Calculation Of Current Distribution Research Articles

Computation of Current Distribution on Superconducting Parallel Wire using an Analytic Approach

Computation of Current Distribution on Superconducting Parallel Wire using an Analytic Approach

Method for operative estimation of current reservoir pressure distribution based on the wells normal production data

In the article there has been proposed method of operative estimation of the current reservoir pressure distribution from normal well operation data. The method is based on the algorithm including current distribution calculation of function values for potential and filtration velocity in the oilfild selected area. The method allows to monitor the current distribution of the reservoir pressure in the productive formation of the area under consideration, as well as to assess the effectiveness of the impact on the reservoir in order to maintain the reservoir pressure. The implementation of the proposed method, demonstrated on the example of the "Neft Dashlary" (X horizon, block V) oilfield data, showed high accuracy of the obtained calculated values. The average value of the relative error of the calculated values of the reservoir pressure to the actual values of the downhole pressure measurements at the wells is not more than 1%, and the average calculated value of the reservoir pressure in the productive formation in the pilot area coincides with its actual present value. Keywords: reservoir; reservoir pressure; reservoir enhanced oil recovery; zonal impact; productive horizon; well productivity; diagnostics; filtration; monitoring; streamlines.

Designing of a multi-frequency vibrator antenna on meander line with resonant loads and fragmented “floating ground”

Problem definition. Many VHF communication devices include multi-frequency vibrator antennas, among which a special place is occupied by the vibrator antennas with reactive loads as the most compact and simplest to produce. However, inductive loads usually used in practice don’t provide current cut-off at higher operating frequencies, which results in deformations of radiation patterns, and resonant circuits loads don’t provide sufficient shortening of the vibrator antenna due to appearance of shunt inductances. There is a need to formulate the new idea of the designing the multi-frequency vibrator antenna, which has absolutely another mechanism of work, is needed. Purpose. The purposes of this article are: to suggest the idea of the design the multi-frequency vibrator antennas, based on hybrid of meander line with parallel LC-circuits and fragmented “floating ground”; to form an equivalent scheme for calculating characteristics; to develop a methodology for calculating this type of antennas characteristics (input impedance, VSWR, current distributions over the vibrator and far-field radiation patterns); to do the calculation of characteristics of the monopole antenna on meander line with loads and to make an experimental check of the theoretical results. Results. A design of the multi-frequency vibrator antenna on meander line with parallel LC-circuits loads and fragmented “floating ground” is shown. An equivalent scheme for calculating antenna characteristics is given, an algorithm of calculation of input characteristics and current distributions over the antenna (both meander and “floating ground”) is described. The calculation of input impedance, VSWR, current distributions and radiation patterns of the vibrator antenna with two LC-circuits loads in meander line is done. An experimental check of the theoretical results in VSWR and far-field radiation patterns is made. Applicability of the proposed idea and methodology for the design the multi-frequency vibrator antennas on meander line is shown by analyzing calculated and experimental data. Practical significance. The results of this work can be used to design the multi-frequency VHF vibrator antennas with resonant loads, which have the identical radiation patterns at all operating frequencies.

Development of a method for optimizing industrial energy storage units placement in electric distribution networks on the basis of ideal current distribution

The object of this study is the process of integrating industrial energy storage units (IESU) into distribution electrical networks. Their connection helps reduce peak loads on the elements of networks and improve the quality of voltage. However, determining the optimal IESU capacities and their places of connection to networks is associated with objective difficulties. It is necessary to apply comprehensive optimality criteria and take into consideration active restrictions. In addition, the trends in the development of distribution networks and pricing in the energy market are partially undefined. The current study proposes the formalization of the problem of optimizing the placement of IESU in distribution networks and reports a new method to solve it. Its application contributes to a reasonable definition of the volume of investments in the development of IESU, taking into consideration technical restrictions on the part of distribution networks. To solve the problem of multifactorial optimization of the energy storage system, the decomposition and method of ideal current distribution (for electricity losses) were applied. It is shown that this problem can be reduced to an iterative calculation of current distribution in the substitution circuit of power grids with active resistances. And, to take into consideration economic factors, a technique to determine and adjust fictitious resistances was devised. An optimization algorithm has been proposed that ensures a decrease in the number of computing operations and an increase in the reliability of obtaining an optimal solution. Its application makes it possible to take into consideration the dynamics of pricing, consumption, and electricity generation processes over long periods. This contributes to the formation of sound design decisions on the connection of IESU to distribution networks

