SpringerLink
Log in

A multi-objective economic emission dispatch problem in microgrid with high penetration of renewable energy sources using equilibrium optimizer

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

In the realm of energy economics and microgrid management, optimizing the multi-objective economic emission dispatch (EED) holds paramount importance. However, the integration of renewable energy sources (RES) introduces challenges due to their inconsistent and unpredictable behaviour. To address this, a novel EED model for microgrids with high RES penetration is developed, aiming to minimize operating fuel costs and pollution while maximizing RES output power availability. Wind and solar energy outputs are modelled using probability density functions, and the 2-m point estimation method is employed for estimation. The complex probabilistic EED model is tackled using an equilibrium optimization approach, tested on microgrid configurations with varying numbers of thermal generators coupled with wind–solar units. Results indicate that the proposed algorithm outperforms other recent techniques, demonstrating quicker convergence and effective handling of EED issues.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Data availability

The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.

Abbreviations

\(a_{i}\), \(b_{i}\), \(c_{i}\), \(e_{i}\), \(f_{i}\) :

Cost variable of the ith thermal unit

\(S_\textrm{rad,stc}\) :

Solar radiation in normal circumstances

N :

Count of connected generators

\(S_\textrm{P,stc}\) :

Solar power in normal circumstances

Ti:

Generated power of ith thermal generator in MW

\(\gamma \) :

Temperature variable in %/\(\circ \)C

\(W_\textrm{p}\), \(S_\textrm{p}\) :

Generated power of wind–solar in MW

\(T_\textrm{cell}\) :

The degree of heat in a solar cell

\(C_\textrm{w}\) :

Cost variable of wind in $/h

\(T_\textrm{cell,stc}\) :

The solar cell’s temperature under the usual test conditions

\(N_\textrm{W}\), \(N_\textrm{s}\) :

Count of wind and solar unit

NOT:

The cell’s typical operating temperature

Bidl:

Bid price of lth solar unit

\(N_\textrm{sc}\), \(N_\textrm{pc}\) :

Number of solar cells in series and parallel

TL:

Transmission loss

\(\mu \),\(\sigma \) :

The average and standard deviation

TD:

Power requirement

\(I_\textrm{k}\) :

Input constant

\(B_{ij}\), \(B_{0i}\), \(B_{00}\) :

Loss matrix

\(S_\textrm{e}\) :

Total electricity production, including solar and wind

\(T_\textrm{imin}\), \(T_\textrm{imax}\) :

Boundary limit minimum–maximum power ith unit

\(z_\textrm{l}\) :

Uncertainty in the input variable

\(S_\textrm{hp}\), \(S_\textrm{cp}\) :

Weibull variables

Qi(t), Qj(t):

Charges of ith and jth fleck

\(v, v_\textrm{r}\) :

Instant and rated haste of wind unit

\(P_\textrm{pv,av}\) and \(P_\textrm{pv,kt}\) :

Available and estimated output power of kth solar unit

\(v_\textrm{in}, v_\textrm{out}\) :

Cut in–cut out the haste of wind unit.

\(C_\textrm{pv}\) :

Cost constant for kth solar unit

\(W_\textrm{p}, W_\textrm{pt}\) :

Instant and rated power of wind unit

\(R_{ij}(t)\) :

The distance in Euclid between two particles

\(\omega \),\(\psi \) :

Beta variables

\(P_\textrm{Wj,av}\) and \(P_\textrm{Wd,jt}\) :

Available and estimated output power of jth wind unit, respectively

\(\Gamma \) :

Gamma objectives

\(K_\textrm{p,wd}, K_\textrm{r,wd}\) :

Penalty factors for underestimation and overestimation of wind power

\(S_\mathrm{rad(t)}\) :

Cellular solar radiation at time t

\(\alpha _\textrm{iT}\), \(\beta _\textrm{iT}\), \(\gamma _\textrm{iT}\), \(\zeta _\textrm{iT}\), \(\lambda _\textrm{iT}\) :

emission parameter

References

  1. Ghorbani N, Babaei E (2016) Exchange market algorithm for economic load dispatch. Int J Electr Power Energy Syst 75:19–27

