Rectangular Busbar Research Articles

Non-Contact Current Measurement for Three-Phase Rectangular Busbars Using TMR Sensors.

This paper proposes a non-contact current measurement method for three-phase rectangular busbars based on TMR (tunneling magneto-resistance) sensors, due to their advantages of large dynamic range, wide bandwidth, light weight, and easy installation. A non-contact current sensor composed of only three TMR sensors is developed and the TMR sensors are respectively placed at a location with a certain distance from the surface of each rectangular busbar to measure the magnetic fields generated by the busbar currents. To calibrate the developed current sensor, i.e., to establish the relationship between the magnetic fields measured by the TMR sensors and the currents flowing in the three-phase rectangular busbars, we designed a thyristor-controlled resistive load as a calibrator, which is connected to a downstream branch of the distribution cabinet. By switching the resistive load, a calibration current, which can be identified from the background current, is generated in one rectangular busbar and its value is measured at the location of the calibrator, and transmitted wirelessly to the location of the TMR sensors. A new and robust method is proposed to extract the voltage components, corresponding to the calibration current, from the voltage waveforms of the TMR sensors. By calculating the proportional coefficients between the calibration currents and the extracted voltage components, online calibration of the current sensor is achieved. We designed and implemented a current measurement system consisting of a current sensor using TMR sensors, a thyristor-controlled resistive load for current sensor calibration, and a data acquisition circuit based on a multi-channel analog-to-digital converter (ADC). Current measurement experiments were performed in a practical distribution cabinet installed in our laboratory. Compared to the measurement results using a commercial current probe with an accuracy of 1%, the relative error of the measured currents in RMS is less than 2.5% and the phase error is less than 1°, while the nonlinearity error of the current sensor is better than 0.8%.

Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars

The purpose of this research is to correctly model steady-state heat transfer in and around rectangular bus bars installed horizontally in an indoor environment and to estimate the corresponding ampacities, considering the effects of horizontal transverse vibrations caused by electromagnetic forces. This thermo-electro-magneto-mechanical problem is solved analytically using correlations determined experimentally by other researchers, while the accuracy of the obtained results is verified numerically using the finite element method (FEM). The novelties of the developed model are as follows. First, modeling the effects of horizontal transverse vibrations on free convection from the top and bottom surfaces of rectangular bus bars via forced convection for different characteristic lengths. Second, modeling the effects of vibration amplitudes and vibration frequencies on the bus bar ampacity. Third, introducing the existing vibration classes (A, B, and C) into the analytical and FEM-based thermal analyses. The results show that with an increase either in the vibration amplitude or the vibration frequency, there is a greater convection-based dissipation of heat from the bus bars and an increase in their ampacity. Finally, for the standard vibration classes, it is found that the effect of horizontal transverse vibrations on the ampacity can be up to 41.99% for Class C.

Rectangular Busbar With Circular Sensing Part for Wideband Current Measurement

Rectangular Busbar With Circular Sensing Part for Wideband Current Measurement

Crosstalk in Elliptical Sensor Arrays for Current Measurement

Contactless current sensors that use arrays of magnetic field sensors are a good alternative to core-based current sensors because the omission of the magnetic core offers many advantages. Particularly, circular sensor arrays have proven to feature good robustness against various error sources. As rectangular bus bars are frequently used for local high-current power distribution systems, elliptic arrays would require less space than circular arrays. Up until now, no publication on magnetic interference errors of elliptic sensor arrays has been presented. This article examines the crosstalk error for different sensor distribution methods, aspect ratios, numbers of sensors, and offset angles with calculations and measurements. Therefore, an interference conductor is positioned at different angles and distances relative to the elliptic arrays. We show that the crosstalk error can be reduced with our elliptic designs in comparison to a circular design with an equal number of sensors and an equal length of the semimajor axis. The projection distribution typically offers a five times smaller crosstalk error compared to the uniform curve segment length distribution. To support the design of elliptical arrays, instructions for the optimization against interference errors for elliptic sensor arrays are given in this article. Thus, an optimal offset angle for the reduction of the crosstalk error is presented.