Calculation of current distribution in parallel-connected transformer winding sections in the case of asymmetric magnetic field during short-circuit test

In this paper, an algorithm for calculating the asymmetric current distribution in parallel-connected high-voltage winding sections of a transformer during a short-circuit test caused by an asymmetric magnetic field is described. This calculation is essential in multi-winding transformers, such as traction transformers and rectifier transformers, which have a high-voltage winding consisting of sections connected in parallel, where the number of sections is equal to the number of low-voltage windings and only one low-voltage winding is shorted during the short-circuit test.An optimization method, combined with a semi-analytical transformer model based on conformal mapping, is used to calculate the magnetic field and find a combination of currents in parallel-connected sections assuming equal induced voltages, i.e. flux linkages, in each section.The results of the calculation show good agreement with measurements carried out on the traction transformer for an electric multiple unit.

3-D Finite-Element Thin-Shell Model for High-Temperature Superconducting Tapes

Thin-shell (TS) models are generally used in the analysis of thin regions with linear constitutive properties, although specialized versions of TS models have been developed for high-temperature superconductor (HTS) tapes. However, due to the intrinsic hypothesis of sheet current density, none of these specialized models can account for all possible configurations of HTS tapes. This article presents a new 3-D time-domain finite-element TS model for the electromagnetic modeling of arbitrary HTS tape configurations. The model is validated against benchmark problems, and it is used to solve a realistic application case, namely the calculation of ac losses in a 14-strand HTS Roebel cable. The 3-D TS model is based on a magnetic field formulation and can take into account the diffusion of the tangential magnetic field into the tapes. The nonlinear behavior of the superconducting tapes is described with an E-J power-law model in a virtual discretization across their thickness. This approach allows the calculation of nonuniform current distributions through the thickness of the tapes, when relevant; thus, losses in multiple HTS tape assemblies in any configuration can be determined accurately. The results of the proposed approach are compared with those obtained with a full 3-D representation of the thin regions and show excellent agreement (a relative difference of less than 2%) while reducing substantially the computational burden (75% fewer DoFs). These features make the new 3-D TS model very promising for simulating large-scale superconducting devices, including high-field magnets and coils of complicated shape.

Calculation of DC current distribution in AC power system near HVDC grounding electrode in subregional layered soil

The DC current from the grounding electrode of a HVDC system may result in great ground potential differences in a large area, and may flow into the widely distributed systems with dispersed grounding points such as AC power grid which may disturb the systems. Soil resistivity is the most important factor that affects the current distribution. The heterogeneous soil has a subregional layered structure on the whole. In this paper, a numerical approach coupling the boundary element method with complex image method is developed to calculate the current fields in the subregional layered soil. By using indirect boundary element method, the subregional layered soil is turned into a uniformly layered soil in which the electric field is calculated with the help of complex image method. The calculation scale is much smaller than that just using the boundary element method, and the complex image method can be extended to calculate the electric field in soil with complex structure. Then, an equivalent circuit network in the complex soil is extracted and is coupled with the equivalent circuit of AC power grid, with which the DC current distribution in an AC power grid around a HVDC grounding electrode is analyzed. The results show that even in the area where the ground electrode is located, the ground potential gradient in the subregional layered soil is different from the result in the uniformly layered soil, which leads to a difference in the current flowing through the neutral point of the substation. The closer the DC grounding electrode or the substation is to the interface of the subregional layered soil, the greater the effect on the ground potential around the DC grounding electrode and the DC current flowing through the substation.

