Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values

2007 IEEE Lausanne POWERTECH, Proceedings

Volumn , Issue , 2007, Pages 98-102

  De Sousa, V A ^b   Baptista, E C ^c   Da Costa, G R M ^a,b  

^a IEEE

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

Modified barrier function; Newton's method; Nonlinear programming; Optimal power flow

Indexed keywords

MATHEMATICAL MODELS; MATRIX ALGEBRA; NEWTON-RAPHSON METHOD; POWER ELECTRONICS;

INEQUALITY CONSTRAINTS; MODIFIED BARRIER FUNCTION; NEWTON'S METHOD; NONLINEAR PROGRAMMING; OPTIMAL POWER FLOW;

LAGRANGE MULTIPLIERS;

EID: 50849096657     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/PCT.2007.4538299     Document Type: Conference Paper

References (13)

1. S. Granville, "Optimal Reactive Dispatch Through Interior Point Method", IEEE Transactions on Power Systems, vol. 9, no. 4, pp. 136-146, February 1994.
2. Y. Wu, A.S. Debs and R. E. Marsten, "A Direct Nonlinear Predictor-Corrector Primal-Dual Interior Point Algorithm for Optimal Power Flow", IEEE Transactions on Power Systems, vol. 9, no. 2, pp. 876-883, May 1994.
3. G. L. Torres, and V. H. Quintana, "An Interior Point Method for Nonlinear Optimal Power Flow Using Voltage Rectangular Coordinates", IEEE Transactions on Power Systems, vol. 13, no. 4, pp. 1211 1218, November 1998.
4. J.A. Momoh and J.Z. Zhu, "Improved interior point for OPF problems", IEEE Transactions on Power Systems, vol. 14, no. 3, pp. 1114-1120, August 1999.
5. Y. Wu, A.S. Debs, "Initialization, decoupling, hot start and warm start in direct nonlinear interior point algorithm for optimal power flow", Generation, Transmission and Distribution, IEE Proceedings, v. 148, no. 1, pp. 67-75, January 2001.
6. 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, vol. 17, no. 3, pp. 654 662, 2002.
7. T. S. P Fernandes and K. C. Almeida, "Methodology for Optimal Power Dispatch Under a Pool-Bilateral Market. IEEE Transactions on Power Systems, vol. 18, no. 1, pp. 182-190, 2003.
8. J. L. M. Ramos, A. G. Expósito and V. H. Quintana, "Transmission power loss reduction by interior-point methods: implementation issues and practical experience" IEE Proc.-Gener. Transm. Distrib., vol. 152, no. 1, pp. 90 98, 2005.
9. E. C. Baptista, E. A. Belati, V. A. Sousa and G. R. M. Da Costa, "Primal-Dual Logarithmic Barrier and Augmented Lagrangian Function to the Loss Minimization in Power Systems", Electric Power Components & Systems, vol. 32, no. 7, pp. 775 784, 2006.
10. M.H. Wright, "Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming", SIAM J. Optmi., vol. 9, no. 1 pp. 84-111, 1998.
11. V. A. Sousa, E. C. Baptista and G. R. M. Da Costa, " Modified Barrier Method for Optimal Power Flow Problem", IEEE Power Engineering Society General Meeting 2004. CD Rom ISBN 0-7803-8466-0. Denver - CO, USA.
12. R. Polyak, "Modified barrier functions", Mathematical Programming, vol. 54, no. 2, pp. 177-222, 1992.
13. A. Melman and R.A. Polyak, "The Newton Modified Barrier Method for QP Problems", Annals of Operations Research, vol. 54, pp. 465 519, 1996.