Hydrothermal Scheduling by Augmented Lagrangian: Consideration of Transmission Constraints and Pumped-Storage Units

This paper presents an augmented Lagrangian (AL) approach to scheduling a generation mix of thermal and hydro resources. AL presents a remedy to duality gap encountered with the ordinary Lagrangian for nonconvex problems. It shapes the Lagrangian function as a hyperparaboloid associating penalty in the direction of the coupling constraints. This work accounts further for the transmission constraints. We use a hydrothermal resource model with pumped-storage units. An IEEE 24-bus test system is used for AL performance illustration. Computational models are all coded in C. The results of the test case show that the AL approach can provide better scheduling results as it can detect optimal on/off schedules of units over a planning horizon at a minimal cost with no constraint violation. It requires no iteration with economic dispatch algorithms. The approach proves accurate and practical for systems with generation diversity and limited transmission capacity.

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

[2]  Peter B. Luh,et al.  An algorithm for solving the dual problem of hydrothermal scheduling , 1998 .

[3]  S. M. Shahidehpour,et al.  Effects of ramp-rate limits on unit commitment and economic dispatch , 1993 .

[4]  Antonio J. Conejo,et al.  A comparison of interior-point codes for medium-term hydro-thermal coordination , 1997 .

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

[6]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[7]  Antonio J. Conejo,et al.  Short-term hydro-thermal coordination by Lagrangian relaxation: solution of the dual problem , 1999 .

[8]  Philip G. Hill,et al.  Power generation , 1927, Journal of the A.I.E.E..

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

[10]  Renjeng Su,et al.  Augmented Lagrangian approach to hydro-thermal scheduling , 1998 .

[11]  Peter B. Luh,et al.  An optimization-based algorithm for scheduling hydrothermal power systems with cascaded reservoirs and discrete hydro constraints , 1997 .

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

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

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

[15]  N. Watanabe,et al.  Decomposition in large system optimization using the method of multipliers , 1978 .

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

[17]  Probability Subcommittee,et al.  IEEE Reliability Test System , 1979, IEEE Transactions on Power Apparatus and Systems.

[18]  G. Stephanopoulos,et al.  The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization , 1975 .