Research and application of Successive Over-Relaxation Iterative Algorithm

Cui, Ruixia; Wei, Mingjun

doi:10.1109/emeit.2011.6023095

Cited by 4 publications

(5 citation statements)

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“…The successive over‐relaxation (SOR) iterative algorithm is used to solve Laplace's equation under the boundary condition U T , U s and E T . The space potential at the ( i +1)th iteration step can be calculated by [26]

U_{x, y, z}^{(i + 1)} = U_{x, y, z}^{(i)} + \frac{ω}{6} (\sum U_{x \pm L, y \pm L, z \pm L}^{false(i false)} - 6 U_{x, y, z}^{false(i false)})

where U x,y,z is the space potential at the point ( x , y , z ), ω is the SOR factor. The factor ω is selected as 1.95 in the subsequent simulation.…”

Section: Proposed Methodsmentioning

confidence: 99%

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A three‐dimensional direct lightning strike model for lightning protection of the substation

Guo

Zhang

Wang

et al. 2021

IET Generation Trans & Dist

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Lightning strikes to a substation happen frequently, which has a serious impact on the safety of the power system. Therefore, it is important to evaluate the effect of the direct lightning to the substation for the sake of protection. However, since the propagation and attachment of the lightning leader is a typical random process, it is hard to sufficiently represent the effect of the direct lightning by some deterministic models. In order to take into consideration the randomness of the lightning propagation process, in this paper, a three dimensional lightning fractal model that reproduces the tortuosity and branching of natural lightning is established. The proposed model is then applied to the effect analysis of the direct lightning to a typical 220 kV substation. Moreover, the protection effect of different distribution and height schemes of lightning rods is investigated using the proposed model. This work helps to understand the lightning strike risk that the substations face and also provides a promising way to improve and optimize the protection design.How to cite this article: Guo J., et al.: A three-dimensional direct lightning strike model for lightning protection of the substation. IET Gener.

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U_{x, y, z}^{(i + 1)} = U_{x, y, z}^{(i)} + \frac{ω}{6} (\sum U_{x \pm L, y \pm L, z \pm L}^{false(i false)} - 6 U_{x, y, z}^{false(i false)})

where U x,y,z is the space potential at the point ( x , y , z ), ω is the SOR factor. The factor ω is selected as 1.95 in the subsequent simulation.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…The successive over-relaxation (SOR) iterative algorithm is used to solve Laplace's equation under the boundary condition U T , U s and E T . The space potential at the (i+1)th iteration step can be calculated by [26]…”

Section: Lightning Strike Modelmentioning

confidence: 99%

A three‐dimensional direct lightning strike model for lightning protection of the substation

Guo

Zhang

Wang

et al. 2021

IET Generation Trans & Dist

View full text Add to dashboard Cite

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“…This process will stop after all subdomains are solved, and the fields are denoted as E(0). For the iteration at the (n + 1)th step, the new fields are computed using a rule of the form where the parameter α is called the (over) relaxation parameter [16], while in each iteration, we define the relative 2 error as…”

Section: Complete System Matrix Equationmentioning

confidence: 99%

Spectral Element Method and Domain Decomposition for Low-Frequency Subsurface EM Simulation

Zhou

Shi

Liu

et al. 2016

IEEE Geosci. Remote Sensing Lett.

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Low-frequency subsurface electromagnetic measurements are important tools for characterizing natural resources and environmental wastes. Rapid simulations of low-frequency subsurface electromagnetic measurements are still a challenge because of the large computational domain and low-frequency breakdown phenomenon. We develop an effective method to simulate these low-frequency subsurface electromagnetic measurements by using the spectral element method together with a domain decomposition method (DDM). A specific mesh has been designed based on the traveling wave nature in the air and the diffusion field nature in the underground space to greatly reduce the number of un- knowns. The frequency-domain version of the Riemann solver (upwind flux) is used as an effective transmission condition to simulate the interactions between neighboring subdomains in DDM.Several numerical examples demonstrate the efficiency of the proposed approach in low-frequency subsurface electromagnetics simulations.Index Terms-Domain decomposition method (DDM), low frequency, Riemann solver, spectral element method (SEM), subsurface EM simulation.

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“…To verify the convergence of NCRG scheme, we compare it with two other benchmark algorithms: the Jacobi iteration approach and the SOR iteration approach . The Jacobi iteration equation is

x_{i}^{(k)} = \frac{β_{i}}{1 + β_{i}} (c_{l} - \sum_{j \neq i} x_{i}^{(k - 1)}) .

The SOR iteration equation is

x_{i}^{(k)} = (1 - ω) * x_{i}^{(k - 1)} + \frac{ω * β_{i}}{1 + β_{i}} (c_{l} - \sum_{j < i} x_{j}^{(k)} - \sum_{j > i} x_{j}^{(k - 1)}),

where ω ∈(0,2).…”

Section: Performance Evaluationmentioning

confidence: 99%

“…To verify the convergence of NCRG scheme, we compare it with two other benchmark algorithms: the Jacobi iteration approach [37] and the SOR iteration approach [39]. The Jacobi iteration equation is…”

Section: Performance Evaluation Of Non-cooperative Cloud Resource Allmentioning

confidence: 99%

A resource allocation game with restriction mechanism in VANET cloud

Tao

Zhang

et al. 2016

Concurrency and Computation

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Summary In Vehicular Ad hoc Networks (VANETs), because of the selfishness of the vehicles, the resource allocation in VANET has become one of the primary tasks. Exploiting the Road Side Units (RSUs), which constructs the Cloud Computing environment, provides more data access opportunities and stable communication time for the vehicles. We investigated the cloud resource allocation for data access with noncooperative game based on a Gauss–Seidel iteration method. We further proposed a repeated game scheme, which can approximately achieve the near Pareto‐optimal flow allocation among the vehicles. Considering the vehicles' irrational behavior, a punishment strategy was designed to prevent the vehicles from behavior deviation. The analysis based on these models lays a theoretical method foundation on cloud resource allocation process. The validity of the modeling and the accuracy of the analysis were verified through the extensive simulations, which also guide the future design of more sophisticated cloud resource allocation schemes. Copyright © 2016 John Wiley & Sons, Ltd.

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Research and application of Successive Over-Relaxation Iterative Algorithm

Cited by 4 publications

References 0 publications

A three‐dimensional direct lightning strike model for lightning protection of the substation

A three‐dimensional direct lightning strike model for lightning protection of the substation

Spectral Element Method and Domain Decomposition for Low-Frequency Subsurface EM Simulation

A resource allocation game with restriction mechanism in VANET cloud

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