Skip to main content
SpringerLink
Log in

An enhanced particle swarm optimization algorithm to solve probabilistic load flow problem in a micro-grid

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper presents an Enhanced PSO (EPSO) method to address the weaknesses associated with the traditional PSO such as high sensitivity to the initial conditions, fast convergence, decline of solutions’ variety, and trapping in the local optimum. For this, several strategies are suggested including segmentation of search space, modification of solution’s updating rule, accepting poor solutions using an intelligent probabilistic function, searching in the regions with poor solutions, gradually removing the regions with poor solutions, and focusing the solutions on the local search after removing all regions with poor solutions. The performance of the EPSO was investigated using the 30 CEC 2014 test functions, 30 CEC 2017 test functions, 10 standard optimization algorithms, and a challenging optimization problem called Probabilistic Load Flow (PLF) in a distribution network. The results of the Wilcoxon signed-rank test on the 2014 and 2017 test functions revealed the superiority of the EPSO over nearly 80% of cases compared to the other algorithms. The obtained results of solving 10 benchmark functions by the proposed EPSO and the other six improved PSO algorithms indicated advantages of the proposed EPSO compared to the other algorithms in finding the optimal value. Meanwhile, the proposed EPSO took the average time of 0.66 s to solve the 10 test functions; it was the shortest time compared to other improved PSO algorithms. According to the results of implementing the EPSO algorithm and other algorithms with random agents for 61 times, in more than 65% of the test functions, the proposed EPSO could find the global optimal solution in a shorter time than the other algorithms. The results of solving the probabilistic load flow problem indicated 89% similarity of the results of the proposed EPSO to those of the most accurate method i.e. Monte Carlo Simulation (MCS). Comparison of the obtained results with the other algorithms as well as outcomes of several improved versions of the PSO indicated the competitive proficiency of the proposed EPSO in various optimization circumstances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Breen M, Murphy MD, Upton J (2019) Development of a dairy multi-objective optimization (DAIRYMOO) method for economic and environmental optimization of dairy farms. Appl Energy 242:1697–1711

    Google Scholar 

  2. Boussaïd I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117

    MathSciNet  MATH  Google Scholar 

  3. Mirjalili SA (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  4. Simpson AR, Dandy GC, Murphy LJ (1994) Genetic algorithms compared to other techniques for pipe optimization. J Water Resour Plan Manag 120:423–443

    Google Scholar 

  5. James C (2003) "introduction to Stochastics search and optimization," ed: Wiley-Interscience, New Jersey

  6. H. R. Lourenço, O. Martin, T. Stützle (2010) Iterated local search: framework and applications, Handbook of Metaheuristics, 2nd. Edition. Kluwer Academic Publishers, International Series in Operations Research & Management Science Vol. 146, pp. 363–397

  7. Cerny V (1985) A thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51

    MathSciNet  MATH  Google Scholar 

  8. Mladenovi’c N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100

    MathSciNet  MATH  Google Scholar 

  9. Feo TA, Resende MGC Greedy randomized adaptive search procedures. Journal of Global Optimization 6(109):1995

  10. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549

    MathSciNet  MATH  Google Scholar 

  11. Voudouris C, Tsang E (1999) Guided local search and its application to the traveling salesman problem. Eur J Oper Res 113(2):469–499

    MATH  Google Scholar 

  12. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press

  13. Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks:1942–1948

  14. Dorigo M, Gambardella LM (Apr. 1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66

    Google Scholar 

  15. D. T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim M. and Zaidi, "The Bees Algorithm, Technical Note, Manufacturing Engineering Centre, Cardiff University, UK, 2005

  16. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471

    MathSciNet  MATH  Google Scholar 

  17. Geem z w, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Google Scholar 

  18. X.-S. Yang (2009) Firefly algorithms for multimodal optimization. In Proceedings of the 5th international conference on stochastic algorithms: foundations and applications. Sapporo, Japan: Springer-Verlag, pp. 169–78

  19. Yang X-S and Deb S (2009) Cuckoo search via levy flights", In Proceedings of the world congress on nature & biologically inspired computing (NaBIC-2009), Coimbatore, India, pp. 210–214

  20. Hosseini SH (2009) The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. International Journal of Bio-Inspired Computing 1(1/2):71–79

    Google Scholar 

  21. Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112

    Google Scholar 

  22. Mousavirad SJ, Ebrahimpour-Komleh H (2017) Human mental search: a new population-based metaheuristic optimization algorithm. Appl Intell 47:850–887. https://doi.org/10.1007/s10489-017-0903-6

    Article  Google Scholar 

  23. Sheng Xin Zhang, Wing Shing Chan, Zi Kang Peng, Shao Yong Zheng, Kit Sang Tang (2020) Selective-candidate framework with similarity selection rule for evolutionary optimization, Swarm and Evolutionary Computation, Volume 56

  24. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. IEEE Congress on Evolutionary Computation 7:4661–4666

    Google Scholar 

  25. Wilde H, Knight V, Gillard J (2020) Evolutionary dataset optimisation: learning algorithm quality through evolution. Appl Intell 50:1172–1191. https://doi.org/10.1007/s10489-019-01592-4

