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A new meta-heuristic programming for multi-objective optimal power flow

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Abstract

In this paper, a new multi-objective approach is suggested, known as multi-objective backtracking search algorithm (MOBSA) in order to formulate and solve the optimal power flow (OPF) problem in power systems. Many objective functions are considered like fuel cost, power losses, and voltage deviation. The structure of the proposed method is simple and has one control parameter. In addition, MOBSA is able to solve the highly constrained objectives. A fuzzy membership technique is integrated into the BSA algorithm to extract the best compromise solution from all the obtained Pareto optimal solutions. Furthermore, the capability of the MOBSA approach is evaluated and verified for bi- and tri-objectives, and tested on three standard IEEE power systems, small network 30-bus, medium network 57-bus, and large network 118-bus test systems. The obtained results reveal that the proposed method is efficient to generate well-distributed Pareto optimal non-dominated solutions. Likewise, the comparison analysis with some re-implemented methods as MODE, SPEA, MALO, and those found in the literature as MOABC/D, QOTLBO, NSGA-II and NSMOGSA, assured the superiority, effectiveness, and robustness of MOBSA.

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Abbreviations

\(a_i\), \(b_i\), \(c_i\) :

Cost coefficients of the \(i^{th}\) generator

BCS :

Best compromise solution

\(B_{ij}\) :

Susceptance of the admittance matrix

D :

Dimension

f(x, u):

Objective function

F :

Scale factor

\(F_C\) :

Fuel cost

\(G_{ij}\) :

Conductance of the admittance matrix

g(x, u):

Equality constraints

histPop :

Historical population

h(x, u):

Inequality constraints

low :

Lower limits of problem

N :

Population size (the number of individuals)

OPF :

Optimal power flow

\(P_{gi}\), \(P_{di}\) :

Active and reactive power generated at \(i^{th}\) unit

\(P_{loss}\) :

Power losses

Pop :

Population

\(Q_C\) :

Shunt VAR compensation

\(Q_{gi}\), \(Q_{di}\) :

Active and reactive power generated at \(i^{th}\) unit

\(S_{li}\) :

Apparent power flow of \(i^{th}\) line

\(T_i\) :

Tap settings of regulating transformer i

\(T_{i,j}\) :

Trial population

u :

Vector of independent variables or control variables

up :

Upper limits of problem

VD :

Voltage deviation

\(V_{gi}\) :

Voltage magnitudes at \(i^{th}\) PV buses

\(V_{li}\) :

Voltage magnitude at load bus i

x :

Vector of dependent variables or state variables

\(\mu _{fi}\) :

Membership function of \(i^{th}\) objective

\(\theta _i\) :

Voltage angles at \(i^{th}\) bus

BSA:

Backtracking search algorithm

MALO:

Multi-objective ant lion optimization

MDE:

Multi-objective differential evolution

MICA3:

Modified imperialist competitive algorithm

MOABC/D:

Multi-objective artificial bee colony algorithm based on decomposition

MODE:

Multi-objective differential evolution

MOO:

Multi-objective optimization

NSMOGSA:

Non-dominated sorting multi-objective gravitational search algorithm

NSGA II:

Non-dominated sorting genetic algorithm

SPEA:

Strength Pareto evolution algorithm

QOTLBO:

Quasi-oppositional teaching learning-based optimization

References

  1. Dommel HW, Tinney WF (1968) Optimal power flow solutions. IEEE Trans Power Syst 87(10):1866–1876

    Article  Google Scholar 

  2. Syai’in M, Soeprijanto A (2012) Improved algorithm of Newton Raphson power flow using GCC limit based on neural network. Int J Electr Comput Sci 12(1):7–12

    Google Scholar 

  3. Al Ameri A, Nichita C, Dakyo B (2014) An efficient algorithm for power load flow solutions by schur complement and threshold technique. Int J Adv Res Electr Electrical Inst Eng 3(8):11062–11069

    Google Scholar 

  4. Singhal K (2014) Comparison between load flow analysis methods in power system using MATLAB. Int J Sci Eng Res 5(5):1412–1419

    Google Scholar 

  5. Habibollahzadeh H, Luo GX, Semlyen (1989) A Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology. IEEE Trans Power Syst 4(2):530–537

