Performance Study of A System with Optimal Location of STATCOM Device using MPMJ Algorithm under Normal Operating Conditions

Performance Study of A System with Optimal Location of STATCOM Device using MPMJ Algorithm under Normal Operating Conditions

Yeshitela Shiferaw Maru

Research Scholar, Andhra University, College of Engineering,

Department of Electrical Engineering, Visakhapatnam-530003, Andhra Pradesh, India

K. Padma

Assistant professor, Andhra University, College of Engineering,

Department of Electrical Engineering, Visakhapatnam-530003, Andhra Pradesh, India

Abstract:- Optimal power flow solution is the backbone of power system operation, power system future design, stability analysis, and power system future expansion. To solve this optimal power flow problem, there are many traditional and meta-heuristics algorithms in the literature. The regular optimal power flow has visible limitations: it takes much time to converge and fails to produce the optimal values within the operating limits. Due to these drawbacks, the researcher shifted to a meta-heuristic algorithm. In this paper mainly devoted to minimize the fuel cost of the generator, improve the voltage magnitude, reduce active power loss, and voltage stability index using the mention meta-heuristic algorithm. The feasibility and effectiveness of the proposed algorithm approach are investigated and exemplarily demonstrated on the IEEE-30 bus test system. The performance of the optimal power flow performed by allocating the proper place of the STATCOM device using the Analytical Hierarchy Process (AHP). From the simulation result for the given objective, the metaheuristic TLBO, JAYA, and MPMJ algorithm compared with and without STATCOM. Besides, the comparison is made with similar studies in the literature. Based on the simulation result, the proposed MPMJ algorithm is the most powerful for the optimization algorithm for the defined objective and selected test system.

Keywords: AHP, MPMJ, OPF, STATCOM, FACTS,

Metaheuristic algorithm.

1. INTRODUCTION

   Optimal power flow (OPF) is part of an integrated power system delivery solution. OPF main goal is to optimize the selected objective feature, including fuel cost, voltage stability indices, active and reactive power loss, and optimum power system control variables change. Nevertheless, it must satisfy reactive power limits on equality and inequality constraints [1]. The OPF problem was and remains one of the most investigated problems in power systems. Earlier, as stated in [2], several classical (deterministic) optimization algorithms were successfully applied, such as Interior point methods[3], [4], Newton's method [5], linear programming methods [6], non-linear programming and gradient method

   [7] are useful to solve optimal power flow besides, the conventional methods have strong limitations in convergence, and they cause complications in obtaining the overall optimal solutions.

   Due to the problems mentioned above, the research focus has already shifted to the meta-heuristic algorithm. The

   varieties of Meta-heuristic Algorithm that can solve optimal power flow complication, like particle swarm optimizations (PSO) [8], a novel hybrid bat algorithm [9], Artificial Bee Colony algorithm (ABC) [10], and Fruit Fly optimization [11].

   Analytical Hierarchy Process effectively supports decision making concerning complex sustainability issues and can help to recognize and define a problem in detail. It is widely used to decompose a decision problem into its essential parts, which are then structured hierarchically. As a result, AHP delivers a ranking of options which facilitate the selection of a strategy option [12].In this paper, the allocation of STATCOM FACTS device is applied on the bus by using Analytical Hierarchy Process (AHP) which in turn compares four parameters namely fuel cost of the generator, active power loss, sum of voltage magnitude on the bus and voltage stability index. We have to select five weakest buses using the voltage stability index. Then, based on these four parameters, we can determine the optimal bus using that AHP method.

2. MATHEMATICAL MODELLING OF STATCOM

   DEVICE

   Active and reactive power flow determined by the phase angle difference between the sources and by the voltage magnitude difference, respectively. Hence, STATCOM can control reactive power flow by changing the fundamental component of the converter voltage concerning the AC bus voltage, both phase and magnitude sensible [12]. In [13], the placement of STATCOM FACTS device based on the PQ bus having low voltage magnitude and the rate STATCOM MVAr rating is between -100 & +100MVAr.

