Optimal Power Generation in Energy-Deficient Scenarios Using Bagging Ensembles

Received August 9, 2019, accepted September 28, 2019, date of publication October 11, 2019, date of current version November 6, 2019.
Digital Object Identifier 10.1109/ACCESS.2019.2946640
Optimal Power Generation in Energy-Deficient
Scenarios Using Bagging Ensembles
KASHIF MEHMOOD 1,2, HAFIZ TEHZEEB UL HASSAN3, ALI RAZA 2,
ALI ALTALBE4, AND HAROON FAROOQ 5
1School of Electrical Engineering, Southeast University, Nanjing 210096, China
2Department of Electrical Engineering, The University of Lahore, Lahore 54000, Pakistan
3Department of Electrical Engineering, University of the Punjab, Lahore 54000, Pakistan
4Department of Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5Department of Electrical Engineering, Rachna College of Engineering and Technology, Gujranwala campus, University of Engineering and Technology, Lahore
54000, Pakistan
Corresponding author: Kashif Mehmood (kashifzealot@gmail.com)
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No.
(DF-656-611-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support.
ABSTRACT This paper presents an improved technique for optimal power generation using ensemble
artificial neural networks (EANN). The motive for using EANN is to benefit from multiple parallel processor
computing rather than traditional serial computation to reduce bias and variance in machine learning. The
load data is obtained from the load regulation authority of Pakistan for 24 hours. The data is analyzed on an
IEEE 30-bus test system by implementing two approaches; the conventional artificial neural network (ANN)
with feed-forward back-propagation model and a Bagging algorithm. To improve the training of ANN and
authenticate its result, first the Load Flow Analysis (LFA) on IEEE 30 bus is performed using Newton
Raphson Method and then the program is developed in MATLAB using Lagrange relaxation (LR) framework
to solve a power-generator scheduling problem. The bootstraps for the EANN are obtained through a disjoint
partition Bagging algorithm to handle the fluctuating power demand and is used to forecast the power
generation. The results of MATLAB simulations are analyzed and compared along with computational
complexity, therein showing the dominance of the EANN over the traditional ANN strategy that closed
to LR.
INDEX TERMS Artificial neural networks, bootstrap aggregation, bagging algorithm, disjoint partition,
economic dispatch, optimal power generation.
I. INTRODUCTION
Interconnected power systems are foundations on which
modern civilization rests. The economy of any developing
country, like Pakistan, is based on the provision of cheap and
abundant sources of electrical energy. Thus, optimal power
generation using better scheduling of available generating
units is essential to supply economical energy to consumers
and thus enhance the sustainability of power systems.
The foremost economic influences on any modern power
system are the cost of generating active power and reduc-
ing system reactive power flow. In practical power systems,
hundreds of generating units run in parallel to meet the load
demand. So, it is essential to run power plants economically.
The associate editor coordinating the review of this manuscript and
approving it for publication was Nan Liu .
The economic operation of a power plant is a sub-problem
of the unit commitment (UC) [1]. The generation schedul-
ing problem for energy deficient scenarios or large UC has
become the subject of considerable discussion during the last
few years [2]–[6]. Mathematical programming and heuristic
methods have been extensively used to define UC for power
plants [2], [5].
Economic dispatch (ED) problems have been investigated
through various heuristic, intelligent and hybrid techniques
such as; evolutionary programming (EP) [7], artificial bee
colony algorithm (ABC) [8], particle swarm optimization
(PSO) [9], hopfield neural network with quadratic program-
ming (HNN-QP) [10] and some others are summarized in
the Table 1. Although the discussed methods are useful in
optimizing the production cost for ED problems, but does
not converge rapidly [11], [12]; particularly in the case when
generation schedule is on an hourly basis to overcome the
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K. Mehmood et al.: Optimal Power Generation in Energy-Deficient Scenarios Using Bagging Ensembles
TABLE 1. Economic dispatch investigation via heuristic, intelligent and
hybrid techniques.
power shedding in an under-developed country like Pakistan.
Artificial neural networks (ANN) attracted attention to solv-
ing ED problems optimally as it has high computational
speed, a high convergence rate even for short intervals and
self-error correction ability, unlike other intelligence tech-
niques [19], [20].