    Article  Google Scholar 

  2. Mareček J, Takáč M (2017) A low-rank coordinate-descent algorithm for semidefinite programming relaxations of optimal power flow. Optim Methods Softw 32(4):849–871

    Article  MathSciNet  Google Scholar 

  3. Hota P, Barisal A, Chakrabarti R (2010) Economic emission load dispatch through fuzzy based bacterial foraging algorithm. Int J Electr Power Energy Syst 32(7):794–803

    Article  Google Scholar 

  4. Vespucci MT, Bertocchi M, Pisciella P, Zigrino S (2016) Two-stage stochastic mixed integer optimization models for power generation capacity expansion with risk measures. Optim Methods Softw 31(2):305–327

    Article  MathSciNet  Google Scholar 

  5. Grimm V, Kleinert T, Liers F, Schmidt M, Zöttl G (2019) Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches. Optim Methods Softw 34(2):406–436

    Article  MathSciNet  Google Scholar 

  6. Rizk-Allah RM, El-Sehiemy RA, Wang G-G (2018) A novel parallel hurricane optimization algorithm for secure emission/economic load dispatch solution. Appl Soft Comput 63:206–222

    Article  Google Scholar 

  7. Shilaja C, Ravi K (2017) Optimization of emission/economic dispatch using Euclidean affine flower pollination algorithm (EFPA) and binary FPA (BFPA) in solar photo voltaic generation. Renew Energy 107:550–566

    Article  Google Scholar 

  8. Güvenc U, Sönmez Y, Duman S, Yörükeren N (2012) Combined economic and emission dispatch solution using gravitational search algorithm. Sci Iran 19(6):1754–1762

    Article  Google Scholar 

  9. Bhattacharjee K, Patel N (2022) A comparative study of economic load dispatch with complex non-linear constraints using Salp swarm algorithm. Sci Iran 29(2):676–692

    Google Scholar 

  10. Barisal A (2013) Dynamic search space squeezing strategy based intelligent algorithm solutions to economic dispatch with multiple fuels. Int J Electr Power Energy Syst 45(1):50–59

    Article  Google Scholar 

  11. Chakraborty S, Senjyu T, Yona A, Saber A, Funabashi T (2011) Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation. IET Gener Transm Distrib 5(10):1042–1052

    Article  Google Scholar 

  12. Zhang Y, Gong D-W, Ding Z (2012) A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf Sci 192:213–227

    Article  Google Scholar 

  13. Shah K, Soni J, Bhattacharjee K (2023) Artificial electric field algorithm applied to the economic load dispatch problem with valve point loading effect: Aefa applied to eld with vple. Int J Swarm Intell Res (IJSIR) 14(1):1–23

    Article  Google Scholar 

  14. Ali ES, Abd-Elazim SM (2011) Bacteria foraging optimization algorithm based load frequency controller for interconnected power system. Int J Electr Power Energy Syst 33(3):633–638

    Article  Google Scholar 

  15. Chatterjee A, Ghoshal S, Mukherjee V (2012) Solution of combined economic and emission dispatch problems of power systems by an opposition-based harmony search algorithm. Int J Electr Power Energy Syst 39(1):9–20

    Article  Google Scholar 

  16. Bhattacharya A, Chattopadhyay PK (2011) Solving economic emission load dispatch problems using hybrid differential evolution. Appl Soft Comput 11(2):2526–2537

    Article  Google Scholar 

  17. Yuan X, Ji B, Zhang S, Tian H, Chen Z (2014) An improved artificial physical optimization algorithm for dynamic dispatch of generators with valve-point effects and wind power. Energy Convers Manag 82:92–105

    Article  Google Scholar 

  18. Hatata AY, Hafez AA (2019) Ant lion optimizer versus particle swarm and artificial immune system for economical and eco-friendly power system operation. Int Trans Electr Energy Syst 29(4):2803

    Article  Google Scholar 

  19. Bhattacharjee K, Bhattacharya A, Nee Dey SH (2014) Oppositional real coded chemical reaction optimization for different economic dispatch problems. Int J Electr Power Energy Syst 55:378–391

    Article  Google Scholar 

  20. Bhattacharjee K, Bhattacharya A, Nee Dey SH (2014) Chemical reaction optimisation for different economic dispatch problems. IET Gener Transm Distrib 8(3):530–541

