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An Innovative Model Based on FCRBM for Load Forecasting in the Smart Grid

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An Innovative Model Based on FCRBM for Load Forecasting in the Smart Grid

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In this paper, an efficient model based on factored conditional restricted boltzmann machine (FCRBM) is proposed for electric load forecasting of in smart grid (SG). This FCRBM has deep layers structure and uses rectified linear unit (RELU) function and multivariate autoregressive algorithm for training. The proposed model predicts day ahead and week ahead electric load for decision making of the SG. The proposed model is a hybrid model having four modules i.e., data processing and features selection module, FCRBM based forecaster module, GWDO (genetic wind driven optimization) algorithm-based optimizer module, and utilization module. The proposed model is examined using FE grid data of USA. The proposed model provides more accurate results with affordable execution time than other load forecasting models, i.e., mutual information, modified enhanced differential evolution algorithm, and artificial neural network (ANN) based model (MI-mEDE-ANN), accurate fast converging short term load forecasting model (AFC-STLF), Bi-level model, and features selection and ANN-based model (FS-ANN).
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An Innovative Model Based on FCRBM
for Load Forecasting in the Smart Grid
Ghulam Hafeez1,2, Nadeem Javaid1(B
), Muhammad Riaz2, Khalid Umar3,
Zafar Iqbal4, and Ammar Ali1
1COMSATS University Islamabad, Islamabad 44000, Pakistan
nadeemjavaidqau@gmail.com
http://www.njavaid.com
2University of Engineering and Technology, Mardan 23200, Pakistan
3Bahria University Islambad, Islamabd 44000, Pakistan
4PMAS Agriculture University, Rawalpindi 46000, Pakistan
Abstract. In this paper, an efficient model based on factored condi-
tional restricted boltzmann machine (FCRBM) is proposed for electric
load forecasting of in smart grid (SG). This FCRBM has deep layers
structure and uses rectified linear unit (RELU) function and multivari-
ate autoregressive algorithm for training. The proposed model predicts
day ahead and week ahead electric load for decision making of the SG.
The proposed model is a hybrid model having four modules i.e., data
processing and features selection module, FCRBM based forecaster
module, GWDO (genetic wind driven optimization) algorithm-based
optimizer module, and utilization module. The proposed model is exam-
ined using FE grid data of USA. The proposed model provides more
accurate results with affordable execution time than other load fore-
casting models, i.e., mutual information, modified enhanced differential
evolution algorithm, and artificial neural network (ANN) based model
(MI-mEDE-ANN), accurate fast converging short term load forecasting
model (AFC-STLF), Bi-level model, and features selection and ANN-
based model (FS-ANN).
1 Introduction
Electric load forecasting is an indispensable decision-making tool for energy man-
agement in both sectors of SG i.e., supply side and demand side. It also plays
an important role in the secure and economic operations of SG [1]. Keeping
aforesaid objectives the recent research in SG focus load scheduling based on
optimization techniques [2,3]. However, the accuracy of electric load forecast-
ing models is compromised due to their influence on stochastic factors such as
climate change, human social activates, and country policies. Consequently, it
is difficult to improve the forecast accuracy and hardly realistic to take all the
influencing factors into account [4]. Thus, an intelligent model is required that
intelligently take the key parameters to improve forecast accuracy.
c
Springer Nature Switzerland AG 2020
L. Barolli et al. (Eds.): IMIS 2019, AISC 994, pp. 49–62, 2020.
https://doi.org/10.1007/978-3-030-22263-5_5
50 G. Hafeez et al.
Numerous models have been proposed and applied for an accurate load fore-
casting over the fast few decades such as legacy classical forecasting models
including exponential smoothing, regression models, autoregressive integrated
moving average (ARIMA) models, grey forecasting model (GM), and kalman
filters [5]. The aforementioned forecasting models forecast the electric load but
the accuracy is not up to the desired level due to their inherent limitations. The
linear regression models depend on historical data and are not suitable to solve
the non-linear problems. The ARIMA models taking into consideration previous
and present data points while ignore other influencing factors. The GM mod-
els can only solve the problems with exponential growth trends. To overcome
the aforementioned problems, in recent years, more effective models have been
proposed to forecast electric load, such as an artificial neural network (ANN),
multi-layer perceptron (MLP), radial basis fuzzy logic, machine learning, and
intelligent system [6]. Though these effective methods outperform legacy meth-
ods, however, the provide accuracy is not satisfactory due to their limitations.