In [19], a dynamic neural network is employed to solve
the combined economic and emission dispatch problem with
fast convergence. Fukuyama et al. employed neural network
techniques to solve the ED problem considering security con-
straints [21]. Liang applied neural network based re-dispatch
method for solving the spinning reserve constrained ED prob-
lem [18]. Chan et al. presented an artificial neural network
and genetic algorithm to optimize the load distribution for a
chiller plant [20]. However, ANN alone may undergo pre-
mature convergence and a tendency to be trapped at a local
optimum [22], which results in a significant error in learning.
The error in ANN learning is reduced by using bootstrap
aggregation [23], which gives better precision, improved gen-
eralization, and prediction along with reduced machine learn-
ing errors like bias and variance. Thus, a research objective
is to overcome the mentioned shortcomings and to explore
economic-dispatch optimally using Lagrange relaxation with
an enhanced neural network (NN) by adopting a bootstrap
aggregation algorithm for energy deficient scenarios. Such an
enhanced neural network is termed an ensemble of artificial
neural networks (EANN).
The proposed neural network ensemble approach is applied
to the IEEE 30-bus system and evaluated for a day on an
hourly basis. There are six generators and twenty load buses.
The constraints considered are generator limits, transmission
line losses, and the power demand. The input data for the
neural network is described by a 20 × 24 matrix which
gives the power demand distribution among 20 buses during
24 hours. The target data for the neural network is via a
6 × 24 matrix that describes the generation of six gener-
ators for a day. Multiple neural networks are incorporated
by applying a Bagging algorithm to create an ensemble of
neural networks. The predictions from the individual neural
networks are aggregated by an algebraic method to get the
ensembled output. Finally, a comparison between ANNs and
EANNs show the predominance of the proposed method.
The remainder of the paper is organized as follows:
problem formulation of economic dispatch is described in
section II. In section III, system description and power
dispatch is discussed. In sections IV and V, the artificial
neural network with feed-forward back-propagation model
and ensemble of artificial neural network with Bagging are
presented, respectively. Simulation results are presented in
section VI, with conclusions then drawn.
II. ECONOMIC DISPATCH PROBLEM FORMULATION
Thermal power plants operate in parallel to fulfill the demand
of different load centers. Typically, cost of power generation
is not the same for each generating unit as this depends
upon the operating efficiency and fuel cost of a unit, and
transmission losses. For optimal generation, minimization
of the cost of real power generated from all units must be
achieved. The amount of fuel consumed by a generating unit,
and in turn the fuel cost, depends upon the produced power
at a specific operating point as shown in Fig. 1 [1].
FIGURE 1. (a) Heat-rate curve (b) Fuel-cost curve.
A generating unit is assumed to have a quadratic cost
function in terms of its produced active power [1]:
CGi = αi + βiPGi + γiP2
Gi (1)
where CGi is the cost of the ith power generating unit, PGi is
the real power generated by the ith generating unit, and αi, βi
and γi are the cost coefficients.
The constraint equations for optimal generation are given
by (2), (3) and (4):
n
i=1
PGi = PD + PL (2)
where ‘n’ is the total number of generating plants, PD is the
load demand, and PL is the total transmission loss.
PL =
n
i=1
n
j=1
PGiBijPGj +
n
i=1
B0iPGi + B00 (3)
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Transmission losses as a function of generator powers are
expressed through B-coefficients and given by Kron’s loss
formula is described in [24]:
Where PGi and PGj are real power generation at the ith
and jth generating units, respectively. Bij and B0i are the loss
coefficients (constant for certain conditions), and B00 is a loss
constant. However, the generation limits of units are given by:
PGi(min) ≤ PGi ≤ Pi(max) (4)
From the Lagrange method, the overall objective func-
tion, including constraint limits and transmission line losses,
becomes:
F = Ct+λ(PD+PL−
n
i=1
PGi) +
n
i=1
µi(max)(PGi − PGi(max))
+
n
i=1
µi(min)(PGi − PGi(min)) (5)
The constant µi(max) = 0 when Pi < Pi(max) and µi(min) =
0 when Pi > Pi(min). These constants play an active role when
constraints are violated, specifically Pi > Pi(max) and Pi <
Pi(min). Ct and λare the total cost and incremental cost of all
generating units, respectively, and Ct is defined as:
Ct =
n
i=1
CGi (6)
The following conditions hold if the function ‘F’ is to be a
minimum:
∂F
∂PGi
= 0
∂F
∂λ
= 0 (7)
∂F
∂µi(max)
= PGi − PGi(max) = 0 (8)
∂F
∂µi(min)
= PGi − PGi(min) = 0 (9)
If PGi is within its limits, then µi(min) and µi(max) are zero
and the Lagrange (λ) of (7) is:
∂Ct
∂PG
+ λ(0 +
∂PL
∂PGi
− 1) = 0 (10)
The incremental transmission line losses are incorporated
as the partial derivative of (3) with respect to the real power
generation PGi:
∂PL
∂PGi
= 2
n
j=1
BijPGj + B0i (11)
Substituting (1) and (11) into (6) and simplifying gives:
γGi
λ
+ Bii PGi +
n
j=1
j=1
BijPGj =
1
2
1 − B0i −
βGi
λ
(12)
Equation (12) for all units, results in matrix form,
equation (13), for all linear equations.