  6. Aoki K, Nishikori A, Yokoyama RT (1987) Constrained load flow using recursive quadratic programming. IEEE Trans Power Syst 2(1):8–16

    Article  Google Scholar 

  7. Momoh JA, Zhu JZ (1999) Improved interior point method for OPF problems. IEEE Trans Power Syst 14(3):1114–1120

    Article  Google Scholar 

  8. Salgado RS, Schiochet AF, Barboza LV (2010) Multi-objective optimal power flow solutions through a parameterized model. In: Eighth world energy system conference, Valahia, Romania

  9. Hayyolalam V, Pourhaji Kazem AA (2020) Black Widow Optimization Algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:103249

    Article  Google Scholar 

  10. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  11. Kamboj VK, Nandi Y, Bhadoria A, Sehgal S (2020) An intensify Harris hawks optimizer for numerical and engineering optimization problems. Appl Soft Comput 89:106018

    Article  Google Scholar 

  12. Dhawale D, Kamboj VK (2020) hHHO–IGWO: A new Hybrid Harris Hawks optimizer for solving global optimization problems. International Conference on Computation, Automation and Knowledge Management (ICCAKM) 19495342

  13. Hashim FA, Houssein EH, Mabrouk MS, Al-Atabany W, Mirjalili S (2019) Henry gas solubility optimization: A novel physics-based algorithm. Future Gener Comput Syst 101:646–667

    Article  Google Scholar 

  14. Bhadoria A, Kamboj VK (2018) Optimal generation scheduling and dispatch of thermal generating units considering impact of wind penetration using hGWO-RES algorithm. Appl Intell 49(4):1517–1547

    Article  Google Scholar 

  15. Weiguo Z, Zhang Z, Wang L (2020) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300

    Article  Google Scholar 

  16. Abou El Ela AA, Abido MA, Spea SR (2011) Differential evolution algorithm for optimal reactive power dispatch. Electr Power Syst Res 81(2):458–464

    Article  Google Scholar 

  17. Suresh V, Sreejith S, Sudabattula SK, Kamboj VK (2019) Demand response-integrated economic dispatch incorporatingrenewable energy sources using ameliorated dragonfly algorithm. Electr Eng 101(2):421–442

    Article  Google Scholar 

  18. Abuella M, Hatziadoniu J (2016) Selection of most effective control variables for solving optimal power flow using sensitivity analysis in particle swarm algorithm. arXiv:1601.04150

  19. Allaoua B, Laouafi A (2008) Collective intelligence for optimal power flow solution using ant colony optimization. Electr J Pract Tech 7(13):88–105

    Google Scholar 

  20. Wankhade CM, Vaidya AP (2012) Optimal power flow evaluation of power system using genetic algorithm. Int J Power Syst Oper Energy Manag 1(4):2231–4407

    Google Scholar 

  21. Ara AL, Kazemi A, Behshad M (2013) Improving power systems operation through multi-objective optimal location of optimal unied power ow controller. Turk J Electr Eng Comput Sci 21:1893–1908

    Article  Google Scholar 

  22. Narimani MR, Azizipanah-Abarghooee R, Zoghdar-Moghadam-Shahrekohne B, Gholami K (2013) A novel approach to multi-objective optimal power flow by a new hybrid optimization algorithm considering generator constraints and multi-fuel type. Energy 49(1):119–136

    Article  Google Scholar 

  23. Sulaiman MH, Mustaffa Z, Mohamed MR, Aliman O (2015) Using the gray wolf optimizer for solving optimal reactive power dispatch problem. Appl Soft Comput 32:286–292

    Article  Google Scholar 

  24. Attia AF, El Sehiemy RA, Hasanien HM (2018) Optimal power flow solution in power systems using a novel Sine-Cosine algorithm. Int J Electr Power Energy Syst 99:331–343

    Article  Google Scholar 

  25. Ghaemi S, Aghdam FH, Safari A, Farrokhifar M (2019) Stochastic economic analysis of FACTS devices on contingent transmission networks using hybrid biogeography-based optimization. Electr Eng 101:829–843

    Article  Google Scholar 

  26. Khorsandi A, Hosseinian SH, Ghazanfari A (2013) Modified artificial bee colony algorithm based on fuzzy multi-objective technique for optimal power flow problem. Electr Power Syst Res 95:206–213

