by Hobbs et al [3]
clearly showed a 1% reduction in load forecasting error of a 10 GW utility can save up to $1.6
million annually. Therefore, utilities tend to increase the accuracy of load forecasting models
to save more, especially in the era of privatization and deregulation of power industries. As
many variables such as time, day, weather, economic aspects, and social activities influence
electricity loads, enhancing the accuracy of load forecasting models has turned out to be a
challenging job.
To improve the forecasting accuracy, many recent STLF methods have included weather or
other variables [4-9] along with historical loads. In many cases, adding such variables not only
increase the complexity of forecasting models, but also make their prediction performance
dependent on accuracy of forecasted variables. Furthermore, due to the expense or
unavailability of required data or low accuracy of weather forecasts, a considerable number of
multi-variate STLF methods that depends on such variables would not be applicable in real
power systems. On the other hand, one of the main problems of univariate STLF methods,
which incorporate only historical loads, is difficulty in estimating and adjusting the model
parameters as these models may be outdated or may not reveal short-term load pattern changes
[10]. Therefore, devising new STLF methods that only use historical load data and predict
accurately and reliably would be of critical importance to power industries.
The power systems, however, are changing rapidly. With deregulation and privatization of the
power industries along with development of renewable energies, traditional forecasting
methods are becoming obsolete and fail to provide generality and interpretability for future
demand prediction [11]. Therefore, introducing new hour-ahead forecast models is needed to
provide timely and reliable load forecasts. Hour-ahead load forecasting is essential in smart
grid paradigms with prosumers that bid load reductions hourly [2]. It is also necessary for
dynamic electricity pricing in deregulated energy systems, real-time control and load
following, congestion management of distribution lines and operational planning of distributed
generation and storage technologies [2,12]. Moreover, with compensating the uncertainty in
load forecasts [12], hour-ahead load forecast can help ISOs to maintain operating reserve and
also reduce costs for ISOs, utilities, and customers. In order to encounter the effects of all
factors on electrical load changing, this paper proposes a new hour-ahead load forecasting
method based on historical loads and defining innovative features. The experimental results
show this strategy has significantly improved the forecasting performance.
1.1 Review of related works and motivation
Increasing the accuracy of load forecasting methods is always challenging because many
factors affect electrical load forecasting. Some factors like time factors, including hour of the
day [4,7,13,14], day of the week [7,14,15], holidays [7,8] and the season of the year [5,6,18] -
or weather variables [4-9] have been receiving more attention from practitioners and scholars.
Nevertheless, investigation on many other important variables like special events, extreme and
sudden weather changes, energy price, consumers’ economic conditions, governmental
policies, etc. makes the load forecasting more difficult task.
Different models have been proposed for STLF that can be classified into three categories:
traditional methods, artificial intelligence algorithms and hybrid techniques. Traditional
methods use statistical and linear forecasting models. Time Series [5,16,17] and regression-
based formulations [18] are the most popular traditional methods [17]. These models use
simple mathematical formulas and are effective in dealing with the linear forecasting problems
but are insufficient in processing the complex nonlinear load time series [16,19]. In recent
studies, researches have used traditional methods in combination with another method to
encounter the exogenous variables [5,17].
To overcome the deficits of traditional methods, artificial intelligence models with learning
capabilities are applied to forecast electricity load [20]. They include knowledge-based systems
[21], support vector machines (SVM) [6,16,22], artificial neural networks (ANN) [7,10,17,23]
and support vector regression (SVR) [13,24,25]. These intelligent methods have been widely
used for forecasting electrical load because of their powerful learning capacity of the complex
and nonlinear nature of load series and consequently their more accurate forecasts. The
comprehensive and systematic literature review of artificial intelligence-based short-term load
forecasting techniques is presented in [20]. The most interesting intelligent method for STLF
is ANN [17]. Many of ANN methods used for STLF are based on similar-day approach
[10,21,22,26]. These methods predict future power load curve by using information of some
days that their weather conditions are similar to forecast day.
Although artificial intelligence model can take into account other influence factors, it still has
its own shortcoming such as dependence on initialization of weight values, local minimum and
over training and slow convergence [20,23]. Therefore, many researchers have proposed hybrid
models and combining traditional and intelligent models with data-driven approaches and
optimization algorithms to improve the accuracy and performance of forecasting. Literature
review results showed that hybrid models can obtain better forecasting than simple models and
single artificial neural network models [6,16,20]. For instance, in ref. [6], a new approach based
on firefly algorithm, SVM and season specific similarity concept has been proposed to capture
seasonality effects and integrate them in STLF process in India during different seasonal
meteorological conditions. In [16], an autocorrelation function is applied to select the
informative input variables and a Least Squares SVM (LSSVM) is used for prediction. In [19],
authors proposed a STLF model based on the hybrid Genetic Algorithm(GA) Particle Swarm
Optimization(PSO) and Backpropagation Neural Network(BPNN) named GA-PSO-BPNN
algorithm in which the GA-PSO algorithm is used to optimize the parameters of BPNN. In ref.
