J. A. Brandão Faria

On the modal analysis of asymmetrical three-phase transmission lines using standard transformation matrices

Fortescues transformation, Clarkes transformation and Karrenbauers transformation are all well-known tools which can be used to conduct a modal analysis of perfectly balanced transposed three-phase power transmission lines. For untransposed asymmetrical lines, however, such standard transformations fail. Nevertheless, all these transformation matrices can still play an important role in determining a first order approximation of the exact modal transformation. This paper shows how this can be done by employing a perturbation technique approach. In addition to the theoretical aspects discussed, some application examples concerning a vertical and a triangular line are also presented for illustrative purposes.

Modal Analysis of Untransposed Bilateral Three-Phase Lines: A Perturbation Approach

Modal analysis of three-phase power lines exhibiting bilateral symmetry leads to modal transformation matrices that closely resemble Clarkes transformation. We develop a perturbation theory approach to justify, interpret, and gain understanding of this well known fact. Further, we show how to find new frequency dependent correction terms that once added to Clarkes transformation lead to improved accuracy.

Electromagnetic foundations of electrical engineering

PREFACE. To the Electrical Engineer Practitioner. To the Student. To the Instructor. ACKNOWLEDGEMENTS. PROJECT PORTFOLIO. Analysis of a power delivery system. Cylindrical type transmission lines. DC current transducer. Determination of the conductivity of a circular conducting disk. Directional coupler analysis. Ill-defined grounding problems. Induction machine analysis. Line matching technique using an exponential transmission-line section. Linear variable differential transformer. Magnetic actuator and sensor device. Overhead-line protection by ground-wires. Power line carrier communication. Pseudo-balanced three-phase lines. Screened high-voltage three-phase installation. Shielded three-phase cable analysis. Three-route microwave splitter. Transmission-line system with balun transformer for even to odd-mode conversion. Transmission-line system with transformer-stage matching. Two-way loudspeaker analysis. Variable reluctance transformer. PART I: A BRIEF OVERVIEW. INTRODUCTION. CHAPTER 1: BASIC FIELD VECTORS. 1.1: The Electric and Magnetic Field Vectors. 1.2: Constitutive Relations. 1.3: Units and Notation. 1.4: Fundamental Concepts of Voltage and Current Intensity. PART II: STATIONARY FIELD PHENOMENA. INTRODUCTION. CHAPTER 2: ELECTROSTATICS. 2.1 Fundamental Equations. 2.2 Gradient Electric Field, Electric Potential, Voltage, Kirchhoffs Voltage Law. 2.3 Electric Charge, Electric Displacement Vector. 2.4 Dielectric Media, Permittivity, Polarization, Dielectric Strength. 2.5 Conductors in Electrostatic Equilibrium. 2.6 Application Example (Filament of charge). 2.7 Capacitor, Capacitance, Electric Energy. 2.8 Application Example (Two-wire transmission line). 2.9 Multiple Conductor Systems. 2.10 Application Example (Electric coupling in printed circuit boards). 2.11 Electric Forces and Torques. 2.12 Homework Proposed Problems. CHAPTER 3: STATIONARY CURRENTS. 3.1 Fundamental Equations. 3.2 Conductivity, Current Density, Electric Circuits. 3.3 Current Intensity, Kirchhoffs Current Law. 3.4 Resistor, Conductance, Resistance, Ohms Law. 3.5 Application Example (The potentiometer). 3.6 Application Example (The Wheatstone bridge). 3.7 Joule Losses, Generator Applied Field. 3.8 Generator Electromotive Force, Power Balance. 3.9 Homework Proposed Problems. CHAPTER 4: MAGNETIC FIELD OF STATIONARY CURRENTS. 4.1 Fundamental Equations. 4.2 Amperes Law, Magnetomotive Force, Magnetic Voltage. 4.3 Magnetic Induction Field, Magnetic Induction Flux. 4.4 Application Example (Power line magnetic fields). 4.5 Magnetic Materials, Ferromagnetic Media, Saturation and Hysteresis. 4.6 Magnetic Circuits. 