COMPLEX-CLOSED POWER SUPPLY SYSTEMS AND CALCULATION OF THEIR ELECTRICAL MODES

When creating and improving power supply systems, steady-state calculations are the most common, they contain nonlinear elements in the form of generators and loads, therefore their steady-state mode is described by nonlinear equations. The solution of such equations is possible only by iterative methods, which is associated with the problem of convergence of the iterative process. Due to some features of electrical systems, which are inherent, including power supply systems of the agro- and forestry complex, the convergence of the iterative process may be slow and not even secured. (Research purpose) The research purpose is developing a method for calculating the steady-state modes of power supply systems that meets the condition of convenience of implementation on an electronic computer and removes the problem of convergence of the iterative counting process. (Materials and methods) Proposed a direct calculation method with cyclic correction of the initial information for each cycle in order to take into account the nonlinearity of elements of power supply systems. (Results and discussion) The calculation formulas for determining the intrinsic and mutual resistances that underlie the proposed method are given, their main feature is that they are distributed with elements included in the nodes corresponding to sources and loads, and obtained by the authors as a result of the transformation and solution of nodal equations. It was established that the method is implemented through the operation of the following algorithms: calculation of intrinsic and mutual resistances; calculation of current distribution, that is, determination of currents in the branches of the network; calculation of voltages in all nodes of the power supply system; calculation of power flow distribution in order to subsequently identify power losses and electric energy consumption. (Conclusions) It was shown that the derived universal calculation expressions can also be used for equivalence purposes. It was revealed that the proposed method and the algorithms implementing it are relatively easy to program and provide the necessary speed and accuracy of calculations; they are designed to solve practical problems related to the design and operation of complex closed power supply systems, increasing their reliability and efficiency.

Multigrid method for numerical modelling of high temperature superconductors

An approach to numerical simulation of three-dimensional electrical and thermal fields in high-temperature superconductors is described. In such a semiconductor, the phenomena of superconductivity are observed at high temperatures above the temperature of liquid nitrogen. The absence of a generally accepted theory of superconductivity leads to the need to study physical processes in semiconductor structures using mathematical simulations. The main attention is paid to the calculation of temperature and electric current distributions in large-size mesas with a self-heating effect. An efficient algorithm for solving the equations describing these distributions is constructed. The basis of the algorithm is an adaptive multigrid method on structured Cartesian grids. The adaptability is based on the Chebyshev iterative method for constructing the smoothing procedures at each grid level and for solving the coarsest grid equations. The adaptive technique allows us to realistically simulate the anisotropic phenomena. The functionality of the algorithm is demonstrated along with an example of solving an anisotropic model problem with discontinuous coefficients.

Advanced parametric model for analysis of the influence of channel cross section dimensions and clamping pressure on current density distribution in PEMFC

The design of the flow field and the channel cross section of a bipolar plate as well as the intrusion effect of gas diffusion layers due to clamping pressure can significantly influence the performance of a fuel cell. The land and channel areas at a channel cross section can have different boundary conditions due to compression, intrusion of gas diffusion layers and transport phenomena. Todayapplication engineers are faced with the challenge of finding advantageous overall solutions from this plurality of multi-criteria parameters. In this thesis, a model approach is presented which combines a fully parametric analytical-empirical intrusion model with a 1D fuel cell model. This allows the calculation of current density distributions at the channel cross section, taking into account clamping pressure, channel parameters and operating conditions. Depending on the operating points considered, the results show that the maximum current densities occur in different areas of the channel cross section. In addition, with regard to the clamping pressure current density optima can be determined. Using this model approach, in an early development process application engineers will be able to compare hundreds of variants in a reasonable short time and thus determine advantageous fuel cell designs.

Rapid Analytical Calculation of Magnetic Field and Critical Current Distributions in HTS Magnets

For the design of superconducting magnets, the magnetic field and critical current distributions are usually calculated based on finite element software such as COMSOL, ANSYS, etc. These software are necessary for accurate structure modeling and field calculation, but they occupy large memory space and comsume long simulation time. Furthermore, they are not easy to use. To achieve an easy-to-implement solution for rapid magnet field and critical current calculations, this paper investigates three types of analytical calculating methods, and builds an autonomously-operated calculating application program (APP) for the uses in various superconducting magnets.

Numerical and experimental evaluation of the general performance in a modular electrochemical reactor and its feasibility for electro-chlorination purposes: Effect of the different electrode assembly configurations