The ANN-based models trapped into local minima and expert systems strongly
rely on supervised learning. In this regard, integrated and hybrid models are
developed [7], which are the combination of different individual models. The
hybrid models outperform than individual models in terms of forecast accuracy.
In this paper, a novel FCRBM based electric load forecasting (FCRBM-
ELF) model is proposed, which is a hybrid model. The major contributions are
demonstrated as follows:
The proposed model takes into account the exogenous influencing parameters
in addition to historical electric load data for accuracy improvement.
The new concept of candidates interaction is introduced for features selec-
tion. Also, the mutual information (MI) technique based features extraction
criteria are extended to measure the candidate’s interaction in addition to
their relevancy and redundancy process.
Due to better accuracy and fast convergence, RELU and is used with FCRBM
which none of the existing models have used.
The proposed GWDO algorithm is used in the optimizer to fine tune the
adjustable parameters for feature selection technique to improve the forecast
accuracy with affordable convergence rate.
The remaining paper is structured as follows: Sect. 2demonstrates related work,
Sect. 3briefly describes the proposed system architecture, in Sect. 4, simulation
results and discussions are described. Finally, Sect.5conclude the paper.
2 State of the Art Work
Electric load forecasting strategies are developed for many years in literature due
to its importance in the decision making of SG. The forecasting strategies are
categorized into four categories according to the forecasting period [8]. The first
category is the very short-term forecasting [9] which corresponds to less than one
day. The second category is the short-term forecasting which corresponds to the
An Innovative Model Based on FCRBM for Load . . . 51
forecasting period of one day to one-week [10]. The third category is medium-
term forecasting which corresponds to one week and a year ahead forecasting [11].
The fourth category is the long-term forecasting which corresponds to more than
a year ahead forecasting [12]. Statistical tools and AI-based tools are commonly
used for electric load forecasting. The recent and related work is summarized in
Table 1.
3 The Proposed System Architecture
In literature, many authors used ANN based forecaster for load prediction due
to its capability to predict the nonlinearity of consumers load. However, the per-
formance of ANN-based models is not satisfactory in terms of accuracy. Thus,
some authors integrated optimization module with ANN based forecaster, which
improves significantly the forecast accuracy. However, the accuracy is improved
at the cost of slow convergence rate. Moreover, the ANN-based models are suit-
able for small data size while their performance is degraded as the data size
increases. Thus, we proposed a new electric load forecasting model based on
FCRBM as shown in Fig. 1. The proposed model is subjected to accuracy, con-
vergence rate, and scalability. The proposed system architecture comprises of
four modules: (1) data processing and feature selection module, (2) FCRBM
based forecaster module, (3) GWDO based optimizer module, and (4) utiliza-
tion module. The detailed description is as follows:
3.1 Data Processing and Features Selection Module
The input data including historical load data and exogenous data (temperature,
humidity, wind speed, and dew point) is fed into the data processing and features
selection module. At first, the data cleansing is performed to recover the missing
and defective values. Then, the clean data is normalized to remove the outliers
and make the data within the limit of the activation function. The input data
(X) includes electric load data (P(h, d)), temperature data (T(h, d)), humidity
data (H(h, d)), dew point (D(h, d)), and wind speed (W(h, d)). The hshows
particular hour and dshows particular day of historical data. The tempera-
ture, humidity, dew point, and wind speed are called exogenous variables. The
normalized data is passed to through irrelevancy filter, redundancy filter, and
candidate interaction phase subjected to removal of irrelevant, redundant, and
nonconstructive information. The detailed description of relevancy, redundancy,
and candidates interaction phases of features selection technique are as follows:
Relevancy Operation The relevance of candidates input to the target vari-
ables is significant for abstractive features selection. For relevancy measurement