   A mathematical model for the controller to the inclusion of load flow algorithm derived from the equivalent circuit diagram of STATCOM in Figure 2.

   Bus

   Transmission line

   AC

   Load

   Load

   to DC

   + VDC

   Modelling of OPF

3. MATHEMATICAL FORMULATIONS OF OPTIMAL POWER FLOW PROBLEM

Mathematically, the OPF problem can be formulated as a nonlinearly constrained optimization problem can be expressed as follows.

Converter –

Figure 1. STATCOM schematic diagram

Minimize

Subject to

F (u, v)

E(u, v) 0

I (u, v) 0

Where F is the objective functions to be minimized, u and v are the vectors of dependent and control variables, respectively. F (u, v), objective function; E (u, v), set of equality constraints; I (u, v), set of inequality constraints.

u can be expressed as

Figure 2. Equivalent diagram of STATCOM device

The STATCOM power flow equations are derived from first principles and assume the following voltage source representation.

It is expressed in Norton equivalent form

The STATCOM voltage injection VvR bound constraint is as

Where NG, NT, and NC are the number of generators, the number of regulating transformers, and the number of VAR compensators, respectively.

The set of state variables for the OPF problem formulation are PG1, active power output at the slack bus, VL, voltage magnitude at PQ buses, load buses; QG, reactive power output of all generating units; Sl, transmission line loading (or line flow).

The following equations give the objective function. Cost minimization

follows:

VvR min

VvR VvR max

Voltage deviation (VD)

Where VvR min and VvR max are the STATCOM's minimum

and maximum voltage.

The current expression in (3) is transformed into a power expression by the VSC and power injection into the bus k as shown in equations (4) and (5) respectively.

Voltage stability index

Where

ij

is the power factor angle and

i & j

are

W

magnitude and angle, respectively.

voltage

voltage angle of the ith and jth bus respectively Active power loss

Equality constraints

1. Real power constraints

   n

   Where RI is a set of given average stochastic consistency, indices and CR is the stochastic consistency ratio.

   For matrices with dimensions ranging from one to nine, respectively, the values of RI have been displayed in [16],[15].

   It is evident that for a matrix with a dimension of one or two, it is not necessary to check the stochastic consistency ratio. Generally, the judgment matrix is satisfied (acceptable) if the

   PGi PDi Vi Vj

   j 1

   Yij cosij i j 0

   stochastic consistency ratio, CR < 0.10.

   1. OVERVIEW OF OPTIMIZATION ALGORITHMS

2. Reactive power constraints

n

Teaching Learning Based Optimization

The TLBO algorithm is a teaching-learning process

QGi QDi Vi

j 1

Vj Yij sin ij i j 0

motivated algorithm proposed by Rao et al and Savsani based on the impact of a teacher on the output of learners in a class

Inequality constraints

The inequality constraints can be considered the minimum and maximum values of Generators, Transformer, shunt var compensation, security or transmission line MVA rating, and STATCOM voltage magnitude, and angles. The voltage of each load bus must be restricted within its lower and upper operating limits. Line flow through each transmission line ought to be restricted by its capacity limits.

1. ANALYTICAL HIERARCHY PROCESS

   METHOD

   The Analytic Hierarchy Process (AHP) is widely used in multi-criteria decision-making tools for tackling multi- attribute decision-making problems in real situations [14]. It represents a powerful technique for solving complicated and unstructured issues that may have interactions and correlations among different objectives and goals [14],[15].

   The mathematical modelling of the AHP methods

   [17], [18].

   The algorithm describes two basic modes of learning:

   1. Teacher phase

   2. Learner phase

      1. Teachers phase

         a group of learners is considered as population and different subjects offered to the learners are considered as other design variables of the optimization problem and a learner's result is analogous to the 'fitness' value of the optimization problem. The best solution in the entire population is considered as the teacher. The design variables are the parameters involved in the objective function of the given optimization problem, and the best solution is the best value of the objective function.

