Content uploaded by Larouci Benyekhlef
Author content
All content in this area was uploaded by Larouci Benyekhlef on Sep 05, 2021
Content may be subject to copyright.
U.P.B. Sci. Bull., Series C, Vol. 79, Iss. 1, 2017 ISSN 2286-3540
CUCKOO SEARCH ALGORITHM FOR SOLVING
ECONOMIC POWER DISPATCH PROBLEM WITH
CONSIDERATION OF FACTS DEVICES
Benyekhlef LAROUCI
1
, Lahouaria BENASLA
2
, Abderrahim BELMADANI
3
,
Mostefa RAHLI
4
The essential objective of an Optimal Power Flow (OPF) algorithm is to find
steady state operation point which minimizes cost of generators, losses etc. while
maintaining an acceptable system performance in terms of limits on generators real
and reactive powers and line flow limits. Traditionally, classical optimization
methods were used to effectively solve OPF. But more recently due to incorporation
of FACTS devices, OPF have become complex and unfortunately these methods are
not able to find an efficient solution. Recently, with the development of computer
science and technology, evolutionary algorithms are used to solve optimal power
flow (OPF) with FACTS devices. In this paper, research work has been carried out
with an objective to applied Cuckoo Search (CS) algorithm for both power flow
optimal and optimal power flow incorporating FACTS devices. To validate the
performance of this algorithm, IEEE 09-bus 3-generators test case system has been
used. Several optimization runs have been approved out on different cases of
problem complexity with consideration of FACTS Devices (SVC and STATCOM).
The results demonstrate that the proposed algorithm is an effective and practical
method for the optimal power flow incorporating FACTS controllers.
Keywords: Cuckoo Search algorithm, FACTS Devices, Optimal Power Flow
1. Introduction
In the last years, many efforts have been made to solve the Economic
Power Dispatch (EPD) problem, incorporating different kinds of constraints or
multiple objectives through various mathematical programming and optimization
techniques. The conventional methods include Newton-Raphson method, Lambda
Iteration method, Gradient method, Non-Linear Programming (NLP), Quadratic
Programming (QP), Newton-based Method, Mixed Integer Programming and
Dynamic Programming [1]. All of these mathematical methods are fundamentally
1
Dept. of Electrical Engineering, University USTO, BP 1505 El Mnaouar, Oran, Algeria, e-mail:
benyekhlef.larouci@univ-usto.dz
2 Dept. of Electrical Engineering, University USTO, BP 1505 El Mnaouar, Oran, Algeria, e-mail:
jbenasla@yahoo.fr
3 Dept. of Computer Science, University USTO, BP 1505 El Mnaouar, Oran, Algeria, e-mail:
abderrahim.belmadani@gmail.com
4 Dept. of Electrical Engineering, University USTO, BP 1505 El Mnaouar, Oran, Algeria, e-mail:
rahlim@yahoo.fr
44 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
based on the convexity of objective function to find the global minimum [2]. To
solve economic dispatch problem effectively, most algorithms require the
incremental cost curves to be of monotonically smooth increasing nature and
continuous [3]. Recently, many attempts to overcome the limitations of the
mathematical programming approaches have been investigated such as meta-
heuristic optimization methods [2]. Some of these algorithms are Particle Swarm
Optimization (PSO) Artificial Bee Colony (ABC), Genetic Algorithms, Firefly
Algorithm, Bat Algorithm, Artificial Chemical Reaction Optimization Algorithm
[4], the Intelligent Water Drops [5], and Modified Bat Algorithm [6].
In this work, CS algorithm is proposed to solve specifically the optimal
power flow and the security constraints optimal power flow problem with
incorporation of the FACTS devices.
2. Problem Formulation
2.1 Economic load dispatch
The basic economic dispatch problem can described mathematically as a
minimization of problem of minimizing the total fuel cost of all committed plants
subject to the constraints [1]:
g
gi
N
igii)P(FPC Minimize 1
1
(1)
)P(F i
gi
is the fuel cost equation of the
th
i
plant. It is the variation of fuel
cost ($/h) with generated power (MW). Normally it is expressed as:
gigiigiigiiN,...,,icPbPa)P(F 21
2
(2)
g
N
is the number of thermal units,
gi
P
is the active power generation at
unit i and
i
a
,
i
b
and
i
c
are the cost coefficients of the
th
i
generator.