in literature many techniques are used in which MI features selection technique
is good. The MI measures the relevance between two variables xand y.The
MI measurement is interpreted as observing yby on xand vice versa. The
52 G. Hafeez et al.
Table 1. Recent and related work summary
Techniques Objectives Dataset Remarks
ARIMA and exponential
smoothing [9]
Forecast accuracy improvement for
real-time scheduling of power
generation
Great Britain
grid
The accuracy is improved for univariate methods while
the accuracy is low for multivariate methods
ANN and self-organizing
map [13]
Decision support system to
commercialize company bidding
Spanish grid This model used meteorological and load data and
ignored exogenous parameters which have a strong
impact on the forecast accuracy
Differential polynomial
neural network [14]
To reduce the generation cost and
spinning reserve capacity
Canadian grid This model has less accuracy and slow convergence which
have a direct impact on spinning reserve and cost
ANN, ARIMA, and GM
[15]
Accuracy improvement of the bulk
power system
Fuj i an pr ovi nce
of China
The accuracy is improved by incorporating large
exogenous parameters at the expense of slow convergence
rateandhighcomplexity
Reglet and Elman neural
network [16]
Improvement of the accuracy and
capability for effective power system
operation
AEMC This model have large complexity that directly impacts
the convergence rate
Support vector regression
[17]
Accurate load forecasting to minimize
energy imbalance and its associated
cost
Irish CER The parameters are optimally adjusted by the intelligent
algorithm which improved the forecast accuracy at the
expense of high execution time
ARMAHX and
quasi-newton algorithm
[18]
Forecast accuracy improvement for a
market agent and system operators
Spanish and
German energy
market
The accuracy is improved by incorporating sigmoidal
function, however, the execution time and complexity is
increased
ANN, SVR, and fuzzy
interaction regression [19]
Resilience improvement against data
integrity attacks
GEFC 2012 The resiliency of the power system is improved at the cost
of high modeling complexity
MI, ANN, and mEDE
[21]and[20]
Accuracy and convergence rate
improvement for EKPC and Daytown
grid of USA
PJM market This model is suitable for small data size and their
performance are degraded for large data size
ANN-based hybrid
models [22]and[23]
Accuracy improvement of microgrid PJM market The ANN-based models improved the forecast accuracy
at the cost of high execution time
An Innovative Model Based on FCRBM for Load . . . 53
Fig. 1. The proposed system architecture
MI for continuous variables xand yis defined I(x;y) for both individual
(p(x),andp(y)) and joint probability distribution (p(x, y)). Assume that
S={x1,x
2,x
3,...,x
M},(1)
where Srepresents the set of candidate inputs and yis the target variable.
The relevance of each candidate input with target variable yare checked. The
relevance of candidate input xiwith target variable yis defined by the following
Equation
D(xi)=I(xi;y),(2)
where D(xi) represents candidate inputs to target variables.
Redundancy Operation Many authors modeled the redundancy operation
between the candidate inputs. The purpose is to remove the redundant infor-
mation from the input data to improve convergence rate. The redundancy is
evaluated in terms of the mutual information among the two candidate inputs.
In literature, authors demonstrated that closely related candidate inputs reduce
the performance of feature selection technique. The reason is that two candidate
inputs have a large number of mutual information and less redundant informa-
tion about the target variable. So, a variable with less redundant information
54 G. Hafeez et al.
about the target variable which may be incorrectly count as redundant and
will be discarded, while it may be the key feature for forecaster. To overcome
the aforementioned problem a redundancy measure based on interaction gain is
modified as:
RM(xi,x
s)=Ig(xi;xs;y)
=I[(xi,x
s); y]I(xi;xs)I(xs;y),(3)
where RM(xi,x
s) is the redundancy measure, xi,x
sare candidate inputs, and
yis the target variable. The Ig can be mathematically modeled in terms joint
and individual entropy as:
Ig(xi;xs;y)=H(xi,x
s)+H(xi,y)+H(xs,y)H(xi)H(xs)H(y)H(xi,x
s,y),
(4)
where H(xi), H(xs), and H(y) denote individual entropy and H(xi,x
s),
H(xi,y), H(xs,y), and H(xi,x
s,y) denote joint entropy.
Interaction Session In [22], used redundancy and irrelevancy filters for fea-
ture selection. However, the individual features may be irrelevant but become
relevant when used together with other input candidates. Thus, the feature selec-
tion technique can be extended to interaction among the candidate inputs. If two
candidate inputs xiand xshave redundant information about target y, then the
joint MI of both candidates with ywill be less than the sum of individual MIs.