Methods for calculation of the impedance of a package of rectangular busbars in an ore-thermal furnace

Methods for calculation of the impedance of a package of rectangular busbars in an ore-thermal furnace

Experimental and theoretical studying simulation of influence of continuous extrusion technological modes on the properties formation of rectangular copper busbars

The influence of temperature and pressing rate parameters on the continuous extrusion process conditions of rectangular busbars with size 1060 mm and made of M1 copper are investigated. With using software for finite element modeling (Q-Form) data on changes in temperature and stresses in the deformation zone at different pressing rates were obtained. The increase of pressing rate from 4 to 6 m/min leads to a slight increase in the average temperature of the extrusion process by 10–20 оC, what can significantly reduce the level of stress triaxiality in the deformation zone. The maximum of stress values are observed in the zone of contact between a metal and a abutment, where the direction of its flow changes. In the same zone, the release of more heat in a metal due to deformation was recorded. For metallographic investigation samples of rods cast at drawing rates of 300 and 500 mm/min and rectangular busbars extruded at workpiece feed rates of 4 and 6 m/min were produced on technological equipment. In result of the study macro- and microstructure images were obtained, indicating a weak effect of casting and pressing rates on the formation of structure in the ranges considered in this work. The macrographs of cast rods indicate an influence of drawing rate on a formation and size of the material structure, however, further deformation processing leads to a complete restructuring of the cast structure. The average grain size of the extruded samples is 15–30 μm. The results of measuring hardness and electrical conductivity also indicate a low effect on influence of the pressing rates in the considered range on the formation of these characteristics. All investigated bus samples show a tendency to increase hardness at edges, which is caused by more intensive cooling of a metal in these zones at an exit from the deformation zone. The average hardness of the tested busbars samples is ~ 66 HV1.The reported study was funded by RFBR, project number 19-38-90104.

Investigation of the stress-strain state and microstructure transformation of copper busbars in the deformation zone during continuous extrusion

The paper describes an extensive study of features peculiar to physical and mechanical processes occurring in metal in the deformation zone during the continuous extrusion of Cu-ETP rectangular busbars 10×60 mm in size. Finite element computer simulation was used to obtain the values of extrusion power parameters. It was noted that moment and force values increase to the point of filling the press chamber free space with metal reaching a maximum of 12.26 kN·m and 1.54 MN, respectively. The stress-strain state analysis of metal in the deformation zone made it possible to obtain distribution fields of accumulated plastic strain, strain rate intensity and average stresses, and to build the graph of metal temperature variation over time during extrusion. Maximum levels of accumulated plastic strain and compressive stresses are observed in the contact zone of the workpiece with the press container abutment. The most intense metal deformation heating also occurs there. The comparison of modeling and microstructural study results indicate that a significant portion of the cast structure grinding work occurs at the entrance to the deformation zone and at the abutment zone subjected to the highest level of compression stresses. Metal deformation during the die passage leads to an oriented crystal structure formed with a grain size of 25–30 μm. Sample hardness measurement results are consistent with the results of structure analysis in the studied areas of the deformation zone. When the workpiece passes through the compression container abutment section, deformation heating occurs, which leads to a decrease in hardness from 93 to 67 HV. After the metal passes through the die, recrystallization processes continue in it leading to a slight increase in grain size and, accordingly, a decrease in hardness from 79 to 74 HV, which continues until the busbar contacts a cooling medium.

A Wideband Current Transducer Based on an Array of Magnetic Field Sensors for Rectangular Busbar Current Measurement

Recently, the current transducer based on an array of magnetic field sensors has attracted a lot of attention. For busbars of circular cross section, many studies have been conducted and many results have been obtained. However, for the rectangular cross section busbar, the skin effect causes the frequency response curve of the magnetic flux density $B$ generated by the current-carrying conductor to appear nonlinear, which brings challenges to the wideband current measurement of the rectangular busbar. This article presents a wideband current transducer based on the array of magnetic field sensors for the current measurement of the rectangular busbar. First, according to the rectangular busbar, select reasonable magnetic field detection points to arrange the sensor array. Then, the frequency response curve of the magnetic flux density $B$ at each detection point around the rectangular busbar is obtained by simulation. After that, all frequency response curves are averaged, and the proper digital filter is designed according to the averaged frequency response curve to perform frequency compensation. The compensated frequency response curve is basically flat, so the wideband current measurement of the rectangular busbar can be realized. The bandwidth and overall performance of the designed wideband current transducer are verified through experiments, and experimental results show that the designed transducer can meet the requirements of relevant standards for the class 0.5 current transducer.

