An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch

This paper deals with the application of an advanced interior point method to the security-constrained economic dispatch (SCED) problems through successive linear programming. The nonlinear SCED problem is linearized, and then solved by a predictor-corrector interior point method. Besides describing the basic algorithm, the paper focuses on several important issues that are critical to its efficient implementation, including the adjustment of barrier parameter, the determination of initial point, and so on. Computational experiments are conducted to evaluate their impact on the performance of the algorithm. Some suggestions, such as using the feasibility condition to adjust the way of computing barrier parameter /spl mu/ and customizing initial point by adopting a relative small threshold, are proposed to reduce the overall iterations required by the algorithm. The computational results on power systems of 236 to 2124 buses have shown that these suggestions are very effective, improving the performance of the algorithm by a factor of 2. Comparison with a pure primal-dual interior point method is also provided to demonstrate the superiority of the proposed predictor-corrector method.

[1]  D. Bertsekas,et al.  Optimal short-term scheduling of large-scale power systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[2]  Stanley C. Eisenstat,et al.  Algorithms and Data Structures for Sparse Symmetric Gaussian Elimination , 1981 .

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

[5]  A.I. Cohen,et al.  Optimization-based methods for operations scheduling , 1987, Proceedings of the IEEE.

[6]  S. Chanas,et al.  Single value simulation of fuzzy variables , 1988 .

[7]  Jonathan F. Bard,et al.  Short-Term Scheduling of Thermal-Electric Generators Using Lagrangian Relaxation , 1988, Oper. Res..

[8]  Luís Ferreira,et al.  Short-term resource scheduling in multi-area hydrothermal power systems , 1989 .

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

[10]  S. Chanas,et al.  Single value simulation of fuzzy variable—some further results , 1989 .

[11]  Vladimiro Miranda,et al.  Fuzzy modelling of power system optimal load flow , 1991 .

[12]  S. Ruzc,et al.  A new approach for solving extended unit commitment problem , 1991, IEEE Power Engineering Review.

[13]  I. Lustig,et al.  Computational experience with a primal-dual interior point method for linear programming , 1991 .

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

[15]  Yuan-Yih Hsu,et al.  Fuzzy dynamic programming: an application to unit commitment , 1991 .

[16]  Clóvis C. Gonzaga,et al.  Path-Following Methods for Linear Programming , 1992, SIAM Rev..

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

[18]  J. A. Amalfi,et al.  An optimization-based method for unit commitment , 1992 .

[19]  E. Lee,et al.  Analysis and simulation of fuzzy queues , 1992 .

[20]  Roy E. Marsten,et al.  On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming , 1992, SIAM J. Optim..

[21]  S. M. Shahidehpour,et al.  Power generation scheduling for multi-area hydro-thermal systems with tie line constraints, cascaded reservoirs and uncertain data , 1993 .

[22]  Robert J. Vanderbei,et al.  ALPO: Another Linear Program Optimizer , 1993, INFORMS J. Comput..

[23]  Peter B. Luh,et al.  Scheduling of hydrothermal power systems , 1993 .

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

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

[26]  Peter B. Luh,et al.  Optimization-based inter-utility power purchases , 1993 .

[27]  Peter B. Luh,et al.  Optimization-based scheduling of hydrothermal power systems with pumped-storage units , 1994 .

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

[29]  R. Adapa,et al.  The effect of load uncertainty on unit commitment risk , 1994 .

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

[31]  Anders Hansson,et al.  A stochastic interpretation of membership functions , 1994, Autom..

[32]  Peter B. Luh,et al.  Power system scheduling with fuzzy reserve requirements , 1996 .

[33]  Victor H. Quintana,et al.  An infeasible interior-point algorithm for optimal power-flow problems , 1996 .