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Interior Point Methods and Applications in Power Systems

  • Xie Kai
  • Y. H. Song
Chapter
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 20)

Abstract

Interior-point methods (IPMs) are a central, striking feature of the constrained optimization landscape today. They have led a fundamental shift in thinking about continuous optimization. Today, in complete contrast to the era before 1984, researchers view linear and nonlinear programming from a unified perspective. The magnitude of this change can be appreciated simply by noting that no one would seriously argue today that linear programming is independent of nonlinear programming. Also, IPMs provide an alternative to active set methods for the treatment of inequality constraints, which permits the effective and efficient handling of large sets of equality and inequality constraints. Therefore, IPMs have been proposed for the solution of a wide range of traditional optimization problems in power systems since the 1990’s, and the numerical experience with these methods has been quite positive.

Keywords

Power System Reactive Power Power Flow Interior Point Method Spot Price 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    K.R. Frisch, 1955, The Logarithmic potential method for convex programming, Institute of Economics, University of Oslo, Oslo, Norway (unpublished manuscript )Google Scholar
  2. 2.
    A.V. Fiacco and G.P.McComick, Non-linear Programming: Sequential Unconstrained Minimisation Techniques, John Wiley & Sons, New York, 1968.Google Scholar
  3. 3.
    I.I. Dikin, Iterative Solution of Problems of Linear and Quadratic Programming, Doklady Akademii Nauk SSSR 174:747–748,1967. Translated into English in Soviet Mathematics Doklady, 8: 674–675.Google Scholar
  4. 4.
    N.K. Karmarkar, 1984. A New Polynomial-Time Algorithm for Linear Programming, Combinatoria 4, 373–395MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    I.J. Lusting, R.E. Marsten, D.F. Shanno, Interior Point Methods for Linear Programming: Computation State of the Art, ORSA Journal on Computing, Vol.6, No.1. Winter 1994Google Scholar
  6. 6.
    G. Strang, Linear Algebra and Its Applications, 405–411, Harcout Brace Jovanovich, 1988Google Scholar
  7. 7.
    J. Gondzio, T. Terlaky, Advanced in Linear Programming, 1996Google Scholar
  8. 8.
    R.J. Vanderbei, Interior Point Methods: Algorithms and Formulations, ORSA Journal on Computing, Vol.6, No.1 Winter 1994Google Scholar
  9. 9.
    K.A. Mcshane, C.L. Monma and D.F. Shanno, 1989, An Implementation of Primary Dual Interior Point Method For Linear Programming, ORSA Journal on Computing 70–83Google Scholar
  10. 10.
    K.A. Clements, P.W. Davis, K.D. Prey, “An Interior Point Algorithm for Weighted Least Absolute Value Power System State Estimation”, IEEE paper 91 WM 235–2 PWRS.Google Scholar
  11. 11.
    G. Irisarri, L.M. Kimball, K.A. Clements, A. Bagchi and P.W. Davis, “Economic Dispatch with Network and Ramping Constraints via Interior Point Methods”, IEEE Trans. PWRS, Vo. 13, No. 1, February 1998Google Scholar
  12. 12.
    L.S. Vargas, V.H. Quintana and A. Vannelli, “A Tutorial Description of An Interior Point Method and Its Applications to Security Constrained Economic Dispatching”, IEEE Trans. PWRS, Vo. 8, No. 3, August 1993Google Scholar
  13. 13.
    X. Yan, V.H. Quintana, “An Efficient Predictor-Corrector Interior Point Algorithm for Security-Constrained Economic Dispatching”, IEEE Trans. PWRS, Vo. 12, No. 2, February 1997Google Scholar
