Skip to main content

Advertisement

SpringerLink
Log in

A multi-objective approach for solving transmission expansion planning problem considering wind power uncertainty

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

Security-constrained transmission expansion planning (SCTEP) is a vital power system problem. In last years, to attain energy sustainability, wind power has received significant attention as one of the popular renewable energy resources. This paper solves multi-objective optimization of TEP considering uncertainty of wind power. The uncertainty is modelled by Weibull probability distribution function and Monte-Carlo simulation is employed to consider the uncertainty into the problem. In the problem, the objectives are investment cost of new lines and expected energy not supplied obtained by N-1 security constraint criterion. Since SCTEP is a complex, large-scale, mixed-integer and non-linear combinatorial optimization problem, multi-objective crow search algorithm and multi-objective particle swarm optimization are utilized to find Pareto front. On modified 24-bus IEEE system, the optimization framework is investigated and the results are discussed.

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
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

\(f_{1} \left( x \right)\) :

Total investment cost

\(c_{i,j}\) :

Investment cost of adding a new line between buses i and j

\(n_{i,j}\) :

Number of added lines between buses i and j

EENS jk :

Expected energy not supplied by demand j due to contigency k

\(\Gamma_{jk}\) :

Involuntary load shedding of demand j due to contigency k

\(\rho_{k}\) :

Probability of contingency k

u k :

State of new component

\(\rho_{all} \) :

Probability of no contigency

FOR k :

Forced outage rate of component k

MTTF :

Mean time to failure

MTTR :

Mean time to repair

λ :

Outage rate

\(n_{i,j}^{0}\) :

Number of lines between buses i and j

\(P_{i,j}^{max}\) :

Maximum power flow between buses i and j

\(P_{i,j }\) :

Power flow between buses i and j

\(n_{i,j}^{max}\) :

Maximum number of lines which can be added between buses i and j

\(b_{i,j }\) :

Susceptance of the line between buses i and j

\(\theta_{i}\) :

Voltage phase angle at bus i

\(\theta_{j}\) :

Voltage phase angle at bus j

\(f\left( {v, c,k} \right)\) :

Weibull PDF

\(F\left( {v, c,k} \right)\) :

Weibull CDF

v :

Wind speed

k :

Shape parameter

c :

Scale parameter

P w :

Output power of wind generator

v rated :

Rated speed

v ci :

Cut-in wind speed

v co :

Cut-out wind speed

\(x_{i}^{iter}\) :

Current position of crow i

\(x_{i}^{iter + 1}\) :

New position of crow i

iter :

Iteration number

\(m_{j}^{iter}\) :

Memorized position of crow j

r :

Random number

\(m_{i}^{iter + 1}\) :

Memorized position of crow i at iteration iter + 1

References

  1. El-bages MS, Elsayed WT (2017) Social spider algorithm for solving the transmission expansion planning problem. Electric Power Syst Res 143:235–243

    Article  Google Scholar 

  2. Baringo L, Baringo A (2017) A stochastic adaptive robust optimization approach for the generation and transmission expansion planning. IEEE Trans Power Syst 33(1):792–802

    Article  Google Scholar 

  3. Alaee S, Hooshmand R, Hemmati R (2016) Stochastic transmission expansion planning incorporating reliability solved using SFLA meta-heuristic optimization technique. CSEE J Power Energy Syst 2(2):79–86

    Article  Google Scholar 

  4. Han X, Zhao L, Wen J, Ai X, Liu J, Yang D (2017) Transmission network expansion planning considering the generators’ contribution to uncertainty accommodation. CSEE J Power Energy Syst 3(4):450–460

    Article  Google Scholar 

  5. Zhang Y, Wang J, Li Y, Wang X (2018) An extension of reduced disjunctive model for multi-stage security-constrained transmission expansion planning. IEEE Trans Power Syst 33(1):1092–1094

