Efficient evaluation of the earth return mutual impedance of overhead conductors over a horizontally multilayered soil

2014 ◽  
Vol 33 (4) ◽  
pp. 1379-1395 ◽  
Author(s):  
Jae-bok Lee ◽  
Jun Zou ◽  
Benliang Li ◽  
Munno Ju
Keyword(s):  
Unit Length ◽  
Oscillatory Integral ◽  
Electromagnetic Transients ◽  
Closed Form Expression ◽  
Computational Time ◽  
Horizontal Distance ◽  
Content Type ◽  
Mutual Impedance ◽  
The Earth ◽  
Highly Oscillatory

Purpose – The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils. Design/methodology/approach – The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands. Findings – The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors. Originality/value – The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil

2018 ◽  
Vol 37 (3) ◽  
pp. 1214-1227 ◽  
Author(s):  
Junjie Ma
Keyword(s):  
Quadrature Rule ◽  
Content Type ◽  
Mutual Impedance ◽  
Numerical Tests ◽  
Sommerfeld Integral ◽  
The Earth ◽  
Finite Integral ◽  
Infinite Integral ◽  
Improper Integrals ◽  
Differential Matrix

Purpose Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule. Findings Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters. Originality/value An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.

High-order fast integration for earth-return impedance between underground and overhead conductors in Matlab

2014 ◽  
Vol 33 (5) ◽  
pp. 1809-1818 ◽  
Author(s):  
Junjie Ma ◽  
Shuhuang Xiang
Keyword(s):  
Numerical Experiments ◽  
Design Methodology ◽  
Integration Method ◽  
Fast Calculation ◽  
Content Type ◽  
Sommerfeld Integrals ◽  
The Earth ◽  
Highly Oscillatory ◽  
Complex Integration ◽  
The Given

Purpose – The earth-return mutual impedances between underground and overhead conductors can be expressed by Pollaczek integrals. Many efforts have been exerted to calculating this kind of integrals. However, most of numerical methods turn out to be time-consuming as integrands become highly oscillatory and strongly singular. Therefore, efficient algorithms should be devised. The paper aims to discuss these issues. Design/methodology/approach – The paper separates the singularity from the whole integral and couple with the singularity and oscillation, respectively. A sinh transformation is applied for the finite part and complex integration method is used to calculate the tail. Findings – Numerical experiments show that the given method shares the property that the stronger the singularity and the higher the oscillation, the better the accuracy of the calculation. Originality/value – The sinh transformation is first proposed to calculate Pollaczek integrals. This efficient algorithm can be used to evaluate mutual impedances between conductors. Also, it provides a new aspect of the research on fast calculation of Pollaczek integrals and Sommerfeld integrals.

A nonlinear magnetic circuit model for periodic eddy current problems using T,ϕ-ϕ formulation

2017 ◽  
Vol 36 (3) ◽  
pp. 649-664 ◽  
Author(s):  
Rene Plasser ◽  
Gergely Koczka ◽  
Oszkár Bíró
Keyword(s):  
Eddy Current ◽  
Magnetic Circuit ◽  
Iteration Process ◽  
Equation System ◽  
Circuit Model ◽  
Computational Time ◽  
Combined Method ◽  
3D Fem ◽  
Content Type ◽  
Transformer Model

Purpose A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time. Design/methodology/approach Using the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process. Findings In fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method. Originality/value To facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.