  14. 14.
    S. Granville, “Optimal Reactive Dispatch Through Interior Point Methods”, IEEE Trans. PWRS, Vo. 9, No. 1, February 1994Google Scholar
  15. 15.
    J.A. Momoh, S.X. Guo, E.C. Ogbuoriri and R. Adapa, “ The Quadratic Interior Point Method Solving Power System Optimisation Problems”, IEEE Trans. PWRS, Vo. 9, No. 3, August 1994Google Scholar
  16. 16.
    G.R. Mda Costa, “Optimal Reactive Dispatch Through Primal-Dual method”, IEEE Trans. PWRS, Vo. 12, No. 2, May 1994Google Scholar
  17. 17.
    J.L Martinez Ramos, A. Gomez Exposito, V.H. Quintana, “ Reactive Power Optimisation by Interior Point Methods: Implementation Issues”, 12h Power Systems Computation Conference, Dresden, August 19–23, 199Google Scholar
  18. 18.
    Y.C. Wu, A.S. Debs and R.E. Marsten, “A Direct Nonlinear PrdictorCorrector Primal-Dual Interior Point Algorithm for Optimal Power Flow”, IEEE Trans. PWRS, Vo. 9, No. 2, May 1994Google Scholar
  19. 19.
    S. Granville, J.C.O. Mello, A.C.G. Melo, “ Application of Interior Point Methods to Power Flow Unsolvability”, IEEE Trans. PWRS, Vo. 11, No. 2, May 1996Google Scholar
  20. 20.
    J.C.O. Mello, A.C.G. Mello, S. Granville, “Simultaneous Transfer Capacity Assessment by Combining Interior Point Methods And Monte Carlo Simulation”, IEEE Summer Meeting, 1996Google Scholar
  21. 21.
    G.D. Irisarri, X. Wang, J. Tong, S. Mokhari, “Maximum Loadability of Power Systems using Interior Point Non-Linear Optimisation Method”, IEEE Trans. PWRS, Vo. 12, No. 1, February 1997Google Scholar
  22. 22.
    K. Xie, Y.H. Song, G.Y. Liu and E.K. Yu, “Real Time Pricing of Electricity Using Interior Point Optimal Power Flow Alogorithm”,UPEC’98, Edinburgh, UK, 1998Google Scholar
  23. 23.
    C.N. Lu, MR. Unum, “Network Constrained Security Control Using Interior Point Algorithm”, IEEE Trans. PWRS, Vo. 8, No. 3, August 1993Google Scholar
  24. 24.
    D.I. Sun, B. Ashley, B. Brewer, A. Hughes, W.F. Tinney, “Optimal Power Flow by Newton Approach”, IEEE Transactions on Power Systems, Vol. PAS-103, No. 10, October 1984Google Scholar
  25. 25.
    Y.G. Hao, “Study of Optimal Power Flow and Short-term Reactive Power Scheduling”, PhD Thesis, Electric Power Research Institute (China), 1997Google Scholar
  26. 26.
    K.A. Mcshane, C.L. Monma and D.F. Shanno, 1989, An Implementation of a Primal-Dual Interior Point for Linear Programming, ORSA Journal on Computing 1, 70–83.zbMATHCrossRefGoogle Scholar
  27. 27.
    F. Schweppe, M. Caramanis, R. Tabors, and R. Bohn, Spot Pricing of Electricity, Kluwer Academic Publishers, Boston, MA, 1988Google Scholar
  28. 28.
    M.L. Baughman, S.N. Siddiqi, “Real Time Pricing of Reactive Power: Theory and Case Study Results ”, IEEE Transactions on Power Systems, Vol. 6, No. 1, February 1993Google Scholar
  29. 29.
    A.A. EL-Keib, X. Ma, “Calculating of Short-Run Marginal Costs of Active and Reactive Power Production”, IEEE Transactions on Power Systems, Vol. 12, No. 1, May 1997Google Scholar
  30. 30.
    J.D. Finney, H.A. Othman, W.L. Rutz, Evaluating Transmission Congestion Constraints in System Planning, IEEE Transactions on Power Systems, Vol. 12, No. 3, August 1997Google Scholar
  31. 31.
    I. Adler, N.K. Karmarkar, M.G.C. Resende and G. Veiga, 1989, An Implementation of Karmarkar’s Algorithm for Linear Programming, Mathematical Programming 44, 297–335MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    R.D.C. Monteiro and I. Adler,1989, Interior Path Following Primal-Dual Algorithms: Part 1: Linear Programming, Mathematical Programming 44, 27–41Google Scholar