Автоматизированная проверка однополосных шин прямоугольного сечения по условиям термической и электродинамической стойкости

Автоматизированная проверка однополосных шин прямоугольного сечения по условиям термической и электродинамической стойкости

Coupled Multiphysics Field Analysis of High-Current Irregular-Shaped Busbar

Conventional rectangular busbars employed in electric power systems suffer from several drawbacks, such as containing excess conductor material and exhibiting low current densities and poor heat dissipation. Therefore, the goal of this paper is to develop an irregular-shaped high-current (2000-A) busbar based on a coupled multiphysics analysis approach in which the influences of the proximity and the skin effects were considered. First, 3-D models based on the finite-element method (FEM) are established for a conventional rectangular busbar and the proposed irregular-shaped busbar, and the current densities of the two are compared. Second, a double coupling method is employed to couple the fluid–thermal field calculations with the electromagnetic power losses, which are considered to be heat sources, to determine the proportion of convective and radiative heat transferred from the surfaces of the busbar conductors. Third, based on the electromagnetic field analysis, the dynamic and thermal stabilities of the irregular-shaped busbar are verified with a new method. The time at which the short-circuit current reached a maximum is determined accurately. The electromagnetic force, temperature, and thermal stress distributions of the irregular-shaped busbar under short-circuit conditions are obtained. Finally, the accuracy of the FEM simulations is verified by experiments, which indicate that the multiphysics field-coupled analytical approach is valid.

The Magnetic Field and Impedances in Three-Phase Rectangular Busbars with a Finite Length

The paper presents an analytical method for calculating impedances of rectangular bus ducts. The method is based on the partial inductance theory—in particular, the impedance of rectangular busbars in a three-phase system with a neutral conductor is described. The results of resistances and reactances of these systems of multiple rectangular conductors were obtained. Skin and proximity effects were taken into account. The measurements of the impedance of shielded and unshielded high-current busducts of rectangular conductors were also carried out. The magnetic field of the busbars was determined with several methods.

Application of Duhamel’s Theorem in the Analysis of the Thermal Field of a Rectangular Busbar

The paper presents the method of thermal field analysis in a rectangular busbar taking into account the variable resistivity. The method is based on the analytical solution of the heat conduction equation. The boundary-initial problem was solved using the Duhamel’s theorem. The suitable step response of the system was determined by the separation of variables method. By means of presented method, a stationary and transient thermal field was determined in the rectangular busbar taking into account variable resistivity. The steady-state currents rating as well as the time constants of the busbar in case of variable and average resistivity were also determined. The results obtained was verified using the finite element method.

Comparison of heating curves of a rectangular busbar in different conditions of heat abstraction during the short-circuit heating

Comparison of heating curves of a rectangular busbar in different conditions of heat abstraction during the short-circuit heating

An analytical algorithm to determine allowable ampacities of horizontally installed rectangular bus bars

The main objective of this paper is to propose an algorithm for the determination of the allowable ampacities of single rectangular-section bus bars without the occurrence of correction factors. Without correction factors, the ampacity computation of the copper and aluminium bus bars is fully automatized. The analytical algorithm has been implemented in a computer program code that along with the allowable ampacity can compute the bus bar temperature and the individual heat transfer coefficient for each side of the bus bar, as well as their corresponding power losses. Natural and forced convection correlations for rectangular bus bars are applied. Effects of the solar radiation and radiation heat losses from the bus bar surface are taken into consideration as well. The finite element method (FEM) has been used for the linear/non-linear steady-state thermal analysis, i.e. for validation of the analytical algorithm. All FEM-based numerical computations were carried out using the COMSOL Heat Transfer Module.