Solving (13) gives ED for an estimated value of λ. An itera-
tive approach is employed to find optimal generation, until all
FIGURE 2. Single line diagram of the IEEE 30-bus test system.
TABLE 2. Cost function parameters of the generators.
constraints are satisfied, the PG matrix from (13) is calculated
and the total cost of generation is obtained from (6). More
details of the Lagrange method can be found in [1].










γG1
λ
+ B11 B12 · · · B1n
B21
...
γG2
λ
+ B22 · · · B2n
Bn1
...
Bn22
...
...
· · ·
γGn
λ
+ Bnn















PG1
PG2
...
PGn





=
1
2









1 − B01 −
βG1
λ
1 − B02 −
βG2
λ
...
1 − B0n −
βGn
λ









(13)
III. SYSTEM DESCRIPTION AND POWER DISPATCH
Lagrange relaxation and the ensembled artificial neural net-
work (EANN) are applied on the IEEE 30-bus system,
as shown in Fig. 2, to not only solve the ED problem optimally
but also to boost and enhance system learning. Generation
scheduling is done on an hourly basis to overcome the power
shedding. EANN is explained in detail in section 5.
The beta loss coefficients matrix ‘Bij’ of order 6×6 for the
IEEE 30-bus system with 6 generators is obtained from the
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TABLE 3. Optimal power generated by employing lagrange relaxation method for supervised learning of the ANN.
power flow calculations using the Newton-Raphson method
and is given by (14), as shown at the bottom of this page, [23].
Other loss coefficients, B0i and B00, are also presented.
The cost function parameters of the six generators in the
IEEE 30-bus system are given in Table 2. [25].
α, β and γ are the cost coefficients in Table 2. The col-
umn ‘Gen. Bus’ give the bus to which a generator is con-
nected. The maximum generation from all the six generators
is 435 MW while the minimum generation is 117 MW. The
daily load data is obtained from the National Power Control
Centre (NPCC) of Pakistan and is shown in Fig. 3, and is used
for optimal generation.
Optimal generation for the IEEE 30-bus system is obtained
by applying the Lagrange method for supervised learning of
the ANN, as given in Table 3.
IV. FEED-FORWARD BACK-PROPAGATION
NEURAL NETWORK
The artificial neural network is derived from the biological
neural network (BNN). ANNs are not as complex but the data
handling method is similar to the BNN. The organization of
FIGURE 3. Daily load curve obtained from NPCC-Pakistan.
an ANN is shown in Fig. 4. It is an interconnected system that
is capable of quickly solving highly non-linear issues.
A multilayer feed-forward back-propagation neural net-
work is employed here instead of a single layer neural
network.
Each layer is associated with the neighboring layer which
means all the neurons in each layer are connected to all
the neurons in a neighboring layer, as shown in Fig. 5 for
a three-layer feed forward back-propagation NN. The first
Bij =








2.18E − 04 1.03E − 04 9.00E − 06 −1.00E − 05 2.00E − 06 2.70E − 05
1.03E − 04 1.81E − 04 4.00E − 06 −1.50E − 05 2.00E − 06 3.00E − 05
9.00E − 06 4.00E − 06 4.17E − 04 −1.31E − 04 −1.53E − 04 −1.07E − 04
−1.40E − 04 −1.50E − 05 −1.31E − 04 2.21E − 04 9.40E − 05 5.00E − 05
2.00E − 06 2.00E − 06 −1.53E − 04 9.40E − 05 2.43E − 04 0.00E + 00
2.70E − 05 3.00E − 05 −5.00E − 05 5.00E − 04 0.00E + 00 3.58E − 04








B0i = [ 1.40E − 05 ]
B00 = [ −3.00E − 06 2.10E − 05 − 5.60E − 05 3.40E − 05 1.50E − 05 7.80E − 05 ] (14)
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FIGURE 4. Basic construction of an ANN.
