Hunting-Based Optimization Technique for Secured Optimal Power

Flow with Lines Outages in Power System

ISMAIL ZIANE1,*, FARID BENHAMIDA1, DJAMAL GOZIM2

1IRECOM Laboratory, Department of Electrical Engineering,

University of SIDI BEL ABBES,

ALGERIA

2University ofZIANE ACHOUR, DJELFA,

ALGERIA

*Corresponding Author

Abstract: - This paper aims to achieve the exact resolution of an optimal power flow (OPF) problem in an

electrical network. In the OPF, the goal is to plan the production and distribution of electrical power flows to

cover, at minimal fuel cost, the consumption at various points in the network. Three variants of the OPF

problem are studied in this manuscript. The first one, OPF corresponds to the case where power production

costs in the network are modeled with a quadratic cost. In the second variant, OPF with outages of some lines,

we clarify the extent to which power flow is affected by the outages and the increasing number of overloaded

lines. Finally, the last variant, secured OPF corresponds to the case where the management of production units

can respect the power limit of each line by rescheduling power production units. The study focuses on

congestion management in the IEEE 30 bus system by applying a model for OPF, incorporating data from both

transmission lines and generators. The research proposes a Hunting Optimization Technique which is named

“Multi-Objective Ant Lion Optimizer (MOALO)” to solve single and multi-objective optimization problems to

find a solution for management pricing, comparing results with other research methods to show the

effectiveness of the applied approach and the mathematical model representing congestion management.

Key-Words: - Optimal power ﬂow; Fuel cost minimization; Line outage; Line overloading; Ant Lion

Optimizer; secured power system.

Received: March 13, 2023. Revised: December 22, 2023. Accepted: February 11, 2024. Published: March 27, 2024.

1 Introduction

The electrical energy is produced simultaneously

with its consumption. Therefore, production must

constantly adapt to consumption. The active and

reactive powers of generators must be adjusted

within their permissible limits to meet fluctuating

electrical loads, [1], with minimal cost and

sometimes with certain environmental protection

while keeping power losses within limits, [2]. This

is called optimal power flow, [3].

The optimal power flow problem has a long

history of development. Over forty years ago,

Carpentier introduced a formulation of the economic

dispatch problem involving constraints on voltages

and other operational constraints. In his approach

(known as the injection method), he framed the

economic dispatch problem as a nonlinear

optimization problem and used the generalized

reduced gradient technique, [4]. In 1968, an

optimization problem involving classical economic

dispatch was introduced and controlled by power

flow equations and operational constraints, where

they used the reduced gradient technique to solve

the Kuhn-Tucker optimality conditions. This

formulation was later named the optimal power flow

(OPF) problem. Since then, it has experienced

considerable growth, as evidenced by the literature.

Excellent synthesis of solution methods and their

applications are provided in [5] and [6].

There are many conventional optimization

methods used for the optimal power flow problem,

like Linear Programming (LP), [7], Interior Point

Method (IPM) [8], Differential Evolution (DE) [9],

and Artificial Bee Colony (ABC) [10]. For secured

optimal power flow, in [11], Sunflower

Optimization (SFO) algorithm was proposed for

solving the problem, and in [12], Self-Organizing

Hierarchical PSO with Time-Varying Acceleration

Coefficients was proposed for Security Constrained

Optimal Power Flow.

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2 Problem Formulation

The OPF solution is used to find a network's

optimum operating state while taking into account

its limitations on control variables and electrical law

constraints. It uses the control variables at its

disposal to maximize a goal while satisfying the

network's power flow equations. Depending on the

situation under study, the goal function

characterizes either the maximizing of power

transmission or the minimization of

losses.Constraints are physical laws that govern a

system's behavior and the design limits of devices

and operating strategies. This type of problem is

usually expressed as a nonlinear static optimization

problem. The objective function is represented as a

nonlinear equation, and the constraints are

represented by nonlinear or linear equations. The

OPF problem can be formulated in the following

equations, [13]:

min max

max/ min ( )

( ) 0, 1,...,

() ( ) 0, 1,...,

obj

i

k k k

f x I

g x i p

Ph x i q

x x x

















(1)

2.1 Objective Function

The main goal of solving the OPF is to determine

the arrangements of control and state variables of

the system that optimize the value of the objective

function. The choice of the objective function

should be based on a better analysis of the security

and economy of the power system. Generally, it is

represented by a second-order nonlinear function.

