The article discusses the determination of the mutual ground resistance of two adjacent metallica... more The article discusses the determination of the mutual ground resistance of two adjacent metallically connected grounding grids. For this purpose, an original analytical expression for calculating the corresponding mutual ground resistance of two adjacent grounding grids has been developed. There is a complex electromagnetic coupling between adjacent grounding grids. The conductive component of this coupling is particularly evident. During a ground fault, this component markedly increases the ground resistance of the corresponding grounding system. It is essential to establish the aforementioned mutual ground resistance correctly in order to determine the distribution of the partial ground fault currents in a system of adjacent grounding grids. The determination of mutual ground resistance is presented using two specifi c grounding grids buried in poorly conductive soil.
Facta universitatis - series: Electronics and Energetics, 2020
In this manuscript, a novel method for computation of per-unit-length internal impedance of a cyl... more In this manuscript, a novel method for computation of per-unit-length internal impedance of a cylindrical multilayer conductor with conductive and dielectric layers is presented in detail. In addition to this, formulas for computation of electric and magnetic field distribution throughout the entire multilayer conductor (including dielectric layers) have been derived. The presented formulas for electric and magnetic field in conductive layers have been directly derived from Maxwell equations using modified Bessel functions. However, electric and magnetic field in dielectric layers has been computed indirectly from the electric and magnetic fields in contiguous conductive layers which reduces the total number of unknowns in the system of equations. Displacement currents have been disregarded in both conductive and dielectric layers. This is justifiable if the conductive layers are good conductors. The validity of introducing these approximations is tested in the paper versus a model ...
2019 International Conference on Software, Telecommunications and Computer Networks (SoftCOM), 2019
In this paper a concise outline of a frequency domain grounding grid analysis based on the finite... more In this paper a concise outline of a frequency domain grounding grid analysis based on the finite element technique is given. Weighted residual method is simultaneously applied to the scalar electric potential integral equation and to the electric field integral equation. The proposed approach represents a basis for development of electromagnetic models for time-harmonic grounding grid analysis as well as transient grounding grid analysis. In the case of transient grounding grid analysis, transformation from the frequency domain into the time domain can be obtained by Fourier transform.
IEEE Transactions on Electromagnetic Compatibility, 2020
This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium t... more This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium that consists of air and multilayer soil. Closed-form kernel functions of the spectral-domain Green's function for scalar electric and vector magnetic potentials (Lorentz potentials) were obtained for every layer of the multilayered medium as analytic solutions of the systems of linear equations. Validation of the proposed closed-form expressions is performed by numerical solving of the system of linear equations and by numerical comparison with expressions derived from existing closed-form expressions developed for the source layer of the multilayer dielectric medium. For an arbitrary-oriented ICS, scalar electric potential of its horizontal component is chosen as a unique scalar electric potential. Accordingly, dyadic Green's function of vector magnetic potential is corrected.
Facta universitatis - series: Electronics and Energetics, 2019
There has been apprehension about the possible adverse health effects resulting from exposure to ... more There has been apprehension about the possible adverse health effects resulting from exposure to power frequency magnetic field, especially in the overhead power lines vicinity. Research work on the biological effects of magnetic field has been substantial in recent decades. Various international regulations and safety guidelines, aimed at the protection of human beings, have been issued. Numerous measurements are performed and different numerical algorithms for computation of the magnetic field, based on the Biot- Savart law, are developed. In this paper, a previously developed 3D quasistatic numerical algorithm for computation of the magnetic field (i.e. magnetic flux density) produced by overhead power lines has been improved in such a way that cylindrical segments of passive conductors are also taken into account. These segments of passive conductors form the conductive passive contours, which can be natural or equivalent, and they substitute conductive passive parts of the over...
Facta universitatis - series: Electronics and Energetics, 2017
In this paper a numerical algorithm for computation of per-unit-length internal impedance of cyli... more In this paper a numerical algorithm for computation of per-unit-length internal impedance of cylindrical conductors under complex arguments of large magnitude is presented. The presented algorithm either numerically solves the scaled exact formula for internal impedance or employs asymptotic approximations of modified Bessel functions when applicable. The formulas presented can be used for computation of per-unit-length internal impedance of solid cylindrical conductors as well as tubular cylindrical conductors.
Journal of Communications Software and Systems, 2007
This paper presents a novel technique for computing dangerous voltages due to direct lightning st... more This paper presents a novel technique for computing dangerous voltages due to direct lightning strike into the communication tower and associated earthing system, which is based on the use of the well-known ATP-EMTP software package. The earthing grid and the communication tower structure are approximated by the circular cross section conductors. In numerical model, conductors are subdivided into segments (1D finite elements) and Clark's model with distributed constant parameters is then applied. Because of the limitations of ATP-EMTP software package, the leakage resistance of buried segments is modelled as additional lumped parameter. Analytical expressions for distributed and lumped segment parameters are derived using the average potential method. Mutual electromagnetic coupling between segments is neglected due to the limitations imposed by the ATP-EMTP software package, which is based on transmission line approach. Separate computer program is developed for obtaining the e...