Thus, the result will be negative according to Eq. 3, which indicates redundant
features xiand xsfor the forecaster. The absolute value of Eq.3shows the
amount of redundancy. On the other hand, if xiand xscandidate inputs inter-
act with target ytheir interaction causes joint (xiand xs) MI with target y
greater than the sum of individual MIs. Thus, the positive value of Eq.3indi-
cates interacting features and its absolute value shows the amount of interaction.
Hence, for redundancy and interaction the Eq. 3can be modified as:
RM(xi,x
s)={Ig(xi;xs;y),if Ig(xi;xs;y)<0
0 otherwise (5)
In(xi,x
s)=Ig(xi;xs;y),if Ig(xi;xs;y)>0
0 otherwise (6)
where Eq. 5is modified equation for redundancy measure and Eq. 6is for inter-
action measure. Thus, the abstractive features are selected and fed into the
forecaster module based on FCRBM.
3.2 FCRBM Based Forecaster Module
The purpose of this module is to devise a framework which is enabled via learn-
ing to forecast the future electric load. From Sect. 2it is concluded that all
forecast models are capable to predict nonlinear electric load profile. Thus, we
chose FCRBM for forecaster module due to two reasons: (a) it predict the non-
linear electric load with reasonable accuracy and convergence rate, (b) and its
An Innovative Model Based on FCRBM for Load . . . 55
performance is improving with the scalability of data. FCRBM is a deep learning
model. It has four layers i.e., hidden layer, visible layer, style layer, and history
layer. Each layer has a particular number of the neuron. In the forecaster module,
FCRBM is activated by rectified linear unit (RELU) activation function. The
RELU is chosen among the activation function because it overcomes the prob-
lems of overfilling and vanishing gradient, and has fast convergence as compared
to other activation functions. The mathematical model of RELU is mentioned
in Eq. 7.
f(x) = max(0,x)
f(x)1ifx0
0 otherwise
(7)
The training and learning procedure iterates for a number of epochs to forecast
the future load. To update weight and biases during training processes authors
used different algorithms, i.e., gradient descent and backpropagation, levenberg-
marquardt algorithm [23], and multivariate autoregressive algorithm [21]. The
levenberg-marquardt algorithm trains the network faster as compared to gradient
descent and backpropagation. Thus, the multivariate autoregressive algorithm
is used for network training due to its fast convergence and better performance.
The selected feature of data processing module S1,S
2,S
3,...S
nis fed into the
forecaster module, where the forecaster constructs training and testing data
samples. The first three years of data samples are used for network training. On
the other hand, the last year data samples are used for testing. The purpose is
to enabled FCRBM based forecaster module via training to forecast the future
load. The forecaster module returns error signal and the weights and biases are
adjusted as per multivariate autoregressive algorithm. This error signal is fed
into the optimization module to improve the forecast accuracy.
3.3 GWDO Based Optimizer Module
The preceding module returns the future predicted load with some error, which
is minimum as per the capability of FCRBM, RELU, and training algorithm.
To further minimize the forecast error the output of the forecaster module is fed
into the optimizer module. The purpose of the optimizer module is to minimize
the forecast error. Thus, the error minimization becomes an objective function
for the optimizer module and can be mathematically modeled as:
Minimize
Rth ,I
th,C
i
Error (x)x∈{h, d}(8)
where Rth is redundancy threshold, Ith is irrelevancy threshold, and Ciis can-
didates interaction. The optimizer module is based on our proposed GWDO
algorithm. The optimizer module optimizes Rth ,Ith ,andCiand feedback these
parameters to data processing module. In data processing module, feature selec-
tion technique use optimized values of Rth ,Ith thresholds and Cicandidates
interaction for optimal selection of features. The integration of optimizer mod-
ule with the forecaster module increase forecast accuracy at the cost of high
56 G. Hafeez et al.
execution time. Usually, the integration of optimizer with the forecaster module
is preferred for those applications where accuracy is of high importance compared
to convergence rate. For optimization, various techniques are available like lin-
ear programming, non-linear programming, convex programming, quadratic pro-
gramming, and heuristic techniques. Linear programming is avoided because the
optimization problem is non-linear. The non-linear programming is applicable
here and returns more accurate results at the cost of large execution time. The
convex optimization and heuristic optimization suffers from slow and premature
convergence, respectively. Similarly, the DE [22] and mEDE [21] are not adopted
because of slow convergence, low precision, and trapped into optimum. To cure
the aforementioned problems we proposed GWDO. In other words, GWDO algo-
rithm is preferred because it provides an optimal solution with a fast convergence
rate. The proposed GWDO algorithm is a hybrid of GA and WDO. The GA
enables the diversity of population and WDO has fast convergence. The fore-
casted future load is utilized in the utilization module for planning, operation,
and unit commitment.
