Mutual Impedance Research Articles

A Study of Mutual Coupling between Vertical Grounding Electrodes

SUMMARYThis paper investigates the mutual grounding impedance between vertical grounding electrodes based on field measurements and FDTD simulations. In the case of vertical electrodes, the mutual impedance between the electrodes is almost completely independent of the electrode length, and thus the induced voltage is nearly constant as the electrode length becomes longer. This characteristic is different from that of an overhead conductor, where the electromagnetic‐induced voltage is proportional to the conductor length. The greater the separation distance between the electrodes, the smaller the induced voltage, as in the case of an overhead conductor. The propagation speed increases as the separation increases. It is found that the speed is not necessarily proportional to the inverse of the relative permittivity of the earth.

Improving the Accuracy of Impedance Calculation for Distribution Power System

This paper compares different approximation methods and develops a new method for simplification of Carson's equations to model distribution lines for unbalanced power flow and short-circuit analysis. The comparisons are made for real and imaginary parts of self and mutual impedances. The impedances obtained by application of different approximation methods are utilized for lines and cables of a long feeder with a load and the IEEE 123-node system. The effect of varying ground resistivity and frequency on impedances is observed. The unbalanced power-flow results of both systems are compared for voltage, current, active, and reactive power flow. It is observed that different approximation methods for impedance calculation have considerable effects on the results of power flow, especially on node voltages which are critical for power quality and steady-state analysis of distribution systems.

A Novel Backup Distance Protection Scheme for Series-Compensated Transmission Lines

Conventional distance protection applies the positive-sequence impedance to protect a line against short-circuit faults. Series-compensated lines may considerably change the positive-sequence impedance of the fault path and cause the distance relays to maloperate. To overcome this problem, the mutual impedance between phases of a transmission line is used for the design of a new distance protection scheme. The voltages and currents of both ends of the line are applied to compute the mutual impedance between the relay and the fault point. The proposed scheme has a reliable performance in protection against single-phase and double-phase-to-ground faults and, therefore, it can be used as a backup protection. Simulation results approve the efficiency of the proposed method in protection of series-compensated transmission lines.

A Method to Model Thin Conductive Layers in the Finite-Difference Time-Domain Method

This paper presents a new approach for modeling of electrically thin conductive shields in the finite-difference time-domain (FDTD) method. The method is based on representation of the relation between the fields at two faces of the shield as an impedance boundary network condition (INBC) in the frequency domain. The INBC includes frequency-dependent self and mutual impedances which are approximated by series of partial fractions in terms of real or complex conjugate pole-residue pairs. A discrete time-domain INBC at the shield is generated, which is then incorporated within the FDTD method. The primary advantages of the proposed approach are: 1) the convolution equations are not used in the formulation, 2) the approximation applied for discretizing the Maxwell equation has second-order accuracy in time and first-order of accuracy in space, and 3) the stability of the method is governed by the classical Courant Friedrichs Lewy stability condition. Numerical examples are presented to validate the new method and to demonstrate its efficiency and accuracy.

Self and mutual ground impedances of cylindrical metal plates buried in homogeneous earth

SUMMARYThis paper presents a numerical procedure for computation of self and mutual impedance of cylindrical metal plates buried in homogeneous earth. Procedure is based on an analytical expression for scalar potential distribution of an equipotential metal plate in homogeneous unbounded medium. The effect of the air–earth boundary condition is taken into account by the exact imaging method. The robustness and accuracy of the computation procedure is based on the combination of analytical integration and 1D and 2D Gaussian quadratures for solving integrals present in expressions for self and mutual ground impedances of metal plates. The attenuation and phase shift is taken into account approximately by introducing the attenuation‐phase shift factor. The numerical procedure developed for the computation of self and mutual ground impedances of cylindrical metal plates buried in homogeneous earth is efficient, numerically stable and generally applicable. Numerical model developed for the computation of self and mutual ground impedances of cylindrical metal plates buried in homogeneous earth represents a basis of a wider numerical model for computation of ground fault current distribution in which grounding grids are approximated by metal cylindrical plates. Copyright © 2014 John Wiley & Sons, Ltd.

Capacitive micromachined ultrasonic transducer arrays as tunable acoustic metamaterials.

