Advertisement

Applications of TRUST-TECH Methodology in Optimal Power Flow of Power Systems

  • Hsiao-Dong Chiang
  • Bin Wang
  • Quan-Yuan Jiang
Part of the Energy Systems book series (ENERGY)

Summary

The main objective of the optimal power flow (OPF) problem is to determine the optimal steady-state operation of an electric power system while sat- isfying engineering and economic constraints. With the structural deregulation of electric power systems, OPF is becoming a basic tool in the power market. In this paper, a two-stage solution algorithm developed for solving OPF problems has several distinguished features: it numerically detects the existence of feasible solutions and quickly locates them. The theoretical basis of stage I is that the set of stable equilibrium manifolds of the quotient gradient system (QGS) is a set of feasible components of the original OPF problem. The first stage of this algorithm is a fast, globally convergent method for obtaining feasible solutions to the OPF problem. Starting from the feasible initial point obtained by stage I, an interior point method (IPM) at stage II is used to solve the original OPF problem to quickly locate a local optimal solution. This two-stage solution algorithm can quickly obtain a feasible solution and robustly solve OPF problems. Numerical test systems include a 2,383-bus power system.

Keywords

Power System Optimal Power Interior Point Method Local Optimal Solution Optimal Power Flow 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Carpentier. Contribution to the economic dispatch problem. Bulletin de la Societ Franhise dElectricit , 8(1):431–437, 1962.Google Scholar
  2. 2.
    H.W. Dommel and W.F. Tinney. Optimal power flow solutions. IEEE Transactions on Power Apparatus and Systems, PAS-87(10):1866–1876, 1968.CrossRefGoogle Scholar
  3. 3.
    O. Alsac and B. Stott. Optimal load flow with steady-state security. IEEE Transactions on Power Apparatus and Systems, PAS-93(3):745–751, 1974.CrossRefGoogle Scholar
  4. 4.
    S.N. Talukdar and F.F. Wu. Computer-aided dispatch for electric power systems. Proceedings of IEEE, 69(10):1212–1231, 1981.CrossRefGoogle Scholar
  5. 5.
    M. Huneault and F.D. Galiana. A survey of the optimal power flow literature. IEEE Transactions on Power Systems, 6(2):762–770, 1991.CrossRefGoogle Scholar
  6. 6.
    J.A. Momoh, M.E. El-Hawary, and R. Adapa. A review of selected optimal power flow literature to 1993: Part-i and part-ii. IEEE Transactions on Power Systems, 14(1):96–111, 1999.CrossRefGoogle Scholar
  7. 7.
    N. Grudinin. Combined quadratic-separable programming opf algorithm for economic dispatch and security control. IEEE Transactions on Power Systems, 12(4):1682–1688, 1997.CrossRefGoogle Scholar
  8. 8.
    R.C. Burchett, H.H. Happ, and D.R. Vierath. Quadratically convergent optimal power flow. IEEE Transactions on Power Apparatus and Systems, PAS-103(11):3267–3276, 1984.CrossRefGoogle Scholar
  9. 9.
    J. Nanda. New optimal power-dispatch algorithm using fletcher's quadratic programming method. IEE Proceedings C, 136(3):153–161, 1989.Google Scholar
  10. 10.
    K.C. Almeida and R. Salgado. Optimal power flow solutions under variable load conditions. IEEE Transactions on Power Systems, 15(4):1204–1211, 2000.CrossRefGoogle Scholar
  11. 11.
    S.A. Pudjianto and G. Strbac. Allocation of var support using lp and nlp based optimal power flows. IEE Proceedings — Generation, Transmission and Distribution, 149(4):377–383, 2002.CrossRefGoogle Scholar
  12. 12.
    T.N. Saha and A. Maitra. Optimal power flow using the reduced newton approach in rectangular coordinates. International Journal of Electrical Power and Energy Systems, 20(6):383–389, 1998.CrossRefGoogle Scholar