[22], grasshopper optimization algorithm (GOA) evaluates the proper parameters for a SVM.
The proposed GOA-SVM model is targeted for forecasting the load using the similar day
approach to satisfy the regional climatic requirements. Ref. [27] combines GOA, ensemble
empirical mode decomposition and extreme learning machine for short-term load forecasting
in five states of Australia. In summary, the hybrid models have been used to capture the
different characteristics associated with electricity load using each model’s advantage [23].
Even though the hybrid models possess novel methodologies and higher accuracy, they usually
have high complexity. Furthermore, their efficiency is not only highly dependent on parameters
which are hard to tune and require higher computational times but also affected by the quality
of data. To improve the quality of data, the forecast models require mining techniques [13].
One of data mining techniques widely used for improving efficiency of load forecasting models
in recent years is Feature Selection (FS) which is the process of selecting an optimal subset of
prominent and independent features in a dataset with the lowest correlation with each other and
the highest correlation with the output [28]. However, a few researchers have used FS
algorithms for STLF [15] to eliminate irrelevant variables, reduce the complexity of forecast
models and overcome drawbacks of ANN forecasting models like overfitting, over training and
slow convergence [28]. These benefits enable the researchers to improve the accuracy and
performance of STLF models when dealing with exogenous variables such as time, day,
weather, seasons, social activities, and economic aspects and capture the features most
correlated with output from the different features affecting electrical loads.
In general, FS approaches can be divided into two main classes: filter approaches and wrapper
approaches [14]. Filter methods are independent of any learning algorithm and choose subset
of features based on evaluation criteria [15] like mutual information (MI) [15,29], Bayesian
‘automatic relevance determination’ [30], or correlation and linear independency [29,31].
Whereas, wrapper approaches use a predetermined learning algorithm as a measure of subset
suitability to select best subset of features by searching through the feature subset space [32].
In comparison with wrapper approaches, Filter approaches are more computationally efficient.
Therefore, they are often suggested for FS in the high dimensional dataset [14]. Ref.
[14,16,29,30] use different types of filter methods and the results demonstrates the
effectiveness of feature selection on improving the efficiency of forecasting models. Koprinska
et al. [31] evaluated the performance of four filter methods-Autocorrelation (AC), Mutual
Information, RReliefF (RF), and Correlation-Based Selection - along with three prediction
algorithms- neural networks, linear regression and model tree rules. The results show that the
better prediction models are RF+NN and AC+NN for the data experiments. Generally, feature
selection methods are very useful tools that can markedly improve the performance of
forecasting models.
In summary, the forecasting accuracy depends either on the quality of data and the ability to
incorporate important exogenous factors into the models or on the numerical efficiency of the
employed algorithms [20,33]. While many research models have focused on introducing new
hybrid forecasting algorithm that usually increase the complexity of forecasting models, this
study proposes new hybrid method to enhance the forecasting performance based on defining
and applying innovative features in order to improve quality of data in pool of features. These
innovative features are simply defined and can identify and tackle time evolving nonlinear load
characteristics. Then, a common feature selection method is used to choose the most relevant
features. Finally, the most popular prediction algorithm for electricity load forecasting, a simple
MLP neural network, has been used to forecast hour-ahead demand. MLP has many advantages
like adaptive learning, self-organization, fault tolerance, real-time operation, and ease of
integration in existing technologies that make it a right choice for STLF. Therefore, we
combine new simple ideas and most simple and popular methods to propose new forecasting
method that enhance the performance and accuracy of electrical load forecasting. The key
contributions of this paper are as follows:
Development of a new efficient data-driven hybrid method for STLF that focuses on
improving the quality of input data of forecasting model instead of using complex
forecasting models.
Introduction of innovative features to predict load changes and identify the nonlinear
and dynamic characteristics of electrical load based merely on historical data.
Demonstration of the effectiveness and quality of our approach for hour-ahead
electrical load forecasting using the energy market data for three years
Based on numerical experiments and analyses in section 4, the proposed method has a better
performance than the benchmarks in four evaluation measures. The results clearly show that
DTF-RF-MLP is a reliable and efficient method that has the ability to improve forecasting
accuracy.