         In TLBO, at each iteration, the mean of decision vectors is computed and denoted by M, the student with the best mark is designated as a teacher. Then, the position of all students is updated via the following equation [16], [18].

         can be:

         Calculate the maximal Eigenvalue

         max

         Xi,new Xi,old r(Xteacher TF .M )

         15

         Xi,new Xi,old r(Xteacher TF .M )

         15

         of the

         judgment matrix

         n ( AW ) j max nW i1 i

         12

         CI max n n 1

         13

         CI max n n 1

         13

         Where (AW ) j represents the jth element in vector AW The consistency index of a hierarchy ranking CI is defined as

         Where max the maximal Eigenvalue of the judgment matrix is n the dimension of the judgment matrix.

         The stochastic consistency ratio is defined as

      2. Learner phase

   As in a real classroom, students learn from each other by discussions, presentations and formal communications; in student phase, for each student i, another student j is randomly picked up, and then, the student with better mark (fitness) is attracted towards (learns from) the other student. That is if student j is fitter than student i, then

   Xi,new Xi,old ri(X j Xi,old )

   16

   JAYA algorithm

   The Jaya algorithm is a met heuristic which is capable of solving both constrained and unconstrained optimization problems. It is a population-based method which repeatedly modifies a population of individual solutions [19].

   CR CI RI

   14

   X ' X r [( X ) ( X )] r [( X ) ( X )] j ,k ,i j ,k ,i 1, j ,i j ,best ,i j ,k ,i 2, j ,i j ,worst ,i j ,k ,i

   17

   CR CI RI

   14

   X ' X r [( X ) ( X )] r [( X ) ( X )] j ,k ,i j ,k ,i 1, j ,i j ,best ,i j ,k ,i 2, j ,i j ,worst ,i j ,k ,i

   17

   Initialize population size, number of design variables, and termination criterion

   Identify best, and worst solution in the population

   Modify the solutions based on best and worst solutions

   X ' X

   • r [( X

   ) ( X

   )] r

   [( X

   ) ( X )]

   j ,k ,i j ,k ,i

   1, j ,i j ,best ,i j ,k ,i

   2, j ,i j ,worst ,i j ,k ,i

   Yes

   Is the modified solution is No

   better

   than the previous solution?

   Accept and replace the previous soltution

   Keep the previous solution

   No

   Is the stopping criterion satisfied?

   Yes

   Report the optimal solution

   Report the optimal solution

   Figure 3. Flow chart of Jaya algorithm

   Proposed Multi Population-Based Modified Jaya (MPMJ) Algorithm

   In the proposed modified JAYA algorithm, an elite member in the population act as a guide to other members in the population to enhance their positions to a place near to the best-known position.

   For the proposed modified Jaya algorithm, the mathematical equation can be shown in equation (18) below [20].

   X ' X r [(X ) ( X )] L *r [( X 2 ) (X )] j,k ,i j,k ,i 1, j,i j,worst,i j,k ,i 2, j,i j,k,i j,best,i

   18

   Where L is a coefficient determined in each iteration as follows:

   if rand > 0.5 then L =1;

   else L=-1;

   end. Since the rand value the number between 0 andone.

   Figure 4, the algorithm steps for the multi-population algorithm can be explained

   Figure 4. The basic flow chart of the MPMJ algorithm

   In the following Figure 5, the application of the multi population based modified Jaya (MPMJ) algorithm for the solution of optimal power flow without and with STATCOM device.

   Start

   Initialize the number of population ,design variable, maximum number of iteration, declare input data of transmission line, transformer tap setting, load and generator data, STATCOM device data

   Generate an initial random population

   Divide the population in to sub population,and apply flow chart on Figure 4.

   Run the load flow using Newton Raphson without and with STATCOM device

   Calculate the optimum power flow of the objective function with the initial population without and with STATCOM device within the accept range of control variables, and save the value of the objective function

   For j=1

   Identify the best and worst solution among the current population

   Modify the candidate solution based on the best and worst solution

   Run load flow for each modified solution, and calculate the value of the objective function without and with STATCOM device

   Yes

   Based on the value of the objective function. No

   Is the modified solution superior than the previous solution ?