    Article  Google Scholar 

  26. Slowik A, Kwasnicka H (2020) Evolutionary algorithms and their applications to engineering problems. Neural Comput & Applic 32:12363–12379. https://doi.org/10.1007/s00521-020-04832-8

    Article  Google Scholar 

  27. Dhiman G, Kumar V (2019) KnRVEA: A hybrid evolutionary algorithm based on knee points and reference vector adaptation strategies for many-objective optimization. Appl Intell 49:2434–2460. https://doi.org/10.1007/s10489-018-1365-1

    Article  Google Scholar 

  28. Moradi H, Ebrahimpour-Komleh H (2018) Development of a multi-objective optimization evolutionary algorithm based on educational systems. Appl Intell 48:2954–2966. https://doi.org/10.1007/s10489-017-1122-x

    Article  Google Scholar 

  29. Garg H (2015) An efficient biogeography based optimization algorithm for solving reliability optimization problems. Swarm and Evolutionary Computation 24:1–10

    Google Scholar 

  30. Garg H (2019) A hybrid GSA-GA algorithm for constrained optimization problems. Information Sciences, Volume 478:499–523

    Google Scholar 

  31. Patwal RS, Narang N, Garg H (2018) A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units. Energy 142:822–837

    Google Scholar 

  32. Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Applied Mathematics and Computation 274:292–305

    MathSciNet  MATH  Google Scholar 

  33. Rezaee Jordehi A, Jasni J Parameter selection in particle swarm optimisation: a survey. J Exp Theor Artif Intell 25:527–542

  34. Alfi A (2011) PSO with adaptive mutation and inertia weight and its application in parameter estimation of dynamic systems. Acta Automat Sin 37(5):541–549

    MATH  Google Scholar 

  35. Zhang L, Tang Y, Hua C et al (2015) A new particle swarm optimization algorithm with adaptive inertia weight based on Bayesian techniques. Applied Soft Computing v:138–149

    Google Scholar 

  36. Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255

    Google Scholar 

  37. Yamaguchi T, Yasuda K (2006) Adaptive particle swarm optimization: self-coordinating mechanism with updating information, Proceedings of the 2006 IEEE International Conference on Systems, Man, and Cybernetics. 3:2303–2308

  38. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Google Scholar 

  39. Pluhacek M, Senkerik R, Davendra D, Oplatkova ZK, Zelinka I (2013) On the behavior and performance of chaos driven PSO algorithm with inertia weight. Comput Math Appl 66:122–134

    MathSciNet  Google Scholar 

  40. Rezaee Jordehi A (2015) Enhanced leader PSO (ELPSO): a new PSO variant for solving global optimisation problems. Appl Soft Comput 26:401–417

    Google Scholar 

  41. Beheshti Z, Shamsuddin SMH (2014) CAPSO: a centripetal accelerated particle swarm optimization. Inf Sci 258:54–79

    MathSciNet  Google Scholar 

  42. Hosseinnezhad V, Babaei E (2013) Economic load dispatch using PSO. Int J Electr Power Energy Syst 49:160–169

    Google Scholar 

  43. Morales JM, Baringo L, Conejo AJ, Minguez R (2010) Probabilistic load flow with correlated wind sources. IET Generation, Transmission & Distribution 4(5):641–651

    Google Scholar 

  44. Gallego-Castillo C, Bessa R, Cavalcante L, Lopez-Garcia O (2016) On-line quantile regression in the RKHS (reproducing kernel Hilbert space) for operational probabilistic forecasting of wind power. Energy 113:355–365

    Google Scholar 

  45. Medellin VAC, Hidalgo IG, Correia PB (2018) Probabilistic valuation for power generation projects from sugarcane in reserve energy auctions. Energy 147:603–611

    Google Scholar 

  46. Morshed MJ, Hmida JB, Fekih A (2018) A probabilistic multi-objective approach for load flow optimization in hybrid wind-PV-PEV systems. Appl Energy 211:1136–1149

    Google Scholar 

  47. Nguyen TT (2019) A high performance social spider optimization algorithm for optimal load flow solution with single objective optimization. Energy 171:218–240

    Google Scholar 

  48. Xiao Q, Zhou S (2018) Probabilistic load flow computation considering correlated wind speeds. Appl Energy 231:677–685

    Google Scholar 

  49. Borkowska B (1974) Probabilistic load flow. IEEE Transactions on Power Apparatus and Systems PAS-93(3):752–759

    Google Scholar 

  50. G.K. Stefopoulos, A.P. Meliopoulos, G.J. Cokkinids (2004) Probabilistic load flow with non conforming electric loads’. Proc. of the Eighth Int. Conf. on Probabilistic Methods Applied to Power Systems, pp. 525–531

  51. Carpinelli G, Caramia P, Varilone P (2015) Multi-linear Monte Carlo simulation method for probabilistic load flow of distribution systems with wind and photovoltaic generation systems. Renew Energy 76:283–295

