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AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES

Yıl 2011, Cilt: 11 Sayı: 2, 1379 - 1390, 08.05.2012

Öz

Abstract: This paper presents an Improved Differential Evolution (IDE) algorithm to solve Economic Load Dispatch (ELD) problem with non-smooth fuel cost curves considering transmission losses, power balance and capacity constraints. The proposed IDE varies from the Standard Differential Evolution (SDE) algorithm in terms of three basic factors. The initial population in IDE is generated through the concept of Opposition Based Learning (OBL), applies tournament based mutation and uses only one population set throughout the optimization process. The performance of the proposed algorithm is investigated and tested with two standard test systems, the IEEE 30 bus 6 unit system and the 20 unit system. The experiments showed that the searching ability and convergence rate of IDE is much better than the SDE. The results of the proposed approach were compared in terms of fuel cost, computational time, power loss and individual generator powers with existing SDE and other meta-heuristics in literature. The proposed method seems to be a promising approach for ELD problems based on the solution quality and the computational efficiency. Keywords: Improved Differential Evolution, Standard Differential Evolution, Economic Load Dispatch, solution quality, robustness.

Kaynakça

  • Lakshmi Devi A., Vamsi Krishna O. "Combined economic and emission dispatch using Evolutionary algorithms-a case study." ARPN Journal of Engineering and Applied Sciences 3, no. 6, 28-35, 2008.
  • C.L., Wadhwa. Electrical Power Systems. New Delhi: New Age International (p) Limited Publishers, 2000.
  • Lowery, P. G. "Generation unit commitment by dynamic programming." IEEE Trans. Power App.Syst., vol. PAS- 102, 1218–1225, 1983.
  • Wilson, J. A. Muckstadt and R. C. "An application of mixed-integer programming duality to scheduling thermal generating systems." IEEE Trans. Power App. Syst vol. PAS-87, no. 12, 1968-1978, 1968.
  • Yoshimura, A. I. Cohen and M. "A branch-and-bound algorithm for unit commitment." IEEE Trans. Power App. Syst. vol. PAS-102, no. 2, 444–451, 1983.
  • J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee. "A particle swarm optimization for economic dispatch with non smooth cost functions." IEEE Trans. on Power Systems vol. 8, no. 3, 1325-1332, August 1993.
  • Wood J., Wollenberg B. F. Power generation operation and control. John Wiley & Sons, 1984.
  • Rayapudi, S. Rao. "An Intelligent Water Drop Algorithm for Solving Economic Load Dispatch Problem." International Journal of Electrical and Electronics Engineering vol. 5, no. 1, 43-49, 2011.
  • H. T. Yang, P. C. Yang and C. L. Huang. "Evolutionary Programming Based Economic Dispatch For Units With Non-smooth Fuel Cost Functions." IEEE Transactions on Power Systems vol. 11, no. 1, 112-118, 1996.
  • T. Jayabarathi, G. Sadasivam and V. Ramachandran. "Evolutionary programming based economic dispatch of generators with prohibited operating zones." Electric Power Systems Research vol. 52, no. 3, 261-266, 1999.
  • Glover, Z. X. Liang and J. D. "A zoom feature for a dynamic programming solution to economic dispatch including transmission losses." IEEE Trans. on Power Systems vol. 7, no. 2, 544-550, May 1992.
  • Lin, C.-T. Su and C.-T. "New approach with a Hopfield modeling framework to economic dispatch." IEEE Trans. Power Syst. vol.15, no. 2, 541, May 2000.
  • G. Damousis, A. G. Bakirtzis, and P. S. Dokopoulos. "Network-constrained economic dispatch using real- coded genetic algorithm." IEEE Trans. Power Syst. vol. 18, no. 1, 198–205, Feb 2003.
  • W.-M. Lin, F.-S. Cheng, and M.-T. Tsay. "An improved tabu search for economic dispatch with multiple minima." IEEE Trans. Power Syst vol. 17, 108 – 112, February 2002.
  • Wong, K. P. Wong and Y. W. "Genetic and genetic/simulated-annealing approaches to economic dispatch." Proc. Inst. Elect. Eng. Gen. Trans. Distrib. vol. 141, 507-513, September 1994.
  • Gaing, Z.-L. "Particle swarm optimization to solving the economic constraints,”." IEEE Trans. Power Syst. vol.18, no. 3, 1187–1195, Aug 2003. the generator
  • Y. H. Hou, Y. W. Wu, L. J. Lu, and X. Y. Xiong. "Generalized ant colony optimization for economic dispatch of power systems." Proc.Int. Conf. Power System Technology, Power-Con., 225–229, Oct. 2002.
  • K. Panigrahi, S. R. Yadav, S. Agrawal. "A clonal algorithm to solve economic load dispatch." Elect. Power Syst. Res. vol.77, no. 10, 1381–1389, 2007.
  • Iba, N. Nomana and H. "Differential evolution for economic load dispatch problems." Elect. Power Syst. Res. vol.78, no. 3, 1322–1331, 2008.
  • Pandi, B. K. Panigrahi and V. R. "Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch." IET Gen.,Transm., Distrib., vol.2, no. 4, 556-565, 2008.