Iron and sulphur speciation and cycling in the sediments of marine systems located in the arid environment: Case of the northern Red Sea

2021 ◽  
pp. jgs2021-027
Author(s):  
Valeria Boyko ◽  
Jürgen Pätzold ◽  
Alexey Kamyshny
Keyword(s):  
Red Sea ◽  
Water Depth ◽  
Iron Content ◽  
Gulf Of Aqaba ◽  
Earth System ◽  
Content Type ◽  
Reactive Iron ◽  
The Earth ◽  
Sulphur Cycle ◽  
Supplementary Material

High fluxes of iron minerals associated with aeolian dry deposition may result in anomalously high reactive iron content and fast reoxidation of hydrogen sulphide in the sediments that prevents pyrite formation and results in “cryptic” sulphur cycle. In this work, we studied cycling of iron and sulphur in the deep-water (> 800 m water depth) sediments of the Red Sea and its northern extension, Gulf of Aqaba. We found that reactive iron content in the surface sediments of the Gulf of Aqaba and the Red Sea is high, while the content of sulphur-bound iron is very low and decreases with water depth. The presence of pyrite traces and zero-valent sulfur as well as isotopic compositions of sulphate and pyrite, which are consistent with sulphate reduction under substrate-limiting conditions, suggest that cryptic sulfur cycling is likely to be a result of fast reoxidation of hydrogen sulfide rather than microbial sulfate reduction suppression. In the sediments of Shaban Deep, which are overlain with hyper-saline hydrothermal brine, low reactive iron and high organic carbon contents result in a non-cryptic sulphur cycle characterized by preservation of pyrite in the sediments.Thematic collection: This article is part of the Sulfur in the Earth system collection available at: https://www.lyellcollection.org/cc/sulfur-in-the-earth-systemSupplementary material:https://doi.org/10.6084/m9.figshare.c.5508155

On modeling a well casing for resistivity and induced polarization

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2061-2063 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Electrical Properties ◽  
Electric Dipole ◽  
Free Space ◽  
Eddy Currents ◽  
Interfacial Polarization ◽  
Induced Polarization ◽  
Mutual Impedance ◽  
The Earth ◽  
Horizontal Electric Dipole ◽  
Displacement Currents

In a previous communication I proposed an analytical model to simulate the electromagnetic (EM) and induced polarization (IP) response of a metal well casing (Wait, 1983). To facilitate the analysis, the earth was idealized as a homogeneous conducting half‐space of electrical properties (σ, ε, μ). The well casing was represented as a filamental vertical conductor of semiinfinite length that was characterized by a series axial impedance to account for eddy currents and interfacial polarization. A further basic simplification was to neglect displacement currents in the air; this was justified when all significant distances were small compared with the free‐space wavelength. Initially, the source was taken to be a horizontal electric dipole or current element I ds on the air‐earth interface. By integration of the results, the mutual impedance between two grounded circuits could be ascertained. In the absence of the vertical conductor (i.e., the well casing) the results reduced to those given by Sunde (1968) and Ward (1967).

A combined effective time series model based on clustering and whale optimization algorithm for forecasting smart meters electricity consumption

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Medhat Abd el Azem El Sayed Rostum ◽  
Hassan Mohamed Mahmoud Moustafa ◽  
Ibrahim El Sayed Ziedan ◽  
Amr Ahmed Zamel
Keyword(s):  
Optimization Algorithm ◽  
Prediction Accuracy ◽  
Electricity Consumption ◽  
Whale Optimization Algorithm ◽  
Computational Time ◽  
Smart Meters ◽  
Content Type ◽  
Individual Level ◽  
Consumption Values ◽  
Whale Optimization

Purpose The current challenge for forecasting smart meters electricity consumption lies in the uncertainty and volatility of load profiles. Moreover, forecasting the electricity consumption for all the meters requires an enormous amount of time. Most papers tend to avoid such complexity by forecasting the electricity consumption at an aggregated level. This paper aims to forecast the electricity consumption for all smart meters at an individual level. This paper, for the first time, takes into account the computational time for training and forecasting the electricity consumption of all the meters. Design/methodology/approach A novel hybrid autoregressive-statistical equations idea model with the help of clustering and whale optimization algorithm (ARSEI-WOA) is proposed in this paper to forecast the electricity consumption of all the meters with best performance in terms of computational time and prediction accuracy. Findings The proposed model was tested using realistic Irish smart meters energy data and its performance was compared with nine regression methods including: autoregressive integrated moving average, partial least squares regression, conditional inference tree, M5 rule-based model, k-nearest neighbor, multilayer perceptron, RandomForest, RPART and support vector regression. Results have proved that ARSEI-WOA is an efficient model that is able to achieve an accurate prediction with low computational time. Originality/value This paper presents a new hybrid ARSEI model to perform smart meters load forecasting at an individual level instead of an aggregated one. With the help of clustering technique, similar meters are grouped into a few clusters from which reduce the computational time of the training and forecasting process. In addition, WOA improves the prediction accuracy of each meter by finding an optimal factor between the average electricity consumption values of each cluster and the electricity consumption values for each one of its meters.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