FIGURE 5. A three-layer feed-forward back-propagation neural network.
layer is the input layer, the last layer is the output layer
and the intermediate layer is termed a hidden layer. The
number of hidden layers and selection of neurons affects the
results [26]. Because of this composition, a multilayer feed
forward neural network is trained (by back-propagation) to
learn non-linear patterns in linear space. Back-propagation is
a form of supervised training, where a network is provided
with both sample inputs and target values.
The input values are fed directly to the output layer via a
weight matrix as in Fig. 4. Inputs (x1, x2..., xN) and their
respective weights (w1j, w2j, . . ., wnj) are sent to the transfer
functions (TF) of the hidden layers. Activation function Oj is
added to TF to check whether or not the output is produced
through comparison with the threshold value θj. TF governs
the threshold values. The difference between the ANN and
desired values gives the error, which controls ANN training.
Thus, the error is fed-back to re-set the weights, until the
ANN outputs resemble the desired values. Neural network
training is a repetitive process. Repetition continues until
the stopping criteria is met, namely a specified mean square
error (MSE).
In this study, the developed supervised neural network is
trained using the parameters in Table 4. The input to the
neural network is power demand which is divided among
20 load busses while the output of the neural network is the
power generated on 6 busses, obtained from the Lagrange
TABLE 4. Training parameter of a single neural network.
relaxation method. This generated power fulfills the system
constraints and hence optimizes generation cost.
V. ENSEMBLE OF ARTIFICIAL NEURAL NETWORK
A. BOOTSTRAP AGGREGATION
Artificial neural network performance is satisfactory for spec-
ified values but when the data values constantly vary, as in
this study, in hours, then the ANN experiences under or
over fitting because of reduced generalization ability. Differ-
ence between the anticipated and actual values occurs even
after several ANN times training periods. This error occurs
because of the flawed learning process. The three main error
factors in learning are: variance, noise and bias [26].
Error = Variance + Noise + Bias (15)
Large variance is the reason of over fitting and large bias
causes under fitting of the data. Generalization of the ANN
to adjust with the new values increases variance and bias are
reduced to a minimum, and then the data-set will not undergo
under and over fitting. Additionally, the percentage change in
input and output values during the learning process decreases,
hence prediction improves.
Thus, bootstrap aggregating is employed to refine and
enhance the precision and stability of the machine learning
algorithm, ANN. It reduces variance and bias which helps
avoid over and under fitting, respectively [26], [27]. The
Bagging structure is shown in Fig. 6. Bootstrap aggregating
is also called bagging and is classified as follows:
1. Disjoint partitions
2. Small bags
3. No replication small bags
4. Disjoint bags
Disjoint partitions bagging is implemented here, by using
MATLAB, as it is more effective and thus outperform other
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FIGURE 6. A typical idea for the ensemble of neural networks.
FIGURE 7. Original dataset D.
FIGURE 8. Disjoint partitions (3 bootstraps).
techniques [28]–[30]. To understanding disjoint partitions,
assume the data set D as shown in Fig. 7. A subset is formed
by random selection of elements from the defined data set
without replication. For this, each certain element is taken
only once as shown in Fig. 8. These subsets are called Boot-
straps.
B. PROPOSED METHOD
The proposed method for optimal generation uses the follow-
ing steps:
1. Real data set generation
2. ANN design
3. Bootstrap design
STEP 1: The employed dataset (power demand against each
hour) is from the National Power Control Centre (NPCC)
in-charge of controlling and monitoring electric power flow
in Pakistan’s power system, shown in Fig. 3. This dataset is
tested on the IEEE 30-bus system. The worst-case scenario
of zero spinning reserve is considered for optimal power
generation.