  • Chattopadhyay, A. Bhattacharya optimization for different "Biogeography-based economic load dispatch problems." IEEE Trans. Power Syst. vol. 25, no. 2, 1064 – 1077, May 2010.
  • Aniruddha Bhattacharya, P.K. Chattopadhyay, “Hybrid Differential Optimization for Solution of Economic Load Dispatch." IEEE Trans. Power Syst. vol. 25. No. 4, 1955-1964, Nov 2010. with Biogeography-Based
  • Kuo, C. C. "A novel coding scheme for practical economic dispatch by." IEEE Trans. Power Syst. vol. 23, no. 4, 1825–1835, Nov. 2008.
  • Mariani, L. D. S. Coelho and V. C. "Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects." Energy Convers. Manage. vol. 49, no. 11, 3080-3085, 2008.
  • K. T. Chaturvedi, M. Pandit, and L. Srivastava. "Self- organizing hierarchical particle swarm optimization for nonconvex economic dispatch." IEEE Trans. Power Syst. vol.23, no. 3, 1079-1087, Aug 2008.
  • K. Panigrahi, V. R. Pandi, and S. Das. "Adaptive particle swarm optimization approach for static and dynamic economic load dispatch." Energy Convers. Manage, vol. 49, no. 6, 1407-1415, 2008.
  • D.-K. He, F.-L. Wang, and Z.-Z. Mao. "Hybrid genetic algorithm for economic dispatch with valve-point effect." Elect. Power Syst. Res., vol. 78, no. 4, 626-633, 2008.
  • Lee, L. D. S. Coelho and C.-S. "Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches." Int. J. Elect. Power Energy Syst., vol.30, no. 4, 297–307, 2008.
  • S.-K. Wang, J.-P. Chiou, and C.-W. Liu. "Non- smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm." IET Gen., Transm., Distrib., vol. 1, no. 5, 793–803, 2007.
  • Chiou, J.-P. "Variable scaling hybrid differential evolution for large scale economic dispatch problems." Elect. Power Syst. Res., vol. 77, no. 1, 212–218, 2007.
  • Chiang, C.-L. "Genetic-based algorithm for power economic load dispatch." IET Gen., Transm., Distrib., vol. 1, no. 2, 261–269, 2007.
  • Mariani, L. D. S. Coelho and V. C. "Correction to “combining of chaotic differential evolution and quadratic optimization with valve-point effect." IEEE Trans. Power Syst. vol.21, no. 3, 1465–1465, Aug 2006.
  • N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay. "Evolutionary programming techniques for economic load dispatch." IEEE Trans. Evol. vol.7, no. 1, 83–94, Feb 2003.
  • R. Storn, K.V. Price. "Differential evolution a simple and efficient heuristic for global optimization over continuous spaces." J. Global Optimization vol.11, no. 4, 341–359, 1997.
  • K.V. Price, R.M. Storn, J.A. Lampinen. Differential Evolution: Optimization. Berlin, Heidelberg: Springer, 2005.
  • Jiriwibhakorn, S. Khamsawang and S. "Solving the Economic Dispatch Problem by Using Differential Evolution." International Journal of Electrical and Electronics Engineering vol.3, no. 10, 641-645, 2009.
  • Shahryar Rahnamayan, H.R. Tizhoosh, M.M.A.Salama. "Opposition based Congress on evolutionary computation, 2010 – 2017, 2006. evolution." IEEE
  • Sailaja Kumari M., Sydulu M. "A Fast Computational Genetic Algorithm for Economic Load Dispatch." International Journal of Recent Trends in Engineering vol.1, no. 1, 349-356, May 2009.
  • Mary, N. Thenmozhi and D. "Economic emission load dispatch using hybrid Genetic Algorithm." Chiang Mai, Thailand, 476-479, 2004.
  • J. Yuryevich, K. P. Wong. "Evolutionary Programming Based Optimal Power Flow Algorithm." IEEE Transaction on power systems vol.14, no. 4, 1245 – 1250, Nov 1999.
  • Y. Labbi, D. Ben Attous. "A hybrid GA–PS method to solve the economic load dispatch problem", Journal of Theoretical and Applied Information Technology vol.15, no. 1, 61-68, 2010.
  • Tarek Bouktir, Linda Slimani, M. Belkacemi. "A Genetic Algorithm for Solving the Optimal Power Flow Problem." Leonardo Journal of Sciences, no. 4, 44-58, June 2004.
  • Boumediène Allaoua, Abdellah Laoufi. "Optimal Power Flow Solution Using Ant Manners for Electrical Network." Advances in Electrical and Computer Engineering vol.9, no. 1, 34-40, 2009.
  • PhanTu Vu, DinhLuong Le, NgocDieu Vo, Tlusty Josef. "A novel weight-improved particle swarm optimization algorithm for optimal power flow and economic load dispatch problem", 1 – 7, 2010.
  • Sumpavakup, I. Srikun, and S. Chusanapiputt. "A solution to the Optimal Power Flow using Artificial Bee Colony algorithm." IEEE. Proc. Int. Conf. Power System Technology . Hangzhou, Oct 2010. 1-5.
  • Thitithamrongchai, B. Eua-arporn. "Self-adaptive
  • Differential Evolution Based Optimal Power Flow for Units with Non-smooth Fuel Cost Functions." Journal of Electrical Systems vol.3, no. 2, 88-99, 2007. L.R.Srinivas.
  • K.Vaisakh, "Differential Evolution Approach for Optimal Power Flow Solutions." Journal of Theoretical and Applied Information Technology vol.4, no. 4, 261-268, 2008.
  • Surekha Paneerselvam is currently a research scholar
  • with the Electrical and Electronics Engineering department
Yıl 2011, Cilt: 11 Sayı: 2, 1379 - 1390, 08.05.2012