    Article  Google Scholar 

  6. Gomez PV, Saraiva JT (2020) A two-stage strategy for security-constrained AC dynamic transmission expansion planning. Electric Power Syst Res 180:106167

    Article  Google Scholar 

  7. Qiu J, Zhao J, Dong Z (2017) Probabilistic transmission expansion planning for increasing wind power penetration. IET Renew Power Gener 11(6):837–845

    Article  Google Scholar 

  8. Dehghan S, Amjady N, Conejo A (2017) Adaptive robust transmission expansion planning using linear decision rules. IEEE Trans Power Syst 32(5):4024–4034

    Article  Google Scholar 

  9. Zhan J, Chung C, Zare A (2017) A fast solution method for stochastic transmission expansion planning. IEEE Trans Power Syst 32(6):4684–4695

    Article  Google Scholar 

  10. Gutiérrez-Alcaraz G, González-Cabrera N, Gil E (2020) An efficient method for contingency-constrained transmission expansion planning. Electric Power Systems Research, Volume 182. Article 106208.

  11. Freitas PFS, Macedo LH, Romero R (2019) A strategy for transmission network expansion planning considering multiple generation scenarios. Electr Power Syst Res 172:22–31

    Article  Google Scholar 

  12. Armaghani S, Naghshbandy AH, Shahrtash SM (2020) A novel multi-stage adaptive transmission network expansion planning to countermeasure cascading failure occurrence. Int J Electr Power Energy Syst Volume 115. Article 105415

  13. Mortaz E, Valenzuela J (2019) Evaluating the impact of renewable generation on transmission expansion planning. Electric Power Syst Res 169:35–44

    Article  Google Scholar 

  14. Taherkhani M, Hosseini SH, Javadi MS, Catalão JPS (Dece) ‘Scenario-based probabilistic multi-stage optimization for transmission expansion planning incorporating wind generation integration. Electric Power Syst Res 189:106601

    Article  Google Scholar 

  15. Mehrtash M, Kargarian A (2020) Risk-based dynamic generation and transmission expansion planning with propagating effects of contingencies. Int J Electr Power Energy Syst Volume 118, Article 105762

  16. Liu D, Zhang S, Cheng H, Zhang X (2021) ‘Reducing wind power curtailment by risk-based transmission expansion planning. Int J Electr Power Energy Syst 124:106349

    Article  Google Scholar 

  17. Stock DS, Harms Y, Mende D, Hofmann L (2020) Robust nonlinear mathematical transmission expansion planning based on German electricity market simulation. Electr Power Syst Res 189:106685

    Article  Google Scholar 

  18. Franken M, Alexander B, Barrios SH, Moser A (2020) Co-optimization of multi-stage transmission expansion planning and grid operation. Electr Power Syst Res 189:106686

    Article  Google Scholar 

  19. Maghouli P, Hosseini SH, Oloomi M, Shahidehpour M (2009) A multi-objective framework for transmission expansion planning in deregulated environments. IEEE Trans Power Syst 24(2):1051–1061

    Article  Google Scholar 

  20. Akbari T, Rahimi-Kian A, Tavakoli M (2012) Security-constrained transmission expansion planning: a stochastic multi-objective approach. Int J Electr Power Energy Syst 43(1):444–453

    Article  Google Scholar 

  21. Arabali A, Ghofrani M, Etezadi-Amoli M, Fadali M, Moeini-Aghtaie M (2014) A Multi-objective transmission expansion planning framework in deregulated power systems with wind generation. IEEE Trans Power Syst 29(6):3003–3011

    Article  Google Scholar 

  22. Ugranlı F, Karatepe E (2015) Multi-objective transmission expansion planning considering minimization of curtailed wind energy. Int J Electr Power Energy Syst 65:348–356

    Article  Google Scholar 

  23. Jadidoleslam M, Ebrahimi A, Latify MA (2017) Probabilistic transmission expansion planning to maximize the integration of wind power. Renew Energy 144:866–878

