Advertisement

Neural Computing and Applications

, Volume 31, Issue 12, pp 8787–8806 | Cite as

Single- and multi-objective optimal power flow frameworks using Jaya optimization technique

  • Salma Abd El-Sattar
  • Salah Kamel
  • Ragab A. El Sehiemy
  • Francisco JuradoEmail author
  • Juan Yu
Original Article
  • 86 Downloads

Abstract

Solution of optimal power flow (OPF) problem is very important for power system operation, planning and energy management. OPF analysis aims to find the optimal solution of system nonlinear algebraic equations with satisfying operational constraints. In this paper, a new and efficient technique called Jaya optimizer is comprehensively applied to solve the OPF problem in power systems. Jaya optimization algorithm is characterized with the movement toward the best solution and avoiding the trapping into local optima. Different frameworks are developed for solving the single- and multi-objective (two- to five-objective functions) OPF problems. These frameworks are developed to achieve the following objective functions: fuel cost minimization, voltage deviation minimization, voltage stability enhancement, power loss minimization and emission minimization. In the developed multi-objective OPF framework, Pareto concept is combined with Jaya optimization algorithm to obtain a set of non-dominated solutions, and then the best compromise solution is extracted using fuzzy set theory. The developed OPF frameworks are validate using two standard IEEE test systems with 23 studied cases. The results prove the effectiveness and superiority of the developed OPF frameworks compared with other well-known optimization algorithms.

Keywords

Optimal power flow Jaya optimizer Pareto front Single- and multi-objective functions Voltage stability enhancement Power loss minimization Voltage profile improvement 

List of symbols

fi

Objective function

M

Number of objectives

gj

Equality constraints

N

Number of equality constraints

hk

Inequality constraints

q

Number of inequality constraints

u

Vector of control variables

x

State vector of dependent variables

PG, QG

Generated active and reactive powers, respectively

VG

Generation bus voltage

QC

Reactive power output of VAR source

T

Transformer tap ratio

VL

Load bus voltage

Sl

Apparent power flow

NG

Number of generators

NT

Number of regulating transformers

NC

Number of existing VAR sources

NL

Number of load buses

Nl

Number of transmission lines

NB

Number of buses

PD, QD

Active and reactive load demand, respectively

G, B

Conductance and substance of line, respectively

\(\delta_{j} , \delta_{i}\)

Voltage angles of buses i and j, respectively

\(a_{i} ,b_{i} ,c_{i}\)

Coefficients of ith generator cost coefficients

\(\gamma_{i} ,\beta_{i} ,\alpha_{i} ,\zeta_{i} ,\lambda_{i}\)

Emission coefficients of ith unit

\(X_{j,k,i}\)

Value of jth variable for the kth candidate solution at ith iteration

\(X_{j,k,i}^{'}\)

Updated value of \(X_{j,k,i}\)

\(X_{{j,{\text{best}},i}}\)

The best solution of variable j

\(X_{{j,{\text{worst}},i}}\)

The worst solution of variable j

\(r_{1} ,r_{2}\)

Random values in interval [0, 1]

\(f_{j}^{\hbox{min} } ,f_{j}^{\hbox{max} }\)

Lower and upper bounds of ith objective function, respectively

\(\lambda_{\text{p}} ,\lambda_{\text{v}} ,\lambda_{\text{Q}} ,\lambda_{\text{s}}\)