   Accept the new solution and

   reject the previous solution

   Keep the previous

   solution

   j=j+1

   No

   Is the stopping criterion satisfied?

   Yes

   Display the optimal values

   stop

   Figure 5. Flow chart of MPMJ algorithm for the application of optimum power flow solution without and with STATCOM device

   1. RESULT AND DISCUSSION

      The effectiveness of the metaheuristic Algorithm TLBO, JAYA, and proposed Multi population Modified- based Jaya (MPMJ) Algorithm without, and with

      STATCOM device are examined on standard IEEE-30, bus system to test the system for OPF problems. The optimal allocation of the STATCOM device is selected by using the Analytical Hierarchy Process (AHP) method. The voltage

      magnitude and phase angle of the STATCOM device are

      0.9 to 1.1pu, and -10 to 10 degree, respectively [21].

      The case studies for simulation are as follows under normal operating conditions:

      Case I: Single-objective optimization without STATCOM device

      Case II: Single-objective optimization with STATCOM device at the selected bus locations

      Case I: Single-objective optimization without STATCOM device

      In this section, the proposed comparison techniques of optimal power flow solutions are evaluated using the IEEE- 30 bus system.

      Figure 6(a) shows the convergence characteristics of the fuel cost of generation for the IEEE 30-bus test system under normal operating conditions without STATCOM device. The minimum costs obtained using TLBO, JAYA, and proposed MPMJ algorithms are798.79$/hr, 797.8$/hr, and 797.5$/hr, respectively. Figure 6(b) shows the convergence characteristics of total real power loss for the IEEE 30-bus system under normal operating conditions. The minimum power losses obtained using TLBO, JAYA, and proposed MPMJ algorithms are 0.046p.u, 0.0288p.u and 0.0286pu respectively. Figure 6(c) shows the convergence characteristics of the sum of voltage deviation for IEEE 30-bus system under normal operating conditions. The minimum sum of voltage deviation obtained using TLBO, JAYA, and proposed MPMJ algorithms are 0.203084p.u, 0.1133pu and0.0987pu, respectively. Figure 6(d) shows the convergence characteristics of the voltage stability index for the IEEE 30-bus system under normal operating conditions.

      Figure 6(a). Convergence characteristics of total fuel cost of generation without STATCOM device

      Figure 6 (b). Convergence characteristics of total active power loss without STATCOM device

      Figure 6 (c). Convergence characteristics of the voltage deviation without STATCOM device

      Figure 6(d). Convergence characteristics of the sum of squared voltage stability index without STATCOM device

      Case II: Single-objective optimization with STATCOM device at the selected line locations

      To get the optimal operation of the power system within the constraint, the selection of the best location of FACTS devices plays an essential role in the process of the power system.

      The considered locations of STATCOM are the bus numbers 19,24,26,29, and 30. These locations are taken based on the first five maximum voltage stability index of load buses from steady-state values of load buses. The value of the voltage stability index at bus 19,24,26,29, and 30. is 0.0621, 0.0690, 0.0812, 0.0697, and 0.0822

      respectively. The voltage stability index for load buses is shown in Figure 7.

      Figure 7. Bus stability index for IEEE-30 bus system

      Table 1 gives the optimized values of different attributes at different alternatives. This OPF results with the STATCOM device are used as a decision matrix for the system and then given as an input to the AHP method.

      In pairwise comparison Table 2, diagonal elements are taken as 1, which means objectives are of equal importance. The upper diagonal elements of the matrix have been taken by giving preferences to the attributes, and the lower diagonal elements of the matrix have been taken as a reciprocal of the upper diagonal elements of the matrix.

      Table 3 is a normalized principal eigenvector called a priority vector or weight matrix of the attributes. Since it is normalized, the sum of all attributes in the priority vector is 1, and the Priority vector shows relative weights among the things that we compare.

