A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows

A new algorithm using the primal-dual interior point method with the predictor-corrector for solving nonlinear optimal power flow (OPF) problems is presented. The formulation and the solution technique are new. Both equalities and inequalities in the OPF are considered and simultaneously solved in a nonlinear manner based on the Karush-Kuhn-Tucker (KKT) conditions. The major computational effort of the algorithm is solving a symmetrical system of equations, whose sparsity structure is fixed. Therefore only one optimal ordering and one symbolic factorization are involved. Numerical results of several test systems ranging in size from 9 to 2423 buses are presented and comparisons are made with the pure primal-dual interior point algorithm. The results show that the predictor-corrector primal-dual interior point algorithm for OPF is computationally more attractive than the pure primal-dual interior point algorithm in terms of speed and iteration count. >

[1]  William F. Tinney,et al.  Optimal Power Flow Solutions , 1968 .

[2]  B Stott,et al.  Linear Programming for Power-System Network Security Applications , 1979, IEEE Transactions on Power Apparatus and Systems.

[3]  O. Alsac,et al.  Review Of Linear Programming Applied To Power System Rescheduling , 1979 .

[4]  Sarosh N. Talukdar,et al.  Quasi-Newton method for optimal power flows , 1981 .

[5]  W. Tinney,et al.  Optimal Power Flow By Newton Approach , 1984, IEEE Transactions on Power Apparatus and Systems.

[6]  H. Happ,et al.  Quadratically Convergent Optimal Power Flow , 1984, IEEE Transactions on Power Apparatus and Systems.

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

[8]  O. Alsac,et al.  Security analysis and optimization , 1987, Proceedings of the IEEE.

[9]  Renato D. C. Monteiro,et al.  Interior path following primal-dual algorithms. part II: Convex quadratic programming , 1989, Math. Program..

[10]  J. Nanda,et al.  New optimal power-dispatch algorithm using Fletcher's quadratic programming method , 1989 .

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

[12]  I. Lustig,et al.  Interior Point Methods for Linear Programming: Just Call Newton, Lagrange, and Fiacco and McCormick! , 1990 .

[13]  B. Stott,et al.  Further developments in LP-based optimal power flow , 1990 .

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

[15]  Sanjay Mehrotra.  On finding a vertex solution using interior point methods , 1991 .

[16]  Anoop Gupta,et al.  Efficient sparse matrix factorization on high performance workstations—exploiting the memory hierarchy , 1991, TOMS.

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

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