Unit Commitment with Identical Units: Successive Subproblem Solving Method Based on Lagrangian Relaxation

When the Lagrangian relaxation based methods are applied to solve power system unit commitment, the identical solutions to the subproblems associated with identical units may cause the dual solution to be far away from the optimal solution and serious solution oscillations. As a result, the quality of the feasible solution obtained may be very unsatisfactory. This issue has been long recognized as an inherent disadvantage of Lagrangian relaxation based methods. In this paper, the homogeneous solution issue is identified and analyzed through a simple example. Based on this analysis, a successtve subproblem solving method is developed. The new method combines the concepts of augmented Lagrangian relaxation and surrogate subgradient to produce a good search direction at the high level. The low-level subproblems including those corresponding to the identical units are solved successively so that the commitments of the identical units may not be homogeneous in the dual solution. Compared with the standard Lagrangian relaxation method, the new method can obtain better dual solutions and avoid the solution oscillations. Numerical testing shows the new method is efficient and the quality of the feasible solution is greatly improved.

[1]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[2]  X. Guan,et al.  New Lagrangian Relaxation Based Algorithm for Resource Scheduling with Homogeneous Subproblems , 2002 .

[3]  Z. Alaywan,et al.  California ISO formation and implementation , 1999 .

[4]  X. Zhao,et al.  Surrogate Gradient Algorithm for Lagrangian Relaxation , 1999 .

[5]  S. M. Shahidehpour,et al.  Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation , 1995 .

[6]  J. J. Shaw,et al.  A direct method for security-constrained unit commitment , 1995 .

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

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

[9]  A. Renaud,et al.  Daily generation management at Electricite de France: from planning towards real time , 1993, IEEE Trans. Autom. Control..

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

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

[12]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[13]  R. Fletcher.  Practical Methods of Optimization , 1988 .

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

[15]  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.