    Article  Google Scholar 

  24. Moradi A, Alinejad-Beromi Y, Kiani K (2017) Multi-objective transmission expansion planning with allocation of fixed series compensation under uncertainties. Int Trans Electr Energy Syst 27:17–24

    Article  Google Scholar 

  25. Khakpoor M, Jafari-Nokandi M, Abdoos AA (2017) Dynamic generation and transmission expansion planning in the power market–based on a multiobjective framework. Int Trans Electr Energy Syst 27:1–17

    Article  Google Scholar 

  26. Kim KJ, Park YM, Lee KY (1988) Optimal long term transmission expansion planning based on maximum principle. IEEE Trans Power Syst 3(4):1494–1501

    Article  Google Scholar 

  27. Aghaei J, Amjady N, Baharvandi A, Akbari MA (2014) Generation and transmission expansion planning: MILP–based probabilistic model. IEEE Trans Power Syst 29(4):1592–1601

    Article  Google Scholar 

  28. Justus CG, Mikhail A (1976) Height variation of wind speed and wind distributions statistics. Geophys Res Lett 3(5):261–264

    Article  Google Scholar 

  29. Ulgen K, Hepbasli A (2002) Determination of Weibull parameters for wind energy analysis of Izmir. Turkey Int J Energy Res 26(6):495–506

    Article  Google Scholar 

  30. Lun IYF, Lam JC (2000) A study of Weibull parameters using long term wind observation. Renew Energy 20(2):145–153

    Article  Google Scholar 

  31. Dorvol ASS (2002) Estimating wind speed distribution. Energy Convers Manag 43(17):2311–2318

    Article  Google Scholar 

  32. Rehman S, Halawani TO (1994) Statistical characteristics of wind in Saudi Arabia. Renew Energy 4(8):949–956

    Article  Google Scholar 

  33. Hoda Zamani, Mohammad H, Nadimi-Shahraki, Amir H, Gandomi CCSA (2019) Conscious neighborhood-based crow search algorithm for solving global optimization problems. Appl Soft Comput Volume 85, Article 105583.

  34. Mohammadi F, Abdi H (2018) A modified crow search algorithm (MCSA) for solving economic load dispatch problem. Appl Soft Comput 71:51–65

    Article  Google Scholar 

  35. Fang C, Hill DJ (2013) A new strategy for transmission expansion in competitive electricity markets. IEEE Trans Power Syst 18(1):374–380

    Article  Google Scholar 

  36. Ugranli F, Karatepe E (2016) Transmission expansion planning for wind turbine integrated power systems considering contingency. IEEE Trans Power Syst 31(2):1476–1485

    Article  Google Scholar 

  37. Silva IJ, Rider MJ, Romero R, Garcia AV, Murari CA (2005) Transmission network expansion planning with security constraints. IET Gener Trans Distrib 152(6):828–836

    Article  Google Scholar 

  38. Rathore C, Roy R (2016) Impact of wind uncertainty, plug-in-electric vehicles and demand response program on transmission network expansion planning. Electr Power Energy Syst 75:59–73

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran

    Basir Rashedi & Alireza Askarzadeh

Authors
  1. Basir Rashedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alireza Askarzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Askarzadeh.

Appendix

Appendix

See Tables

Table 5 Transmission line data for modified IEEE 24-bus system (base = 100 MVA)
Full size table

5,

Table 6 Transformer data for modified IEEE 24-bus system (base = 100 MVA)
Full size table

6 and

Table 7 Data of new lines added to existing branches of modified IEEE 24-bus system (base = 100 MVA) [23]
Full size table

7.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rashedi, B., Askarzadeh, A. A multi-objective approach for solving transmission expansion planning problem considering wind power uncertainty. Evol. Intel. 15, 497–511 (2022). https://doi.org/10.1007/s12065-020-00525-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-020-00525-2

Keywords

Search

Navigation