Enhanced Lagrangian relaxation solution to the generation scheduling problem

Benhamida, Farid; Abdelbar, Bendaoud

doi:10.1016/j.ijepes.2010.06.007

Cited by 26 publications

(13 citation statements)

References 17 publications

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“…violate the constraint-Equation (9) u is 3 hours; therefore, the UC solution in the squared-bold-italic part violates Equation (9).…”

Section: Methodsmentioning

confidence: 99%

“…It involves the determination of an optimum start-up and shut-down schedule of generating units that minimizes operating cost, while satisfying a set of system constraints over a time period [1] [2]. Numerous efficient and robust UC methods have been developed and can be classified into two main categories [3]: The first category represents numerical optimization techniques such as priority list methods (PL) [4] [5] [6], dynamic programming method (DP) [7] [8], Lagrangian relaxation (LR) [9] [10] [11], and the popular branch-and-bound method (BB) [12] [13] [14] [15]. The PL method is fast but highly heuristic and gives schedules with relatively high operation costs.…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods

Wu¹,

Chih-Cheng²,

Lin³

et al. 2017

SGRE

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This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system's operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to largescale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL); however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.

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“…violate the constraint-Equation (9) u is 3 hours; therefore, the UC solution in the squared-bold-italic part violates Equation (9).…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods

Wu¹,

Chih-Cheng²,

Lin³

et al. 2017

SGRE

View full text Add to dashboard Cite

show abstract

“…The e↵ects of indistinguishable generation units in UC problems has been studied before in the context of LR (Alemany et al, 2014;Benhamida and Abdelbar, 2010;Dekrajangpetch et al, 1999;Dentcheva et al, 1997;Zhai et al, 2002). In LR the symmetry was identified as a source of convergence problems, leading to suboptimal solutions or even infeasible solutions Dekrajangpetch et al (1999).…”

Section: Symmetry In Unit Commitment Problemsmentioning

confidence: 99%

Symmetry breaking in MILP formulations for Unit Commitment problems

Lima

Novais

2016

Computers & Chemical Engineering

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Please cite this article as: Ricardo M. Lima, Augusto Q. Novais, Symmetry Breaking in MILP Formulations for Unit Commitment Problems, Computers and Chemical Engineering (2015), http://dx.doi.org/10. 1016/j.compchemeng.2015.11.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. • Symmetry issues are discussed in the context of UC formulations.• Three sets of SBC are proposed and analyzed.• Three well-known UC MILP models are used to implement the SBC.• The results presented are completely disruptive compared with the results presented in the literature.• The SBC derived have a clear advantage over general methods available in two MILP solvers. *HighlightsPage 2 of 43 show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed.The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.

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“…If not, update according to (9) increment iteration counter and go to step 3. In the unit commitment problem, a 10 unit system is shown which is committed to serve a 24 hour load pattern [3]. Table I shows the generator data namely cost coefficients and generation constraints.…”

Section: Steps To Solve Unit Commitment Problemmentioning

confidence: 99%

“…Reference [2] has applied the Lagrange relaxation technique for 4 unit, 5 unit and 10 unit systems and has showed that convergence can be achieved by the selection of proper value of Lagrangian multiplier. Reference [3] has proposed a new method of updating the Lagrange multiplier which leads to lesser number of iterations to attain the optimal solution and the total fuel cost has also been observed to be lesser than the cost calculated through other methods. Reference [4] has proposed the application of genetic algorithm in updating the Lagrangian multiplier and hence proved that the combined approach of Lagrange Relaxation technique and genetic algorithm can yield better results for large systems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of unit commitment problem through Lagrange relaxation and priority listing method

Raj

Chanana

2014

2014 6th IEEE Power India International Conference (PIICON)

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This paper shows how the Lagrange Relaxation dual optimization algorithm is incorporated in solving a thermal unit commitment problem. The Lagrange relaxation procedure solves the unit commitment problem by temporarily relaxing the coupling constraints and solving the problem as if they do not exist. The performance of this technique is tested by running the algorithm on MATLAB using a 10-unit system with a 24-hour load requirement data. The same problem is solved using Priority listing method on MATLAB and the results obtained are compared with the results obtained through the dual optimization algorithm to check the performance of the relaxation technique. Minimum up time, down time constraints and startup costs are considered in this case study. Ramp rate constraints and reserve capacity constraints are ignored and shut down cost is taken as zero.

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Enhanced Lagrangian relaxation solution to the generation scheduling problem

Cited by 26 publications

References 17 publications

A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods

A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods

Symmetry breaking in MILP formulations for Unit Commitment problems

Analysis of unit commitment problem through Lagrange relaxation and priority listing method

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