Inequality constraints: Generation power should be within the minimum
output
min
gi
P
and the maximum output
max
gi
P
:
max
gigi
min
gi PPP
Equality constraints: The total generation should meet the total demand
D
and transmission losses
l
P
[7]:
l
N
igi PDP
g
1
(3)
2.2 Optimal Power Flow dispatch
The active power-planning problem is considered as a general
minimization problem with constraints, and can be written in the following form
[8]: Min
)u,x(f
(4)
Cuckoo Search Algorithm for solving EPD problem with consideration of FACTS devices 45
S.t:
0)u,x(g
(5)
0)u,x(h
(6)
T
L
Vx
(7)
T
SVClGgi ...]QPVP[u
(8)
)u,x(f
is the objective function,
)u,x(g
and
)u,x(h
are respectively the
power flow equations and the limits on physical devices in the power system as
well as the limits created to ensure system security. The control variables
u
are
generator active and reactive power outputs, bus voltages, power losses. The state
variables are voltage and angle of load buses. For optimal active power dispatch,
the objective function
i
F
is total generation cost as expressed follows [9]:
g
N
igiigiii PcPbaMinimize 1
2
(9)
2.3 Optimal Power Flow with STATCOM; Static model and
mathematical analysis of STATCOM [10, 11]
The STATCOM is modeled as a controllable voltage source (Ep) in series
with an impedance [12]. The real part of this impedance represents the cupper
losses of the coupling transformer and converter, while the imaginary part of this
impedance represents the leakage reactance of the coupling transformer.
STATCOM absorbs requisite amount of reactive power from the grid to keep the
bus voltage within reasonable range for all power system loading. Fig. 1 shows
the circuit model of a STATCOM connected to the
th
i
bus of a power system. The
injected active and reactive power flow equation of the
th
i
bus is given below:
n
j)
ijji
cos(
ij
Y
j
V
i
V)cos(YEVVGP ppkpkkkpp 1
2
(10)
n
j)
ijji
sin(
ij
Y
j
V
i
V)sin(YEVVBQ ppkppkkpp 1
2
(11)
The implementation of STATCOM in transmission system introduces two
state variables (|Ep| and
p
); however, |Vk| is known for STATCOM connected
bus. It may be assumed that the power consumed by the STATCOM source is
zero in steady state.
0
2 )cos(YVEE)G(IEalRePpkppkppp
*
ppEp
(12)
Where
k
V
is the voltage at the
th
i
bus;
p
Y
is the admittance of the
STATCOM;
p
G
,
p
B
are the conductance and susceptance, respectively, of the
46 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
STATCOM;
ij
is the admittance angle of transmission line connected between
the
th
i
bus and
th
j
bus, respectively;
k
is the voltage source angle of the
STATCOM;
k
E
is the voltage sources of STATCOM converters.
Fig.1. Schematic static model of STATCOM
2.4 Optimal Power Flow with FACTS devices cost (SVC)
The cost function for SVC is developed as follows [14]:
2
000303051038127 S.S..CSVC
(13)
Where
SVC
C
is $/kVar and S is the operating range of the FACTS devices
in MVar.
The formulation of the optimal allocation of FACTS devices can be
expressed as follows [13, 14]:
fCPCCMin gi
Total 21
(14)
0
1)g,f(E
(15)
00 21 )g(B,)f(B
(16)
Where:
C1: Total generation costs.
C2: Average investment costs of FACTS devices.
CTotal: Overall cost of objective function.
1
E
: Equality constraints with respect to active and reactive power flow.
21 B,B
: Inequality constrains for FACTS devices and power flow.
gi
P,f
: are the variables of FACTS devices and real power generated.
The unit for generation cost is US$/hour and for the investment costs of
FACTS devices are US$. They must be unified into US$/hour [10, 12]. In this
paper, tree years are applied to evaluate the cost function. Therefore, the average
value of the investment costs are calculated using the following equation:
Cuckoo Search Algorithm for solving EPD problem with consideration of FACTS devices 47
38760
1
)f(c
fC
($/Hour) (17)
C(f) is the total investment costs of FACTS devices.