The remainder of this paper is as follows. In Section 2, the detail of the proposed forecasting
model is elaborated. Section 3 presents experimental setup, dataset, selected variables and the
measures used to evaluate the performance of the proposed method. The experiment results are
presented and discussed in Section 4. Finally, Section 5 summarizes the conclusions and future
works.
2. Proposed method
This section briefly describes the proposed hybrid method called DTF-RF-MLP, which is
composed of three stages: Candidate features that include innovative Demand Tracking Features
(DTF), RreliefF (RF) feature selection and feedforward Multi-Layer Perceptron (MLP) neural
network.
2-1 Candidate Features
In the field of STLF, appropriate features are crucial for accurate forecasting [14]. Besides
simply including the lag variables—used in most forecasting models—many researchers have
proposed different approaches to construct the pool of features, such as seasonal patterns
[5,6,10,18] and variables related to weather information [4-10,21]. In order to choose lag
variables and construct an initial pool of candidate features we examined some characteristics
of the hourly loads. Fig. 1 illustrates the hourly load demand of a one week from Monday (02
March 2015) to Sunday (08 March 2015) of New England grid. Although, the load level during
the weekends and holidays is lower than that of the working days due to different social
activities of the peoples, Fig. 1 clearly shows the load profiles of the individual days are similar
throughout the week. It therefore indicates that the historical data, load profiles and time are
influential factors and should be considered in constructing pool of candidate features.
Fig. 1 Daily electricity load profiles for different days of a week (02-08 Mar 2015).
Fig. 2 depicts the load demand of four specific months (i.e., January, April, July and October)
of 2013. These months are chosen because they are typical representatives of summer, winter,
and transitional periods of the year. This figure illustrates that the seasons and their associated
weather changeshave a great impact on load profile and electrical load changes. As described,
investigation on all influential variables on load demand changes is impossible. To identify the
electrical load changes, we propose innovative variables to predict nonlinear time-evolving
characteristics of electrical load that is fully described in next section.
Fig.2 Electrical load demand of four specific months (January, April, July and October) of New England ISo in
2013.
2-1-1 Defining innovative features
To take into consideration the impact of all influential variables into a forecasting model and
efficiently forecast the future demand, this paper proposes and defines innovative features from
the original dataset to extract the nonlinear time-evolving characteristics of load series called
Demand Tracking Features (DTF). To track the load change, we used to concepts:
Daily Load Change (DLC), Difference between Electrical load of a specific hour and
a day before.
Hourly Load Change (HLC), Electrical load change of two consecutive hours.
innovative features have been introduced as follows:
LTF1D,H = LD,H-1+ DLCD-1,H (1)
LTF2D,H = DLCD-1,H (2)
LTF3D,H = LD-1,H+ HLCD-1,H
(3)
LTF4D,H = LD,H-1+ mean(HLCD-1,H & HLCD-2,H) (4)
LTF5D,H = LD,H-1+ HLCD-7,H (5)
LTF6D,H = LD,H-1+ mean(HLCD-1,H & HLCD-7,H) (6)
In which, “L” represents for Load and indices “D” and “H” indicate “forecasting day” and
“forecasting hour”, respectively. For instance, LD,H represent for load in current hour of
forecasting day.
To clearly illustrates these definitions, Fig 3 graphically details the definition of the three of
innovative features.
Fig.3 Illustration of three innovative features.
2-1-2 Pool of features
Inspired by proposed idea, this paper constructs a pool of features based on lag variables and
new proposed variables. Based on the experiments, a 1-week sliding window is chosen as
historical load, i.e. 168 lag inputs. The last 10 values for each newly defined variable are added
to construct the pool. Although more historical data could have been included, the inclusion of
more data would increase model complexity and computational costs without any significant
improvement in forecasting accuracy. Table 1 demonstrates the detailed information of
proposed pool of features which includes 228 features.
Table 1. Proposed pool of features.
Variable Types Description The Variable Number
Lag Variables A 1-week sliding window as lag
variables 1-168
New proposed Variables LTF1D,H-9 - LTF1D,H 169-178
New proposed Variables LTF2D,H-9 - LTF2D,H 179-188
New proposed Variables LTF3D,H-9 - LTF3D,H 189-198
New proposed Variables LTF4D,H-9 - LTF4D,H 199-208
New proposed Variables LTF5D,H-9 - LTF5D,H 209-218
New proposed Variables LTF6D,H-9 - LTF6D,H 219-228
2-2 RRreliefF(RF)
RF [34,35] is an instance-based feature ranking method for feature selection. The key idea
behind the original Relief algorithm is to estimate the quality of attributes according to their
instances values and distinguish the instances that are near to each other [34]. The extended
version of algorithm, which is called RReliefF, is an efficient algorithm for regression problems
such as load forecasting [35]. RReliefF randomly selects some instances from the training data
and then searches for K-nearest neighbors from the same class. This algorithm ranks the feature
based on assignment of a weight to each feature [35].