Öz

Kaynakça

  • Lakshmi Devi A., Vamsi Krishna O. "Combined economic and emission dispatch using Evolutionary algorithms-a case study." ARPN Journal of Engineering and Applied Sciences 3, no. 6, 28-35, 2008.
  • C.L., Wadhwa. Electrical Power Systems. New Delhi: New Age International (p) Limited Publishers, 2000.
  • Lowery, P. G. "Generation unit commitment by dynamic programming." IEEE Trans. Power App.Syst., vol. PAS- 102, 1218–1225, 1983.
  • Wilson, J. A. Muckstadt and R. C. "An application of mixed-integer programming duality to scheduling thermal generating systems." IEEE Trans. Power App. Syst vol. PAS-87, no. 12, 1968-1978, 1968.
  • Yoshimura, A. I. Cohen and M. "A branch-and-bound algorithm for unit commitment." IEEE Trans. Power App. Syst. vol. PAS-102, no. 2, 444–451, 1983.
  • J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee. "A particle swarm optimization for economic dispatch with non smooth cost functions." IEEE Trans. on Power Systems vol. 8, no. 3, 1325-1332, August 1993.
  • Wood J., Wollenberg B. F. Power generation operation and control. John Wiley & Sons, 1984.
  • Rayapudi, S. Rao. "An Intelligent Water Drop Algorithm for Solving Economic Load Dispatch Problem." International Journal of Electrical and Electronics Engineering vol. 5, no. 1, 43-49, 2011.
  • H. T. Yang, P. C. Yang and C. L. Huang. "Evolutionary Programming Based Economic Dispatch For Units With Non-smooth Fuel Cost Functions." IEEE Transactions on Power Systems vol. 11, no. 1, 112-118, 1996.
  • T. Jayabarathi, G. Sadasivam and V. Ramachandran. "Evolutionary programming based economic dispatch of generators with prohibited operating zones." Electric Power Systems Research vol. 52, no. 3, 261-266, 1999.
  • Glover, Z. X. Liang and J. D. "A zoom feature for a dynamic programming solution to economic dispatch including transmission losses." IEEE Trans. on Power Systems vol. 7, no. 2, 544-550, May 1992.
  • Lin, C.-T. Su and C.-T. "New approach with a Hopfield modeling framework to economic dispatch." IEEE Trans. Power Syst. vol.15, no. 2, 541, May 2000.
  • G. Damousis, A. G. Bakirtzis, and P. S. Dokopoulos. "Network-constrained economic dispatch using real- coded genetic algorithm." IEEE Trans. Power Syst. vol. 18, no. 1, 198–205, Feb 2003.
  • W.-M. Lin, F.-S. Cheng, and M.-T. Tsay. "An improved tabu search for economic dispatch with multiple minima." IEEE Trans. Power Syst vol. 17, 108 – 112, February 2002.
  • Wong, K. P. Wong and Y. W. "Genetic and genetic/simulated-annealing approaches to economic dispatch." Proc. Inst. Elect. Eng. Gen. Trans. Distrib. vol. 141, 507-513, September 1994.
  • Gaing, Z.-L. "Particle swarm optimization to solving the economic constraints,”." IEEE Trans. Power Syst. vol.18, no. 3, 1187–1195, Aug 2003. the generator
  • Y. H. Hou, Y. W. Wu, L. J. Lu, and X. Y. Xiong. "Generalized ant colony optimization for economic dispatch of power systems." Proc.Int. Conf. Power System Technology, Power-Con., 225–229, Oct. 2002.
  • K. Panigrahi, S. R. Yadav, S. Agrawal. "A clonal algorithm to solve economic load dispatch." Elect. Power Syst. Res. vol.77, no. 10, 1381–1389, 2007.
  • Iba, N. Nomana and H. "Differential evolution for economic load dispatch problems." Elect. Power Syst. Res. vol.78, no. 3, 1322–1331, 2008.
  • Pandi, B. K. Panigrahi and V. R. "Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch." IET Gen.,Transm., Distrib., vol.2, no. 4, 556-565, 2008.
  • Chattopadhyay, A. Bhattacharya optimization for different "Biogeography-based economic load dispatch problems." IEEE Trans. Power Syst. vol. 25, no. 2, 1064 – 1077, May 2010.
  • Aniruddha Bhattacharya, P.K. Chattopadhyay, “Hybrid Differential Optimization for Solution of Economic Load Dispatch." IEEE Trans. Power Syst. vol. 25. No. 4, 1955-1964, Nov 2010. with Biogeography-Based
  • Kuo, C. C. "A novel coding scheme for practical economic dispatch by." IEEE Trans. Power Syst. vol. 23, no. 4, 1825–1835, Nov. 2008.
  • Mariani, L. D. S. Coelho and V. C. "Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects." Energy Convers. Manage. vol. 49, no. 11, 3080-3085, 2008.