3. Cuckoo Search
Cuckoo search (CS) is one of the latest nature-inspired metaheuristic
algorithms, developed in 2009 by Xin-She Yang and Suash Deb . CS is based on
the brood parasitism of some cuckoo species. In addition, this algorithm is
enhanced by the so-called Lévy flights, rather than by simple isotropic random
walks. For simplicity in describing the standard Cuckoo Search, we now use the
following three idealized rules [15, 16]:
• Each cuckoo lays one egg at a time, and dumps it in a randomly chosen
nest;
• The best nests with high-quality eggs will be carried over to the next
generations;
• The number of available host nests is fixed, and the egg laid by a cuckoo
is discovered by the host bird with a probability pa ϵ [0, 1]. In this case, the host
bird can either get rid of the egg, or simply abandon the nest and build a
completely new nest.
The steps of the CSA are as follows [17]:
1. Select values for CSA parameters, which are the number of nests (eggs)
(n), the step size parameter (β), discovering probability (pa), and maximum
number of iterations for termination of the cycles.
2. Generate initial population of n host nests
)n,...,,i(,xi21
randomly each of which represents a candidate solution to the optimization
problem with objective function of
xf
and decision variables
3. Get a cuckoo randomly by Levy flights using
)(Levyxx ii
1
and evaluate its fitness
i
F
. Here Levy(λ) is a
random walk based on Levy flights and the product ⊕ means entry-wise
multiplications.
4. Choose randomly a nest among n (say j) and evaluate its fitness Fj.
If Fj <Fi, replace j by the new solution.
5. Abandon a fraction of worst nests and built new ones. First find out
whether each nest keeps its current position (Eq. (18)). R matrix stores 0 and 1
values such that any one of them is assigned to each component of ith nest, in
which 0 means that current position is kept and 1 implies that the current position
is to be updated:
48 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
a
a
iprandif
prandif
R0
1
(18)
New nests are conducted by means of Eq. (19):
iii
t
i
t
ipermpermRrxx 21
1
(19)
Where r is a random number between 0 and 1. perm1 and perm2 are two
row permutations of the corresponding nest. R defines the probability matrix.
6. Rank solutions and find the current best one.
7. Repeat steps 3-6 until termination criterion is satisfied which is usually
taken as the maximum number of iterations.
4. Simulation results and discussions
The EPD problem with and without FACTS device is applied to the
standard IEEE 09-bus system (Fig. 2) using Cuckoo Search algorithm (CS).
Fig.2. Structure of the IEEE 9 Bus test system
This approach has been developed by the use of Matlab 9. To demonstrate the
effectiveness of the proposed approach three cases to be discussed:
4.1. Case 1: Optimal Power Flow with variable losses
In this case, the proposed CS-OPF is applied to standard IEEE 9-bus
system (Optimal Power Flow with variable losses), the load demand D=315 MW.
The input parameters of CS-algorithm are: nest set to 30 and discovery rate of
alien eggs or fraction probability, Pa equals to 0.25 was run for 100 iterations. The
obtained results using CS-OPF are given in Tables 1, 2 and compared with those
of MATPOWER software [18].
Table 1
Comparison of simulation results obtained of Optimal Power Flow
Variable
PG1(MW)
PG2(MW)
PG3(MW)
∑PG (MW)
PL(MW)
cost in($/h)
CS-OPF
86.596
138.638
93.724
318.959
4.182
5194.92
MATPOWER [18]
89.802
134.345
94.159
318.306
3.306
5296.7
Cuckoo Search Algorithm for solving EPD problem with consideration of FACTS devices 49
Table 2
Optimal Power Flow with variable losses (CS-OPF)
Bus
V
Angle
Injection
Generation
Load
No
Pu
Degree
MW
MVar
MW
Mvar
MW
MVar
1
1.04
0.000
86.82
39.636
86.82
39.636
0.000
0.000
2
1
6.8464
138.638
-0.249
138.638
-0.249
0.000
0.000
3
1
4.4125
93.724
-14.782
93.724
-3.882
0.000
10.9
4
1.0192
-2.7042
0.000
0.000
0.000
0.000
0.000
0.000
5
0.9841
-5.0477
-125
-50
0.000
0.000
125
50
6
1.0001
-4.329
-90
-30
0.000
0.000
90
30
7
1.0039
1.895
0.000
0.000
0.000
0.000
0
0.000
8
0.9933
-0.714
-100
-35
0.000
0.000
100
35
9
1.0102
1.2958
0.000
0.000
0.000
0.000
0.000
0.000
Total
4.182
-90.396
319.182
35.504
315
125.9
The results show that CS-OPF algorithm gives much better results than the
MATPOWER software. The difference in generation cost between these methods
clearly shows the advantage of this method. In addition, it is important to point
out that the CS algorithm OPF converge in an acceptable time. For this system
was converged to highly optimal solutions set after 30 iterations (Fig. 3).