Some common objective functions used in OPF

studies include:

 Minimum production costs.

 Minimum active transmission losses.

 Minimum reactive transmission losses.

 Maximum transmissible active powers.

 Minimum costs of injected reactive power

(to determine the optimal location for

installing new batteries or compensation

coils).

 Minimum costs of injected active power (to

determine the optimal location for installing

new production units).

 Minimum of emissions, [14].

2.1.1 Equality Constraints

These constraints are translated by the physical laws

governing the electrical system. In steady-state

conditions, the generated power must satisfy the

load demand plus the transmission losses. This

energy balance is described by the power flow

balance equations (Mismatch), formulated as

follows, [15]:

1

cos( ) sin( )

n

Gi Di i j ij i i ij i i

j

P P V V G B

   





     





(2)

1

sin( ) cos( )

n

Gi Di i j ij i j ij i j

j

Q Q V V G B

   





    





(3)

2.1.2 Inequality Constraints

The inequality constraints consist of constraints on

the active powers P and reactive powers Q

generated, the voltage magnitudes V and their

angles θ at each PV node, and on the line currents.

min maxi i i

P P P

(4)

maxij ij

LL

(5)

min maxn n n

V V V

(6)

Where:

Pi: real power generation of generator i.

Pimax/min: maximum/minimum real power generation

of generator i.

Lij: power flow in line (i-j).

Lijmax/min: maximum/minimum power flow limit in

line (i-j).

Vn max/min: maximum/minimum voltage magnitude.

2.2 Economic Dispatch Problem

The main objective of economic dispatch is to find

the active power contribution of each generation

group in the electrical system so that the total

production cost is minimized for any load condition.

The production cost of a unit varies depending on

the power provided by the unit in question, [16].

For an electro-energetic system with ng

production units, the total fuel cost is equal to the

sum of the elementary fuel costs of the different

units, as follows:

1

min ( ) ( )

N

T G i Gi

i

F P F P





(7)

Where:

PGi: is the active power produced by the ith

generator.

Ft: Represents the total production cost.

Fi(PGi): Represents the production cost of the ith

generator.

The production cost function of a generator can be

expressed by a quadratic form of a second-order

polynomial as follows:

2

()

i Gi i Gi i Gi i

F P a P b P c  

(8)

where:

ai, bi, ci: are the coefficients of the cost function.

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2.3 Multi-Objective Ant Lion Optimizer

Methodology

The Multi-Objective Ant Lion Optimizer (MOALO)

was developed in 2016, [17]. This is an updated

version of the Ant Lion Optimizer (ALO), which

was first introduced by in 2015, [18]. A stochastic

method Ant Lion Optimizer method (ALO) was

developed in response to ant lion hunting behavior,

[18].

The (ALO) algorithm emulates the interplay

observed between lion ants and regular ants within

the trap scenario. In these interaction models, ants

are mandated to traverse the search space, while

other ants are sanctioned to pursue and enhance

their fitness using traps. Given the stochastic nature

of ant movement during food foraging in nature, a

random walk is selected as the modeling approach

for ant locomotion, where the graphical presentation

of ant lion hunting and Antlion optimization

algorithm are presented in Figure 1 and Figure 2

respectively.

Fig. 1: Graphical presentation of ant lion hunting

The following flowchartpresents the ant lion

optimization algorithm, [19]:

Fig. 2: Antlion optimization algorithm

3 Problem Solution

In this paper, research has tested Multi-Objective

Ant Lion Optimizer for Congestion Management, so

that, this approach is presented to mitigate

congestion in IEEE 30 buses shown in Figure 4,

which includes 41 transmission lines and 30 buses,

6 generator units, [20]. The load in each system is

283.4 MW, with a total active and reactive power of

126.2 MVar.

3.1 Case Study I:

In this case, we test the performance of our

proposed method to minimize the quadratic fuel cost

without an outage of lines (normal case).

Table 1 presents the effectiveness of (MOALO)

by comparing it with other optimization techniques

like GA, FPA, MDE, GAMS, and GWO techniques.