  • K. T. Chaturvedi, M. Pandit, and L. Srivastava. "Self- organizing hierarchical particle swarm optimization for nonconvex economic dispatch." IEEE Trans. Power Syst. vol.23, no. 3, 1079-1087, Aug 2008.
  • K. Panigrahi, V. R. Pandi, and S. Das. "Adaptive particle swarm optimization approach for static and dynamic economic load dispatch." Energy Convers. Manage, vol. 49, no. 6, 1407-1415, 2008.
  • D.-K. He, F.-L. Wang, and Z.-Z. Mao. "Hybrid genetic algorithm for economic dispatch with valve-point effect." Elect. Power Syst. Res., vol. 78, no. 4, 626-633, 2008.
  • Lee, L. D. S. Coelho and C.-S. "Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches." Int. J. Elect. Power Energy Syst., vol.30, no. 4, 297–307, 2008.
  • S.-K. Wang, J.-P. Chiou, and C.-W. Liu. "Non- smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm." IET Gen., Transm., Distrib., vol. 1, no. 5, 793–803, 2007.
  • Chiou, J.-P. "Variable scaling hybrid differential evolution for large scale economic dispatch problems." Elect. Power Syst. Res., vol. 77, no. 1, 212–218, 2007.
  • Chiang, C.-L. "Genetic-based algorithm for power economic load dispatch." IET Gen., Transm., Distrib., vol. 1, no. 2, 261–269, 2007.
  • Mariani, L. D. S. Coelho and V. C. "Correction to “combining of chaotic differential evolution and quadratic optimization with valve-point effect." IEEE Trans. Power Syst. vol.21, no. 3, 1465–1465, Aug 2006.
  • N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay. "Evolutionary programming techniques for economic load dispatch." IEEE Trans. Evol. vol.7, no. 1, 83–94, Feb 2003.
  • R. Storn, K.V. Price. "Differential evolution a simple and efficient heuristic for global optimization over continuous spaces." J. Global Optimization vol.11, no. 4, 341–359, 1997.
  • K.V. Price, R.M. Storn, J.A. Lampinen. Differential Evolution: Optimization. Berlin, Heidelberg: Springer, 2005.
  • Jiriwibhakorn, S. Khamsawang and S. "Solving the Economic Dispatch Problem by Using Differential Evolution." International Journal of Electrical and Electronics Engineering vol.3, no. 10, 641-645, 2009.
  • Shahryar Rahnamayan, H.R. Tizhoosh, M.M.A.Salama. "Opposition based Congress on evolutionary computation, 2010 – 2017, 2006. evolution." IEEE
  • Sailaja Kumari M., Sydulu M. "A Fast Computational Genetic Algorithm for Economic Load Dispatch." International Journal of Recent Trends in Engineering vol.1, no. 1, 349-356, May 2009.
  • Mary, N. Thenmozhi and D. "Economic emission load dispatch using hybrid Genetic Algorithm." Chiang Mai, Thailand, 476-479, 2004.
  • J. Yuryevich, K. P. Wong. "Evolutionary Programming Based Optimal Power Flow Algorithm." IEEE Transaction on power systems vol.14, no. 4, 1245 – 1250, Nov 1999.
  • Y. Labbi, D. Ben Attous. "A hybrid GA–PS method to solve the economic load dispatch problem", Journal of Theoretical and Applied Information Technology vol.15, no. 1, 61-68, 2010.
  • Tarek Bouktir, Linda Slimani, M. Belkacemi. "A Genetic Algorithm for Solving the Optimal Power Flow Problem." Leonardo Journal of Sciences, no. 4, 44-58, June 2004.
  • Boumediène Allaoua, Abdellah Laoufi. "Optimal Power Flow Solution Using Ant Manners for Electrical Network." Advances in Electrical and Computer Engineering vol.9, no. 1, 34-40, 2009.
  • PhanTu Vu, DinhLuong Le, NgocDieu Vo, Tlusty Josef. "A novel weight-improved particle swarm optimization algorithm for optimal power flow and economic load dispatch problem", 1 – 7, 2010.
  • Sumpavakup, I. Srikun, and S. Chusanapiputt. "A solution to the Optimal Power Flow using Artificial Bee Colony algorithm." IEEE. Proc. Int. Conf. Power System Technology . Hangzhou, Oct 2010. 1-5.
  • Thitithamrongchai, B. Eua-arporn. "Self-adaptive
  • Differential Evolution Based Optimal Power Flow for Units with Non-smooth Fuel Cost Functions." Journal of Electrical Systems vol.3, no. 2, 88-99, 2007. L.R.Srinivas.
  • K.Vaisakh, "Differential Evolution Approach for Optimal Power Flow Solutions." Journal of Theoretical and Applied Information Technology vol.4, no. 4, 261-268, 2008.
  • Surekha Paneerselvam is currently a research scholar
  • with the Electrical and Electronics Engineering department
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