A discrete numerical method for magnetic field determination in three-phase busbars of a rectangular cross-section

This paper presents a discrete numerical computation method for determining the magnetic field distributions in finite-length high-current bus ducts of rectangular busbars. This method is based on the integral equation method and the partial element equivalent circuit method. It takes into account the skin effect and proximity effects, as well as the complete electromagnetic coupling between phase bars and the neutral bar. In particular, the magnetic fields in busbars of unshielded three-phase systems with rectangular phase and neutral busbars and the use of the method are described. Finally, two applications to three-phase unshielded systems busbars are presented.

IMPEDANCJE WŁASNE I WZAJEMNE SZYNOPRZEWODÓW PROSTOKĄTNYCH O SKOŃCZONEJ DŁUGOŚCI

In this paper, a new numerical method of calculating rectangular busbar impedance is proposed. This method is based on integral equation method and partial inductance theory. Results for resistances and reactances for these systems of multiple rectangular conductors have been obtained. Skin and proximity effects have also been taken into consideration. The validation of the proposed method is carried out through FEM and laboratory measurements, and a reasonable level of accuracy is demonstrated.

Alternating current loss reduction for rectangular busbars by covering their edges with low permeable magnetic caps

A method to reduce ac conductive losses in a thin rectangular busbar made of copper is presented. The method is based on a technique, which makes the distribution of the ac current in the cross section of a busbar flatter. Edges of a thin busbar are covered with low permeability magnetic thin layers as caps. The magnetic cap makes the impedance experienced by the current flowing near the edge comparatively larger so that currents cannot get crowded near the edges of a busbar. This method is numerically verified.

Initial magnetic field distribution around high rectangular bus bars

The one-dimensional transient electromagnetic field in and around a system of two nonmagnetic homogenous rectangular high thin bars can be analytically evaluated if the ratio of average initial magnetic field on the two sides of thin bar, or of the ratio of initial magnetic fields in middle of the bar height is known. In this paper, using appropriate conformal mappings, an exact analytical solution for these ratios are proposed in the case of very thin bars. Obtained values are compared with FEM results for relatively thick bars.

POLE MAGNETYCZNE SZYNOPRZEWODÓW PROSTOKĄTNYCH O SKOŃCZONEJ DŁUGOŚCI

W artykule przedstawiono nową analityczną metodę obliczania pola magnetycznego układów szyn prostokątnych. Metoda wykorzystuje prawa Biota-Savarta. Zaproponowana metoda pozwala na wyznaczanie rozkładu pola magnetycznego w układach równoległych szynoprzewodów prostokątnych o dowolnych wymiarach w tym szynoprzewodów o skończonej długości. W szczególności wyznaczono pola magnetyczne w nieekranowanych trójfazowych torach wielkoprądowych z prostokątnymi szynoprzewodami fazowymi i z szynoprzewodem neutralnym.

The Current Distribution, Resistance and Internal Inductance of Linear Power System Conductors—A Review of Explicit Equations

This paper reviews the present state of knowledge of explicit equations for calculating the dc and ac current distributions and the resistances and internal inductances per-unit length of linear electrical conductors used in power transmission and distribution systems. These conductors may be homogeneous wire or rod, tubular, triangular, elliptical or rectangular busbars, helically stranded nonmagnetic conductors (AAC or AAAC), or bimetallic stranded conductors, such as the commonly used aluminum conductor steel reinforced (ACSR). In general, the current density in an isothermal homogeneous conductor is uniform with direct current (dc), but with alternating current (ac), skin effect, and proximity effect, can cause nonuniform distribution of current, hence, increased resistance and decreased internal inductance. With stranded steel-cored conductors, the dc density within each section is inversely proportional to its resistivity. However, with ac at power frequency, the spiraling of the currents in the nonferrous layers causes a longitudinal magnetic flux in the steel core, which results in hysteresis and eddy current power loss in the core, and a circular magnetic flux in the nonferrous wires, which results in a nonuniform distribution of current density between the layers of nonferrous wires. These effects give rise to increased resistance and reduced internal inductance. The effects of current amplitude, frequency, temperature, and tensile stress on conductor properties are discussed.