Capacitive Micromachined Ultrasonic Transducers (CMUTs) operating in immersion support dispersive evanescent waves due to the subwavelength periodic structure of electrostatically actuated membranes in the array. Evanescent wave characteristics also depend on the membrane resonance which is modified by the externally applied bias voltage, offering a mechanism to tune the CMUT array as an acoustic metamaterial. The dispersion and tunability characteristics are examined using a computationally efficient, mutual radiation impedance based approach to model a finite-size array and realistic parameters of variation. The simulations are verified, and tunability is demonstrated by experiments on a linear CMUT array operating in 2-12 MHz range.

CALCULATION OF THE MUTUAL COUPLING PARAMETERS AND THEIR EFFECTS IN 1-D PLANAR ALMOST PERIODIC STRUCTURES

This paper proposes a new modal analysis based on Floquet's theorem which is needful for the study of a 1-D periodic phased array antenna excited by arbitrary located sources. This analysis requires an accurate estimation for calculation of the mutual coupling parameters (for example: mutual impedances or admittances ...) between the array elements and their efiects integrating a large planar radiating structure. Two difierent formulations are suggested, in spectral and spatial domains, to solve the problem and to calculate the coupling coe-cients between the neighbouring elements in a periodic environment. Important gain in the running time and used memory is obtained using Floquet analysis. One numerical method is used for modeling the proposed structures: the moment method combined with Generalized Equivalent Circuit (MoM-GEC).

A MATHEMATICAL MODEL FOR THE TRANSIENT LIGHTNING RESPONSE FROM GROUNDING SYSTEMS

With the Fast Fourier Transform (FFT), a mathematical model for accurately computing distribution of a lightning currents ∞owing along a high voltage a.c. substation's grounding system buried in half inflnite homogenous earth has been developed in this paper. It is a hybrid of Galerkin's method of moment (MoM) and a conventional nodal analysis method. The model can directly calculate the distribution of both branch and leakage currents along the grounding system. A dynamic state complex image method and a closed form of Green's function of a dipole or monopole in the half inflnite homogenous earth model are introduced into this model to accelerate calculations of mutual impedance and induction coe-cients. Analytical formulae for the mutual induction and impedance coe-cients have been developed to accelerate the calculation for near fleld case by using Maclaurin expansion. With the inverse FFT, the model can be used to study the transient lightning response of a grounding system.

Sensitivity Analysis of Characteristic Parameters of Railway Electric Traction System

The modal analysis, which decouples the contact wire and rail track conductors, is used to develop an integrated model of single rail track and contact wire. The characteristic impedance and propagation constant matrices of integrated model have been computed. The authors have studied effects of various parameters of interest on characteristic impedance and propagation constant using sensitivity analysis. The sensitivity functions of series impedance and shunt admittance related to contact wire and catenary have been developed and validated in this paper. Index Terms—railway traction lines, characteristic parameters, sensitivity analysis, parameter sensitivity  I. INTRODUCTION Railway electric traction system is a fast and green transportation system with enhanced load carrying capacity. The analysis and design of power and signaling system of railway electric traction system needs mathematical model of the system. The authors in this paper have used the multi-conductor transmission line theory to develop the mathematical model of the electric traction system and to compute the characteristic impedance and propagation constant of this system. This approach can then be extended to find the voltage and current distribution of the system. The characteristic impedance and propagation constant are the functions of line parameters i.e. self and mutual impedances and admittances of contact wire and rail track. The numerical values of these parameters are not accurately known under practical conditions as they are dependent on varying/uncertain parameters like permeability, supply frequency and shape of the conductor. In order to study the effect of these uncertain parameters on the characteristic parameters of the railway electric traction system, the authors have carried out the sensitivity analysis of characteristic impedance and propagation constant with respect to the above mentioned parameters of interest for the first time in the literature. In a rail track ferromagnetic material, both saturation and hysteresis are

Calculation of a Transient Line-to-Ground Voltage of a Solar Panel Caused by a Direct and an Indirect Lightning by means of Circuit Analysis Method

A circuit analysis method of a line-to-ground voltage of a solar panel when a structure for a solar panel is struck by a lightning is discussed in this paper. The transient voltage is influenced by the current distribution within the structure. A characteristic of a voltage of an output terminal of a solar panel to ground caused by a lightning is also investigated in this paper. The resonant frequency and the maximum voltage of the overvoltage are clarified. The resonant frequency is determined by inductances of the structure, a capacitance between a frame and an output terminal of a solar panel, and a stray capacitance of a solar panel. An oscillation determined by the length of the struck structure is superimposed in the case of an indirect lightning. The characteristic of the maximum induced voltage depends on the electromotive force generated by the magnetic flux which links with a frame of a solar panel. An overvoltage caused by an indirect lightning can be obtained by an equivalent circuit with mutual impedances between a struck structure and a structure for a solar panel. The calculation can be easily carried out by the Electro-Magnetic Transients Program.