It can be observed that MOALO can find an optimal

solution for fuel cost, which equals 801.8436 $

where the electrical losses are 9.3760 MW. In

Figure 3, we can see that the fuel cost convergence

without an outage by using (MOALO) optimization.

Fig. 3: Fuel cost convergence without an outage

3.2 Case Study II:

In this case, the test system is exposed to some

outages on transmission lines, so, we proposed 4

scenarios to determine the impact of outages on the

optimal power flow, the fuel cost, and overloading

on lines.

- Scenario 1: Outage of line 1-2

- Scenario 2: Outage of line 1-3

- Scenario 3: Outage of line 2-6

- Scenario 4: Outage of line 4-6

020 40 60 80 100

801.5

802

802.5

803

803.5

804

804.5

805

805.5

806

Iteration

Fuel cost($/hr)

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Fig. 4: Line diagram of 30 IEEE bus Systems with 4

scenarios

Table 2 and Table 3 present the optimal solution

for the 4 scenarios by comparing them with two

methods proposed in [22]. It can be observed that

the outage on the line caused an increase in fuel cost

due to a change in the electrical system. For

example, in the normal case, the fuel cost was

801.8436 $, but in Scenarios 1, 2, 3, and 4 the fuel

cost becomes 839.2833$, 815.1970$, 805.8811$,

and 806.7213$ respectively.

Table 1.Fuel cost comparison obtained by different optimization techniques

MOALO

GA [21]

FPA [21]

MDE [22]

Gradient

method

[23]

EEA [24]

GAMS

[24]

GWO[25]

P1

176.7303

176.6374

176.7294

175.974

187.219

173.4593

177.1

176.1721

P2

48.8300

48.7022

48.8300

48.884

53.781

47.7363

48.8

48.0926

P3

21.4738

21.6967

21.4750

21.51

16.955

23.7692

21.4

21.1376

P4

21.6482

21.5941

21.6475

22.24

11.288

23.2234

21.5

23.3591

P5

12.0937

11.9399

12.0940

12.251

11.287

11.3724

12

11.3591

P6

12.0000

12.1910

12.0000

13.355

2.2530

12

12.0000

Losses (MW)

9.3760

9.3613

9.3753

9.459

10.486

/

8.4137

9.1528

Fuel cost ($/h)

801.8436

801.8566

801.8436

802.376

804.853

802.060

800.0831

801.176

Table 2. Fuel cost comparison obtained by different optimization techniques (Scenario 1 and 2)

1-2

1-3

MOALO

GA [22]

FPA [22]

MOALO

GA [22]

FPA [22]

P1

151.1891

151.3525

151.1886

168.7236

168.4838

168.8781

P2

59.2042

59.2858

59.2040

49.1312

49.4219

49.1360

P3

24.0579

24.0334

24.0580

21.8775

21.7093

21.8775

P4

33.9503

33.9226

33.9500

27.6647

27.5947

27.6750

P5

16.3833

16.1131

16.3840

14.3261

14.5627

14.3140

P6

14.8979

15.0079

14.8980

13.9215

13.8633

13.9236

Losses (MW)

16.2827

16.3153

16.2826

12.2448

12.2356

12.4042

Fuel cost ($/h)

839.2833

839.2858

839.2833

815.1970

815.21

815.1970

Table 3. Fuel cost comparison obtained by different optimization techniques (Scenario 3 and 4)

2-6

4-6

MOALO

GA [22]

FPA [22]

MOALO

GA [22]

FPA [22]

P1

173.8089

172.8813

173.7989

172.9537

172.6048

172.9495

P2

47.6827

47.6091

47.6720

48.4095

48.4625

48.4100

P3

21.4508

22.4618

21.4540

21.6101

21.2781

21.6115

P4

25.0345

25.6042

25.0825

25.6087

25.4855

25.6100

P5

13.3432

12.8147

13.3280

13.1694

13.3780

13.1700

P6

12.2469

12.0940

12.2296

12.0000

12.1629

12.0000

Losses (MW)

10.1670

10.0650

10.1650

10.3514

9.3883

10.3510

Fuel cost ($/h)

805.8811

805.9622

805.8811

806.7213

806.7550

806.7213

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Fig. 5: Fuel cost convergence with outage of line 1-