4.7 Application Example (Three-legged transformer). 4.8 Magnetic Reluctance. 4.9 Inductor, Inductance, Magnetic Flux Linkage, Magnetic Energy. 4.10 Application Example (Coaxial cable). 4.11 Hysteresis Losses. 4.12 Multiple Circuit Systems. 4.13 Magnetic Forces and Torques. 4.14 Application Example (U-shaped electromagnet). 4.15 Homework Proposed Problems. PART III: SLOW TIME-VARYING FIELDS. INTRODUCTION. CHAPTER 5: MAGNETIC INDUCTION PHENOMENA. 5.1 Fundamental Equations. 5.2 Gradient and Induction Electric Fields, Potential Vector. 5.3 Revisiting the Voltage Concept. 5.4 Induction Law. 5.5 Application Example (Magnetic noise effects). 5.6 Voltages and Currents in Magnetically Multicoupled Systems. 5.7 Application Example (Magnetic coupling in printed circuit boards). 5.8 Eddy Currents. 5.9 Generalization of the Induction Law to Moving Circuit Systems. 5.10 Application Example (Electromechanical energy conversion). 5.11 DC Voltage Generation. 5.12 AC Voltage Generation. 5.13 Homework Proposed Problems. CHAPTER 6: ELECTRIC INDUCTION PHENOMENA. 6.1 Fundamental Equations. 6.2 Displacement Current, Generalized Amperes Law. 6.3 Charge Continuity Equation. 6.4 Revisiting the Current Intensity Concept. 6.5 Application Example (Capacitor self-discharge). 6.6 Voltages and Currents in Electrically Multicoupled Systems. 6.7 Homework Proposed Problems. CHAPTER 7: LUMPED PARAMETERS CIRCUIT ANALYSIS. 7.1 Introduction. 7.2 Steady-State Harmonic Regimes. 7.3 Transformer Analysis. 7.4 Transient Regimes. 7.5 Homework Proposed Problems. PART IV: RAPID TIME-VARYING FIELDS. INTRODUCTION. CHAPTER 8: ELECTROMAGNETIC FIELD PHENOMENA. 8.1 Electromagnetic Waves. 8.2 Poyntings Theorem, Poyntings Vector, Power Flow. 8.3 Time-Harmonic Fields, Field Polarization, RMS Field Values. 8.4 Phasor-Domain Maxwell Equations, Material Media Constitutive Relations. 8.5 Application Example (Uniform plane waves). 8.6 Complex Poyntings Vector. 8.7 Application Example (Skin effect). 8.8 Homework Proposed Problems. CHAPTER 9: TRANSMISSION LINE ANALYSIS. 9.1 Introduction. 9.2 Time-Domain Transmission-Line Equations for Lossless Lines. 9.3 Application Example (Parallel-plate transmission line). 9.4 Frequency-Domain Transmission-Line Equations for Lossy Lines. 9.5 Frequency-Domain Transmission-Line Equations for Lossless Lines. 9.6 Application Example (Line matching techniques). 9.7 Multiconductor Transmission Lines. 9.8 Application Example (Even and odd modes). 9.9 Homework Proposed Problems. APPENDICES. Appendix 1: Formulas from Vector Analysis. Appendix 2: Lorentz Transformation. Appendix 3: Elements of Complex Algebra. Appendix 4: Elements of Fourier Analysis. BIBLIOGRAPHY. INDEX.

Overhead three-phase transmission lines-nondiagonalizable situations

Physically realizable transmission lines exist to which the standard modal theory does not apply, since ZY diagonalization cannot always be undertaken successfully. The nondiagonalizable conditions for typical overhead three-phase lines are established. Algorithms are described and implemented to synthesize concrete nondiagonalizable configurations. Numerical examples are presented and discussed. >

Wave Propagation in Polyphase Transmission Lines a General Solution to Include Cases Where Ordinary Modal Theory Fails

The solution of transmission line equations is usually written as a superposition of so called natural modes of exponential type. These are obtained through the use of a suitable transformation that decouples the original sets or N simultaneous 2nd order wave equations for voltages and currents into N independent equations. For such a transformation to exist the fundamental product matrix ZY must be diagonalizable. In a previous paper it has been shown that physically realizable transmission lines are possible for which ZY is not diagonalizable and to which ordinary modal theory does not apply. In the present paper a new generalized modal theory is developed for the purpose of including non-diagonalizing cases.