STEP 2: The initial step for the formation of the ANN
classifier, is the selection of the target and input datasets. The
input data for the neural network is power demand, a 20 ×
24 matrix, among 20 buses during 24 hours. The target values
for the NN are a 6 × 24 matrix that describes the generation
of six generators for a day. The target data is obtained from
the Lagrange method for supervised learning. The biases
and weights of each neuron are randomly generated. The
specifications in Table 4 are used for ANN classifiers.
The training of the classifiers employs the Levenberg–
Marquardt Back Propagation algorithm, for fast convergence
with reduced error. Gradient descent is employed to reset the
bias and weights in the adaption learning process since the
convergence of ‘batch gradient descent with momentum’ is
fast enough for feed-forward networks. Gradient descent also
reduces the mean square error (MSE) [31]:
MSE =
1
n
n
I=1
e(i)2
=
1
n
n
i=1
(xi − zi)2
(16)
where n is the number of samples, xi is the prediction and is
the target value.
The data is divided as: 70% is used for training, 15% is for
validation to reduce over-fitting, and the remaining 15% is
used to predict the ANN final value.
STEP 3: Several ANN training sessions reveal a devia-
tion from the target value; mainly when the input dataset
varies abruptly. So Hypothetical 30 bootstraps are created
with different Network topology and Training Algorithms.
Bootstraps re-sample the initial data before ANN training
to improve the generalization ability. The Bootstrap ANN
(EANN) result is closer to the target with reduced percentage
error. EANN and ANN outputs are compared and presented
in the result section.
The proposed methodology is described in the algorithm
as:
1. Initialization of the original training data set D for
i = 1, 2, 3 . . . n.
2. Formation of a fresh data set Di called bootstrap of
the same size D by arbitrary choosing some data of
training samples from the set D (several samples can
be selected recurrently, and some of the samples may
not be selected at all, i.e. with or without replacement).
3. Training and learning of a specific classifier Ni of Di
by some machine learning procedures which depend on
the actual training set Di.
4. Combining the predictions of n classifiers by taking an
average.
The flow chart of optimal power generation, using a Bag-
ging/Bootstrap algorithm, is shown in Fig. 9 and further
explained via following algorithm:
1. START
2. Define system for economic dispatch:
a. IEEE 30 bus system which includes 6 generator
buses, 20 load busses
3. Obtained the data for economic dispatch:
a. Sum of power demands at 20 load busses at a par-
ticular hour from daily load curve
b. Beta loss coefficients matrix (Transmission losses)
obtained after Load Flow Analysis
c. Generator maximum and minimum power gener-
ated limits in MW including cost coefficients
4. Find out the dispatch using Lagrange Relaxation (LR)
method in MATLAB:
a. Active power generation in MW at 6th generator
busses to fulfil the daily load demand
b. The cost in $/hr to fulfil power demands
5. Prepared the N number of Neural Networks in MAT-
LAB:
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FIGURE 9. Flowchart of ensemble neural network using bootstrap
aggregating.
a. For each Neural Network, selection of the input data
set i.e. bootstraps of order 20∗24
b. Selection of target data set of order 6∗24 obtained
from LR
6. Setting the parameters of Neural Network:
a. Data division, hidden layers, number of neurons in
the hidden layers, training function, performance
function etc.
7. Separate training, testing and validation data for Neural
Network
8. Run ANN
9. Check ANN converge. If YES, go to step 10. Otherwise
go to step 6
10. Create N Bootstraps by applying bagging algorithm on
input data
11. Create N classifiers similar to ANN
12. Aggregating the Ensemble Neural Network to get final
prediction
13. Check EANN converge. If YES, go to step 14. Other-
wise, go to step 10
14. Print the output results
15. END
VI. SIMULATION RESULTS
The performance of ANN with regression analysis, compar-
ison of ANN prediction with target data, the formation of an
ensemble of neural networks with bootstrap aggregation, and
its influence on the predicted values along with regression
analysis and error histograms, are discussed in this section.
The optimal solution for the IEEE 30-bus system in Table 3,
is obtained by applying the Lagrange method.
The training window is presented in appendix, Fig. 10,
representing the mapping of IEEE 30-bus system into the
neural network.
FIGURE 10. Training window of the artificial neural network.
The data division is ‘Random’ and Levenberg-Marquardt is
selected as a training method which is further employed with
MSE performance functions. This is the most effective train-
ing method for feed-forward neural networks with respect to
the training precision [32].