2

Fig. 6: Fuel cost convergence with outage of line 1-

3

Fig. 7: Fuel cost convergence with outage of line 2-

6

Fig. 8: Fuel cost convergence with outage of line 4-

6

0,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

30

29

28

27

26

25

24

23

22

21

20

19

17 16 15 14

13

12

11

10

9

8

7

6

5

4

3

2

1

18

Lower Voltage (p.u)

Voltage magnitude (p.u)

Upper Voltage (p.u)

Fig. 9: Voltage magnitude in p.uwith outage of line

1-2

0,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

30

29

28

27

26

25

24

23

22

21

20

19

17 16 15 14

13

12

11

10

9

8

7

6

5

4

3

2

1

18

Lower Voltage (p.u)

Voltage magnitude (p.u)

Upper Voltage (p.u)

Fig. 10: Voltage magnitude in p.uwith outage of line

1-3

0,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

30

29

28

27

26

25

24

23

22

21

20

19

17 16 15 14

13

12

11

10

9

8

7

6

5

4

3

2

1

18

Lower Voltage (p.u)

Voltage magnitude (p.u)

Upper Voltage (p.u)

Fig. 11: Voltage magnitude in p.uwith outage of line

2-6

0,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

30

29

28

27

26

25

24

23

22

21

20

19

17 16 15 14

13

12

11

10

9

8

7

6

5

4

3

2

1

18

Lower Voltage (p.u)

Voltage magnitude (p.u)

Upper Voltage (p.u)

Fig. 12: Voltage magnitude in p.uwith outage of line

4-6

020 40 60 80 100

839

839.5

840

840.5

841

841.5

842

842.5

Iteration

Fuel cost($/hr)

020 40 60 80 100

815

815.5

816

816.5

817

817.5

818

Iteration

Fuel cost($/hr)

020 40 60 80 100

805.5

806

806.5

807

807.5

808

808.5

809

809.5

810

Iteration

Fuel cost($/hr)

020 40 60 80 100

806.5

807

807.5

808

808.5

809

809.5

810

Iteration

Fuel cost($/hr)

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Table 4. Results of power flow in lines after4

scenarios

Line

limit

(MVA)

