Abstract
Geometric programming is an important tool for solving certain optimization problems. In this paper, multi objective geometric programming with \(\epsilon \)-constraint method is used to find the maximum radius of a circular power supply substation to supply power in a particular region. The main aim of the proposed method is to formulate a mathematical model for the efficient distribution of the power supply to maximum area from a circular substation with least investment and minimum waste. The proposed multi-objective optimization model has been solved to generate Pareto optimal solutions using weighted sum method. The results so obtained have been compared with that of \(\epsilon \)-constraint method by considering suitable numerical examples.
Similar content being viewed by others
References
Albadi, M.H., El-Saadany, E.F.: Demand response in electricity markets: an overview. In: Proceedings of the IEEE Power Engineering Society General Meeting (2007)
Beightler, C.S., Phillips, D.T.: Applied Geometric Programming. Wiley, New York (1976)
Chinwuko, C.E., Chukwuneke, J.L., Okolie, P.C., Dara, E.J.: Modeling and optimization of electricity distribution planning system using dynamic programming techniques: a case of power holding company of Nigeria (PHCN). Int. J. Multidiscip. Sci. Eng. 3(6), 39–46 (2012)
Chakravorty, S., Ghosh, S.: Power distribution planning using multi-criteria decision making method. Int. J. Comput. Electr. Eng. 1(5), 596 (2009)
Cao, Bing-Yuan: Power supply radius optimized with fuzzy geometric program in substation. Fuzzy Optim. Decis. Mak. 5, 123–139 (2006)
Duffin, R.J., Peterson, E.L., Zener, C.M.: Geometric Programming Theory and Application. Wiley, New York (1967)
Dhar, S.B.: Power system long-range decision analysis under fuzzy environment. IEEE Trans. Power Appar. 2, 585–596 (1979)
Gonen, T., Ramrez-Rosado, I.J.: Optimal multi-stage planning of power distribution systems. IEEE Trans. Power Deliv. 2, 512–519 (1987)
Gonen, T., Foote, B.L.: Mathematical dynamic optimization model for electrical distribution system planning. Electr. Power Energy Syst. 4, 129–136 (1982)
Haddad, J., Lambert-Torres, G., Costa, C.I.A., Jannuzzi, G.M.: Long-term power system planning using a fuzzy treatment. In: Proceedings of IFSA, So Paulo, July (1995)
Haimes, Y.Y., Lasdon, L.S., Wismer, D.A.: On a Bacterion formulation of problems integrated System identification and system optimization. IEEE Trans. Syst. Man Cybern. 1, 296–297 (1971)
Litvinov, E.: Design and operation of the locational marginal pricesbased electricity markets. IET Gener. Transm. Distrib. 4(2), 315323 (2010)
Miettinen, K.M.: Non-linear Multi-objective Optimization. Kluwer Academic Publishers, Boston (1999)
Obrad, M.M.: Mathematical dynamic model for long-term distribution system planning. IEEE Trans. Power Syst. 1, 34–41 (1986)
Ojha, A.K., Biswal, K.: Multi-objective geometric programming problem with \(\epsilon \)-constraint method. Appl. Math. Model. 38, 747–758 (2014)
Peterson, E.L.: The fundamental relations between geometric programming duality, parametric programming duality and ordinary lagrangian duality. Ann. Oper. Res. 105, 109–153 (2001)
Rajgopal, J., Bricker, D.L.: Solving posynomial geometric programming problems via generalized linear programming. Comput. Optim. Appl. 21, 95–109 (2002)
Su, C.L., Kirschen, D.: Quantifying the effect of demand response on electricity markets. IEEE Trans. Power Syst. 24(3), 1199–1207 (2009)
Yang, Q.Y., Zhang, Z.L., Yang, M.Z.: Transformer substation capacity dynamic optimizing in city power network planning. In: Proceedings of Colleges and Unv. Specially of Power System and Its Automation in the Third Academic Annual Conference, pp. 7–11. Xian Jiao Tong University Press (1987)
Yang J.H., Cao B.Y.: The origin and its application of geometric programming. In: Proceedings of the Eighth National Conference of Operational Research Society of China, pp. 358–363. Global-Link Publishing Company, Hong Kong. ISBN:962-8286-09-9 (2006)
Yu, Y.Y., Wang, X.Z., Yang, Y.W.: Optimizational selection for substation feel economic radius. J. Chang. Norm. Univ. Water Resour. Electr. Power 6(1), 118–124 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ota, R.R., Pati, J.C. & Ojha, A.K. Geometric programming technique to optimize power distribution system. OPSEARCH 56, 282–299 (2019). https://doi.org/10.1007/s12597-019-00363-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-019-00363-6