3.4 Utilization Module
The forecasted load is utilized for long term planning that needed state permits
financing, right of ways, transmission and generation equipment, power lines
(transmission lines and distribution lines), and substation construction.
4 Simulations Results and Discussions
For the performance evaluation of the proposed FCRBM-ELF model simulations
are conducted in Matlab 2016, which is installed on a laptop having specifica-
tions of Intel(R) Corei3-CPU @2.4GHz and 6GB RAM with Windows 10. The
proposed FCRBM-ELF model is compared with existing models i.e., MI-mEDE-
ANN [20], AFC-STLF [21], Bi-level [22], and FS-ANN [23]. The aforementioned
models are chosen due to closer similarity with the proposed model. For testing
the proposed model real time hourly load data of FE grid is used. The dataset
is taken from publicly available pennsylvania jersey maryland (PJM) [25]. The
dataset is also considered in [21]. The dataset is of four years from 2014 to 2017.
The first three years of data is used for training the FCRBM and last year data
is for testing. The parameters used in simulations can be justified in [21]. The
parameters listed are kept constant for existing and proposed model subjected
to a fair comparison. The proposed model is tested in terms of four performance
metrics, i.e., MAPD, RMSD, correlation coefficient (R) and execution time.
The first three performance metrics correspond to accuracy, which is defined
as:
Forecast accuracy: accurcay = 100-Error().
The last performance metric (execution time) corresponds to convergence rate,
which is defined as:
An Innovative Model Based on FCRBM for Load . . . 57
Convergence rate: execution time, the time required for a forecast model to
complete its execution. The forecast model which have small execution time
converges fast and vice versa. The execution time in this paper is measured
in seconds.
The detailed description as follows:
4.1 Hourly Electric Load Prediction
The evaluation of hourly forecasted electric load of FE grid for the proposed fore-
cast model (FCRBM-ELF) vs existing models (MI-mEDE-ANN, AFC-STLF,
Bi-level, and FS-ANN) is illustrated in Fig. 2. It is clear that the proposed
FCRBM-ELF model effectively forecasts the future load of FE grid. Both ANN
and FCRBM based forecasters are capable to capture the nonlinearities of his-
torical load time series data. The nonlinear prediction capability is due to the
use of nonlinear activation functions (AFs) i.e., sigmoidal, rectified linear unit
(RELU), and tangent hyperbolic (Tanh). The existing models (MI-mEDE-ANN,
AFC-STLF, Bi-level, and FS-ANN) used sigmoidal AF and our proposed model
select RELU because it has a fast convergence rate and solves the problems of
overfitting and vanishing gradient. Figure 2depicts that the proposed FCRBM-
ELF model profile closely follows the target load profile as compared to exist-
ing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN). It is clearly
seen that the percentage error of the proposed FCRBM-ELF model is 1.10%,
MI-mEDE-ANN is 2.2%, AFC-STLF is 2.1%, Bi-level is 2.6%, and FS-ANN is
3.6%, respectively.
0 2 4 6 8 10 12 14 16 18 20 22 24
620
640
660
680
700
720
740
760
780
800
Target
Fig. 2. Hourly load prediction of FE grid
58 G. Hafeez et al.
4.2 Seasonal Electric Load Forecasting: Weekly Prediction with
Hourly Resolution
The weekly electric load forecasting with hourly resolution is depicted in Fig. 3.
