Interior Point Methods and Applications in Power Systems

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.

[1]  Francisco D. Galiana,et al.  A survey of the optimal power flow literature , 1991 .

[2]  Clyde L. Monma,et al.  An Implementation of a Primal-Dual Interior Point Method for Linear Programming , 1989, INFORMS J. Comput..

[3]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[4]  S. Granville,et al.  Application of interior point methods to power flow unsolvability , 1996 .

[5]  A.C.G. Melo,et al.  Simultaneous transfer capability assessment by combining interior point methods and Monte Carlo simulation , 1997 .

[6]  N. Megiddo.  Pathways to the optimal set in linear programming , 1989 .

[7]  F. Alvarado,et al.  Point of collapse methods applied to AC/DC power systems , 1992 .

[8]  Mauricio G. C. Resende,et al.  An implementation of Karmarkar's algorithm for linear programming , 1989, Math. Program..

[9]  G.R.M. da Costa,et al.  Optimal reactive dispatch through primal-dual method , 1997 .

[10]  Hua Wei,et al.  An interior point method for power system weighted nonlinear L/sub 1/ norm static state estimation , 1998 .

[11]  Kumaraswamy Ponnambalam,et al.  A fast algorithm for power system optimization problems using an interior point method , 1991 .

[12]  K. D. Frey,et al.  Treatment of inequality constraints in power system state estimation , 1995 .

[13]  F. Schweppe.  Spot Pricing of Electricity , 1988 .

[14]  V. Quintana,et al.  An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch , 1997 .

[15]  Hua Wei,et al.  An interior point nonlinear programming for optimal power flow problems with a novel data structure , 1997 .

[16]  Hiroshi Sasaki,et al.  A decoupled solution of hydro-thermal optimal power flow problem by means of interior point method and network programming , 1998 .

[17]  R. E. Marsten,et al.  A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows , 1993 .

[18]  Robert J. Vanderbei,et al.  An Interior-Point Algorithm for Nonconvex Nonlinear Programming , 1999, Comput. Optim. Appl..

[19]  A. El-Keib,et al.  Calculating short-run marginal costs of active and reactive power production , 1997 .

[20]  V. Quintana,et al.  A tutorial description of an interior point method and its applications to security-constrained economic dispatch , 1993 .

[21]  S. Granville.  Optimal reactive dispatch through interior point methods , 1994 .

[22]  H. A. Othman,et al.  Evaluating transmission congestion constraints in system planning , 1997 .

[23]  Robert J. Vanderbei,et al.  Commentary - Interior-Point Methods: Algorithms and Formulations , 1994, INFORMS J. Comput..

[24]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[25]  R. Adapa,et al.  The quadratic interior point method solving power system optimization problems , 1994 .

[26]  A. Bagchi,et al.  Economic dispatch with network and ramping constraints via interior point methods , 1998 .

[27]  G. Irisarri,et al.  Maximum loadability of power systems using interior point nonlinear optimization method , 1997 .

[28]  Michael A. Saunders,et al.  On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method , 1986, Math. Program..

[29]  Renato D. C. Monteiro,et al.  Interior path following primal-dual algorithms. part I: Linear programming , 1989, Math. Program..

[30]  M. L. Baughman,et al.  Real-time pricing of reactive power: theory and case study results , 1991, IEEE Power Engineering Review.

[31]  G. C. Ejebe,et al.  Preventive/corrective control for voltage stability using direct interior point method , 1997 .

[32]  Chan-nan Lu,et al.  Network constrained security control using an interior point algorithm , 1993 .

[33]  Roy E. Marsten,et al.  Feature Article - Interior Point Methods for Linear Programming: Computational State of the Art , 1994, INFORMS J. Comput..