International Review of Electrical Engineering-iree, Feb 28, 2014
Computation of the internal impedance per unit length of solid and tubular cylindrical conductors... more Computation of the internal impedance per unit length of solid and tubular cylindrical conductors, energized by time-harmonic current, needs to take into account the skin effect. Computation algorithm involves direct numerical manipulations with Bessel functions. These functions are defined by infinite series, which yield unstable and often erroneous results, particularly for large magnitudes of the function argument at high frequencies. Therefore, different approximate formulas are used in order to alleviate this problem. In this paper, exact formulas, with scaled Bessel and Neumann functions and scaled coefficients, for internal impedance of two-layer cylindrical conductors are presented. In two numerical examples presented, results for internal impedances per unit length of two-layer conductors computed by exact formulas are compared with results based on Amos subroutines, which are used in program package MATLAB
International Review on Modelling and Simulations, Dec 31, 2013
In this paper a model of a two-winding transformer based on the finite element technique is propo... more In this paper a model of a two-winding transformer based on the finite element technique is proposed. The model employs a T-equivalent circuit of the transformer. Local systems of equations are derived both for the case of a single-phase transformer and for the case of the three-phase transformer. Three most often used transformer connections are observed in the case of the three-phase transformer. These models of a two-winding single-phase or three-phase transformers will be used in an electromagnetic model for analysis of ground fault current distribution based on the finite element technique.
In this paper an effective numerical algorithm for computation of double-exponential function par... more In this paper an effective numerical algorithm for computation of double-exponential function parameters based on the available input data is presented. The parameter estimation is achieved using the Marquardt least squares method.
A numerical algorithm for segmentation of overhead power line conductors, which form a catenary, ... more A numerical algorithm for segmentation of overhead power line conductors, which form a catenary, for 3D electric and magnetic power frequency field computation is presented. The overhead power line conductor catenary is approximated by a set of straight thin-wire segments. The segmentation algorithm requires only three input data per power line span conductor - the global coordinates of power line span conductor endpoints and the height of the lowest conductor point. On the basis of the presented theory, a FORTRAN program was developed and results of the overhead power line conductor segmentation with different number of straight segments along the span are compared and graphically presented.
The article discusses the determination of the mutual ground resistance of two adjacent metallica... more The article discusses the determination of the mutual ground resistance of two adjacent metallically connected grounding grids. For this purpose, an original analytical expression for calculating the corresponding mutual ground resistance of two adjacent grounding grids has been developed. There is a complex electromagnetic coupling between adjacent grounding grids. The conductive component of this coupling is particularly evident. During a ground fault, this component markedly increases the ground resistance of the corresponding grounding system. It is essential to establish the aforementioned mutual ground resistance correctly in order to determine the distribution of the partial ground fault currents in a system of adjacent grounding grids. The determination of mutual ground resistance is presented using two specifi c grounding grids buried in poorly conductive soil.
Facta universitatis - series: Electronics and Energetics, 2020
In this manuscript, a novel method for computation of per-unit-length internal impedance of a cyl... more In this manuscript, a novel method for computation of per-unit-length internal impedance of a cylindrical multilayer conductor with conductive and dielectric layers is presented in detail. In addition to this, formulas for computation of electric and magnetic field distribution throughout the entire multilayer conductor (including dielectric layers) have been derived. The presented formulas for electric and magnetic field in conductive layers have been directly derived from Maxwell equations using modified Bessel functions. However, electric and magnetic field in dielectric layers has been computed indirectly from the electric and magnetic fields in contiguous conductive layers which reduces the total number of unknowns in the system of equations. Displacement currents have been disregarded in both conductive and dielectric layers. This is justifiable if the conductive layers are good conductors. The validity of introducing these approximations is tested in the paper versus a model ...
2019 International Conference on Software, Telecommunications and Computer Networks (SoftCOM), 2019
In this paper a concise outline of a frequency domain grounding grid analysis based on the finite... more In this paper a concise outline of a frequency domain grounding grid analysis based on the finite element technique is given. Weighted residual method is simultaneously applied to the scalar electric potential integral equation and to the electric field integral equation. The proposed approach represents a basis for development of electromagnetic models for time-harmonic grounding grid analysis as well as transient grounding grid analysis. In the case of transient grounding grid analysis, transformation from the frequency domain into the time domain can be obtained by Fourier transform.