    Article  Google Scholar 

  21. Jadhav H, Roy R (2013) Gbest guided artificial bee colony algorithm for environmental/economic dispatch considering wind power. Expert Syst Appl 40(16):6385–6399

    Article  Google Scholar 

  22. Qu B-Y, Liang JJ, Zhu Y, Wang Z, Suganthan PN (2016) Economic emission dispatch problems with stochastic wind power using summation based multi-objective evolutionary algorithm. Inf Sci 351:48–66

    Article  Google Scholar 

  23. Hagh MT, Kalajahi SMS, Ghorbani N (2020) Solution to economic emission dispatch problem including wind farms using exchange market algorithm method. Appl Soft Comput 88:106044

    Article  Google Scholar 

  24. Liao G-C (2011) A novel evolutionary algorithm for dynamic economic dispatch with energy saving and emission reduction in power system integrated wind power. Energy 36(2):1018–1029

    Article  Google Scholar 

  25. Soni J, Bhattacharjee K (2023) Equilibrium optimiser for the economic load dispatch problem with multiple fuel option and renewable sources. Int J Ambient Energy 44(1):2386–2397

    Article  Google Scholar 

  26. Azizipanah-Abarghooee R, Niknam T, Roosta A, Malekpour AR, Zare M (2012) Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method. Energy 37(1):322–335

    Article  Google Scholar 

  27. Mondal S, Bhattacharya A, Nee Dey SH (2013) Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration. Int J Electr Power Energy Syst 44(1):282–292

    Article  Google Scholar 

  28. Wang L, Singh C (2006). PSO-based multi-criteria economic dispatch considering wind power penetration subject to dispatcher’s attitude. In: 2006 38th North American power symposium, pp 269–276. IEEE

  29. Jiang S, Ji Z, Wang Y (2015) A novel gravitational acceleration enhanced particle swarm optimization algorithm for wind-thermal economic emission dispatch problem considering wind power availability. Int J Electr Power Energy Syst 73:1035–1050

    Article  Google Scholar 

  30. Guesmi T, Farah A, Marouani I, Alshammari B, Abdallah HH (2020) Chaotic sine-cosine algorithm for chance-constrained economic emission dispatch problem including wind energy. IET Renew Power Gener 14(10):1808–1821

    Article  Google Scholar 

  31. Hagh MT, Kalajahi SMS, Ghorbani N (2020) Solution to economic emission dispatch problem including wind farms using exchange market algorithm method. Appl Soft Comput 88:106044

    Article  Google Scholar 

  32. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190

    Article  Google Scholar 

  33. Seleem SI, Hasanien HM, El-Fergany AA (2021) Equilibrium optimizer for parameter extraction of a fuel cell dynamic model. Renew Energy 169:117–128

    Article  Google Scholar 

  34. Soni J, Bhattacharjee K (2024) Integrating renewable energy sources and electric vehicles in dynamic economic emission dispatch: an oppositional-based equilibrium optimizer approach. Eng Optim 1–35

  35. Nourianfar H, Abdi H (2021) Solving power systems optimization problems in the presence of renewable energy sources using modified exchange market algorithm. Sustain Energy Grids Netw 26:100449

    Article  Google Scholar 

  36. Chang TP (2011) Estimation of wind energy potential using different probability density functions. Appl Energy 88(5):1848–1856

    Article  Google Scholar 

  37. **n-gang Z, Ji L, ** M, Ying Z (2020) An improved quantum particle swarm optimization algorithm for environmental economic dispatch. Expert Syst Appl 152:113370

    Article  Google Scholar 

  38. Niknam T, Doagou-Mojarrad H (2012) Multiobjective economic/emission dispatch by multiobjective thetas-particle swarm optimisation. IET Gener Transm Distrib 6(5):363–377

    Article  Google Scholar 

  39. Sayah S, Hamouda A (2013) A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems. Appl Soft Comput 13(4):1608–1619

    Article  Google Scholar 

  40. Namilakonda S, Guduri Y (2021) Chaotic Darwinian particle swarm optimization for real-time hierarchical congestion management of power system integrated with renewable energy sources. Int J Electr Power Energy Syst 128:106632