      Table 4 shows the relative ranking of alternatives under five objective functions, which are the minimization of fuel cost of the generator, minimizing the sum of voltage deviation, minimizing active power loss, and enhancement of voltage stability index by the AHP method.

      Table 1. OPF results and decision table for the AHP method for IEEE-30 bus

      Alternatives	Attributes
      Load bus	Fuel cost ($/h)	Power loss (pu)	VSI	VD (pu)
      Bus 19	797.47	0.0252	0.1023	0.0970
      Bus 24	797.34	0.0280	0.1031	0.096
      Bus 26	797.3	0.0265	0.1016	0.0924
      Bus 29	797.2	0.0285	0.1040	0.0990
      Bus 30	797.3	0.0272	0.1020	0.0918

      Table 2. Pairwise comparison matrix for attributes

      Objective	Attributes
      	Fuel cost	Power loss	VSI	VD
      Fuel cost	1	2	3	3
      Power loss	0.5	1	2	5
      VSI	0.33	0.5	1	2
      VD	0.33	0.2	0.5	1

      Table 3. Weight matrix and value of attributes

      Attributes	Weightage	Subjective measurement of attributes	Assigned values
      Fuel cost	0.3905
      Power loss	0.2761	Eigen value	4.1213
      VIS	0.1953	Consistency index	0.0404
      VD	0.1381	Consistency ratio	0.0454

      Table 4. Weakest bus ranking by AHP methods

      Alternatives load bus	AHP ranking
      Bus 19	2
      Bus 24	5
      Bus 26	1
      Bus 29	3
      Bus 30	4

      Figures 8(a)-8(d) show the convergence characteristic of each objective function with STATCOM at bus 26 for IEEE-30

      bus system, showing smooth convergence to the optimum value without spontaneous oscillations for best run under normal operating conditions.

      Figure 8(a). Convergence characteristics of total fuel cost of the generator using STATCOM at bus 26

      Figure 8(b). Convergence characteristics of real power loss using STATCOM at bus 26

      Figure8(c). Convergence characteristics of sum of squared voltage stability index with STATCOM at bus 26

      Figure 8(d). Convergence characteristics of voltage deviation using STATCOM at bus 26

   2. CONCLUSION

The optimal power flow solution is the critical power system network resources, and various optimization strategies exist to solve the optimal power flow problems. In this paper, we applied the proposed MPMJ algorithm without and with STATCOM device, compared to the recent literature algorithm Results from the proposed

algorithm method are contrasted with the recent literature in Table 5. From the result, it is clear that the proposed method can achieve better results concerning other algorithms for IEEE-30 bus test system. These values are not negligible because of the continuous operations of power dispatch throughout the years.

Table 5. Comparison of proposed MPMJ algorithm with other recent methods reported in the literature

The only parameters to be set for TLBO and JAYA algorithms are population size, several iterations and number of runs, the only difference for proposed MPMJ algorithms is the number of initial sub-population and modified original JAYA algorithm. The optimal values of the proposed MPMJ algorithm are converged early, including the STATCOM device, and optimal values are obtained for the objective function of generation fuel cost, active power loss, minimizing voltage summation and enhancing voltage stability index.

The proposed MPMJ algorithm is constructed using the exclusive collection of best group values and subpopulations. The key benefit of the proposed MPMJ algorithm to solve the OPF problem is that there is no tuning parameter and simple divergence control. Therefore, due to not using external settings, the result obtained is more desirable than the other metaheuristic algorithm. Thus, the proposed MPMJ algorithm can be easily extended to solve the OPF problem with a quick convergence rate and the optimal result in the power system operating limits.

REFERENCE

1. H. Bouchekara, "Solution of the optimal power flow problem considering security constraints using an improved chaotic electromagnetic field optimization algorithm," Neural Comput. Appl., vol. 32, no. 7, pp. 26832703, Apr. 2020, doi: 10.1007/s00521-019-04298-3.

