Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 207428, 12 pages.

Multiobjective Transmission Network Planning considering the Uncertainty and Correlation of Wind Power

Yuan Hu, Zhaohong Bie, Yanling Lin, Guangtao Ning, Mingfan Chen, and Yujie Gao

Full-text: Open access


In order to consider the uncertainty and correlation of wind power in multiobjective transmission network expansion planning (TNEP), this paper presents an extended point-estimation method to calculate the probabilistic power flow, based on which the correlative power outputs of wind farm are sampled and the uncertain multiobjective transmission network planning model is transformed into a solvable deterministic model. A modified epsilon multiobjective evolutionary algorithm is used to solve the above model and a well-distributed Pareto front is achieved, and then the final planning scheme can be obtained from the set of nondominated solutions by a fuzzy satisfied method. The proposed method only needs the first four statistical moments and correlation coefficients of the output power of wind farms as input information; the modeling of wind power is more precise by considering the correlation between wind farms, and it can be easily combined with the multiobjective transmission network planning model. Besides, as the self-adaptive probabilities of crossover and mutation are adopted, the global search capabilities of the proposed algorithm can be significantly improved while the probability of being stuck in the local optimum is effectively reduced. The accuracy and efficiency of the proposed method are validated by IEEE 24 as well as a real system.

Article information

J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 207428, 12 pages.

First available in Project Euclid: 1 October 2014

Permanent link to this document

Digital Object Identifier


Hu, Yuan; Bie, Zhaohong; Lin, Yanling; Ning, Guangtao; Chen, Mingfan; Gao, Yujie. Multiobjective Transmission Network Planning considering the Uncertainty and Correlation of Wind Power. J. Appl. Math. 2014, Special Issue (2014), Article ID 207428, 12 pages. doi:10.1155/2014/207428.