  13. 13.
    Y.Y. Hong, C.M. Liao, and T.G. Lu. Application of newton optimal power flow to assessment of var control sequences on voltage security: case studies for a ractical power system. IEE Proceedings C, 140(6):539–544, 1993.Google Scholar
  14. 14.
    J.A. Momoh. Improved interior point method for opf problems. IEEE Transactions on Power Systems, 14(3):1114–1120, 1999.CrossRefGoogle Scholar
  15. 15.
    Y.C. Wu and A.S. Debs. Initialization, decoupling, hot start, and warm start in direct nonlinear interior point algorithm for optimal power flows. IEE Proceedings — Generation, Transmission and Distribution, 148(1):67–75, 2001.CrossRefGoogle Scholar
  16. 16.
    K.C. Almeida, F.D. Galiana, and S. Soares. A general parametric optimal power flow. IEEE Transactions on Power Systems, 9(1):540–547, 1994.CrossRefGoogle Scholar
  17. 17.
    P. Ristanovic. Successive linear programming based opf solution. Technical report, IEEE Tutorial Course Manual #96 TP 111-0, Piscataway, NJ, 1996.Google Scholar
  18. 18.
    N. Grudinin. Reactive power optimization using successive quadratic programming method. IEEE Transactions on Power Systems, 13(4):1219–1225, 1998.CrossRefGoogle Scholar
  19. 19.
    D. Sun, B. Ashley, B. Brewer, A. Hughes, and W. Tinney. Optimal power flow by newton approach. IEEE Transactions on Power Apparatus and Systems, PAS-103(10):2864–2880, 1984.CrossRefGoogle Scholar
  20. 20.
    Y.C. Wu, A.S. Debs, and R.E. Marsten. A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Transactions on Power Systems, 9(2):876–883, 1994.CrossRefGoogle Scholar
  21. 21.
    F.F. Wu, G. Gross, J.F. Luini, and P.M. Lock. A two-stage approach to solving large scale optimal power flow. In IEEE Proceedings of Power Industry Computer Applications Conference (PICA'79), pages 126–136, Cleveland, OH, May 1979.Google Scholar
  22. 22.
    V.H. Quintana, G.L. Torres, and J. Medina-Palomo. Interior-point methods and their applications to power systems: a classification of publications and software codes. IEEE Transactions on Power Systems, 15(1):170–176, 2000.CrossRefGoogle Scholar
  23. 23.
    G.L. Torres and V.H. Quintana. An interior-point methods for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Transactions on Power Systems, 13(4):1211–1218, 1998.CrossRefGoogle Scholar
  24. 24.
    S. Granville. Optimal reactive dispatch through interior point methods. IEEE Transactions on Power Systems, 9(1):136–146, 1994.CrossRefGoogle Scholar
  25. 25.
    Pjm manual 06, 11, 12: Scheduling operations, 2006. Available at: http://www.pjm.com/contributions/pjm-manuals/manuals.html.
  26. 26.
    Federal Energy regulatory Commission. Principles for efficient and reliable reactive power supply and consumption. FERC Staff reports, Docket No. AD05-1-000, pages 161–162, February 2005. Available at: http://www/ferc.gov/legal/staff-reports.asp.
  27. 27.
    H. Wei, H. Sasaki, J. Kubokawa, and R. Yohoyama. An interior point methods for power systems weighted nonlinear l1 norm static state estimation. IEEE ransactions on Power Systems, 13(2):617–623, 1998.CrossRefGoogle Scholar
  28. 28.
    G.D. Irisarri, X. Wang, J. Tong, and S. Mokhtari. Maximum loadability of power systems using interior point method nonlinear optimization. IEEE Transactions on Power Systems, 12(1):162–172, 1997.CrossRefGoogle Scholar
  29. 29.
    S. Granville, J.C.O. Mello, and A.C.G. Melo. Application of interior point methods to power flow unsolvability. IEEE Transactions on Power Systems, 11(2):1096–1103, 1996.CrossRefGoogle Scholar
  30. 30.
