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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Vydáno v:IEEE transactions on power systems Ročník 10; číslo 2; s. 772 - 778
Hlavní autoři: Xiaohong Guan, Luh, P.B., Lan Zhang
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.05.1995
Institute of Electrical and Electronics Engineers
Témata:
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
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Shrnutí: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