Export citation


  • H. Sun and D. C. Yu, “A multiple-objective optimization model of transmission enhancement planning for independent transmission company (ITC),” in Proceedings of the 2000 Power Engineering Society Summer Meeting, pp. 2033–2038, usa, July 2000.
  • T. S. Chung, K. K. Li, G. J. Chen, J. D. Xie, and G. Q. Tang, “Multi-objective transmission network planning by a hybrid GA approach with fuzzy decision analysis,” International Journal of Electrical Power and Energy Systems, vol. 25, no. 3, pp. 187–192, 2003.
  • Z. Xu, Z. D. Dong, and K. P. Wong, “A hybrid planning method for transmission networks in a deregulated environment,” IEEE Transactions on Power Systems, vol. 21, no. 2, pp. 925–932, 2006.
  • E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999.
  • K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.
  • K. Deb, M. Mohan, and S. Mishra, “Evaluating the $\varepsilon $-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions,” Evolutionary Computation, vol. 13, no. 4, pp. 501–525, 2005.
  • P. Maghouli, S. H. Hosseini, M. O. Buygi, and M. Shahidehpour, “A multi-objective framework for transmission expansion planning in deregulated environments,” IEEE Transactions on Power Systems, vol. 24, no. 2, pp. 1051–1061, 2009.
  • P. Maghouli, S. H. Hosseini, M. Oloomi Buygi, and M. Shahidehpour, “A scenario-based multi-objective model for multi-stage transmission expansion planning,” IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 470–478, 2011.
  • M. Moeini-Aghtaie, A. Abbaspour, and M. Fotuhi-Firuzabad, “Incorporating large-scale distant wind farms in probabilistic transmission expansion planning–-part I: theory and algorithm,” IEEE Transactions on Power Systems, vol. 27, no. 3, pp. 1585–1593, 2012.
  • Y. Wang, H. Cheng, C. Wang et al., “Pareto optimality-based multi-objective transmission planning considering transmission congestion,” Electric Power Systems Research, vol. 78, no. 9, pp. 1619–1626, 2008.
  • W. F. Esser, P. Ghose, and K. Chen, “Decision analysis for electric power systems engineering and management,” IEEE Transactions on Power Apparatus and Systems, vol. 96, no. 2, pp. 447–456, 1977.
  • C. Chompoo-Inwai, L. Wei-Jen, P. Fuangfoo, M. Williams, and J. R. Liao, “System impact study for the interconnection of wind generation and utility system,” IEEE Transactions on Industry Applications, vol. 41, no. 1, pp. 163–168, 2005.
  • X. Cui, W. Li, X. Ren, F. Xue, and Y. Fang, “Review of transmission planning with large-scale wind power integration,” in Proceedings of the Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC \textquotesingle 12), pp. 285–288, Singapore, May 2012.
  • H. Yu, C. Y. Chung, K. P. Wong, and J. H. Zhang, “A chance constrained transmission network expansion planning method with consideration of load and wind farm uncertainties,” IEEE Transactions on Power Systems, vol. 24, no. 3, pp. 1568–1576, 2009.
  • G. A. Orfanos, P. S. Georgilakis, and N. D. Hatziargyriou, “Transmission Expansion Planning of Systems With Increasing Wind Power Integration,” IEEE Transactions on Power Systems, 2012.
  • A. M. Leite da Silva, S. M. P. Ribeiro, V. L. Arienti, R. N. Allan, and M. B. do Coutto, “Probabilistic load flow techniques applied to power system expansion planning,” IEEE Transactions on Power Systems, vol. 5, no. 4, pp. 1047–1053, 1990.
  • A. M. Leite Da Silva, L. Manso, W. D. S. Sales, S. A. Flavio, G. J. Anders, and L. C. de Resende, “Chronological power flow for planning transmission systems considering intermittent sources,” IEEE Transactions on Power Systems, vol. 27, no. 4, pp. 2314–2322, 2012.
  • J. M. Morales and J. Pérez-Ruiz, “Point estimate schemes to solve the probabilistic power flow,” IEEE Transactions on Power Systems, vol. 22, no. 4, pp. 1594–1601, 2007.
  • P. Sánchez Martín, A. Ramos, and J. F. Alonso, “Probabilistic midterm transmission planning in a liberalized market,” IEEE Transactions on Power Systems, vol. 20, no. 4, pp. 2135–2142, 2005.
  • X. Ai, J. Wen, T. Wu, S. Sun, and G. Li, “A practical algorithm based on point estimate method and Gram-Charlier expansion for probabilistic load flow calculation of power systems incorporating wind power,” in Proceedings of the CSEE, pp. 16–23, 2013.
  • H. P. Hong, “An efficient point estimate method for probabilistic analysis,” Reliability Engineering & System Safety, vol. 59, pp. 261–267, 1998.
  • P. Karki, P. Hu, and R. Billinton, “A simplified wind power generation model for reliability evaluation,” IEEE Transactions on Energ Conversion, vol. 21, no. 5, pp. 533–540, 2006.
  • I. Abouzahr and R. Ramakumar, “An approach to assess the performance of utility-interactive wind electric conversion systems,” IEEE Transactions on Energy Conversion, vol. 6, no. 2, pp. 627–638, 1991.
  • W. Li, Risk Assessment of Power Systems: Models, Methods, and Applications, John Wiley & Sons, New York, NY, USA, 2005.
  • T. Niknam, F. Golestaneh, and A. Malekpour, “Probabilistic energy and operation management of a microgrid containing wind/photovoltaic/fuel cell generation and energy storage devices based on point estimate method and self-adaptive gravitational search algorithm,” Energy, vol. 43, no. 1, pp. 427–437, 2012.
  • R. Azizipanah-Abarghooee, T. Niknam, A. Roosta, A. R. Malekpour, and M. Zare, “Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method,” Energy, vol. 37, pp. 322–335, 2012.
  • J. M. Morales, L. Baringo, A. J. Conejo, and R. Minguez, “Probabilistic power flow with correlated wind sources,” IET Generation, Transmission& Distribution, vol. 4, no. 5, pp. 641–651, 2010.
  • H. Wei, H. Zijun, C. Junzhao, and Z. Li, “Transmission network planning with N-1 security criterion based on improved multi-objective genetic algorithm,” in 2011 4th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, DRPT 2011, pp. 1250–1254, chn, July 2011.
  • M. Laumanns, L. Thiele, K. Deb, and E. Zitzler, “Combining convergence and diversity in evolutionary multiobjective optimization,” Evolutionary Computation, vol. 10, no. 3, pp. 263–282, 2002.
  • M. Zhang, W. Luo, X. Pei, and X. Wang, “The self-adaption strategy for parameter $\varepsilon $ in $\varepsilon $-MOEA,” in 2008 IEEE Congress on Evolutionary Computation, CEC 2008, pp. 2940–2947, chn, June 2008.
  • J. Jing and Su. Yong, “An improved adaptive genetic algorithm,” Computer Engineering and Applications, pp. 64–69, 2005. \endinput