RReliefF’s good performance and robustness and its ability to detect higher order pairwise
feature interactions between features and deal with incomplete and noisy data indicate its
appropriateness for feature selection [31]. In order to increase the performance of the feature
selection, we use all the training data and also choose k=10 nearest neighbors.
Feature selection is done offline for each hour based on the constructed pool of features. This
pool consists of the historical load data and related innovative features. 30 of the best ranked
features has been selected for each hour and then updated hourly based on more recent hourly
data and applied for online hour-ahead load forecasting.
2.3 Multilayer perceptron neural networks
NNs, in particular multi-layer perceptrons, are the most popular prediction algorithms for
electricity load forecasting [31]. ANNs are able to model complex nonlinear relationships
between input and output variables in complex environments that makes ANNs especially
attractive for use in problems such as demand forecasting. They have many advantages like:
adaptive learning, self-organization, fault tolerance, real-time operation, and ease of integration
in existing technologies. Therefore, we used a feedforward multi-layer perceptron with one
hidden layer including ten neurons for forecasting engine. The Levenberg-Marquardt algorithm
has been chosen as training algorithm due to its faster convergence relative to the standard
steepest gradient descent backpropagation algorithm [31]. The flowchart of proposed method
is illustrated in Fig. 4.
Fig. 4 Basic flowchart of DTF-LF-MLP method.
3. Experimental Setup
All experiments are conducted in MATLAB R2019a on a PC with 2.50 GHz Intel Core i5, 64
bit and 8 GB RAM.
3.1 Data sets
To verify the hour-ahead forecasting performance of the proposed STLF model, a real-world
hourly load dataset from New England Independent System Operator (New England-ISO) from
January 1, 2013 to November 31, 2015 [37] is used as the experimental data.
The data are sampled at every hour giving 24 observations a day, 168 observations a week and
a total of 26280 observations.
3-2 Evaluation criteria
To assess the accuracy of the proposed forecasting model, four standard evaluating measures,
including the Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and
Daily Absolute Maximum Error(DAME) have been used in this study which are defined as
follows:
1ˆ
1
N
M
AE x x
ii
i
N
(7)
ˆ
1100%
1
Nx x
ii
MAPE i
Nx
i
(8)
ˆ
max{ }
D
AM E x x i=1,...,24
ii
(9)
Where xi and x
idenote the actual value and predicted value for ith hour of day, respectively,
and N is the length of data to compare and evaluate. For instance, N is 24 for daily computations
and is 720 and 744 for monthly calculations of months which have 30 and 31 days, respectively.
Maximum Daily MAPE (MDMAPE) is computed for a year or month and equals to the
maximum of calculated MAPE of each day.
3-3 Data Pre-Processing
Data pre-processing includes some necessary operations to be performed on load data based
on the behavior and variation in load data, to acquire the good forecast results [20]. For
example, load data usually include missing or poor data that decrease the efficiency of
forecasting model and in some cases it makes the forecasting model fail [33].
The outlier data has not been detected and all hours have been treated equally. In other words,
any data smoothing method which might have resulted in lower accuracy [14] has not been
used. To deal with missing values in this study, a simple and straightforward technique of
substituting them with an average of the neighboring observations is employed [33].
Data normalization is another pre-processing method which can be applied on the basis load
profile analysis. In this paper, the input load series data, xj ϵ ℝ, j=1,2,…,M are linearly
normalized between [0,1] using the minimum and maximum values of all variables to avoid
unit and scaling issues and is performed as:
min
max min
xx
j
xixx
(10)
where i,j ϵ [1, 2,…,M], x
i denotes the normalized elements of xj, xmin and xmax denotes the
minimum and maximum values in x. Further, the forecasted load, xP, is de-normalized to the
original data range (as we normalized the data initially) using Eq.10:
ˆˆ
()
max min min
Dnorm
xxxxx
(11)
In which, x and x D-norm is normalized and de-normalized forecasted load data vector, respectively.
3.5 Selected Features
As described before, feature selection is done offline for each hour based on the constructed
pool features from 01 January 2013 to 31 December 2014. The 30 highly ranked features based
on RReliefF are selected. In other words, for forecasting of each hour, 228 features including
168 lag variables and 60 new defined features in Table 1 are used as FS inputs and filtered out
based on the RreliefF method that reduces the number of features to 30 to establish the
forecasting model. The resulting feature set is denoted by NF+RF in Table 2. In Table 2, the
selected feature set, denoted by RF, represents a feature selection from the pool that only
contains lag variables.
