Short term hydroelectric scheduling combining network flow and interior point approaches

Abstract In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal–dual and predictor–corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested.

[1]  Secundino Soares,et al.  Minimum loss predispatch model for hydroelectric power systems , 1997 .

[2]  Secundino Soares,et al.  Optimal active power dispatch combining network flow and interior point approaches , 2003 .

[3]  Secundino Soares,et al.  A network flow model for short-term hydro-dominated hydrothermal scheduling problems , 1994 .

[4]  Janis A. Bubenko,et al.  Application of Decomposition Techniques to Short-Term Operation Planning of Hydrothermal Power System , 1986 .

[5]  Ge Shaoyun,et al.  Optimal active power flow incorporating FACTS devices with power flow control constraints , 1998 .

[6]  Gerald B. Sheblé,et al.  Unit commitment literature synopsis , 1994 .

[7]  V. Quintana,et al.  An interior-point/cutting-plane method to solve unit commitment problems , 1999 .

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

[9]  M. Innorta,et al.  The problem of the active and reactive optimum power dispatching solved by utilizing a primal-dual interior point method , 1998 .

[10]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[11]  D. Chattopadhyay.  Daily generation scheduling: quest for new models , 1998 .

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

[13]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods , 1999 .

[14]  Juan M. Ramirez,et al.  Solving state estimation in power systems by an interior point method , 2000 .

[15]  A. Garzillo,et al.  The flexibility of interior point based optimal power flow algorithms facing critical network situations , 1999 .

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

[17]  S. M. Shahidehpour,et al.  Real power loss minimization using interior point method , 2001 .

[18]  T. S. Chung,et al.  Optimal active power flow incorporating power flow control needs in flexible AC transmission systems , 1999 .

[19]  Antonio J. Conejo,et al.  Multiperiod optimal power flow using Benders decomposition , 2000 .

[20]  P. Luh,et al.  Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling , 1995 .

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

[22]  Ross Baldick,et al.  The generalized unit commitment problem , 1995 .

[23]  T. Dillon,et al.  Optimal Operations Planning in a Large Hydro-Thermal Power System , 1983, IEEE Transactions on Power Apparatus and Systems.

[24]  O. Nilsson,et al.  Hydro unit start-up costs and their impact on the short term scheduling strategies of Swedish power producers , 1997 .

[25]  Victor H. Quintana,et al.  Interior-point methods and their applications to power systems: a classification of publications and software codes , 2000 .

[26]  Hong-Tzer Yang,et al.  A parallel genetic algorithm approach to solving the unit commitment problem: implementation on the transputer networks , 1997 .

[27]  A. Renaud,et al.  Daily generation scheduling optimization with transmission constraints: a new class of algorithms , 1992 .

[28]  Takaaki Ohishi,et al.  A short term hydrothermal scheduling approach for dominantly hydro systems , 1991 .

[29]  S. M. Shahidehpour,et al.  Unit commitment with transmission security and voltage constraints , 1999 .

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

[31]  O. Nilsson,et al.  Variable splitting applied to modelling of start-up costs in short term hydro generation scheduling , 1997 .

[32]  A. J. Svoboda,et al.  A new unit commitment method , 1997 .

[33]  Md. Sayeed Salam,et al.  Hydrothermal scheduling based Lagrangian relaxation approach to hydrothermal coordination , 1998 .