FULL-WAVE SEMI-ANALYTICAL MODELING OF PLANAR SPIRAL INDUCTORS IN LAYERED MEDIA

In this paper, we present a full-wave semi-analytical solution to calculate the self and mutual impedances of two coupled spiral inductors with rectangular cross sections. In low-frequency electromagnetism, the self and mutual impedance of planar spiral inductors can be obtained based on the eddy current approximation, where the displacement current is disregarded. As the frequency increases, the size of the system can be designed to be smaller. However, the displacement current becomes more important in inductively-coupled systems. By directly deriving the Maxwell's equations without the eddy current assumption, the obtained full-wave model could be applied to both homogeneous and planarly layered media for wireless power transfer systems. Compared to the traditional methods, the newly derived impedances show a considerable discrepancy at GHz frequencies for millimeter-sized inductors, indicating the significance of the displacement current if the operating frequency of wireless power transmission reaches the GHz-range.

An Improvement of Closed-Form Formula for Mutual Impedance Computation

In this paper, we present an improvement of a closed-form formula for mutual impedance computation. Depending on the center-to-center spacing between two rectangular microstrip patch antennas, the mutual impedance formula is separated into two parts. The formula based on synthetic asymptote and variable separation is utilized for spacings of more than 0.5 λ0. When the spacing is less than 0.5 λ0, an approximate formula is proposed to improve the computation for closely spaced elements. Simulation results are compared to computational results of mutual impedances and mutual coupling coefficients as functions of normalized center-to-center spacing in both E- and H-plane coupling configurations. A good agreement between simulation and computation is achieved.

Stray Capacitance Between Magnetic Resonance Imaging Coil Elements: Models and Application to Array Decoupling

The role of capacitive coupling between RF coil elements of MRI arrays is studied extensively in this paper and comprehensive models are obtained. At higher MRI frequencies, capacitive coupling greatly impacts coil coupling and therefore cannot be neglected. We compare lumped and distributed capacitance models and show that they correctly predict impedance variations due to stray and intentional mutual capacitance. The distributed model takes into account the dispersed nature of the mutual impedance, and it is more accurate than the lumped model. The value of stray capacitance obtained by fitting simulated results is shown to depend strongly on substrate and phantom permittivity, while being mostly invariant to changes in frequency. A novel result of this investigation is a method of completely eliminating mutual impedance between adjacent coils, including the mutual resistance. Until recently it was believed that only mutual reactance could be eliminated with lossless passive circuits. The SNR performance of two and four coil arrays with varying degrees of coupling is compared, showing that there is no SNR degradation when the mutual resistance is eliminated in addition to mutual reactance. This result has applications in arrays used in transmission, where mutual resistance leads to losses that degrade transmit efficiency.

Numerical Analysis of Isotropy Electromagnetic Sensor Measurement Error

Abstract The article deals with classification and quantification of electromagnetic field measurement errors in case an isotropic sensor as a field probe is used. The focus is mainly on the error of measurement method, resulting from mutual interaction of the field probe sensors associated with the origin of the so-called mutual impedance.

New accurate fault location algorithm for parallel transmission lines using local measurements

This paper presents a new accurate fault location algorithm for parallel transmission lines based on the distributed parameter line model. The new method requires only voltages and currents from one end of parallel lines. Based on sequence networks and boundary conditions, equations can be derived to obtain the fault location. The new method fully considers shunt capacitance of the line, and mutual impedance and mutual admittance between the lines by using accurate model for both positive- and zero- sequence circuits, and obviates the need of iterative process to compensate for the capacitance. The method is independent of fault resistance, remote infeed and source impedances. EMTP simulation studies have been conducted to generate fault cases under various fault conditions to validate the proposed method. The results have shown that the developed algorithm can achieve highly accurate fault location estimates.