Evaluation of electrochemical reactors consisting of different electrode assemblies, stacks, or modular units, by the employing of computational techniques and its comparison with experimental data is desirable for its applications and scaling up for electrochemical processes like the mediated electro-chlorination. This work aimed to evaluate the effect of three different electrode configurations (flat, interspersed, and C-stack assemblies) on the general performance of a homemade modular reactor, based on former ElectroSyn design with an improved inlet-outlet system, through studies of hydrodynamics, electrical characteristics, and mass transfer. Additionally, a secondary potential-current distribution study was carried out to evaluate the feasibility of different electrode configurations tested for the electro-chlorination process, that can be applied mainly for environmental purposes like mediated oxidation of organic pollutants and disinfection by the production of active chlorine species.From the hydrodynamic study, velocity profiles and RTD curves obtained in all electrode configurations tested, suggest that the flat electrode configuration exposes a low fluid dispersion and resistance than the other configurations, because of the diminishing of the high-velocity zones and by its higher cross-sectional area, which was confirmed by the pressure drop measurements. On the other hand, calculation of primary and secondary current distribution suggests that the presence and modification of edge effect in the different configurations tested generate strong non-uniformities in the electrode corners and the reactor walls, which could affect the distribution of reaction rate during the mass transport evaluations. Also, the secondary potential-current distribution study indicates that the flat and C-stack configurations are the more electrical feasible configurations (since the effect of the flow field and mass transfer was not taken into account) to be applied in the electro-chlorination process.

Accurate off-axis magnetic field calculation of axisymmetric cylindrical current distributions

This paper proposes an accurate, simple, and versatile approach for calculation of the off-axis magnetic field of any axisymmetric cylindrical current distribution, eliminating the need for complicated elliptical integrals and sophisticated numerical methods, e.g., finite element method. The results obtained from both integral and series forms not only confirm the validity of the proposed method against well-established analytical techniques but also outperform them in terms of accuracy, simplicity, and calculation time. The integral method yields greater convergence (14 decimal places) compared to the ill-posed series method, which depends on the highest order of derivatives; this would yield an error below 1% at the highest order of derivatives (i.e., 14 for axial-H and 11 for radial-H in the range of 0 < ρ < 0.8R). The off-axis solution to the case of a thin shell of finite length with cylindrical current distribution is calculated using the proposed method irrespective of the current density function, though only the most common case of uniform current has been included in the solved special cases. Given that no known formula is available to solve this case, the results of this work have been validated against the results of the well-known software ANSYS Maxwell simulator.

Effects of Endplate Assembly on Cold Start Performance of Proton Exchange Membrane Fuel Cell Stacks

A proton exchange membrane fuel cell (PEMFC) stack has two endplate assemblies (EAs) to stabilize the multilayered structure and distribute the preload evenly on each cell. Thermal inertia of and heat loss through the EA are crucial factors for developing novel thermal and water management strategies for PEMFC stacks. Herein, a 3D multidisciplinary transient model is established to assess the effects of EAs on the cold start performance of PEMFC stacks. The underlying mechanism linked to the EA effects is revealed through the analysis of temperature distribution, current density distribution, ice formation, and water balance calculation. The predicted results show that the EA has a significant impact on temperature and ice distributions in the end cell, thus negatively affecting the end cell performance. It is found that the smaller water diffusivity caused by the lower temperature in end cells results in more ice accumulation in the middle of cathode catalyst layer (CCL). The temperature of the end cells is greatly influenced by the thermal mass of the bus plate. For a low start‐up temperature of −30 °C, the impact of EA becomes more significant and the end cell is completely filled up by ice and therefore shuts down.

INFLUENCE OF SKIN EFFECT ON THE CALCULATION OF BUSBAR SYSTEMS HAVING RECTANGULAR CROSS SECTION

One method for the calculation of current density distribution in a finite number of long parallel conductors, having rectangular cross section, is proposed in this paper. Numerical results aim to highlight the importance of the skin effect, which can be combined with the proximity effect. The method of superposition of these two effects was applied to the calculation of the electromagnetic field in electric power busbars systems. It has been shown that the skin effect has a much greater impact, especially when the conductors are thin and strong electric currents flow through them, so special attention is paid to its calculation. For numerical solution the integral equations are used. The function of current density is approximated by the finite functional series. This way leads to a very accurate solution with only two terms. Differential evolution method is applied for minimization of error function. To demonstrate the application of the proposed approach, numerical values for busbars are presented and compared with values obtained by using the finite elements method.