S. Sumathi Bu kişi benim

Surekha P, S.sumathı Bu kişi benim

Yayımlanma Tarihi 8 Mayıs 2012
Yayımlandığı Sayı Yıl 2011 Cilt: 11 Sayı: 2

Kaynak Göster

APA Sumathi, S., & S.sumathı, S. P. (2012). AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES. IU-Journal of Electrical & Electronics Engineering, 11(2), 1379-1390.
AMA Sumathi S, S.sumathı SP. AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES. IU-Journal of Electrical & Electronics Engineering. Mayıs 2012;11(2):1379-1390.
Chicago Sumathi, S., ve Surekha P, S.sumathı. “AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES”. IU-Journal of Electrical & Electronics Engineering 11, sy. 2 (Mayıs 2012): 1379-90.
EndNote Sumathi S, S.sumathı SP (01 Mayıs 2012) AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES. IU-Journal of Electrical & Electronics Engineering 11 2 1379–1390.
IEEE S. Sumathi ve S. P. S.sumathı, “AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES”, IU-Journal of Electrical & Electronics Engineering, c. 11, sy. 2, ss. 1379–1390, 2012.
ISNAD Sumathi, S. - S.sumathı, Surekha P,. “AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES”. IU-Journal of Electrical & Electronics Engineering 11/2 (Mayıs 2012), 1379-1390.
JAMA Sumathi S, S.sumathı SP. AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES. IU-Journal of Electrical & Electronics Engineering. 2012;11:1379–1390.
MLA Sumathi, S. ve Surekha P, S.sumathı. “AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES”. IU-Journal of Electrical & Electronics Engineering, c. 11, sy. 2, 2012, ss. 1379-90.
Vancouver Sumathi S, S.sumathı SP. AN IMPROVED DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMAL LOAD DISPATCH IN POWER SYSTEMS INCLUDING TRANSMISSION LOSSES. IU-Journal of Electrical & Electronics Engineering. 2012;11(2):1379-90.