Table 2. Selected features.
DTF+RF RF
Hour
of
day
1-5, 169-174, 179-182, 189-194, 199-204, 209, 219-220 1-28, 32, 33 1
1-5, 169-174, 179-181, 189-194, 199-204, 209, 210, 219-220 1-29, 34 2
1-5, 169-174, 179-181, 189-192, 199-204, 209-211, 219-221 1-30 3
1-4, 169-173, 179-181, 189-193, 199-203, 209-212, 219-222 1-30 4
1-4, 169-172, 179-181, 189-192, 199-204, 209-212, 219-223 1-29, 45 5
1-4, 169-173, 179-180, 189-193, 199-203, 209-212, 219-223 1-26, 46, 47, 165, 166 6
1-2, 10, 23, 24, 46-48, 119, 165-170, 178-181, 189-190, 199-200, 208-211,
219-221
1-18, 22-24, 46-48, 119, 164-168 7
1-2, 11, 24, 47-49, 120, 165-171, 179-182, 189-191, 199-200, 209-211, 219-
221
1-18, 23, 24, 47-49, 119, 120, 164-168 8
1-3, 11, 12, 25, 167-171, 179-184, 188-191, 199-201, 209-211, 219-221 1-21, 24, 25, 48-50, 165-168 9
1-3, 10-13, 18, 169-171, 179-182, 189-191, 198-201, 209-212, 219-222 1-25, 49, 50, 166-168 10
1-3, 11-14, 19, 20, 169-171, 179-183, 189-192, 199-201, 209-211, 219-221 1-25, 51, 165-168 11
1-3, 13-15, 20-22, 169-171, 179-183, 189-192, 199-201, 209-211, 219-221 1-25, 164-168 12
1-4, 15, 21, 169-172, 179-183, 189-192, 199-202, 209-211, 219-222 1-26, 165-168 13
1-4, 169-172, 179-184, 189-192, 199-202, 209-212, 219-222 1-27, 166-168 14
1-4, 169-172, 179-183, 189-193, 199-202, 209-212, 219-222 1-28, 167, 168 15
1-4, 169-172, 179-183, 189-193, 199-202, 209-212, 219-222 1-29, 168 16
1-4, 169-172, 179-183, 189-193, 199-202, 209-212, 219-222 1-29, 168 17
1-4, 169-172, 179-183, 189-193, 199-202, 209-212, 219-222 1-29, 168 18
1-4, 169-173, 179-181, 189-193, 199-203, 209-212, 219-222 1-30 19
1-4, 169-173, 179-182, 189-193, 199-202, 209-212, 219-222 1-30 20
1-4, 169-173, 179-181, 189-193, 199-202, 209-212, 219-223 1-25, 27-31 21
1-5, 169-172, 179-181, 189-194, 199-202, 209-212, 219-222 1-26, 28-32 22
1-5, 169-173, 179-181, 189-193, 199-202, 209-212, 219-222 1-26, 30-33 23
1-4, 169-172, 179-181, 189-192, 199-203, 209-213, 219-223 1-27, 31-33 24
Table 2 demonstrates that innovative features can significantly improve the quality of data in
pool of features. For instance, at least 17 of top 30 best ranked features are the newly defined
variables whereas the maximum is 26. It must be noted that 582 of the 720 selected features
for 24 hours, are innovative features i.e. approximately 81 percent. It is clearly indicated that
these features have significant relevance and independency to output and can be used for
hour-ahead forecasting.
4- Simulation Results
To simulate real-world applications, the test and training sets are completely independent.
Hourly data from 1 Jan. 2013 to 29 Nov. 2014 and the newly defined features are used as inputs
of offline feature selection methods that described in the preceding section. As indicated before
the STLF error is greatly influenced by special events, such as rapid load fluctuation or sudden
change in weather conditions, that might have not been investigated if the time period of
simulation was short. Therefore, for overall validation of the effectiveness of proposed model
in a long run, it is run against all hourly electricity loads of 2015. Fig. 5 presents a forecast load
curve and the corresponding error for the whole year of 2015. It indicates that the proposed
method has a low prediction error for all days of 2015. To clearly compare the precision of the
proposed method with, the real and forecasted load and the corresponding prediction error are
plotted for 1 Jan. 2015 to 31 Jan. 2015 in Fig. 6.
Fig.5 Forecast for whole year of 2015.
Fig.6 Forecast for January of 2015.
