Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling

When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the...

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Bibliographic Details
Published in:IEEE transactions on power systems Vol. 10; no. 2; pp. 772 - 778
Main Authors: Xiaohong Guan, Luh, P.B., Lan Zhang
Format: Journal Article Conference Proceeding
Language:English
Published: New York, NY IEEE 01.05.1995
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Approximation algorithms
Approximation methods
Cost function
Electrical engineering. Electrical power engineering
Electrical power engineering
Exact sciences and technology
Lagrangian functions
Linear approximation
Operation. Load control. Reliability
Power engineering and energy
Power networks and lines
Relaxation methods
Scheduling algorithm
Systems engineering and theory
Testing
ISSN:0885-8950
Online Access:Get full text
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Summary:When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are undetermined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.< >
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ISSN:0885-8950
DOI:10.1109/59.387916