    Article  Google Scholar 

  41. Soni J, Bhattacharjee K (2024) Multi-objective dynamic economic emission dispatch integration with renewable energy sources and plug-in electrical vehicle using equilibrium optimizer. Environ Dev Sustain 26(4):8555–8586

    Article  Google Scholar 

  42. Soni JM, Pandya MH (2018) Power quality enhancement for PV rooftop and BESS in islanded mode. In: 2018 4th international conference on electrical energy systems (ICEES), pp 242–247. IEEE

  43. Aydin D, Özyön S, Yaşar C, Liao T (2014) Artificial bee colony algorithm with dynamic population size to combined economic and emission dispatch problem. Int J Electr Power Energy Syst 54:144–153

    Article  Google Scholar 

  44. Chamandoust H, Derakhshan G, Hakimi SM, Bahramara S (2019) Tri-objective optimal scheduling of smart energy hub system with schedulable loads. J Clean Prod 236:117584

    Article  Google Scholar 

  45. Mohammadi S, Mozafari B, Solimani S, Niknam T (2013) An adaptive modified firefly optimisation algorithm based on Hong’s point estimate method to optimal operation management in a microgrid with consideration of uncertainties. Energy 51:339–348

    Article  Google Scholar 

  46. Abarghooee RA, Aghaei J (2011) Stochastic dynamic economic emission dispatch considering wind power. In: 2011 IEEE power engineering and automation conference, vol 1, pp 158–161. IEEE

  47. Chamandoust H, Derakhshan G, Bahramara S (2020) Multi-objective performance of smart hybrid energy system with multi-optimal participation of customers in day-ahead energy market. Energy Build 216:109964

    Article  Google Scholar 

  48. Chamandoust H, Derakhshan G, Hakimi SM, Bahramara S (2020) Tri-objective scheduling of residential smart electrical distribution grids with optimal joint of responsive loads with renewable energy sources. J Energy Storage 27:101112

    Article  Google Scholar 

  49. Chamandoust H, Bahramara S, Derakhshan G (2020) Day-ahead scheduling problem of smart micro-grid with high penetration of wind energy and demand side management strategies. Sustain Energy Technol Assess 40:100747

    Google Scholar 

  50. Soni J, Bhattacharjee K (2024). Equilibrium optimizer for multi-objective dynamic economic emission dispatch integration with plug-in electric vehicles and renewable sources. Multiscale Multidiscip Model Exp Des 1–17

  51. Bhattacharjee K, Bhattacharya A, Nee Dey SH (2014) Solution of economic emission load dispatch problems of power systems by real coded chemical reaction algorithm. Int J Electr Power Energy Syst 59:176–187

    Article  Google Scholar 

  52. Jiang S, Ji Z, Shen Y (2014) A novel hybrid particle swarm optimization and gravitational search algorithm for solving economic emission load dispatch problems with various practical constraints. Int J Electr Power Energy Syst 55:628–644

    Article  Google Scholar 

  53. Bhattacharjee K, Bhattacharya A, Nee Dey SH (2014) Solution of economic emission load dispatch problems of power systems by real coded chemical reaction algorithm. Int J Electr Power Energy Syst 59:176–187

  54. Das D, Bhattacharya A, Ray RN (2020) Dragonfly algorithm for solving probabilistic economic load dispatch problems. Neural Comput Appl 32(8):3029–3045

    Article  Google Scholar 

  55. Woolson RF (2007) Wilcoxon signed-rank test. Wiley encyclopedia of clinical trials, pp 1–3

Download references

Author information

Authors and Affiliations

  1. Institute of Technology, Nirma University, Ahmedabad, Gujarat, 382481, India

    Jatin Soni & Kuntal Bhattacharjee

Authors
  1. Jatin Soni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kuntal Bhattacharjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jatin Soni.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

Ethical approval is not applicable for this article.

Human and animal rights

This article does not contain any studies with human or animal subjects.

Informed consent

There are no human subjects in this article, and informed consent is not applicable.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soni, J., Bhattacharjee, K. A multi-objective economic emission dispatch problem in microgrid with high penetration of renewable energy sources using equilibrium optimizer. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02526-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00202-024-02526-1

Keywords

Search

Navigation