IEEE Transactions on Electromagnetic Compatibility, 2020
This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium t... more This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium that consists of air and multilayer soil. Closed-form kernel functions of the spectral-domain Green's function for scalar electric and vector magnetic potentials (Lorentz potentials) were obtained for every layer of the multilayered medium as analytic solutions of the systems of linear equations. Validation of the proposed closed-form expressions is performed by numerical solving of the system of linear equations and by numerical comparison with expressions derived from existing closed-form expressions developed for the source layer of the multilayer dielectric medium. For an arbitrary-oriented ICS, scalar electric potential of its horizontal component is chosen as a unique scalar electric potential. Accordingly, dyadic Green's function of vector magnetic potential is corrected.
Facta universitatis - series: Electronics and Energetics, 2019
There has been apprehension about the possible adverse health effects resulting from exposure to ... more There has been apprehension about the possible adverse health effects resulting from exposure to power frequency magnetic field, especially in the overhead power lines vicinity. Research work on the biological effects of magnetic field has been substantial in recent decades. Various international regulations and safety guidelines, aimed at the protection of human beings, have been issued. Numerous measurements are performed and different numerical algorithms for computation of the magnetic field, based on the Biot- Savart law, are developed. In this paper, a previously developed 3D quasistatic numerical algorithm for computation of the magnetic field (i.e. magnetic flux density) produced by overhead power lines has been improved in such a way that cylindrical segments of passive conductors are also taken into account. These segments of passive conductors form the conductive passive contours, which can be natural or equivalent, and they substitute conductive passive parts of the over...
Facta universitatis - series: Electronics and Energetics, 2017
In this paper a numerical algorithm for computation of per-unit-length internal impedance of cyli... more In this paper a numerical algorithm for computation of per-unit-length internal impedance of cylindrical conductors under complex arguments of large magnitude is presented. The presented algorithm either numerically solves the scaled exact formula for internal impedance or employs asymptotic approximations of modified Bessel functions when applicable. The formulas presented can be used for computation of per-unit-length internal impedance of solid cylindrical conductors as well as tubular cylindrical conductors.
Journal of Communications Software and Systems, 2007
This paper presents a novel technique for computing dangerous voltages due to direct lightning st... more This paper presents a novel technique for computing dangerous voltages due to direct lightning strike into the communication tower and associated earthing system, which is based on the use of the well-known ATP-EMTP software package. The earthing grid and the communication tower structure are approximated by the circular cross section conductors. In numerical model, conductors are subdivided into segments (1D finite elements) and Clark's model with distributed constant parameters is then applied. Because of the limitations of ATP-EMTP software package, the leakage resistance of buried segments is modelled as additional lumped parameter. Analytical expressions for distributed and lumped segment parameters are derived using the average potential method. Mutual electromagnetic coupling between segments is neglected due to the limitations imposed by the ATP-EMTP software package, which is based on transmission line approach. Separate computer program is developed for obtaining the e...
International Review of Electrical Engineering-iree, Feb 28, 2014
Computation of the internal impedance per unit length of solid and tubular cylindrical conductors... more Computation of the internal impedance per unit length of solid and tubular cylindrical conductors, energized by time-harmonic current, needs to take into account the skin effect. Computation algorithm involves direct numerical manipulations with Bessel functions. These functions are defined by infinite series, which yield unstable and often erroneous results, particularly for large magnitudes of the function argument at high frequencies. Therefore, different approximate formulas are used in order to alleviate this problem. In this paper, exact formulas, with scaled Bessel and Neumann functions and scaled coefficients, for internal impedance of two-layer cylindrical conductors are presented. In two numerical examples presented, results for internal impedances per unit length of two-layer conductors computed by exact formulas are compared with results based on Amos subroutines, which are used in program package MATLAB
International Review on Modelling and Simulations, Dec 31, 2013
In this paper a model of a two-winding transformer based on the finite element technique is propo... more In this paper a model of a two-winding transformer based on the finite element technique is proposed. The model employs a T-equivalent circuit of the transformer. Local systems of equations are derived both for the case of a single-phase transformer and for the case of the three-phase transformer. Three most often used transformer connections are observed in the case of the three-phase transformer. These models of a two-winding single-phase or three-phase transformers will be used in an electromagnetic model for analysis of ground fault current distribution based on the finite element technique.
In this paper an effective numerical algorithm for computation of double-exponential function par... more In this paper an effective numerical algorithm for computation of double-exponential function parameters based on the available input data is presented. The parameter estimation is achieved using the Marquardt least squares method.
A numerical algorithm for segmentation of overhead power line conductors, which form a catenary, ... more A numerical algorithm for segmentation of overhead power line conductors, which form a catenary, for 3D electric and magnetic power frequency field computation is presented. The overhead power line conductor catenary is approximated by a set of straight thin-wire segments. The segmentation algorithm requires only three input data per power line span conductor - the global coordinates of power line span conductor endpoints and the height of the lowest conductor point. On the basis of the presented theory, a FORTRAN program was developed and results of the overhead power line conductor segmentation with different number of straight segments along the span are compared and graphically presented.
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