Fig.3. Convergence characteristics of CS algorithms for fuel cost with variable losses
50 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
4.2. Case 2: Optimal Power Flow with FACTS devices (STATCOM)
In order to check the feasibility of the proposed method, it is applied to
solve OPF-CS with STATCOM of the same test system. We increase the load
demand from 315 to 390 MW. The input parameters of CS-algorithm are: nest set
to 30 and discovery rate of alien eggs or fraction probability, Pa equals to 0.25
was run for 100 iterations.
From the results of OPF-CS without STATCOM (Table 3), we conclude
that increasing load; decrease the voltage of all buses. Here node 5 can be
considered as the weakest node (0.933pu) and the drop of voltage is 6.7 %, so to
maintain the voltage magnitude at the specified value, the STATCOM is installed
at this bus. Table 3
Optimal Power Flow without FACTS devices
Bus
V
Angle
Injection
Generation
Load
No
Pu
Degree
MW
MVar
MW
Mvar
MW
MVar
1
1.04
0
107.869
77.229
107.869
77.229
0.000
0.000
2
1
9.6217
173.346
24.921
173.346
24.921
0.000
0.000
3
1
7.1713
117.403
-2.925
117.403
7.975
0.000
10.900
4
0.999
-3.4284
0.000
0.000
0.000
0.000
0.000
0.000
5
0.933
-7.7478
-200.000
-80.000
0.000
0.000
200.000
80.000
6
0.983
-4.1976
90.000
-30.000
0.000
0.000
90.000
30.000
7
0.99
3.3412
0.000
0.000
0.000
0.000
0.000
0.000
8
0.983
0.8917
-100.000
-35.000
0.000
0.000
100.000
35.000
9
1.004
3.2424
0.000
0.000
0.000
0.000
0.000
0.000
Total
8.618
-45.774
398.618
110.126
390.000
155.900
The simulation results of fuel cost power generators, the controlled
variables, and its voltage rating obtained by CS are shown in Table 4, 5 and Fig.
4. The simulation results show that the bus voltages have considerably improved:
at bus 5 (from 0.933pu to 1.000pu).
Moreover, the results indicate that with the proposed CS algorithm,
acceptable fuel cost (7262.5414$/h) compared without STATCOM
(7282.3345$/h) is obtained and the power losses has considerably decreased with
9.888%, from 8.618 MW to 7.766 MW. Therefore, the OPF problem with
STATCOM using Cuckoo Search algorithm represented a good solution were the
cost and the transmission loss are reduced and voltage magnitude are maintained
at the specified value.
Cuckoo Search Algorithm for solving EPD problem with consideration of FACTS devices 51
Table 4
Optimal Power Flow with FACTS devices (STATCOM)
Bus
V
Angle
Injection
Generation
Load
No
Pu
Degree
MW
MVar
MW
Mvar
MW
MVar
1
1.0400
0.0000
108.621
31.748
108.621
31.748
0.000
0.000
2
1.0000
9.3383
172.997
-1.951
172.997
-1.951
0.000
0.000
3
1.0000
7.0652
116.635
-15.999
116.635
-5.099
0.000
0.000
4
1.0242
-3.3674
0.000
0.000
0.000
0.000
0.000
0.000
5
1.0000
-7.5551
-200.487
-10.201
-0.487
69.799
200.000
80.000
6
1.0026
-4.0988
-90.000
-30.000
0.000
0.000
90.000
30.000
7
1.0070
3.1747
-0.000
0.000
0.000
0.000
0.000
0.000
8
0.9959
0.8349
-100.000
-35.000
0.000
0.000
100.000
35.000
9
1.0117
3.1915
-0.000
0.000
0.000
0.000
0.000
0.000
Total
7.766
-61.402
397.766
94.498
390.000
155.900
Fig.4. Convergence characteristics of CS algorithms for fuel cost with STATCOM
Table 5
Comparison of simulation results obtained without and with STATCOM.