Simple Approach to Predict Near Field Electromagnetic Interference in SMPS Using the Induced EMF Method

The electromagnetic interference generated by a switched-mode power supply on a victim circuit is analysed representing their electromagnetic field coupling by two-port networks. The essential electromagnetic interference sources of the switched-mode power supplies are individuated and their mutual impedances with the victim circuit are calculated by the induced EMF method. The two-port representation of the field coupling allows the noise voltage on a victim circuit to be predicted. As a victim circuit a circular loop representing a magnetic field probe used in near field measurements is considered. The approach is applied to a flyback converter and validated through experimental measurements.

A Two Element Plasma Antenna Array

This theoretical study presents the characteristics of plasma monopole antennas in the VHF/UHF range using finite difference time domain (FDTD) simulation. Results show that more broadband characteristics can be obtained by increasing the diameter of the plasma tube and that the minor lobes diminish in intensity as diameter increases. Furthermore, the nulls are replaced by low level radiation. Since the collision frequency, which is a function of gas pressure, represents the loss mechanism of plasma, decreasing its value increases the gain and radar cross section (RCS) of the antenna. Theoretical modeling shows that at higher plasma frequencies with respect to the signal frequency, the gain and radar cross section of the plasma antenna are high enough and that the impedance curves are altered as the plasma frequency varies. Using these preliminary studies, mutual impedance and gain of a broadside array of two parallel side-by-side plasma elements is presented.

Mutual coupling compensation for a practical VHF/UHF Yagi‐Uda antenna array

The performance of an antenna array is considerably affected by mutual coupling effects between antenna elements. When a large number of antenna elements are located close to each other, mutual coupling becomes more significant. In this study, by using a new mutual impedance matrix, a decoupling methodology for compensating mutual coupling effects in a practical very high frequency (VHF)/ultra high frequency (UHF) Yagi-Uda antenna array is introduced. No previous publications have studied VHF/UHF Yagi-Uda antenna arrays in this context. In the proposed scheme, extreme care has been taken to account for both self- and mutual impedance related to mutual coupling effects. Experimental and simulation results show that using the proposed method, a perfect decoupling is achieved. The application of high-resolution direction of arrival (DOA) estimation algorithms in decoupled experimental data leads to excellent performance of DOA estimation, in terms of accuracy and resolution. In addition, it is concluded (from experimental and simulation results) that mutual coupling effects between array elements as well as the root-mean-square error of estimated parameters depend on the direction of arrival. It is also deduced that in the presence of mutual coupling, estimation of signal parameter via rotation invariance techniques algorithm performs better than other subspace-based algorithms.

Beam-Steering Antenna using Bending Fluidic Actuators

A beam steering antenna is described which uses bending parasitic elements controlled by bending fluidic actuators (BFAs). The structure is a monopole antenna surrounded by four parasitic elements on a groundplane. The BFAs are controlled by linear controllers located below the groundplane. In this way, the parasitic elements comprise BFAs and the action of bending them away from the monopole to alter the mutual impedances is analogous to the reactance variation of switched parasitic antenna. When a parasitic element is not bent, it can act as a reflector or director for low-gain beam formation, while the other parasitic element is bent away from the monopole and hence not affecting the beam. Two configurations have been realized with different numbers of bent parasitic elements, and experimental results for these configurations are presented. Patterns with low cross correlations can be attained while keeping the return loss below a reasonable limit.

Fault Current Distribution and Pole Earth Potential Rise (EPR) Under Substation Fault

Abstract New high-voltage (HV) substations are fed by transmission lines. The position of these lines necessitates earthing design to ensure safety compliance of the system. Conductive structures such as steel or concrete poles are widely used in HV transmission mains. The earth potential rise (EPR) generated by a fault at the substation could result in an unsafe condition. This article discusses EPR based on substation fault. The pole EPR assessment under substation fault is assessed with and without mutual impedance consideration. Split factor determination with and without the mutual impedance of the line is also discussed. Furthermore, a simplified formula to compute the pole grid current under substation fault is included. Also, it includes the introduction of the n factor which determines the number of poles that required earthing assessments under substation fault. A case study is shown.