Simulating swing dynamics of a power system model using nonlinear model order reduction

2019 ◽  
Vol 38 (6) ◽  
pp. 1918-1930
Author(s):  
Satyavir Singh ◽  
Mohammad Abid Bazaz ◽  
Shahkar Ahmad Nahvi
Keyword(s):  
Power System ◽  
System Dynamics ◽  
Interpolation Method ◽  
Computational Cost ◽  
Nonlinear Function ◽  
Computational Time ◽  
Reduced Basis ◽  
Power System Dynamics ◽  
Content Type ◽  
On Line

Purpose The purpose of this paper is to demonstrate the applicability of the Discrete Empirical Interpolation method (DEIM) for simulating the swing dynamics of benchmark power system problems. The authors demonstrate that considerable savings in computational time and resources are obtained using this methodology. Another purpose is to apply a recently developed modified DEIM strategy with a reduced on-line computational burden on this problem. Design/methodology/approach On-line computational cost of the power system dynamics problem is reduced by using DEIM, which reduces the complexity of the evaluation of the nonlinear function in the reduced model to a cost proportional to the number of reduced modes. The on-line computational cost is reduced by using an approximate snap-shot ensemble to construct the reduced basis. Findings Considerable savings in computational resources and time are obtained when DEIM is used for simulating swing dynamics. The on-line cost implications of DEIM are also reduced considerably by using approximate snapshots to construct the reduced basis. Originality/value Applicability of DEIM (with and without approximate ensemble) to a large-scale power system dynamics problem is demonstrated for the first time.

A parallel multi-fidelity optimization approach in induction hardening

2019 ◽  
Vol 39 (1) ◽  
pp. 133-143
Author(s):  
Marco Baldan ◽  
Alexander Nikanorov ◽  
Bernard Nacke
Keyword(s):  
Parallel Computing ◽  
Optimization Technique ◽  
Computational Cost ◽  
Induction Hardening ◽  
Computational Time ◽  
High Fidelity ◽  
Optimization Approach ◽  
Content Type ◽  
Fidelity Model ◽  
Hardening System

Purpose Reliable modeling of induction hardening requires a multi-physical approach, which makes it time-consuming. In designing an induction hardening system, combining such model with an optimization technique allows managing a high number of design variables. However, this could lead to a tremendous overall computational cost. This paper aims to reduce the computational time of an optimal design problem by making use of multi-fidelity modeling and parallel computing. Design/methodology/approach In the multi-fidelity framework, the “high-fidelity” model couples the electromagnetic, thermal and metallurgical fields. It predicts the phase transformations during both the heating and cooling stages. The “low-fidelity” model is instead limited to the heating step. Its inaccuracy is counterbalanced by its cheapness, which makes it suitable for exploring the design space in optimization. Then, the use of co-Kriging allows merging information from different fidelity models and predicting good design candidates. Field evaluations of both models occur in parallel. Findings In the design of an induction heating system, the synergy between the “high-fidelity” and “low-fidelity” model, together with use of surrogates and parallel computing could reduce up to one order of magnitude the overall computational cost. Practical implications On one hand, multi-physical modeling of induction hardening implies a better understanding of the process, resulting in further potential process improvements. On the other hand, the optimization technique could be applied to many other computationally intensive real-life problems. Originality/value This paper highlights how parallel multi-fidelity optimization could be used in designing an induction hardening system.

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