    X. Wang, G.C. Ejebe, J. Tong, and J.G. Waight. Preventive/corrective control for voltage stability using direct interior point method. IEEE Transactions on Power Systems, 13(3):878–883, 1998.CrossRefGoogle Scholar
  31. 31.
    J. Medina, V.H. Quintana, A.J. Conejo, and F.P. Thoden. A comparison of interior-point codes for medium-term hydrothermal coordination. IEEE Transactions on Power Systems, 13(3):836–843, 1998.CrossRefGoogle Scholar
  32. 32.
    X. Yan and V.H. Quintana. An efficient predictor — corrector interior point algorithm for security-constrained economic dispatch. IEEE Transactions on Power Systems, 12(2):803–810, 1997.CrossRefGoogle Scholar
  33. 33.
    S. Mehrotra. On the implementation of a primal-dual interior point method. SIAM Journal on Optimization, 2(4):575–601, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    J. Gondzio. Multiple centrality corrections in a primal-dual method for linear programming. Computational Optimization and Applications, 6(2):137–156, 1996.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    G.L. Torres and V.H. Quintana. On a nonlinear multiple-centrality corrections interior-point method for optimal power flow. IEEE Transactions on Power Systems, 16(2):222–228, 2001.CrossRefGoogle Scholar
  36. 36.
    Y.C. Wu and A.S. Debs. Initialisation, decoupling, hot start, and warm start in direct nonlinear interior point algorithm for optimal power flows. IEE-Proceeding, 148(1):67–75, 2001.Google Scholar
  37. 37.
    R.A. Jabr, A.H. Coonick, and B.J. Cory. A primal-dual interior point method for optimal power flow dispatching. IEEE Transactions on Power Systems, 17(3):654–662, 2002.CrossRefGoogle Scholar
  38. 38.
    H. Wei, H. Sasaki, J. Kubakawa, and R. Yokoyama. An interior point nonlinear programming for optimal power flow problems with a novel data structure. IEEE Transactions on Power Systems, 13(3):870–877, 1998.CrossRefGoogle Scholar
  39. 39.
    J. Lee and H.D. Chiang. A dynamical trajectory-based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems. IEEE Transactions on Automatic Control, 49(6):888–899, 2004.MathSciNetCrossRefGoogle Scholar
  40. 40.
    H.D. Chiang and C.C. Chu. A systematic search method for obtaining multiple local optimal solutions of nonlinear programming problems. IEEE Transactions on Circuits and Systems, 43(2):99–109, 1996.MathSciNetCrossRefGoogle Scholar
  41. 41.
    H.D. Chiang and J. Lee. TRUST-TECH Paradigm for computing high-quality optimal solutions: method and theory, pages 209–234. Wiley-IEEE, New Jersey, February 2006.Google Scholar
  42. 42.
    C.R. Karrem. TRUST-TECH Based Methods for Optimization and Learning. PhD thesis, Cornell University, Ithaca, NY, 2007.Google Scholar
  43. 43.
    J.H. Chen. Hybrid TRUST-TECH Algorithms and Their Applications to Mixed Integer and Mini-Max Optimization Problems. PhD thesis, Cornell University, Ithaca, NY, 2007.Google Scholar
  44. 44.
    M.S. Bazaraa, H.D. Sherali, and C.M. Shetty. Nonlinear Programming, Theory and Algorithms. Wiley, Hoboken, NJ, third edition, 2006.CrossRefzbMATHGoogle Scholar
  45. 45.
    C.T. Kelley and D.E. Keyes. Convergence analysis of pseudo-transient continuation. SIAM Journal on Numerical Analysis, 35(2):508–523, 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    T.S. Coffey, C.T. Kelley, and D.E. Keyes. Pseudo-transient continuation and differential-algebraic equations. SIAM Journal of Scientific Computing, 25(2):553–569, 2003.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hsiao-Dong Chiang
    • 1
  • Bin Wang
    • 1
  • Quan-Yuan Jiang
    • 2
  1. 1.School of Electrical and Computer EngineeringCornell UniversityIthacaUSA
  2. 2.School of Electrical EngineeringZhejiang UniversityHangzhouP.R. China

Personalised recommendations