Penalty factors

D

Non-dominated solutions number

Notes

Acknowledgements

The authors gratefully acknowledge the contribution of the NSFC (China)-ASRT (Egypt) Joint Research Fund, Project No. 51861145406, for providing partial research funding to the work reported in this research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Dommel HW, Tinney WF (1968) Optimal power flow solutions. IEEE Trans Power Appar Syst 10:1866–1876Google Scholar
  2. 2.
    Shaheen AM, El-Sehiemy RA, Farrag SM (2019) A reactive power planning procedure considering iterative identification of VAR candidate buses. Neural Comput Appl 31(3):1–22Google Scholar
  3. 3.
    Yan X, Quintana VH (1999) Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Trans Power Syst 14(2):709–717Google Scholar
  4. 4.
    Habibollahzadeh H, Luo GX, Semlyen A (1989) Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology. IEEE Trans Power Syst 4(2):530–537Google Scholar
  5. 5.
    Burchett RC, Happ HH, Vierath DR (1984) Quadratically convergent optimal power flow. IEEE Trans Power Appar Syst 11:3267–3275Google Scholar
  6. 6.
    Ebeed M, Kamel S, Jurado F (2018) Optimal power flow using recent optimization techniques. In: Classical and recent aspects of power system optimization. Elsevier, Amsterdam.  https://doi.org/10.1016/B978-0-12-812441-3.00007-0 Google Scholar
  7. 7.
    El-sattar SA, Kamel S, Tostado M, Jurado F (2018) Lightning attachment optimization technique for solving optimal power flow problem. In: 2018 twentieth international Middle East power systems conference (MEPCON). IEEE, pp 930–935Google Scholar
  8. 8.
    Abido MA (2002) Optimal power flow using particle swarm optimization. Int J Electr Power Energy Syst 24(7):563–571Google Scholar
  9. 9.
    Liang RH, Tsai SR, Chen YT, Tseng WT (2011) Optimal power flow by a fuzzy based hybrid particle swarm optimization approach. Electr Power Syst Res 81(7):1466–1474Google Scholar
  10. 10.
    Bouchekara HREH (2014) Optimal power flow using black-hole-based optimization approach. Appl Soft Comput 24:879–888Google Scholar
  11. 11.
    Bhattacharya A, Chattopadhyay PK (2011) Application of biogeography-based optimisation to solve different optimal power flow problems. IET Gener Transm Distrib 5(1):70–80Google Scholar
  12. 12.
    Mandal B, Roy PK (2014) Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization. Appl Soft Comput 21:590–606Google Scholar
  13. 13.
    Youssef H, Kamel S, Ebeed M (2018) Optimal power flow considering loading margin stability using lightning attachment optimization technique. In: 2018 twentieth international Middle East power systems conference (MEPCON). IEEE, pp 1053–1058Google Scholar
  14. 14.
    Abdo M, Kamel S, Ebeed M, Yu J, Jurado F (2018) Solving non-smooth optimal power flow problems using a developed Grey Wolf Optimizer. Energies 11(7):1692Google Scholar
  15. 15.
    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 95:206–213Google Scholar
  16. 16.
    Sivasubramani S, Swarup KS (2011) Multi-objective harmony search algorithm for optimal power flow problem. Int J Electr Power Energy Syst 33(3):745–752Google Scholar
  17. 17.
    El Ela AA, Abido MA, Spea SR (2010) Optimal power flow using differential evolution algorithm. Electr Power Syst Res 80(7):878–885Google Scholar
  18. 18.
    Varadarajan M, Swarup KS (2008) Solving multi-objective optimal power flow using differential evolution. IET Gener Transm Distrib 2(5):720–730Google Scholar
  19. 19.
    Sivasubramani S, Swarup KS (2011) Sequential quadratic programming based differential evolution algorithm for optimal power flow problem. IET Gener Transm Distrib 5(11):1149–1154Google Scholar
  20. 20.
    Abido MA, Al-Ali NA (2012) Multi-objective optimal power flow using differential evolution. Arab J Sci Eng 37(4):991–1005zbMATHGoogle Scholar
  21. 21.
    Taher MA, Kamel S, Jurado F, Ebeed M (2019) An improved moth-flame optimization algorithm for solving optimal power flow problem. Int Trans Electr Energy Syst 29(3):e2743Google Scholar
  22. 22.
    Kumari MS, Maheswarapu S (2010) Enhanced genetic algorithm based computation technique for multi-objective optimal power flow solution. Int J Electr Power Energy Syst 32(6):736–742Google Scholar
  23. 23.
    Taher MA, Kamel S, Jurado F, Ebeed M (2019) Modified grasshopper optimization framework for optimal power flow solution. Electr Eng 29(3):1–28Google Scholar
  24. 24.
    Bouchekara HREH, Abido MA (2014) Optimal power flow using differential search algorithm. Electr Power Compon Systms 42(15):1683–1699Google Scholar
  25. 25.
    Bouchekara HR, Chaib AE, Abido MA, El-Sehiemy RA (2016) Optimal power flow using an Improved Colliding Bodies Optimization algorithm. Appl Soft Comput 42:119–131Google Scholar
  26. 26.
    Roy PK, Paul C (2015) Optimal power flow using Krill Herd algorithm. Int Trans Electr Energy Syst 25(8):1397–1419Google Scholar
  27. 27.
    Rao R (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7(1):19–34Google Scholar
  28. 28.