1-2

1-3

2-6

4-6

1-2

130

0

168.9020

103.9468

129.1996

1-3

130

151.2313

0

70.0516

43.8798

2-4

65

13.3401

58.5122

53.1723

12.9914

3-4

130

139.6031

2.4000

65.6479

40.6727

2-5

130

44.8153

70.9142

74.8976

73.1521

2-6

65

6.0290

61.9943

0

66.9042

4-6

90

82.7810

17.5150

74.6626

0

5-7

70

26.2196

3.5958

0.2943

1.7699

6-7

130

50.1231

26.6147

23.2581

24.7500

6-8

32

0.2023

5.4482

7.4629

6.7088

6-9

65

14.0385

17.9911

16.8770

11.3156

6-10

32

11.2404

13.0913

12.2471

9.0575

9-11

65

16.3834

14.3173

13.2670

13.1693

9-10

65

30.4218

32.3084

30.1441

24.4849

4-12

65

32.9956

29.1921

34.5275

45.7167

12-13

65

14.8979

13.9472

12.2288

12.0000

12-14

32

8.2745

7.7788

8.1618

9.3022

12-15

32

19.6063

17.5512

19.0972

23.7977

12-16

32

8.8127

6.6094

8.2973

13.4168

14-15

16

1.9935

1.5054

1.8825

3.0038

16-17

16

5.2399

3.0626

4.7303

9.7616

15-18

16

6.8136

5.6383

6.5549

9.2974

18-19

16

3.5652

2.4034

3.3094

6.0108

19-20

32

5.9426

7.1005

6.1975

3.5110

10-20

32

8.2278

9.4055

8.4856

5.7641

10-17

32

3.7930

5.9624

4.2996

0.6797

10-21

32

16.0510

16.2871

16.0296

15.3352

10-22

32

7.7904

7.9447

7.7764

7.3228

21-22

32

1.5616

1.3275

1.5825

2.2709

15-23

16

6.3253

5.0014

5.9741

8.9333

22-24

16

6.1748

6.5617

6.1400

5.0017

23-24

16

3.0824

1.7701

2.7339

5.6564

24-25

16

0.4960

0.4274

0.1153

1.8829

25-26

16

3.5447

3.5446

3.5447

25-27

16

3.0506

3.9754

3.4317

1.6685

28-27

65

16.3450

17.2749

16.7279

14.9583

27-29

16

6.1901

6.1898

6.1900

6.1902

27-30

16

7.0922

7.0918

7.0921

7.0923

29-30

16

3.7038

3.7037

3.7038

8-28

32

3.7465

3.0591

2.6178

2.3083

6-28

32

12.6350

14.2565

14.1486

12.6815

0

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26 25 24 23 22 21 20 19 18 17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1 Line limit (MVA)

Line flow (MVA)

Fig. 13: Power flow in lines with outage of line

1-2

-200

0

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26 25 24 23 22 21 20 19 18 17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1 Line limit (MVA)

Line flow (MVA)

Fig. 14: Power flow in lines with outage of line

1-3

-200

0

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26 25 24 23 22 21 20 19 18 17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1 Line limit (MVA)

Line flow (MVA)

Fig. 15: Power flow in lines with outage of line

2-6

-200

0

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26 25 24 23 22 21 20 19 18 17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1 Line limit (MVA)

Line flow (MVA)

Fig. 16: Power flow in lines with outage of line

4-6

In Figure 5, Figure 6, Figure 7 and Figure 8 it

can be observed the fuel cost convergence for each

scenario from the four scenarios by the application

of (MOALO) optimization, and in Figure 9, Figure

10, Figure 11 and Figure 12, we note that the

voltage magnitude respected the lower and the

upper voltage for each scenario.

In Table 4 and Figure 13, Figure 14, Figure 15

and Figure 16, the impact of line outages can be

seen on the power flow of each line, and it can be

observed that some of the power flow exceeds the

limit of some transmission lines (overloaded lines).

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Table 5.Results of line limits problem by securedOPF

line

Outage

Overloaded

line

Line limit

(MVA)

Power flowbefore secured

OPF (MVA)

Power flowafter secured OPF

(MVA)

Violation(MVA)

1-2

1-3

130

151.2313

130

21.2313

3-4

130

139.6031

52.2188

87.3843

1-3

1-2

130

168.9020

122.4327

46.4693

4-6

2-6

65

66.9042

50.9818

15.9224

Table 6. Fuel cost result after secured OPF (4 scenarios)

1-2

1-3

4-6

P1

129.9991

122.3032

133.5647

P2

79.8120

69.4864

49.0689

P3

15.5871

29.9095

26.8427

P4

18.5757

28.1856

33.1922

P5

23.7541

12.9890

29.0994

P6

29.3149

29.1476

18.7686

Losses (MW)

13.6428

8.6214

7.1365

Fuel cost ($/h)

863.3217

842.6816

824.5087

The blue curve represents the limits of the

transmission lines and the red curve represents the

power flow on each line.In Figure 13, we notice an

overload on lines (1-3) (3-4), and in Figure 14, we

can notice an increase in the load on the line (1-2),

while in Figure 16 the increase in load is present on

the line (2-6). As for Figure 15, it can be seen that

there is no crossing of the limitson each line.

In scenario 1, we can see that the three lines (1-

3) and (3-4) are overloaded, and in this case, the

problem will inevitably lead to damage to

overloaded lines and an increase in electrical losses,

from 9.3760 MW to 16.2827 MW. In scenario 3, it

can be noted that there are no overloaded lines, and

a small increase in fuel cost compared with the other

scenarios.

3.3 Case Study III:

Due to the problem of outages on transmission lines

and the issue of overloaded lines, this aspect of the

study will be a solution to these two problems by

managing the congestion in the network and

reducing the load on some power lines. Therefore,

we will attempt to reformulate the objective by

taking into account the permissible power limits for

each transmission line (secured OPF). The results

are presented in Table 5 and Table 6. It can be

observed that the secured OPF causes an increase in

fuel cost due to a change in the management of the

electrical system.