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FIGURE 11. Regression plots obtained during the training of artificial
neural network.
FIGURE 12. Comparison between target data and ANN prediction.
The relation between the anticipated value (target data) and
the actual value (ANN output) is shown in the regression plots
of Fig. 11. The regression plots (R) gives the relation between
the desired and actual output for training, testing, validation,
and overall data. Ideally, data division (circles) should be on
the line for good generalization, representing y = x, which
shows output is equal to the target value and thus ‘R’ is unity.
The ANN value at R = 0.86 does not match with the target
value because of the load change each hour which indicates
the lack of good generalization ability of ANN.
Comparison of the target value (real power generation) and
the ANN prediction is shown in the Fig. 12. The compar-
ative analysis shows that the ANN forecast does not match
precisely with the actual power demand resulting in the
sub-optimal and uneconomical dispatch. The closer differ-
ence is represented by the error histogram of ANN as shown
in the Fig. 13.
The error histogram in Fig. 13 shows the percentage error
between the target power generation and the EANN forecast
against each hour of the day. The maximum percentage error
FIGURE 13. Error histogram of target and ANN predictions.
FIGURE 14. Regression plots obtained during the training of ensembled
artificial neural network.
is at the 8th hour that is 0.747% and the minimum percent-
age change is at 21st hour, which is 0.247%. Although the
percentage error is small against each hour, but the appli-
cation of EANN reflects the significant improvement in the
percentage error, better generalization ability and faster con-
vergence with the reduction in bias and variance under the
same training parameters and operating conditions. The ANN
has trained again for the re-sampled data to enhance its ability
and to adapt to new values speedily, after creating the Boot-
strap data by using the Bagging algorithm for the formation
of EANN. The Bagging algorithm to produce Bootstraps is
implemented in MATLAB by following the steps described
in section V.
The trials are done 50 times, and average value is taken to
analyze the results. It is shown in the results that the neural
network ensembles make fewer errors than the simple ANN
alone. The regression analysis of EANN is provided in the
Fig. 14. R = 0.98 shows the improved performance of the
classifiers. The data division is so aligned that y = x and have
a very little deviation in training, validation and test data sets
as compared to ANN.
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TABLE 5. Accuracy percentage of EANN.
FIGURE 15. Comparison between target data and EANN prediction.
FIGURE 16. Error histogram of target and EANN predictions.
Comparison of the target value and the EANN prediction
is shown in the Fig. 15. The EANN prediction is more close
to the target value (power generation) incorporating better
generalization ability as than ANN. The percentage change
of the EANN is shown via error histogram of Fig. 16.
FIGURE 17. Comparison of percentage errors between ANN and EANN.
It is noticed that the maximum percentage error is at the 9th
hour that is 0.199% and the minimum percentage error is
at the 13th hour, which is 0.031%. The signiﬁcant reduction
in the percentage error shows the superiority of EANN over
ANN with reduced bias and variance due to the inherent
property of the Bootstrap aggregation.
Fig. 17 shows the comparison of percentage errors between
ANN and the proposed EANN. The comparison graphically
portrays the dominance of the Bootstraps algorithm over the
conventional ANN.
To summarize the results of ANN and EANN, the accuracy
percentage is measured and is shown in the Table 5.
A. VALIDATION OF PROPOSED ALGORITHM
As the load data could change day by day, so the pro-
posed algorithm is implemented on seven days’ data sets.
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FIGURE 18. Weekly load curve obtained from NPCC-Pakistan.
FIGURE 19. Error histogram of ANN predictions for a week.
FIGURE 20. Error histogram of EANN predictions for a week.
The weekly load curve is shown in Fig. 18 for twenty-four
hours.
The error analysis of ANN forecast for a full week is shown
in the Fig. 19. It is noted that the error is 1% percent, resulting
in the sub-optimal and uneconomical dispatch.
The error analysis of EANN forecast for a full week is
shown in the Fig. 20 of appendix and noted that the error
ranges from 0.0%-0.3%, which is far less than the errors
produced by ANN. Thus, the proposed algorithm is valid for
the variation in datasets.
The regression analysis of EANN during a week is pro-
vided in the Fig. 21. R = 0.99 shows the significant improve-
ment in the proposed algorithm when the dataset is varied.