This is the week ahead forecasted electric load of FE grid. It is worth mention-
ing that the proposed FCRBM-ELF model has better results as compared to
the existing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN). The
proposed FCRBM-ELF model closely follows the target load which is clearly
depicted in the zoomed box. The observation in terms of numerical values is
that the percentage error of the proposed FCRBM-ELF model is 1.12%, MI-
mEDE-ANN is 2.23%, AFC-STLF is 2.0%, Bi-level is 2.5%, and FS-ANN is
3.4%, respectively. The well-grounded reasons the for better performance of the
proposed FCRBM-ELF model are the use of deep layer layout of FCRBM with
RELU and integration of GWDO based optimization module.
Fig. 3. Seasonal electric load forecasting for a week with an hourly resolution of FE
grid
4.3 Performance Evaluation in Terms of Error and Convergence
Rate
The performance analysis in terms of accuracy (error) and convergence rate (exe-
cution time) is illustrated in Figs. 4and 5. The error indicates how much the
forecasted value deviates from the target value. The smaller value of error results
in high accuracy and vice versa. The error performance in terms of numerical val-
ues for both day and week ahead forecast is shown in Figs.4and 5, respectively.
The percentage error of FCRBM-ELF, MI-mEDE-ANN, AFC-STLF, Bi-level,
and FS-ANN, 1.10, 2.2, 2.23, 2.6, and 3.6%, respectively. From the above dis-
cussion, it is concluded that Bi-level strategy is better than FS-ANN strategy
in terms of error performance. The reason for this better performance is that
An Innovative Model Based on FCRBM for Load . . . 59
forecast error is minimized by the integration of EDE based optimization mod-
ule. However, this percent error is minimized at the cost of more execution time
as depicted in Fig. 5. This Figure shows that the execution increases from 20 to
95 s as the optimization module is integrated. Thus, it is concluded that there
exists a tradeoff between accuracy and convergence rate. The proposed FCRBM-
ELF model reduces this execution time due to the following reasons: (i) GWDO
3is used in the optimization module instead of EDE and mEDE due to faster
convergence, (ii) RELU is used instead of sigmoidal AF and multivariate autore-
gressive algorithm, (iii) FCRBM is used which performs better than ANN, (iv)
for data pre-processing data cleansing and normalization are used, and (v) for
features selection redundancy, irrelevancy, and candidate interaction process are
used, while the existing models only use redundancy and irrelevancy. The afore-
mentioned modifications in the existing models (MI-mEDE-ANN, AFC-STLF,
and Bi-level) leads to reduce the execution time of 38 seconds. On the other
hand, the proposed FCRBM-ELF model accuracy is improved as compared to
existing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN) [refer to
Fig. 4]. However, the execution time of the proposed FCRBM-ELF model is more
as compared to FS-ANN because with FS-ANN model no optimization module
is used [refer to Fig. 5]. Thus, it is concluded from the above discussion that
the proposed FCRBM-ELF model outperforms the existing models in terms of
convergence rate and accuracy.
Fig. 4. FE grid Electric load forecast: accuracy analysis in terms of percentage error
60 G. Hafeez et al.
Fig. 5. FE grid Electric load forecast: accuracy analysis in terms of Convergence rate
5 Conclusion
In this paper, the electric load forecasting problem is described. This problem is
very complex due to the nonlinear behavior of consumers and influencing factors.
Thus, an efficient electric load forecasting model based on FCRBM is proposed
to provide accurate load forecast with affordable execution time. The proposed
model is examined on FE grid data of USA. The obtained results are compared
with other load forecasting models (MI-mEDE-ANN, AFC-STLF, Bi-level, and
FS-ANN) in terms of both accuracy and convergence rate. It is validated that
our proposed FCRBM-ELF model outperforms the other models in terms of
forecast accuracy and convergence rate.
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Chapter
This chapter addresses the status of artificial intelligence (AI) as a central element in smart grid (SG) while focusing on the recent progress of research on machine learning techniques to pave the future work in the SG area. The SG framework provides a performance toolkit based on information and communication technologies. The SG paradigm supervises and promotes grid operations at a high level of expertise. AI systems have attributed to the realization of sustainable development goals including the vital integration of renewable energy sources (RES). The scarcity of conventional energy resources in the near future and their increasing threats to the environment extremely require the transition toward RES. The bulk penetration of RES into the electrical grid leads to unstable and volatile power generation. The chapter presents the commonly applied AI methods to the SG system and the key elements of the evaluation procedure.
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