Theory of Magnetic Transmission Lines

This paper presents, for the first time, the frequency-domain theory of magnetic transmission lines, i.e., transmission lines where electromagnetic energy guidance is assured by means of two magnetic-flux carrying parallel magnetic wires, as opposed to the ordinary situation of two current carrying parallel electric wires (an electric transmission line). Propagation equations for the fundamental quasi-TEM mode are established and solved. Wave parameters are analyzed. A transmission matrix is described.

The effect of randomly earthed ground wires on PLC transmission-a simulation experiment

The analysis of an almost periodic lattice of cascaded line segments with individual lengths randomly distributed around a typical mean value is presented. The analysis considers an interphase balanced antisymmetric-type carrier transmission and makes use of a modal decomposition technique. Each line segment is assigned a two-port network representation whose intrinsic propagation parameters are established. The transmission matrix of the overall chain is obtained, and from it the chain propagation parameters (attenuation, velocity, surge impedances) are computed. The analysis and numerical results presented show that even slight random perturbations of line periodicity are sufficient to render unnoticeable any sharp variations in attenuation, velocity, and surge impedance. >

Direct TD analysis of PLC channels in HV transmission lines with sectionalized shield wires

The continuity of shield wires is often broken for losses reduction purposes in high voltage transmission lines. The accurate simulation of the effects of this practice on power line communications in multiconductor transmission lines is performed in the time domain by means of a finite-difference method. Losses in wires and ground are accounted for by means of transient per unit length parameters and recursive convolution. The method overcomes most of the usual problems encountered by frequency-domain modal analysis techniques.

Approximate evaluation of the wave propagation parameters of MF TL communication systems for mine tunnels using image theory

Mine tunnel communications are migrating to wireless; however, medium frequency (MF) communications based on conductor-to-wall transmission line (TL) structures still exist and can be used as emergency or backup systems. This research, addressing MF TL communication systems, is aimed at the finding of simple approximated expressions of the wave propagation parameters characterizing the transmission properties of such systems: attenuation, phase velocity, and characteristic impedance. Bearing in mind the variety of tunnels’ geometries and the lack of rigorous information about the surrounding soil electromagnetic properties, it turns clear that general accurate solutions of the problem are out of reach in a general formulation. In this work, a tunnel model with an equivalent circular cross section and a homogeneous soil with average conductivity is adopted and analyzed. The novelty of the analysis is its intrinsic simplicity due to the employment of image theories, which are applied not only to obtain the ...Mine tunnel communications are migrating to wireless; however, medium frequency (MF) communications based on conductor-to-wall transmission line (TL) structures still exist and can be used as emergency or backup systems. This research, addressing MF TL communication systems, is aimed at the finding of simple approximated expressions of the wave propagation parameters characterizing the transmission properties of such systems: attenuation, phase velocity, and characteristic impedance. Bearing in mind the variety of tunnels’ geometries and the lack of rigorous information about the surrounding soil electromagnetic properties, it turns clear that general accurate solutions of the problem are out of reach in a general formulation. In this work, a tunnel model with an equivalent circular cross section and a homogeneous soil with average conductivity is adopted and analyzed. The novelty of the analysis is its intrinsic simplicity due to the employment of image theories, which are applied not only to obtain the capacitance and external inductance of the TL but also to obtain the soil return impedance. Closed-form approximate expressions of the MF TL wave propagation parameters are offered and discussed, their dependence on the frequency and on the position of the signal carrying conductor located inside the tunnel being disclosed.

Application of a harmonic expansion method approach to the computation of L and C matrices for open-boundary inhomogeneous multiconductor transmission-line structures with strong proximity effects present

A harmonic expansion method is utilised to determine the capacitance and inductance parameters of a few multiconductor transmission-line (MTL) structures comprising a set of dielectric-coated conductors in close contact seated on a ground plane. Results are presented in tabular form in order to provide microwave software developers with useful data for benchmarking purposes. In addition, an analysis of the effective permittivity characterizing the normal modes of the inhomogeneous MTL structures is presented.