B. COMPARATIVE STUDY
To check the accuracy of the proposed method, we uti-
lized four standard performance measures: Mean Square
Error (MSE), Mean Absolute Percentage Error (MAPE) and
Root Mean Square Error (RMSE) and Mean Error Devia-
tion (MAD) on various persistence models. The MSE is dis-
cussed before while others performance measures are defined
FIGURE 21. Regression plots obtained during the training of ensembled
artificial neural network for a week.
as:
MAD =
1
n
n
i=1
(xi − zi) (17)
RMSE =
1
n
n
i=1
(xi − zi)2
(18)
MAPE =
100%
n
n
i=1
(xi − zi)
xi
(19)
The errors have been computed independently for training,
testing and the Validation data. Their values are important
indicators of the practical usefulness of the forecasting frame-
work. The performance of EANN is compared with other
state-of-the-art machine learning algorithms namely Arti-
ficial Neural Network-Multilayer perceptron (ANN-MLP),
Support vector machines (SVM), Radial basis function
(RBF). Table 6 shows the performance metric of these
models.
The results show that using an EANN resulted in higher
accuracy than using other classifiers, for all four performance
metric. The improvements in terms of MAPE for the val-
idation data, averaged over all case studies are 0.14, 0.46,
0.95 and 0.87 for EANN, ANN, SVM, RBF respectively. The
computational cost of training an ensemble is higher than for
a single ANN but suitable for both offline and online practical
applications.
C. COMPUTATIONAL COMPLEXITY ANALYSIS
EANN is a bootstrapping technique, mainly influenced by
the learning phase. The resampling step, along with training
155926 VOLUME 7, 2019

TABLE 6. Models performance metric.
TABLE 7. Computational complexity analysis.
of the classifier for a certain number of bags leads to an
expensive approach than a simple ANN and SVM. Three
phases are considered, distinguished as training, search of
the optimal ensemble and inference, to show computational
complexity of ensemble techniques. Let N represents the
number of classifiers, R represents number of replacements
and B represents number of bags. If σ represents the time
complexity in terms of learning a computational complexity
of EANN, ANN and SVM is presented in the Table 7.
In terms of optimal searching, the SVM is the most time
intense approach characterized by an exponential time com-
plexity of σ(2N) compared to the linear ANN and Bagging.
However, EANN (bagging) shows a bit computational com-
plexity due to number of bags (B) and replacements(R),
defined by the term σ(B (N + R)) which is by definition
greater than one. However, this can be tolerated as compared
with SVM and ANN.
To measure the time complexity of the model with experi-
mental dataset at a particular load, comparisons of 50 individ-
ual trials have been done and the values are averaged. RMSE
(for training, testing and validation), and prediction accuracy
(under the tolerance of 15%) are used as indicators to evaluate
the models. The time complexity of SVM, ANN and EANN
(15 bootstraps) ANN and SVM is given in Table 8.
In general, the forecast results of any classifiers are accept-
able that have lower RMSEs. Table 8 show that the EANN
have lowest RMSEs (1.28) and having the prediction accu-
racy of 99.50% with the tolerance of 15%.
TABLE 8. Time complexity analysis.
FIGURE 22. EANN performance over the number of bootstraps.
However, with increase in number of classifiers the error
of ensemble learning is greatly reduced but the total time
including (training, testing and validation) is increased subse-
quently. To show the effectiveness of the proposed approach,
further EANN performance over the number of bootstraps
is analyzed. In Fig. 22, EANN performance varies over the
number of bootstraps employed in the model. Higher the
bootstraps in the model higher the accuracy and time it
takes. EANN is bit computationally intensive because of the
complex network architecture and greater spatial dimensions.
However, the runtime still allows the use of the model for a
real-time estimation with the advantage of a better and robust
performance.
VII. CONCLUSION
A solution for the optimal power generation problem using
an ensemble of artificial neural networks through bootstrap
aggregation is proposed in this paper. Load demand data for
Pakistan’s power system has been considered for a day and
then validated for a week. Lagrange Relaxation method is
developed and used to train the several conventional ANNs.
The proposed algorithm EANN is then applied to analyze the
results.