Variable
PG1(MW)
PG2(MW)
PG3(MW)
∑PG (MW)
PL(MW)
Cost in($/h)
CS with STATCOM
108.1237
172.9974
116.6347
397.7557
7.766
7262.5414
CS without STATCOM
107.6832
173.3462
117.4029
398.4324
8.6182
7282.3345
4.3. Case 3: Optimal Power Flow with FACTS devices cost (SVC).
In this case, we solve the optimal Power Flow with the investment cost of
FACTS devices (SVC). We increase the load demand from 315 to 390 MW.
52 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
The input parameters of CS-algorithm are: nest set to 30 and discovery
rate of alien eggs or fraction probability, Pa equals to 0.25 was run for 500
iterations.
Generally, the FACTS devices are very expensive, and the choice the
placement of these flexible devices is essential to insure the efficient operation of
electrical power systems and to avoid the improvidence. In our approach, the SVC
is installed at critical buses (bus 5). We consider the cost of SVC and the
generators to minimize the both total cost.
The solving results show that when using SVC, the security constraints are
checked for voltage magnitudes (table 6). As shown in table 7, it is clear that the
obtained optimal SVC location brings a considerable reduction of both the total
fuel cost and the power losses (6.9460 MW compared to the CS without SVC
8.6182MW). Table 6
Optimal Power Flow with FACTS devices (SVC)
Bus
V
Angle
Injection
Generation
Load
No
pu
Degree
MW
MVar
MW
Mvar
MW
MVar
1
1.04
0.000
127.109
30.752
127.109
30.752
0.000
0.000
2
1.05
4.6436
152.614
-14.506
152.614
-14.506
0.000
0.000
3
1.05
3.9063
117.223
-32.374
117.223
-21.474
0.000
10.9
4
1.0254
-3.9368
0.000
0.000
0.000
0.000
0.000
0.000
5
0.982
-8.6375
-200
-80
0.000
0.000
200
80
6
1.0261
-5.2272
-90
-30
0.000
0.000
90
30
7
1.0625
-0.261
0.000
0.000
0.000
0.000
0.000
0.000
8
1.0875
-2.2339
-100
49.353
0.000
0.000
100
-49.353
9
1.0701
0.4012
0.000
0.000
0.000
0.000
0.000
0.000
Total
6.946
-76.774
396.946
-5.227
390.000
71.547
Table 7
Optimal Power Flow results with FACTS devices cost (SVC)
PG1 (MW)
PG2 (MW)
PG3 (MW)
Qsvc (MVAr)
Total PG (MW)
126.95
117.2232
152.6137
84.3534
396.946
Losses (MW)
Total Cost ($/h)
Fuel cost ($/h)
SVC Cost ($/KVAr)
SVC Cost in ($/h)
6.946
7422.8027
7422.5709
105.70161
0.231863
Convergence characteristic of the 3 generators system for total fuel cost is
shown in Fig. 5.
Cuckoo Search Algorithm for solving EPD problem with consideration of FACTS devices 53
Fig.5. Convergence characteristics of CS algorithms for total cost with SVC
5. Conclusions
In this paper, the CS algorithm has been proposed, and successfully
applied to solve both power flow optimal and optimal power flow incorporating
FACTS devices. This algorithm which is one of the recent heuristic algorithms for
solving optimization problems has several advantages including its few control
variables, fast results, easy using process and simple structure.
The proposed algorithm is tested on IEEE 9 bus test power system to
demonstrate its effectiveness. The simulation results indicate the robustness of the
proposed approach to solve the OPF problem of power systems with and without
FACTS. It is observed that the FACTS devices (STATCOM and SVC) can reduce
the transmission losses, voltage deviation and the fuel cost. This work can be
extended by including other FACTS devices like Unified Power Flow Controller
(UPFC) and Thyristor Controlled Series Capacitor (TCSC).