From these figures, it can be seen that the forecast curve accurately follows the real curve-
except for some minor deviations. Fig. 6 indicates that the proposed method is accurate, not
only for regular days but also for holidays like 1th and 19th of January.
The lower MAPE suggests that the model is efficient, accurate and robust for STLF [4]. The
daily MAPE and MAE of the proposed method and New England-ISO hourly-load forecasts
for the whole year of 2015 is depicted in Fig. 7 and Fig. 8, respectively. For a whole year, the
proposed strategy has considerably lower MAPE value than the STLF of the New England
ISO. These figures further illustrate the proposed STLF strategy are a reliable and accurate
method.
Fig.7 Comparison of MAPE of proposed method and ISO Forecast for whole year of 2015.
Fig.8 Comparison of MAE of proposed method and ISO Forecast for whole year of 2015.
4.1 Comparison of the proposed method and other STLF models
In order to assess the performance of proposed model, we compare it with four forecasting
models: Support Vector Regression (SVR) [24], RReliefF feature selection with SVR(RF-
SVR) [32], MLP neural network trained by Levenberg-Marquardt algorithm (MLP-LM) [36],
and RReliefF feature selection with MLP Neural Network (RF+NN) [31]. All neural networks
include one hidden layer with 10 neurons with the mean squared error (MSE) as the objective
function. The kernel function of SVR models is Gaussian and its input parameters are
determined by searching the space of all possible parameter values until an optimal
combination is found by grid search as the tuning method.
The MAPE of hour-ahead load forecasting results of the proposed and benchmark models for
all days of 2015 is plotted in Fig. 9. In addition, the variations of MAE of forecasting models
during the year are depicted in Fig. 10 to show how they scatter over the forecast period. It
clearly shows that the proposed hybrid DTF-RF-MLP method outperforms SVR, RF-SVR,
MLP-LM, RF+NN models in terms of lower MAPE and MAE.
Fig.9 Comparison of MAPE of proposed method with other forecasting modes for all days of 2015.
Fig.10 Comparison of MAE of proposed method with other forecasting modes for all days of 2015.
Based on Fig. 9 and Fig. 10, it is obvious that the proposed method has a significant
performance for all days of 2015 including working days, weekend and special days. All these
examinations indicate that the proposed model can capture the complex time-evolving
characteristics of electricity load.
To verify the efficiency of the proposed method, the resulting MAPE, MAE, MDMAPE and
DAME of load forecasting models for the 12 test months and the whole year of 2015 are
presented in Table 3. The lowest value for each evaluation measures is highlighted in bold for
the test months. They clearly demonstrate the efficiency of proposed method. In respect to the
daily absolute maximum error, except for two months, the DAME of the proposed DTF-RF-
MLP method is the lowest for all test months and the whole year of 2015.
Table 3. The MAPE, MAE, MDMAPE and DAME of proposed and benchmark methods for the year of 2015.
Forecasting
Method
Evaluation
Criteria Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Year
SVR[24]
MAPE 3.22 2.93 2.88 3.93 3.53 3.52 3.64 3.64 4.03 3.44 3.41 3.39 3.45
MDMAPE 4.65 4.09 4.23 6.32 5.50 5.98 6.86 6.56 6.78 6.25 4.62 5.25 6.86
MAE 514.41 484.33 429.25 499.05 455.35 491.35 603.89 611.52 633.06 445.33 451.32 469.50 502.76
DAME 2399.6 2278.4 2147.7 2012.8 1896.5 2167.0 2808.9 2461.6 2163.9 2112.5 2046.4 2160.3 2808.9
RF‐SVR[32]
MAPE 3.32 2.79 2.75 2.99 2.95 2.86 2.93 2.73 2.95 3.13 3.64 3.58 3.07
MDMAPE 4.62 3.82 3.68 4.06 4.01 4.44 5.24 4.71 4.67 5.02 5.11 4.74 5.24
MAE 526.83 458.41 407.75 381.23 384.59 397.06 483.27 453.72 .14 403.90 479.86 495.07 445.70
DAME 2337.4 2133.7 1983.1 1973.1 1364.3 2061.6 2205.7 2043.9 1653.2 2080.8 2018.0 2265.4 2337.4
MLP‐LM[36]
MAPE 2.13 2.01 2.16 2.10 1.98 1.92 1.93 2.02 2.38 2.35 2.71 2.58 2.20