    Article  Google Scholar 

  27. Shang R, Wang J, Jiao L, Wang Y (2014) An improved decomposition-based memetic algorithm for multi-objective capacitated arc routing problem. Appl Soft Comput 19:343–361

    Article  Google Scholar 

  28. Liang RH, Wu CY, Chen YT, Tseng WT (2015) Multi-objective dynamic optimal power flow using improved artificial bee colony algorithm based on Pareto optimization. Int Trans Electr Energy Syst 26(4):692–712

    Article  Google Scholar 

  29. Medina AM, Das S, Carlos ACC, Ramirez MJ (2014) Decomposition-based modern metaheuristic algorithms for multi-objective optimal power flow a comparative study. Eng Appl Artif Intel 32:10–20

    Article  Google Scholar 

  30. Ghasemi M, Ghavidel S, Ghanbarian MM, Gitizadeh M (2015) Multi-objective optimal electric power planning in the power system using Gaussian bare-bones imperialist competitive algorithm. Inf Sci 294:286–304

    Article  MathSciNet  MATH  Google Scholar 

  31. Yuan X, Zhang B, Wang P, Ji L, Yuan Y, Huang Y, Lei X (2017) Multi-objective optimal power flow based on improved strength Pareto evolutionary algorithm. Energy 122:70–82

    Article  Google Scholar 

  32. Warida W, Hizama H, Mariuna N, Wahaba NIA (2018) A novel quasi-oppositional modified Jaya algorithm for multi-objective optimal power flow solution. Appl Soft Comput 65:360–373

    Article  Google Scholar 

  33. Zhanga J, Tang Q, Li P, Deng D, Chen Y (2016) A modified MOEA/D approach to the solution of multi-objective optimal power flow problem. Appl Soft Comput 47:494–514

    Article  Google Scholar 

  34. Sivasubramani S, Swarup K (2011) Multi-objective harmony search algorithm for optimal power flow problem. Int J Electr Power Energy Syst 33:745–752

    Article  Google Scholar 

  35. Rahmati M, Effatnejad R, Safari A (2014) Comprehensive Learning Particle Swarm Optimization (CLPSO) for Multi-objective Optimal Power Flow. Indian J Sci Tech 7(3):262–270

    Google Scholar 

  36. Barocio E, Regalado J, Cuevas E, Uribe F, Zúñga P, Torres PJR (2017) Modified bio-inspired optimisation algorithm with a centroid decision making approach for solving a multi-objective optimal power flow problem. IET Gener Trans Distri 11(4):1012–1022

    Article  Google Scholar 

  37. Abido MA, Al-Ali NA (2012) Multi-Objective Optimal Power Flow Using Differential Evolution. Arab J Sci Eng 37:991–1005

    Article  MATH  Google Scholar 

  38. Shaheen AM, Farrag SM, El-Sehiemy RA (2017) A Novel Multi-Objective Optimal Power Flow Solution Methodology. IET Proceedings Gener Trans Distrib 11(2):570–581

    Article  Google Scholar 

  39. Pulluri H, Naresh R, Sharma V (2017) An Enhanced Self-adaptive Differential Evolution Based Solution Methodology for Multiobjective Optimal Power Flow. Appl Soft Comput 54:229–245

    Article  Google Scholar 

  40. Shaheen AM, El-Sehiemy RA, Farrag SM (2015) Solving multi-objective optimal power flow problem via forced initialised differential evolution algorithm. IET Gener Trans Distrib 10(7):1634–1647

    Article  Google Scholar 

  41. Ghasemi M, Ghavidel S, Ghanbarian MM, Massrur HR, Gharibzadeh M (2014) Application of imperialist competitive algorithm with its modified techniques for multi-objective optimal power flow problem: a comparative study. Inf Sci 281:225–247

    Article  MathSciNet  Google Scholar 

  42. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144

    MathSciNet  MATH  Google Scholar 

  43. Chatzipavlis A, Tsekouras GE, Trygonis V, Velegrakis AF, Tsimikas J, Rigos A, Hasiotis T, Salmas C (2019) Modeling beach realignment using a neuro-fuzzy network optimized by a novel backtracking search algorithm. Neural Comput Appl 31:1747–1763