R E F E R E N C E S
[1] Deepti Gupta, Rupali Parmar “Optimization of Economic Load Dispatch Thermal Power
Plant Using Differential Evolution Technique” International Journal of Engineering Trends
and Technology (IJETT) – Volume22 Number 4- April2015
[2] Mimoun Younes, Fouad Khodja and Riad Lakhdar Kherfane ‘Multi-objective economic
emission dispatch solution using hybrid FFA ( fire fly algorithm) and considering wind power
penetration’ Energy 67 (2014 ) 595 -606http://dx.doi.org/10.1016/j.energy.2013.12.043
[3] Ingrida Radziukyniene ‘C-Grasp application to the economic dispatch problem’ Thesis the
degree of Master of Science University of Florida 2010
54 Benyekhlef Larouci, Lahouaria Benasla, Abderrahim Belmadani, Mostefa Rahli
[4] B. Alatas, “ACROA: artificial chemical reaction optimization algorithm for global
optimization”, Expert Systems with Applications, vol. 38, no. 10, pp. 13170–13180, 2011.
[Online]. Available: http://dx.doi.org/10.1016/j.eswa.2011.04.126
[5] H.Shah-Hosseini,“An approach to continuous optimization by the Intelligent Water Drops”,
Procedia Social and Behavioural Sciences, vol. 32, pp. 224–229, 2012. [Online]. Available:
http://dx.doi.org/ 10.1016/j.sbspro.2012.01.033
[6] S. Yilmaz, E. U. Kucuksille, Y. Cengiz, “Modified bat algorithm”, Elektronika IR
Elektrotechnika, vol.20, no.2, pp.71–78,2014. [Online] Available:
http://dx.doi.org/10.5755/j01.eee.20.2.4762
[7] S.Roshni, C.R.Pradhan, Biswajit Mohapatra,’ A Comparitive Study of Economic Load
Dispatch Problems Using Classical method and Artificial Intelligence Method’ International
Journal of Advanced Research in Electrical,Electronics and Instrumentation Engineering,
Vol. 4, Issue 3, March 2015
[8] Belkacem Mahdad, Kamel Srairi, Tarek Bouktir, Mohamed Benbouzid. Optimal Power Flow
for Large-Scale Power System with Shunt FACTS using Efficient Parallel GA. IEEE
IECON’08, Nov 2008, Orlando, United States. pp.867-972, 2008
[9] Mehdi Samimi Rad, Reihaneh Kardehi Moghaddam ‘A Novel PSOGSA_SQP Algorithm for
Solving Optimal Power Flow (OPF) Problem Based on Specific Switching Condition’
American Journal of Research Communication, Rad, et al., 2013: Vol 1(11)
[10] Dutta Setal., Optimal location of STATCOM using chemical reaction optimization for
reactive power dispatch problem, Ain Shams Eng J (2015), http://dx.doi.o rg/10.1016/ j.asej.
2015.04.013
[11] Xiao Y, Song YH. Power flow studies of a large practical power network with embedded
FACTS devices using improved optimal multiplier Newton–Raphson method. Eur Trans
Electr Power 2001;11(4):247–56
[12] Ghadir R, Reshma SR. Power flow model/calculation for power systems with multiple
FACTS controllers. Electr Power Syst Res 2007;77:1521–31
[13] E. J. Oliveira, J. W. M. Lima, and K. C. Almeida, “Allocation of FACTS devices in
hydrothermal system,” IEEE Trans.power systems, vol. 15, pp. 276-282, February. 2000.
[14] Lijun Cai and Istvan Erlich Georgios Stamtsis Yicheng Luo “Optimal Choice and Allocation
of FACTS Devices in Deregulated Electricity Market using Genetic Algorithms”
[15] Xin-She Yang,Zhihua Cui, Renbin Xiao, Amir Hossein Gandomi, Mehmet Karamanoglu
‘Swarm Intelligence and Bio-Inspired Computation Theory and Applications’ Elsevier-32
Jamestown Road, London NW1 7BY-225 Wyman Street, Waltham, MA 02451, USA First
edition 2013
[16] Yang, X.S., Deb, S., 2009. Cuckoo search via Le´vy flights. Proceedings of the World
Congress on Nature & Biologically Inspired Computing (NaBic 2009). IEEE Publications,
USA, pp. 210-214.
[17] Yang, X.S., Deb, S., 2010. Engineering optimization by cuckoo search. Int. J. Math. Model.
Num. Opt. 1 (4), 330343.
[18] Christopher L. DeMarco “New System Control Methodologies: Adapting AGC and Other
Generator Controls to the Restructured Environment” Power Systems Engineering Research
Center- Cornell University 428 Phillips Hall - PSERC Publication 05-64 November 2005