MDMAPE 2.82 2.73 3.08 2.54 2.76 2.72 2.59 2.80 3.31 3.13 4.08 3.31 4.08
MAE 338.97 333.05 320.22 267.62 255.21 265.18 310.18 332.85 365.55 304.82 357.41 357.09 317.11
DAME 1897.2 2457.0 2187.4 1491.4 1139.1 1338.1 1883.0 1744.4 1701.0 1615.3 2073.7 1917.3 2457.0
RF‐NN[31]
MAPE 2.01 1.74 1.94 2.01 1.70 1.61 1.42 1.47 1.79 1.96 2.51 2.40 1.90
MDMAPE 2.78 2.47 3.28 2.59 2.63 2.43 1.88 2.03 2.62 2.74 3.64 2.97 3.64
MAE 319.93 287.36 287.40 257.81 219.19 223.79 229.05 239.45 280.88 256.89 331.94 334.71 273.61
DAME 1623.2 1589.0 2372.8 1448.4 1141.7 1440.1 1341.1 1060.2 1716.9 1489.0 1783.6 1627.3 2372.8
DTF‐RF‐MLP
(Proposed
Method)
MAPE 0.29 0.29 0.32 0.36 0.50 0.51 0.59 0.51 0.46 0.40 0.42 0.37 0.42
MDMAPE 0.71 0.66 0.72 0.74 1.04 1.20 1.06 0.99 0.85 0.64 0.82 0.82 1.20
MAE 41.75 43.48 42.70 40.27 56.60 61.54 80.85 69.96 61.33 44.78 47.00 43.63 52.45
DAME 1103.8 1268.5 721.4 743.0 1497.1 1459.5 1205.5 974.5 1115.9 601.3 1497.1 788.1 1497.1
Table 3 clearly illustrates that the proposed strategy produces considerably lower MAPE, MAE
and MDMAPE values than other methods for all the test months and also for the whole year of
2015. That highlights its superiority in predicting the future demand values accurately. For
instance, MAPE value of the proposed method for the whole year is 0.42% which is
significantly lower than the MAPE of SVR (3.45%), RF-SVR (3.07%), MLP-LM (2.2%) and
RF-NN (1.9%). The minimum and maximum monthly MAPE are 0.29% and 0.59%,
respectively. Table 3 also shows that the MDMAPE of the proposed method is the lowest where
the maximum daily MAPE in 2015 is only 1.2% while the second lowest value is 3.64% for
RF-NN. Compared with the benchmarks, DTF-RF-MLP has a better performance for almost
all the test months and the whole year of 2015 as shown in Fig. 11. This consistency clearly
demonstrates that the proposed method is more reliable than benchmark models.
Fig.11 Comparison of proposed method with other forecasting modes for 12 test months of 2015 in the case of
(a) MAPE, (b) MAE(MW), (c) MDMAPE, (d) DAME(MW).
4.2 Assessment of defining innovative feature on load forecasting
To evaluate the impact of the proposed strategy of defining innovative features on the hour-
ahead load forecasting method, we select two cases: RF-NN [31] and DTF-RF-MLP as case 1
and RF-SVR [32] and DTF-RF-SVR as case 2. Note that RF-NN [31] has used MLP neural
network as well as proposed method. The MAPE and MAE of forecasting result of these four
models for the 12 test month of 2015 are depicted in Fig. 12 and Fig.13, respectively.
Fig. 12 Impact of proposed strategy of defining innovative features - Case 1: (a) MAPE, (b) MAE(MW)
Fig. 13. Impact of proposed strategy of defining innovative features - Case 2: (a) MAPE, (b) MAE(MW).
According to the figures 12 and 13, the defined features incredibly decrease the forecasting
error in all the test months. Comparison of the methods in case 1 illustrates that the impact of
defining innovative features on improvement of forecasting results is substantial where it
brings down the monthly MAPE, 58.56% in July to 85.3% in January. The MAE is improved
too. For example, it diminished significantly from 334.71 to 43.63 i.e. 87% for December. For
case 2, the defined features reduce the monthly MAPE between 45.84% in May and 60% in
January while decreasing the monthly MAE 47.32% for April and 60.04% for January. The
whole year MAE and MAPE improvements are 80.8% and 77.99% for case 1 and 54.9% and
54.2% for case 2. The results of the comparison for four selected months can also be seen in
Table 4. It shows the impact of defining innovative features on improvement of forecasting
performance for four test months and the whole year of 2015. Overall, adding these features
reduces the MAPE and MAE considerably. This results indicates that the innovative features
are not only significantly relevant to output as shown in section 3, but also have considerable
impact on the precision of load forecasting.
Table 4. Impact of defining innovative features on forecasting accuracy.