2. P. K. Roy, S. P. Ghoshal, and S. S. Thakur, "Biogeography based optimization for multi-constraint optimal power flow with emission and non-smooth cost function," Expert Syst. Appl., vol. 37, no. 12, pp. 82218228, Dec. 2010, doi: 10.1016/j.eswa.2010.05.064.

3. T. Wadayama, "Interior Point Decoding for Linear Vector Channels Based on Convex Optimization," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 49054921, Oct. 2010, doi: 10.1109/TIT.2010.2060030.

4. R. Ramos de Souza, A. Roberto Balbo, L. Nepomuceno, E. Cassia Baptista, E. Martins Soler, and R. Bento Nogueira Pinheiro, "A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems," IEEE Lat. Am. Trans., vol. 15, no. 8, pp. 14131421, 2017, doi: 10.1109/TLA.2017.7994787.

5. B Brandstatter, C. Magele, and W. Ring, "A full step Newton method for the solution of a non-linear magnetostatic optimization problem," IEEE Trans. Magn., vol. 37, no. 5, pp. 32123215, Sep. 2001, doi: 10.1109/20.952579.

6. R. T. Meyer, M. efran, and R. A. DeCarlo, "A Comparison of the Embedding Method with Multiparametric Programming, Mixed- Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based Methods," IEEE Trans. CONTROL Syst. Technol., vol. 22, no. 5, p. 17, 2014.

7. H. Dalman and M. Bayram, "Interactive Fuzzy Goal Programming Based on Taylor Series to Solve Multiobjective Non-linear Programming Problems with Interval Type-2 Fuzzy Numbers," IEEE Trans. FUZZY Syst., vol. 26, no. 4, p. 16, 2018.

8. Khalid. H. Mohamed, K. S. R. Rao, and K. N. B. Md. Hasan, "Optimal power flow and interline power flow controllers using particle swarm optimization technique," in TENCON 2009 – 2009 IEEE Region 10 Conference, Singapore, Nov. 2009, pp. 16, doi: 10.1109/TENCON.2009.5395876.

9. G. Chen, J. Qian, Z. Zhang, and Z. Sun, "Applications of Novel Hybrid Bat Algorithm with Constrained Pareto Fuzzy Dominant Rule on Multiobjective Optimal Power Flow Problems," IEEE Access, vol. 7, pp. 5206052084, 2019, doi: 10.1109/ACCESS.2019.2912643.

10. L. Le Dinh, D. Vo Ngoc, and P. Vasant, "Artificial Bee Colony Algorithm for Solving Optimal Power Flow Problem," Sci. World J., vol. 2013, pp. 19, 2013, doi: 10.1155/2013/159040.

11. M. Balasubbareddy, "Multiobjective optimization in the presence of ramp-rate limits using non-dominated sorting hybrid fruit fly algorithm," Ain Shams Eng. J., vol. 7, no. 2, pp. 895905, Jun. 2016, doi: 10.1016/j.asej.2016.01.005.

12. C. Pisani and D. Villacci, "A novel AHP framework for Decision Making in Power Systems sustainable development," no. 0954, p. 6, 2011.

13. Annapurna Bhargava, "load flow study of large power system with STATCOM FACTS devices.",2014.

14. C. Pisani and D. Villacci, "A novel AHP framework for Decision Making in Power Systems sustainable development," no. 0954, p. 6, 2011.

15. Yeshitela Shiferaw, K.Padma, "The Optimal Power Flow Solution by Optimal Location of STATCOM Device using AHP Method," Int. J. Innov. Technol. Explor. Eng., vol. 9, no. 4, pp. 25612569, Feb. 2020, doi: 10.35940/ijitee.D1944.029420.

16. T. Niknam, R. Azizipanah-Abarghooee, and J. Aghaei, "A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch," IEEE Trans. Power Syst., vol. 28, no. 2, pp. 749763, May 2013, doi: 10.1109/TPWRS.2012.2208273.