    Article  Google Scholar 

  44. Ahandani MA, Ghiasi AR, Kharrati H (2018) Parameter identification of chaotic systems using a shuffled backtracking search optimization algorithm. Soft Comput 22:8317–8339

    Article  Google Scholar 

  45. Lu J, Ding J (2019) Construction of prediction intervals for carbon residual of crude oil based on deep stochastic configuration networks. Inf Sci 486:119–132

    Article  Google Scholar 

  46. Khan WU, Ye Z, Chaudhary NI, Raja MAZ (2018) Backtracking search integrated with sequential quadratic programming for nonlinear active noise control systems. Appl Soft Comput 73:666–683

    Article  Google Scholar 

  47. Thai V, Cheng J, Nguyen V, Daothi P (2019) Optimizing SVM’s parameters based on backtracking search optimization algorithm for gear fault diagnosis. J Vibroeng 21(1):66–81

    Article  Google Scholar 

  48. Sriram M, Ravindra K (2020) Backtracking Search Optimization Algorithm Based MPPT Technique for Solar PV System. in: Adv Decis Sci, Image Process, Secur Comput Vis, Springer 498–506

  49. Abdolrasol MGM, Hannan MA, Mohamed A, Amiruldin UAU, Abidin IBZ, Uddin MN (2018) An optimal scheduling controller for virtual power plant and microgrid integration using the binary backtracking search algorithm. IEEE Trans Ind Appl 54:2834–2844

    Article  Google Scholar 

  50. Shaheen AM, El-Sehiemy RA, Farrag SM (2016) Optimal reactive power dispatch using backtracking search algorithm. Aust J Electr Electron Eng 13:200–210

    Article  Google Scholar 

  51. Chaib AE, Bouchekara H, Mehasni R, Abido MA (2016) Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm. Int J Electr Power Energy Syst 81:64–77

    Article  Google Scholar 

  52. El-Fergany A (2016) Multi-objective allocation of multi-type distributed generators along distribution networks using backtracking search algorithm and fuzzy expert rules. Electric Power Compon Syst 44(3):252–267

    Article  Google Scholar 

  53. Lin J (2019) Backtracking search based hyper-heuristic for the flexible job-shop scheduling problem with fuzzy processing time. Eng Appl Artif Intell 77:186–196

    Article  Google Scholar 

  54. Badawy MM, Ali ZH, Ali HA (2019) QoS provisioning framework for service-oriented internet of things (IoT). Cluster Comput 1–17

  55. Zadeh LA (1965) Fuzzy sets. Information and Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  56. Bellman R, Zadeh LA (1970) Decision-making in a fuzzy environment. Manage Sci 17:141–164

    Article  MathSciNet  MATH  Google Scholar 

  57. Alsac O, Stott B (1974) Optimal load flow with steady-state security. IEEE Trans Power Apparatus Syst 93(3):745–751

    Article  Google Scholar 

  58. Zimmerman RD, Murillo-Sánchez CE, Thomas, RJ, Matpower Available at: http://www.pserc.cornell.edu/matpower

  59. Bhowmik AR, Chakraborty AK (2014) Solution of optimal power flow using non-dominated sorting multi objective gravitational search algorithm. Int J Electr Power Energy Syst 62:323–334

    Article  Google Scholar 

  60. Mandal B, Roy PK (2014) Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization. Appl Soft Comput 21:590–606

    Article  Google Scholar 

  61. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. Evol Comput IEEE Trans 1:67–82

    Article  Google Scholar 

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Authors and Affiliations

  1. Engineering for Smart and Sustainable Systems Research Center, Mohammadia School of Engineers, Mohammed V University, Rabat, Morocco

    Fatima Daqaq, Mohammed Ouassaid & Rachid Ellaia

  2. Laboratory of Study and Research for Applied Mathematics, Mohammadia School of Engineers, Mohammed V University, Rabat, Morocco

    Fatima Daqaq & Rachid Ellaia

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  1. Fatima Daqaq
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  2. Mohammed Ouassaid
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  3. Rachid Ellaia
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Correspondence to Fatima Daqaq.

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Daqaq, F., Ouassaid, M. & Ellaia, R. A new meta-heuristic programming for multi-objective optimal power flow. Electr Eng 103, 1217–1237 (2021). https://doi.org/10.1007/s00202-020-01173-6

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