January April July October Year(2015)
MAPE MAE MAPE MAE MAPE MAE MAPE MAE MAPE MAE
RF-NN[31] 2.01 319.93 2.01 257.81 1.42 229.05 1.96 256.89 1.90 273.61
Proposed
Method 0.29 41.75 0.36 40.27 0.59 80.85 0.40 44.78 0.42 52.45
Improvement
of Case 1 85.35% 86.95% 82.21% 84.38% 58.56% 64.70% 79.59% 82.57% 77.99% 80.83%
RF-SVR[32] 3.32 526.83 2.99 381.23 2.93 483.27 3.13 403.90 3.07 445.70
DTF-RF-SVR 1.33 210.53 1.61 200.84 1.27 213.56 1.51 190.94 1.41 200.86
Improvement
of Case 2 60.03% 60.04% 46.02% 47.32% 56.44% 55.81% 51.72% 52.73% 54.17% 54.93%
4-3 Load forecasting in holidays
Although the electrical load forecasting is a complex nonlinear problem linked with holidays
are more difficult to forecast than non-holidays and weekends because of their relative
infrequent occurrence [1]. Actually, most of the existing methods in the literature of electric
load forecasting focus only to evaluate the performance in normal days, includes working days
and weekends, or typical conditions and they often ignore the effect of anomalous loads that
occur on special days [25]. Ref [15,29] indicated necessity of specific forecasting model for
special days like holidays. Ref [2] investigated the difference between day-ahead and hour-
ahead load forecasting for four holidays very briefly. In ref [38], large errors for holiday days
due to infrequency and low number of patterns with similar characteristics are demonstrated.
We evaluate the accuracy of proposed methods in all holidays of 2015 and show the proposed
method has improved the prediction precision of special days as well as normal days.
Fig. 14 graphically compares hour ahead forecasts of the proposed DTF-RF-MLP with the four
benchmarks and ISO forecasts for all holidays of 2015. The proposed method clearly
outperforms SVR [24], RF-SVR [32], MLP-LM [36], RF-NN [31] and ISO forecast models in
terms of lower MAPE. These results establish the significant performance and accuracy of the
method for electrical hour-ahead load forecasting for special days.
The proposed method outperforms the benchmarks in four evaluation measures. It indicates the
method is consistently and significantly more accurate than its peers during all the test months
of 2015.
4-4 Simulation time
To accurately measure the computational time required for the proposed hour-ahead load
forecasting method, the mean of total required time for training and prediction of all the hours
of 2015, that includes 8760 samples, is taken as the simulation time. The FS has been done
offline based on the data of two last years (2013 and 2014 in this paper). The average simulation
time of proposed method for each hour-ahead prediction is 2.33 seconds. We ignore the time
for extracting new defined features due to their negligible required time (about a few Hundredth
of a second). This computational time indicates that the proposed method could successfully
be used for hour-ahead load forecasting application.
Fig. 14 Forecasting MAPE for all holidays of 2015
5- Conclusion
The major contribution of this paper is to propose a new data-driven method to forecast the
hour-ahead electricity. To improve the accuracy of the hour-ahead electrical load forecasting,
innovative features have been extracted from original load data to exploit the dynamics of the
time-evolving load data and applied with lag variables as FS inputs. FS not only reduces the
number of features but also improves the quality of data and forecasting performance.
The efficiency of the proposed model is demonstrated through various comparative
experiments using the three years’ real energy market data from New England ISO.
The experimental results show the advantages of the proposed method as follows:
The Defined features are not only significantly relevant to the output but also have
considerable impact on improving precision of hour-ahead load forecasting.
The accuracy and performance of the proposed model are satisfactory compared to
other benchmark models for STLF. The significantly lower forecasting error measures
such as MAPE, MAE, MDMAPE and DAME for approximately all test periods in 2015
confirm the predictive performance of the proposed model.
The results clearly prove the superiority of the proposed method in all 12 test months
of 2015. The proposed strategy produces good STLF results for one year as well. This
consistency proves the proposed method are more reliable and efficient than benchmark
models.
The proposed method also improves the precision of holidays’ load forecasting
considerably.
The comparative results show the proposed innovative feature definitions reduce
MAPE of STLF and increase the accuracy of models.
This method, though having considerable accuracy, only uses historical demand data.
Note that most of STLF methods rely on external inputs such as meteorological
forecasts or complicated forecast models to improve accuracy.
Besides being an accurate and reliable method, the proposed DTF-RF-MLP is easy to
implement due to its simplicity which makes it a right choice for industrial applications. The
acceptable computation burden of the proposed model also facilitates its application.
Further research could include a more extensive comparison of the proposed method with other
state-of-the-art models, as well as applying or modifying the proposed method for day-ahead
load forecasting, solar energy forecasting and electricity price forecasting.
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