Results show that the feed forward back propagation of
the ANN model alone is not suitable for power scheduling
as it produces significant errors for the simulated and actual
generations. It is shown that when the proposed EANN is
used to deal with ED problem, a great deal of improvement is
witnessed compared with the ANN. EANN approach shows
better generalization ability, faster convergence with reduced
bias and variance due to the inherent property of the Bootstrap
aggregation, under the same operating conditions.
VOLUME 7, 2019 155927

The ANN is accurate for the given set of data during
different scenarios of overloading and contingencies in the
Pakistan’s power system but when load changes are rapid
or change in the following hour, the ANN suffers under or
overfitting. These ANN limitations lead to inaccuracy dur-
ing load shedding and disturb power system stability. The
computational complexity analysis for the proposed EANN
shows real-time estimation with better and robust perfor-
mance. Thus, proposed EANN algorithm is preferred for
scenarios where the load sheds/changes rapidly, solving the
shortcomings of an ANN.
APPENDIX
See Figure. 10.
ACKNOWLEDGMENT
This project was funded by the Deanship of Scientific
Research (DSR), King Abdulaziz University, Jeddah, under
Grant No. (DF-656-611-1441). The authors, therefore, grate-
fully acknowledge DSR technical and financial support.
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KASHIF MEHMOOD received the B.Sc. and
M.Sc. degrees (Hons.) in electrical engineering
from The University of Lahore, Lahore, Pakistan,
in 2011 and 2015, respectively. He is currently pur-
suing the Ph.D. degree with Southeast University
Nanjing China. In 2012, he joined The University
of Lahore, where he is currently with the Depart-
ment of Electrical Engineering. He has supervised
several projects, and authored and coauthored in
several research articles. His current research inter-
ests include power system operation and control, flexible AC transmission
and distribution systems (FACTS), the application of metaheuristic opti-
mization (artificial intelligence) techniques in power system’s problem, and
the UHV magnetically saturable controllable reactor for reactive power
compensation.
155928 VOLUME 7, 2019

HAFIZ TEHZEEB UL HASSAN received the
bachelor’s degree in electrical engineering and the
master’s degree in power engineering from
the University of Engineering and Technology,
Lahore, Lahore, Pakistan, in 1975 and 1981,
respectively. He is currently an Associate Profes-
sor with the University of the Punjab, Pakistan.
He has more than 30 years of experience in
research and teaching with dozens of project
supervisions at both graduate and post graduate
level. He has authored more than 30 scholarly articles published in interna-
tionally recognized journals.
ALI RAZA received the B.S. and M.Sc. degrees
in electrical engineering from the University of
Engineering and Technology, Lahore, Pakistan,
in 2010 and 2013, respectively, and the Ph.D.
degree in electrical engineering from the Harbin
Institute of Technology, Harbin, China, in 2016.
He is currently with the Department of Electrical
Engineering, The University of Lahore, Pakistan.
He has authored and coauthored several technical
journal articles and technical conference proceed-
ings. His current research interests include operation and the control of
M-VSC-HVDC including its effects on power systems, protection, optimiza-
tion, and the topological evaluation of MT-HVDC transmission systems for
large offshore wind power plants.
Dr. Ali has been a TPC Member of the International Symposium on
Wireless Systems and Networks (ISWSN), since 2017. He received the ﬁrst
Best Paper Award 2014 IEEE International Conference on Control Science
and Systems Engineering. He is the Co-Chair of Asia Paciﬁc International
Conference on Electrical Engineering 2019 (APICEE 2019).
ALI ALTALBE received the M.Sc. degree in
information technology from Flinders Univer-
sity, Australia, in 2011, and the Ph.D. degree in
information technology from The University of
Queensland, Australia, in 2018. He is currently
an Assistant Professor with the Department of IT,
King Abdulaziz University, Jeddah, Saudi Arabia.
His current research interest includes protection of
multiterminal HVDC grids using machine learning
approaches.
HAROON FAROOQ received the Ph.D. degree
in electrical engineering from Glasgow Caledo-
nian University, U.K., in 2012. He is currently an
Assistant Professor with the Electrical Engineer-
ing Department, Rachna College of Engineering
and Technology, Gujranwala campus, University
of Engineering and Technology, Lahore, Pakistan.
His current research interests include power qual-
ity, renewable energy systems, electric vehicles,
and demand side management.
VOLUME 7, 2019 155929

Optimal Power Generation in Energy-Deficient Scenarios Using Bagging Ensembles

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