17. R. V. Rao, V. J. Savsani, and D. P. Vakharia, "Teaching Learning-Based Optimization: An optimization method for continuous non-linear large-scale problems," Inf. Sci., vol. 183, no. 1, pp. 115, Jan. 2012, doi: 10.1016/j.ins.2011.08.006.

18. R. V. Rao and V. Patel, "An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems," Int. J. Ind. Eng. Comput., vol. 3, no. 4, pp. 535560, Jul. 2012, doi: 10.5267/j.ijiec.2012.03.007.

19. R. Venkata Rao, "Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems," Int. J. Ind. Eng. Comput., pp. 1934, 2016, doi: 10.5267/j.ijiec.2015.8.004.

20. E. E. Elattar and S. K. ElSayed, "Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement," Energy, vol. 178, pp. 598609, Jul. 2019, doi: 10.1016/j.energy.2019.04.159.

21. B. S. Rao and K. Vaisakh, "Application of ACSA to solve single/multi objective OPF problem with FACTS devices," in 2013 15th International Conference on Advanced Computing Technologies (ICACT), Rajampet, India, Sep. 2013, pp. 16, doi: 10.1109/ICACT.2013.6710536.

22. D. P. Ladumor, I. N. Trivedi, R. H. Bhesdadiya, and P. Jangir, "Optimal Power Flow problems solution with SVC using meta- heuristic algorithm," in 2017 Third International Conference on Advances in Electrical, Electronics, Information, Communication and Bio-Informatics (AEEICB), Chennai, India, Feb. 2017, pp. 283288, doi: 10.1109/AEEICB.2017.7972430.

23. A. A. El-Fergany and H. M. Hasanien, "Single and Multiobjective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms," Electr. Power Compon. Syst., vol. 43, no. 13, pp. 15481559, Aug. 2015, doi: 10.1080/15325008.2015.1041625.

24. S. Surender Reddy, P. R. Bijwe, and A. R. Abhyankar, "Faster evolutionary algorithm based optimal power flow using incremental variables," Int. J. Electr. Power Energy Syst., vol. 54, pp. 198210, Jan. 2014, doi: 10.1016/j.ijepes.2013.07.019.

25. A.-A. A. Mohamed, "Optimal power flow using moth swarm algorithm," Electr. Power Syst. Res., p. 17, 2017.

26. 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 Comput. Appl., vol. 30, no. 6, pp. 18891904, Sep. 2018, doi: 10.1007/s00521-016-2794-6.

27. A.-F. Attia, "Optimal power flow solution in power systems using a novel Sine-Cosine algorithm," p. 13, 2018.

28. T. T. Nguyen, "A high performance social spider optimization algorithm for optimal power flow solution with single objective optimization," p. 23, 2019.

29. H. Tehzeeb-Ul-Hassan, R. Zafar, S. A. Mohsin, and O. Lateef, "Reduction in power transmission loss using fully informed particle swarm optimization," Int. J. Electr. Power Energy Syst., vol. 43, no. 1, pp. 364368, Dec. 2012, doi: 10.1016/j.ijepes.2012.05.028.

30. W. Warid, H. Hizam, N. Mariun, and N. Abdul-Wahab, "Optimal Power Flow Using the Jaya Algorithm," Energies, vol. 9, no. 9, p. 678, Aug. 2016, doi: 10.3390/en9090678.

31. A. Bhattacharya and P. K. Chattopadhyay, "Application of biogeography-based optimization to solve different optimal power flow problems," IET Gener. Transm. Distrib., vol. 5, no. 1, p. 70, 2011, doi: 10.1049/iet-gtd.2010.0237.

32. A.-F. Attia, Y. A. Al-Turki, and A. M. Abusorrah, "Optimal Power Flow Using Adapted Genetic Algorithm with Adjusting Population Size," Electr. Power Compon. Syst., vol. 40, no. 11, pp. 12851299, Aug. 2012, doi: 10.1080/15325008.2012.689417.