  33. 33.
    P.E. Gill, W. Murray, M.A. Saunders, J.A. Tomlin and MH. Wright, 1986. On Projected Newton Barrier Method for Linear Programming and an Equivalence to Karmarkar’s Projective Method, Mathematical Programming 36, 409–429CrossRefGoogle Scholar
  34. 34.
    N. Megiddo, 1989, Pathways to Optimal Set in Linear Programming, pp.131138 in Progress in Mathematical Programming,: Interior Point and Related Methods, N.Megiddo (ed.), Springer Verlag, NYGoogle Scholar
  35. 35.
    S. Mehrotra, 1992, On the Implementation of a Primal-Dual Interior Point Method, SIAM Journal on Optimisation 2: 4, 575–601MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    A. Canizares, F.L. Alvarado, C.L. DeMarco, I. Dobson, W.F. Long, “ Point of Collapse Methods Applied to AC/DC Power Systems”, IEEE Transactions on Power Systems, Vol. 7, No. 2, August 1992Google Scholar
  37. 37.
    V.H. Quitana, A. Gomez and J.L. Martinez, “Nonlinear Optimal Power Flow by a Logrithmic-Barrier Primal-Dual Algorithm”, Proc. Of NAPS, 1995Google Scholar
  38. 38.
    K.A. Clements, P.W. Davis and K.D. Frey, “Treatment of Inequality Constraints in Power System State Esitimation”, IEEE Transactions on Power Systems, Vol. 10, No. 2, 567–573, May 1995CrossRefGoogle Scholar
  39. 39.
    J. Carpentier, “Contribution to the Economic Dispatch problems”, Bull. Soc. France Elect, Vol.8, 431–437, August, 1962Google Scholar
  40. 40.
    R. J. Vanderbei, D.F. Shanno, “ An Interior Point Algorithm for Nonconvex Nonlinear Programming, ” 1991 Mathematics Subject Classification Primary 90C30, Secondary 49M37, 65K05Google Scholar
  41. 41.
    M. Huneault, F.D. Galliana, “A Survey of the Optimal Power Flow Literature,” IEEE Transactions on Power Systems, Vol. 6, No. 2, 762–770, May 1991Google Scholar
  42. 42.
    H. Wei, H. Sasaki, J. kubokawa, R. Yokoyama, “ An Interior Point Nonlinear Programming for Optimal Power Flow Problems with a Novel Data Structure”, IEEE Transactions on Power Systems, Vol. 13, No. 3, 870877, August 1998Google Scholar
  43. 43.
    H. Wei, H. Sasaki, J. Kubokawa, R. Yokoyama, “ An Interior Point Nonlinear Programming for Power System Weighted Nonlinear L1 Norm State Estimation”, IEEE Transactions on Power Systems, Vol. 13, No. 2, 870–877, May 1998Google Scholar
  44. 44.
    X. Wang, G.C. Ejebe, J. Tong, J.G. Waight, “Preventive/Corrective Control for Voltage Stability Using Direct Interior Point Method”, IEEE Trans on PWRS, Vol. 13, No. 3, August 1998Google Scholar
  45. 45.
    K.A. Mcshane, C.L. Monma, D.F. Shanno, An Implementation of a Primal-Dual Interior Point Methods For Linear Programming, ORSA Journal on Computing 1, 70–83Google Scholar
  46. 46.
    H. Wei, H. Sasaki, J. kubokawa, “ A Decoupled Solution of Hydro-thermal Optimal Power Flow by Means of Interior Point Method and Network Programming”, IEEE Transactions on Power Systems, Vol. 13, No. 2,, May 199Google Scholar
  47. 47.
    K. Ponnambalam, V.H. Quintana, A. Vannelli, “ A Fast Algorithm for Power System Optimization Problems Using An Interior Point Method”, IEEE Transactions on Power Systems, Vol. 7, No. 2, May 1992.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Xie Kai
    • 1
  • Y. H. Song
    • 1
  1. 1.Department of Electrical Engineering and ElectronicsBrunel UniversityUxbridgeUK

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