Method for determining the two-dimensional current density distribution function over the radiating structure based on chiral metamaterials

The article is devoted to the development of a method of electrodynamic analysis and a two-dimensional mathematical model of strip radiating structures based on the apparatus of hypersingular equations in order to ensure the correct calculation of their characteristics when using relatively small computational resources. A system of hypersingular integral equations with respect to the unknown transverse and longitudinal components of the current density distribution functions is obtained. This system of hypersingular equations was solved using the collocation method, where Gaussian nodes (zeros of Legendre polynomials) were used as collocation points. This approach allows for faster convergence compared to uniform partitioning. Numerical results of calculations of current density distribution functions for various parameters of the radiating structure based on chiral metamaterials are obtained. It is shown that in the case of wide emitters, it is necessary to take into account both components of the current density distribution function. The advantage of this method in comparison with universal analogues is the ability to accurately calculate the characteristics of radiating structures based on chiral metamaterials with wide emitters.

Efficiency Optimization of IPOP DC/DC System for HEV

Input parallel output parallel (IPOP) DC/DC system is widely utilized in many occasions like data center and hybrid electric vehicle (HEV). However, the efficiency characteristics of different converters usually differs from each other, and the conventional control strategy has difficult to realize efficient conversion of overall power of the system. To address this issue, Buck converter is taken as the module and whose efficiency model under current continuous conduction mode (CCM) is presented. Meantime, parameter identification method based on least square (LS) algorithm is proposed as well. In order to realize the efficiency optimization of the whole parallel system, the constraint conditions of each module are analyzed, and the current distribution calculation method based on sequential quadratic programming (SQP) algorithm for the parallel system is introduced. On this basis, a control strategy of proportional current distribution (PCD) is proposed, which not only ensures that the parallel system can always run as efficiently as possible under different loads, but also realizes the flexible switching between the current-sharing mode and current distribution mode. Finally, the simulation and experimental results prove that the proposed method can achieve 4.46% higher efficiency than conventional method within the given power range of each converter, and realize the efficiency optimization of the IPOP DC/DC system to the greatest extent.

Specific aspects of calculating electrical energy losses in electricity networks

The paper present modes of operation of 10(6) kV distribution networks, which are determined by the loads of consumers. The network scheme is based on an open circuit, which allows you to perform calculations for each 10(6) kV distribution line (feeder) separately. The calculation of power losses in the electric network is carried out by the method of average loads. The paper determines the integral characteristics of the operational parameters of the head branch, determines the parameters of the equivalent power loss of the feeder equivalent circuit, and the equivalent circuit determines the energy loss in the feeder. The paper compiles the equivalent circuit of the considered network section, calculated the parameters of the equivalent circuit elements and determines the total power loss in all linear sections. The paper presents an algorithm for calculating the steady state using the example of a feeder and shows the sequence of calculation of current distribution in the branches of the equivalent circuit.

Increase of Input Resistance of a Normal-Mode Helical Antenna (NMHA) in Human Body Application

In recent years, the development of healthcare monitoring devices requires high performance and compact in-body sensor antennas. A normal-mode helical antenna (NMHA) is one of the most suitable candidates that meets the criteria, especially with the ability to achieve high efficiency when the antenna structure is in self-resonant mode. It was reported that when the antenna was placed in a human body, the antenna efficiency was decreased due to the increase of its input resistance (Rin). However, the reason for Rin increase was not clarified. In this paper, the increase of Rin is ensured through experiments and the physical reasons are validated through electromagnetic simulations. In the simulation, the Rin is calculated by placing the NMHA inside a human’s stomach, skin and fat. The dependency of Rin to conductivity (σ) is significant. Through current distribution calculation, it is verified that the reason of the increase in Rin is due to the decrease of antenna current. The effects of Rin to bandwidth (BW) and electrical field are also numerically clarified. Furthermore, by using the fabricated human body phantom, the measured Rin and bandwidth are also obtained. From the good agreement between the measured and simulated results, the condition of Rin increment is clarified.

Calculation of current distribution in tungsten plate under exposure to a pulsed electron beam

In the mathematical model of melting of a tungsten plate exposed to a pulsed electron beam, the calculation of the current distribution in the medium is added. The model takes into account the heterogeneity of the resistivity. This enables modeling of non-uniform heated material. The current is expected to spread into the depth due to the increased resistance of the heated part. Changing the thickness of the tungsten plate, one can increase the current density in the melt. The calculation results for parameters corresponding to those used on the BETA facility at BINP SB RAS show that no current concentration occur. The Ampere force is not large enough for the rotation observed in the experiments.