Implementation of a Lagrangian relaxation based unit commitment problem

Virmani, S.; Adrian, E.C.; Imhof, K.; Mukherjee, Shishir K.

doi:10.1109/59.41687

Cited by 232 publications

(41 citation statements)

References 9 publications

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“…Swarms display fluidity and uniformity in response, which emerge in dynamic behavioural patterns, such as in fish schools [26]–[28], in the fast ephemeral rolling patterns of starlings flocks (in particular under predation by falcons or gulls [24], [29]), in the huddles of emperor penguins [30] or in groups of moving mammals [28], [31]. The simplest mathematical model of an animal swarm defines individual agents with a Lagrangian approach [24], [31]–[32], which have a gradient of repulsion and alignment around them following three rules: (a) move in the same direction as your neighbours , (b) remain close to your neighbours , and (c) avoid collisions with your neighbours . However, shimmering in giant honeybees does not match this swarm model: shimmering-active bees do not change their relative position in the bee curtain, and they move only parts of their body (Movies S1, S2, S3; [12]), although with the potential to generate directed moving patterns.…”

Section: Discussionmentioning

confidence: 99%

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Speeding Up Social Waves. Propagation Mechanisms of Shimmering in Giant Honeybees

et al. 2014

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Shimmering is a defence behaviour in giant honeybees (Apis dorsata), whereby bees on the nest surface flip their abdomen upwards in a Mexican wave-like process. However, information spreads faster than can be ascribed to bucket bridging, which is the transfer of information from one individual to an adjacent one. We identified a saltatoric process that speeds up shimmering by the generation of daughter waves, which subsequently merge with the parental wave, producing a new wave front. Motion patterns of individual “focus” bees (n = 10,894) and their shimmering-active neighbours (n = 459,558) were measured with high-resolution video recording and stereoscopic imaging. Three types of shimmering-active surface bees were distinguished by their communication status, termed “agents”: “Bucket-bridging” agents comprised 74.98% of all agents, affected 88.17% of their neighbours, and transferred information at a velocity of v = 0.317±0.015 m/s. “Chain-tail” agents comprised 9.20% of the agents, were activated by 6.35% of their neighbours, but did not motivate others to participate in the wave. “Generator agents” comprised 15.82% of agents, showed abdominal flipping before the arrival of the main wave front, and initiated daughter waves. They affected 6.75% of their neighbourhood and speeded up the compound shimmering process compared to bucket bridging alone by 41.5% to v = 0.514±0.019 m/s. The main direction of shimmering was reinforced by 35.82% of agents, whereas the contribution of the complementing agents was fuzzy. We discuss that the saltatoric process could enable the bees to instantly recruit larger cohorts to participate in shimmering and to respond rapidly to changes in flight direction of preying wasps. A third, non-exclusive explanation is that at a distance of up to three metres from the nest the acceleration of shimmering could notably contribute to the startle response in mammals and birds.

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Section: Discussionmentioning

confidence: 99%

“…For the analysis of shimmering, concentric zones of neighbourhood were implemented around each focus bee , similar to the Lagrangian swarm models [25], [32]–[33]. This concept allows the assessment of topological properties (cf.…”

Section: Discussionmentioning

confidence: 99%

Speeding Up Social Waves. Propagation Mechanisms of Shimmering in Giant Honeybees

et al. 2014

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“…In the literature survey, reference [1] has tracked the variation of Lagrange multipliers over every iteration of the Lagrange relaxation technique and checked the viability of the technique for large systems. 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.…”

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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“…Next, the cheaper unit will be turn on with high priority. The heat rate ($/MW) of each unit is represented as (11). As shown in Figure 1, most of load is supplied by base units and the remaining load is supplied by other units k p ′ .…”

Section: Production Of All Possible Candidate Units For Each Time Periodmentioning

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%

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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Implementation of a Lagrangian relaxation based unit commitment problem

Cited by 232 publications

References 9 publications

Speeding Up Social Waves. Propagation Mechanisms of Shimmering in Giant Honeybees

Speeding Up Social Waves. Propagation Mechanisms of Shimmering in Giant Honeybees

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

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

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