4 Conclusion

This paper allowed us to address the issue of

optimal power flow, which is one of the most

prominent problems in the field of operation of

electrical networks, especially as the demand for

electrical energy continues to increase with growing

socio-economic needs in all societies worldwide.

This paper attempted to provide a brief overview of

methods that have been used to solve this problem,

whether conventional methods based on analytical

techniques of functions derived from power system

modeling or unconventional methods mainly based

on artificial intelligence techniques. It is worth

noting that we focused on the case of economic

dispatch, which is one of the most important

problems in optimal power flow.This paper

elucidated the impact of lineoutages on production

costs and the increase in load on other lines, and it

provided the proposed methodMulti-Objective Ant

Lion Optimizer (MOALO) with mathematical

solutions to solve the problem without the

intervention of other devices or tools.

Acknowledgement:

The authors thank everyone who assisted in the

study. The author would also like to thank the

reviewers for their valuable comments.

References:

[1] M. A. Elhameed, M. M. Elkholy, Optimal

Power Flow Using Cuckoo Search

Considering Voltage Stability, WSEAS

Transactions On Power Systems, Vol. 11,

2016, pp 18-26.

[2] I. N. Trivedi, P. Jangir, S. A. Parmar, and N.

Jangir, “Optimal power flow with voltage

stability improvement and loss reduction in

power system using Moth-Flame Optimizer,

Neural Computing & Applications, vol. 30,

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2024.19.11

Ismail Ziane, Farid Benhamida, Djamal Gozim

E-ISSN: 2224-350X

85

Volume 19, 2024

no. 6, 2018, pp 1889-1904,

https://doi.org/10.1007/s00521-016-2794-6

[3] A. Ginidi ,E. Elattar ,A. Shaheen , A. Elsayed,

R. El-Sehiemy , and H. Dorrah, Optimal

Power Flow Incorporating Thyristor-

Controlled Series Capacitors Using the

Gorilla Troops Algorithm, International

Transactions on Electrical Energy Systems

(Hindawi), 2022, pp 1-23,

https://doi.org/10.1155/2022/9448199.

[4] J. L. Carpentier, Optimal Power Flows:

Uses, Methods and Developments, IFAC

Electric Energy Systems Rio de Janeiro.

Brazil, 1985, pp. 11-21.

[5] M. Huneault et F. Galiana, A survey of the

optimal power flow literature, IEEE

Transactions on Power Systems, Vol.6(2),

1991, pp 762-770, DOI: 10.1109/59.76723.

[6] J. Momoh , R. Adapa and M. El-Hawary , A

review of selected optimal power flow

literature to 1993. I. Nonlinear and quadratic

programming approaches, IEEE Transactions

on Power Systems, Vol. 14(1), 1999, pp. 96-

104, DOI: 10.1109/59.744492.

[7] D.Harini, M.Ramesh Babu, C.Venkatesh

Kumar, LP based solution for Security

Constrained Optimal Power Flowincluding

Power Routers, WSEAS Transactions on

Power Systems, Vol. 20, 2020, pp 30-40,

https://doi.org/10.37394/232016.2020.15.4.

[8] E. D. Castronuovo, Jorge M. Campagnolo and

Roberto Salgado, New versions of interior

point methods applied to the optimal power

flowproblem, proceedings of the IEEE/PES

T&D 2002, Sao Paulo, Brazil, 2002, pp 1-7.

[9] M. Varadarajan, K.S. Swarup, Differential

evolutionary algorithm for optimal reactive

power dispatch, Journal Electrical Power and

Energy Systems, Elsevier, pp 435 - 441, 2008,

https://doi.org/10.1016/j.ijepes.2008.03.003.

[10] K. Ayan, U. Kiliç, B. Barakli, Chaotic

artificial bee colony algorithm based solution

of security and transient stability constrained

optimal power flow,journal Electrical Power

and Energy Systems Elsevier, 2015, pp 136 –

147,

https://doi.org/10.1016/j.ijepes.2014.07.018.

[11] T. L. Duong, T. T. Nguyen, Application of

Sunflower Optimization Algorithm for

Solving the Security Constrained Optimal

Power Flow Problem, Engineering,

Technology & Applied Science Research,

Vol. 10(3), 2020, pp. 5700-5705,

https://doi.org/10.48084/etasr.3511.