    Google Scholar 

  52. Yu H, Chung CY, Wong KP, Lee HW, Zhang JH (2009) Probabilistic load flow evaluation with hybrid Latin hypercube sampling and Cholesky decomposition. IEEE Trans Power Syst 24:661–667

    Google Scholar 

  53. Allan RN, Al-Shakarchi MRG (1977) Probabilistic techniques in A.C. load-flow analysis. Proceedings of the Institution of Electrical Engineers 124:154–160

    Google Scholar 

  54. Zhang P, Lee ST (2004) Probabilistic load flow computation using the method of combined cumulants and gram-Charlier expansion. IEEE Trans Power Syst 19:676–682

    Google Scholar 

  55. Fan M, Vittal V, Heydt GT, Ayyanar R (2012) Probabilistic load flow studies for transmission systems with photovoltaic generation using Cumulants. IEEE Trans Power Syst 27:2251–2261

    Google Scholar 

  56. Su CL (2005) Probabilistic load-flow computation using point estimate method. IEEE Trans Power Syst 20:1843–1851

    Google Scholar 

  57. G. Verbic, , C.A. Canizares, ‘Probabilistic optimal load flow in electricity markets based on a two-point estimate method’, IEEE Trans Power Syst, vol. 21, no. 4, pp. 1883–1893, 2006

    Google Scholar 

  58. I. S. Arneja, B. Venkatesh (2012) Probabilistic OPF using linear fuzzy relation. Conf on Power & Energy, Ho Chi Minh City, pp. 601–605

  59. Fu X, Sun H, Guo Q, Pan Z, Zhang X, Zeng S (2017) Probabilistic load flow analysis considering the dependence between power and heat. Applied Energy 191:582–592

    Google Scholar 

  60. Nikmehr N, Najafi Ravadanegh S (2015) Heuristic probabilistic load flow algorithm for microgrids operation and planning. IET Generation, Transmission & Distribution 9(11):985–995

    Google Scholar 

  61. Liang J, Qu B, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization, Computational intelligence laboratory, Zhengzhou University, Zhengzhou China and technical report, Nanyang Technological University. Singapore

  62. Cheng M-Y, Lien L-C (2012) Hybrid artificial intelligence-based PBA for benchmark functions and facility layout design optimization. J Comput Civ Eng 26:612–624

    Google Scholar 

  63. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behavior: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617–644

    MATH  Google Scholar 

  64. Zhang J, Xiao M, Gao L, Pan Q (2018) Queuing search algorithm: a novel metaheuristic algorithm for solving engineering optimization problems. Appl Math Model 63:464–490

    MathSciNet  MATH  Google Scholar 

  65. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl Based Syst 75:1–18

    Google Scholar 

  66. Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12:702–713

    Google Scholar 

  67. Kazikova A, Pluhacek M, Senkerik R (2018) Regarding the behavior of Bison runners within the Bison algorithm. MENDEL. 24(1):63–70

    Google Scholar 

  68. Yang X-S, Deb S (2009) Cuckoo search via Levy flights. In: Proceedings of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), December 2009, India, USA, pp. 210–214. IEEE Publications

  69. Awad NH, Ali MZ, Liang JJ, Qu BY, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization, technical report. Nanyang Technological University, Singapore

    Google Scholar 

  70. Kazikova A, Pluhacek M, Senkerik R (2019) Performance of the Bison algorithm on benchmark IEEE CEC 2017. In: Silhavy R (ed) Artificial intelligence and algorithms in intelligent systems., CSOC2018 2018. Advances in intelligent systems and computing, vol 764. Springer, Cham

    Google Scholar 

  71. Zhang X, Du Y, Qin G, Qin Z (2005) Adaptive particle swarm algorithm with dynamically changing inertia weight. J Xi'an Jiaotong Univ 39(10):1039–1042

    MATH  Google Scholar 

  72. Wang D-F, Meng L (2016) Performance analysis and parameter selection of PSO algorithms. Acta Automat Sin 42(10):1552–1561

    MATH  Google Scholar 

  73. Tong JQ, Zhao Q, Li M (2019) Particle swarm optimization algorithm based on adaptive dynamic change. Microletronics & Computer 36(2):6–10

    Google Scholar 

  74. Jiang GJ, Ye H, Ma YH (2015) Particle swarm optimization algorithm via sampling strategy. Control and Decision 10:1779–1784

    MATH  Google Scholar 

  75. L. Sun, X. Song, Tianfei Chen (2019) An improved convergence particle swarm optimization algorithm with random sampling of control parameters. Journal of Control Science and Engineering, Article in press, https://doi.org/10.1155/2019/7478498

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran

    Hajar Bagheri Tolabi & Afshin Lashkar Ara

  2. Department of Computer Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

    Rahil Hosseini

Authors
  1. Hajar Bagheri Tolabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Afshin Lashkar Ara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rahil Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Afshin Lashkar Ara.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bagheri Tolabi, H., Lashkar Ara, A. & Hosseini, R. An enhanced particle swarm optimization algorithm to solve probabilistic load flow problem in a micro-grid. Appl Intell 51, 1645–1668 (2021). https://doi.org/10.1007/s10489-020-01872-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-01872-4

Keywords

Search

Navigation