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International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35

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MATHEMATICAL MODELING APPROACH FOR DETERMINING TYPE-1 LOAD-FLOW SOLUTIONS OF POWER SYSTEMS

Research Paper Open Access

International Journal of Latest Research in Science and Technology Vol.4 Issue 6, pp 29-38,Year 2015

MATHEMATICAL MODELING APPROACH FOR DETERMINING TYPE-1 LOAD-FLOW SOLUTIONS OF POWER SYSTEMS

Chen-Sung Chang

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Received : 03 December 2015; Accepted : 16 December 2015 ; Published : 31 December 2015

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Abstract

A mathematical modeling approach based on the continuation power flow (CPFLOW) analysis method is proposed for locating the Type-1 load-flow solutions of a power system. Importantly, the proposed method enables all of the Type-1 load-flow solutions to be obtained by tracing just a small number of homotopy curves. The validity of the proposed approach is demonstrated using 5-bus and 7-bus power systems for illustration purposes. The results show that the proposed method not only has the ability to locate all of the Type-1 load-flow solutions, but also has a lower computational complexity than existing schemes.

Key Words   
Type-1 solutions; Continuation power flow (CPFLOW) analysis; Stable equilibrium point (SEP); Manifol

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References
  1. Chang, C.S. “Voltage Security Monitoring and Control in Electric Power Transmissi on Systems,” Ph.D. Thesis, National Taiwan University, 1999.
  2. Mozina, C.J. “A shot in the dark,” IEEE Ind. Appl. Vol. 14, pp. 45-52, 2008.
  3. Chang, C.S. “A Matrix-based VaR Model for Risk Identification in Power Supply Networks.” Applied Mathematical Modeling, Vol. 35, pp. 4567-4574, 2011.
  4. Tamura, Y., Mori, H., Iwamoto, S. “Relationship between voltage instability and multiple load-flow solutions in electric power systems,” IEEE Trans. Power App. Syst. Vol. 102, pp. 1115-1125, 1983.
  5. Alvarado, F.L., Dobson, I., Thomas, R.J., Hu, Y. “Computation of closest bifurcation in power systems,” IEEE Trans. Power Syst. 9,  pp. 918-928, 1994.
  6. Lu, J., Liu, C.W., Thorp, J.S. “New methods for computing a saddlenode bifurcation point for voltage stability analysis,” IEEE Trans. Power Syst. Vol. 10, pp. 978-989, 1995.
  7. Dimitrovski, A., Tomsovic, K. “Boundary load flow solutions,” IEEE Trans. Power Syst. Vol. 19, pp. 348-355, 2004.
  8. Guedes, R.B.L., Alberto, L.F.C., Bretas, N.G. “Power System Low-Voltage Solutions Using an Auxiliary Gradient System for Voltage Collapse Purposes,” IEEE Trans. Power Syst. Vol. 20, pp. 1528-1537, 2005.
  9. Salam, F.M.A., Ni, L., Guo,S., Sun, X. “Parallel processing for the load flow of power systems: the approach and applications,” In Proc. 28th Decision and Control Conf., Tampa, FL, pp. 2173-2178, Dec. 1989.
  10. Ma, W., Thorp, J.S. “An efficient algorithm to locate all the load-flow solutions,” IEEE Trans. Power Syst., Vol. 8, pp. 1077-1083, 1993.
  11. Chiang, H.D., Dobson, I., Thomas, R.J., Thorp, J.S., Lazhar, F.A. “On voltage collapse in electric power systems,” IEEE Trans. Power Syst. Vol. 5, pp. 601-611, 1990.
  12. Sauer, P.W., Pai, M.A. “Power system steady-state and the load-flow Jacobian,” IEEE Trans. Power Syst. Vol. 5, pp. 1374-1383, 1990.
  13. Overbye, T.J., Klump, R.P. “Effective calculation of power system low-voltage solution,” IEEE Trans. Power Syst. Vol. 11, pp. 75-82, 1996.
  14. Liu, C.W., Thorp, J.S. “A novel method to compute the closest unstable equilibrium point for transient stability region estimate in power system,” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat. Vol. 44, pp. 630-635, 1997.
  15. Ting, T.O., Wong, K.P., Chung, C.Y. “Locating Type-1 Load Flow Solutions using Hybrid Evolutionary Algorithm,” In Proceedings of the Fifth International Conference on Machine Learning and Cybernetics, pp. 4093-4098, Aug. 2006.
  16. Liu, C.W., Chang, C.S., Jiang, J.A. Yeh, G.H “Toward a CPFLOW-based algorithm to compute all the type-1 load-flow solutions in electric power systems,” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat. Vol. 52, pp. 625-630, 2005.
  17. Guillemin, V., Pollack, A. Differential Topology, AMS Chelsea Publishing, 2010.
  18. Sotomayor, J. “Generic bifurcations of dynamic systems,” Dynamical Systems, Peixoto, M.M. Ed., Academic Press: New York, 1973.
  19. Zhang, T., Wang, W. “Hopf bifurcation and bistability of a nutrient–phytoplankton–zooplankton model,” Applied Mathematical Modeling, Vol. 36, pp. 6225-6235, 2012.
  20. Ma, Z.P. “Stability and Hopf bifurcation for a three-component reaction–diffusion population model with delay effect,” Applied Mathematical Modeling , Vol. 37, pp. 5984-6007, 2013.
  21. Bairagi, N., Jana, D. “On the stability and Hopf bifurcation of a delay-induced predator-prey system with habitat complexity,” Applied Mathematical Modeling, Vol. 35, pp. 3255-3267, 2011.
  22. Chow, S.N., Hale, J. Methods of Bifurcation Theory, Springer Verlag: New York, 1982.
  23. Allgower, E.L., Georg, K. “Introduction to Numerical Continuation Methods,” Society for Industrial & Applied , 2003.
  24. Krauskopf, B., Osinga, H.M., Galan-Vioque, J. Numerical Continuation Methods For Dynamical Systems: Path Following And Boundary Value Problems, Springer Verlag, 2007.
  25. Soriano, M., Ordoñez Cabrera, M. “Continuation methods and condensing mappings,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 102, pp. 84-90, 2014.
To cite this article

Chen-Sung Chang , " Mathematical Modeling Approach For Determining Type-1 Load-flow Solutions Of Power Systems ", International Journal of Latest Research in Science and Technology . Vol. 4, Issue 6, pp 29-38 , 2015

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