[12] J. Polprasert, W. Ongsakul and D. Vo Ngoc,

Security Constrained Optimal Power Flow

Using Self-Organizing Hierarchical PSO with

Time-Varying Acceleration Coefficients,

Global Journal of Technology &

Optimization, Vol. 5(1), 2014, pp 1-6, DOI:

10.4172/2229-8711.1000163.

[13] L. Abderaouf, Intelligent Optimal Power

Flow of a Multi-Source Power System

(Écoulement de Puissance Optimal Intelligent

d’un Système de Puissance Multi-Sources),

Doctorat thesis, National school of

polytechinics, Algeria, 2022.

[14] P. Pao-La-Or, A. Oonsivilai, and T.

Kulworawanichpong, Combined Economic

and Emission Dispatch Using Particle Swarm

Optimization, WSEAS Transactions On

Environment and Development, Vol. 6( 4), pp.

296-305, 2010.

[15] K. Aurangzeb, S. Shafiq, M.Alhussein,Pamir,

N. Javaidand and M. Imran, An effective

solution to the optimal power flow problem

using meta-heuristic algorithms, Front.

Energy Research, 2023, pp. 1-17, DOI

10.3389/fenrg.2023.1170570.

[16] I. Ziane, F. Benhamida, A. Graa, Optimizing

Weight Factors in Multi-Objective Simulated

Annealing for Dynamic Economic/Emission

Dispatch, WSEAS Transactions on Power

Systems, Vol. 10,2015, pp 89-96.

[17] S.Mirjalili, P.Jangir and Saremi, S. Multi-

objective ant lion optimizer: a multi-objective

optimization algorithm for solving

engineering problems. Appl Intell, Vol.

46,2017, pp. 79–95,

https://doi.org/10.1007/s10489-016-0825-8.

[18] S.Mirjalili, The antlion optimizer. Adv. Eng.

Softw, Vol. 83, 2015, pp. 80–98,

https://doi.org/10.1016/j.advengsoft.2015.01.0

10.

[19] S. Gupta, P. K. Biswas, T. S. Babu, and H.

H.Alhelou, Hunting Based Optimization

Techniques Used in Controlling an Active

Magnetic Bearing System, IEEE access, 10,

pp 62702-62721, 2022, DOI:

10.1109/ACCESS.2022.3182875.

[20] Alsac, O. & Stott B, Optimal load flow with

steady-state security, IEEE Transaction on

Power Application System, Vol. 93, 1974, pp,

745-751,

https://doi.org/10.1109/TPAS.1974.293972.

[21] R. H. Salem, M. E. Abdelrahman, A. Y.

Abdelaziz, Security constrained optimal

power flow by modern optimization tools,

International Journal of Engineering, Science

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2024.19.11

Ismail Ziane, Farid Benhamida, Djamal Gozim

E-ISSN: 2224-350X

86

Volume 19, 2024

and Technology, Vol. 9(3), 2017, pp. 22-30,

DOI: 10.4314/ijest.v9i3.3.

[22] S. Sayah, K. Zehar, Modiﬁed differential

evolution algorithm for optimal power ﬂow

with non-smooth cost functions,Energy

Convers Manage,Vol. 49,2008, 3036–42,

https://doi.org/10.1016/j.enconman.2008.06.0

14.

[23] AA .Abou El Ela, MA. Abido, SR. Spea,

Optimal power ﬂow using differential

evolution algorithm,Electric Power Syst Res,

Vol. 80, 2010, 875–85,

https://doi.org/10.1016/j.epsr.2009.12.018.

[24] S. Surender Reddy, P.R. Bijwe, A.R.

Abhyankar, Faster evolutionary algorithm

based optimal power ﬂow using incremental

variables, Electrical Power and Energy

Systems,Vol.54,2014,198–210,

https://doi.org/10.1016/j.ijepes.2013.07.019.

[25] S. Haddi, O. Bouketir, T. Bouktir, Improved

Optimal Power Flow for a Power System

Incorporating Wind Power Generation by

Using Grey Wolf Optimizer Algorithm,

Power Engineering And Electrical

Engineering, Vol.16(4), 2018, pp. 471-488,

DOI: 10.15598/aeee.v16i4.2883.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

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