    Warid W, Hizam H, Mariun N, Abdul-Wahab N (2016) Optimal power flow using the Jaya algorithm. Energies 9(9):678Google Scholar
  29. 29.
    Rao R, Rai DP, Ramkumar J, Balic J (2016) A new multi-objective Jaya algorithm for optimization of modern machining processes. Adv Prod Eng Manag 11(4):271Google Scholar
  30. 30.
    Barakat AF, El-Sehiemy RA, Elsaid M, Osman E (2018) Solving reactive power dispatch problem by using JAYA optimization algorithm. Int J Eng Res Afr 36:12–24Google Scholar
  31. 31.
    Kumar N, Hussain I, Singh B, Panigrahi BK (2017) Rapid MPPT for uniformly and partial shaded PV system by using JayaDE algorithm in highly fluctuating atmospheric conditions. IEEE Trans Ind Inform 13(5):2406–2416Google Scholar
  32. 32.
    Rao RV, Saroj A (2017) A self-adaptive multi-population based Jaya algorithm for engineering optimization. Swarm Evol Comput 37:1–26Google Scholar
  33. 33.
    Rao RV, More K, Taler J, Ocłoń P (2016) Dimensional optimization of a micro-channel heat sink using Jaya algorithm. Appl Therm Eng 103:572–582Google Scholar
  34. 34.
    Mishra S, Ray PK (2016) Power quality improvement using photovoltaic fed DSTATCOM based on JAYA optimization. IEEE Trans Sustain Energy 7(4):1672–1680Google Scholar
  35. 35.
    Laumanns M, Thiele L, Zitzler E (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. Eur J Oper Res 169(3):932–942MathSciNetzbMATHGoogle Scholar
  36. 36.
    Hazra J, Sinha AK (2011) A multi-objective optimal power flow using particle swarm optimization. Eur Trans Electr Power 21(1):1028–1045Google Scholar
  37. 37.
    Adaryani MR, Karami A (2013) Artificial bee colony algorithm for solving multi-objective optimal power flow problem. Int J Electr Power Energy Syst 53:219–230Google Scholar
  38. 38.
    Barocio E, Regalado J, Cuevas E, Uribe F, Zúñiga 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 Transm Distrib 11(4):1012–1022Google Scholar
  39. 39.
    Shaheen AM, El-Sehiemy RA, Farrag SM (2016) Solving multi-objective optimal power flow problem via forced initialised differential evolution algorithm. IET Gener Transm Distrib 10(7):1634–1647Google Scholar
  40. 40.
    Niknam T, rasoul Narimani M, Jabbari M, Malekpour AR (2011) A modified shuffle frog leaping algorithm for multi-objective optimal power flow. Energy 36(11):6420–6432Google Scholar
  41. 41.
    Mahdad B, Srairi K (2015) Blackout risk prevention in a smart grid based flexible optimal strategy using Grey Wolf-pattern search algorithms. Energy Convers Manag 98:411–429Google Scholar
  42. 42.
    Shaheen AM, Farrag SM, El-Sehiemy RA (2017) MOPF solution methodology. IET Gener Transm Distrib 11(2):570–581Google Scholar
  43. 43.
    IEEE power Systems test case. http://www.ee.washington.edu/research/pstca/
  44. 44.
    Yang XS (2012) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation. Springer, Berlin, pp 240–249Google Scholar
  45. 45.
    Coelho LDS, Mariani VC, Leite JV (2012) Solution of Jiles–Atherton vector hysteresis parameters estimation by modified differential evolution approaches. Expert Syst Appl Int J 39(2):2021–2025Google Scholar
  46. 46.
    El-Fergany AA, Hasanien HM (2015) Single and multi-objective optimal power flow using Grey Wolf optimizer and differential evolution algorithms. Electr Power Compon Syst 43(13):1548–1559Google Scholar
  47. 47.
    Khorsandi A, Alimardani A, Vahidi B, Hosseinian SH (2011) Hybrid shuffled frog leaping algorithm and Nelder–Mead simplex search for optimal reactive power dispatch. IET Gener Transm Distrib 5(2):249–256Google Scholar
  48. 48.
    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 49:119–136Google Scholar
  49. 49.
    Bouchekara HREH, Abido MA, Boucherma M (2014) Optimal power flow using teaching-learning-based optimization technique. Electr Power Syst Res 114:49–59Google Scholar
  50. 50.
    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 99:331–343Google Scholar
  51. 51.
    El-Sehiemy RA, Shafiq MB, Azmy AM (2014) Multi-phase search optimisation algorithm for constrained optimal power flow problem. IJBIC 6(4):275–289Google Scholar
  52. 52.
    Barakat AF, El-Sehiemy RA, Elsayd MI, Osman E (2019) An enhanced Jaya optimization algorithm (EJOA) for solving multi-objective ORPD problem. In: 2019 international conference on innovative trends in computer engineering (ITCE). IEEE, pp 479–484Google Scholar
  53. 53.
    Ghasemi M, Ghavidel S, Ghanbarian MM, Gharibzadeh M, Vahed AA (2014) Multi-objective optimal power flow considering the cost, emission, voltage deviation and power losses using multi-objective modified imperialist competitive algorithm. Energy 78:276–289Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringAswan UniversityAswânEgypt
  2. 2.State Key Laboratory of Power Transmission Equipment and System Security and New TechnologyChongqing UniversityChongqingChina
  3. 3.Department of Electrical Engineering, Faculty of EngineeringUniversity of KafrelsheikhKafrelsheikhEgypt
  4. 4.Department of Electrical Engineering, EPS LinaresUniversity of JaénJaénSpain

Personalised recommendations