Parallel Lagrangian relaxation in power scheduling

Oliveira, Pedro; Blair-Fish, John A.; McKees, S.; Coles, C.

doi:10.1016/0956-0521(92)90029-i

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…Many methods of optimisation have been proposed in the context of control systems, such as Lagrangian relaxation (LR) [1][2][3][4], dynamic programming (DP) [5][6][7], mixed-integer programming [8,9], branch and bound [10,11], and logic programming [12]. Although the introduction of the Lagrangian multiplier simplifies the calculation by structuring the dual problem in the LR, it is challenging to deal with coupling constraints between units.…”

Section: Introductionmentioning

confidence: 99%

Two‐stage glowworm swarm optimisation for economical operation of hydropower station

Wang

Yang

Zhou

2018

IET Renewable Power Generation

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This study proposes a two-stage glowworm swarm optimisation (GSO) algorithm for the economical operation of the inner plant of a hydropower station. Binary GSO and real-coded GSO (RCGSO) algorithms are applied with different types of encodings to solve the unit commitment sub-problem and the economic load distribution (ELD) sub-problem, respectively. Moreover, an improved dynamic patching mechanism is developed to avoid invalid calculations and enrich the diversity of the solutions. A luciferin transfer mechanism helps the algorithm escape the local optimum and a local research mechanism enhances the diversity of the solution space by selecting from among the derived solutions. The RCGSO algorithm uses a variable-step mechanism to avoid missing the optimal solution. In comparison with the genetic algorithm and particle swarm optimisation, the RCGSO is significantly robust and provides better solutions to ELD sub-problems. Numerical simulations exhibited the superiority of the two-stage GSO algorithm in terms of stably and quickly solving the economical operation problem of hydropower stations.

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Section: Introductionmentioning

confidence: 99%

Two‐stage glowworm swarm optimisation for economical operation of hydropower station

Wang

Yang

Zhou

2018

IET Renewable Power Generation

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“…Over many years, numerous researchers have developed various mathematical programming and optimization techniques, including equal increment method, branch and bound algorithm, mixed integer linear programming (MILP), decomposition approach, Lagrangian relaxation, and dynamic programming (DP) to solve inner-plant economical operation of hydropower stations (Allen & Bridgeman 1986;Cohen & Yoshimura 1987;Snyder et al 1987;Oliveira et al 1992;Guan et al 1995;Georgakakos et al 1997;Cheng et al 2000;Martin 2000;Siu et al 2001;Baltar et al 2002;Yi et al 2003). Among the different optimization approaches, DP has enjoyed much popularity, because it can offer convenient and efficient solutions for optimizing committed hydro units' load scheduling.…”

Section: Introductionmentioning

confidence: 99%

Limited adaptive genetic algorithm for inner-plant economical operation of hydropower station

Zheng

Yang

2012

Hydrology Research

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A limited adaptive genetic algorithm (LAGA) is proposed in the paper for inner-plant economical operation of a hydropower station, in the LAGA, limited solution strategy, with the feasible solution generation method for generating an initial population and the limited perturbation mutation operator, is presented to avoid hydro units operating in cavitation-vibration regions. The adaptive probabilities of crossover and mutation are introduced to improve the convergence speed of the genetic algorithm (GA). Furthermore, the performance of the limited solution strategy and the adaptive parameter controlling improvement are checked against the historical methods, and the results of simulating inner-plant economical operation of the Three Gorges hydropower station demonstrate the effectiveness of the proposed approach. First, the limited solution strategy can support the safety operations of hydro units by avoiding cavitation-vibration region operations, and it achieves a better solution, because the non-negative fitness function Is achieved. Second, the adaptive parameter method is shown to have better performance than other methods, because it realizes the twin goals of maintaining diversity in the population and advancing the convergence speed of GA. Thus, the LAGA is feasible and effective in optimizing inner-plant economical operation of hydropower stations.

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“…where SSR is the sum of squares of reserves as in (19), TMV is the total manpower violation of (21), and TLV is the total load violation of (22). The weighting coefficients ω O, , ω M and ω L are chosen so that the penalty values for the constraint violations dominate over the objective function, and the violation of the relatively hard load constraint (22) gives a greater penalty value than for the relatively soft crew constraint.…”

Section: Test Gms Problemmentioning

confidence: 99%

“…Recent work has favoured Lagrangian Relaxation [18], in which the global constraints of demand and reserve are admitted into the objective function, and the problem decomposed into master problem and unit subproblems. This natural algorithmic decomposition admits parallelisation [19]. The method provides bounds on the original optimum but a heuristic must be employed to construct a feasible solution for the original problem.…”

Section: Introductionmentioning

confidence: 99%