Damir Cavka

A Comparison of Frequency-Dependent Soil Models: Application to the Analysis of Grounding Systems

We present a review and comparison of different models representing the frequency dependence of the soil electrical parameters (conductivity and permittivity). These models are expressed in terms of curve-fit expressions for the soil conductivity and relative permittivity, which are based on experimental data. Six available models/expressions are discussed and compared making reference to two sets of experimental data. It is shown that the soil models by Scott, Smith-Longmire, Messier, and Visacro-Alipio predict overall similar results, which are in reasonable agreement with both sets of experimental data. Differences between the soil models are found to be more significant at high frequencies and for low-resistivity soils. The causality of the considered models is tested using the Kramers-Kronig relationships. It is shown that the models/expressions of Smith-Longmire, Messier, and Portela satisfy the Kramers-Kronig relationships and thus provide causal results. The soil models are applied to the analysis of grounding systems subject to a lightning current. A full-wave computational model is adopted for the analysis. The analysis is performed considering two cases: 1) a simple horizontal grounding electrode, and 2) a realistic grounding system of a wind turbine. Two current waveforms associated with typical first and subsequent return strokes are adopted for the representation of the incident lightning current. In agreement with recent studies, simulations show that the frequency dependence of the soil parameters results in a decrease of the potential of the grounding electrode, with respect to the case where the parameters are assumed to be constant. It is found that the models/expressions by Scott, Smith-Longmire, Messier, and Visacro-Alipio predict similar levels of decrease, which vary from about 2% (ρLV = 20 Ω·m and first stroke) up to 45% (ρLV = 10 000 Ω·m and subsequent stroke). On the other hand, the models of Portela and Visacro-Portela predict significantly larger levels of the decrease, especially for very high resistivity soils. Furthermore, in the case of a high resistivity soil (10 000 Ω·m), the Visacro-Alipio expression predicts a longer risetime for the grounding potential rise, compared to the predictions of Scott, Smith-Longmire, and Messier models.

A Simple Finite Element Model of Heat Transfer in the Human Eye

A simple finite element 2D model of the human eye is developed to calculate the steady-state temperature distribution. The mathematical model of the eye is based on the Pennes bio-heat transfer equation. Problem is solved using the weak formulation and the Galerkin-Bubnov procedure. The study was performed to determine the effects of various values of thermal conductivity of lens on temperature distribution inside human eye and also the effects due to changes in ambient temperature and blood temperature

Some computational aspects of using current and voltage sources in electromagnetic models of lightning return strokes

The paper deals with some computational aspects of modeling the lightning return strokes using the full wave model. The electromagnetic model of lightning return stroke is based on the thin wire antenna theory and the related Pocklington integro-differential equation in the frequency domain while the corresponding transient response is obtained by means of hybrid (analytical and numerical) version of the Inverse Fourier Transform. The Pocklington equation is solved by the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). Special attention is given to the computational differences arising from the usage of current and voltage source, respectively.

Finite element model of the human head exposed to electrostatic field generated by Video Display Units

The goal of this paper is to investigate interaction between electrostatic field of video display units (VDUs) and human head in front of it. Special attention is given to the field at the surface of the face. The finite element model for assessment of the electrostatic field, by solving Laplace equation for the electric potential, is implemented. The electrostatic field is calculated for two different faces and for two different types of the domain and then compared with results obtained by the finite difference method. The advantage of the presented numerical method is a high resolution and a higher accuracy

GB-IBEM model of vertical antenna above, below and penetrating ground

This paper deals with an assessment of current distribution along vertical antenna penetrating the ground. The model is based on the integro-differential equation of Pocklinghton type together with rigorous Sommerfeld representation of the fields due to an interface. The corresponding integral equation is treated with the Galerkin-Bubnov variant of Indirect Boundary Element Method. The antenna is excited by the voltage source, as well as by the equivalent current source, which is incorporated into the model as a boundary condition.

Transient analysis of ring shaped grounding electrode using isoparametric quadratic elements

The paper deals with transient analysis of ring shaped grounding electrodes using isoperametric quadratic elements. The formulation in the frequency domain is based on the thin wire antenna theory and the related Pocklington integro-differential equation while the corresponding transient response is obtained by means of the Inverse Fourier Transform (IFT). The Pocklington integro-differential equation is solved by the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) featuring the use of isoparametric quadratic elements for the current distribution approximation.

Electrostatic field around human head in front of Video display unit: Field as a function of display - face distance

The goal of this paper is to investigate correlation between electrostatic field of video display units (VDUs) generated around human head located in front of VDU and display-face distance. The mathematical model is based on the Laplace equation for the electrostatic potential. The finite element model for the assessment of the electrostatic field is derived. The electrostatic field is calculated for different distances between display and the human head and for different sizes of display, respectively. Results were compared with results obtained by the finite difference method (FDM). The advantage of the presented numerical method is a high resolution and a higher accuracy, compared to the FDM results.

On the Concept of Grounding Impedance of Multipoint Grounding Systems

An N-port equivalent circuit approach is adopted to model a multipoint grounding system, N being the number of injection points. A methodology is proposed to determine the parameters of the N-port equivalent circuit from either numerical simulations or experimental measurements. For the case of a symmetrical grounding system, analytical closed-form expressions are derived for the equivalent parameters of the N-port circuit. We show that the concept of the equivalent input impedance (harmonic impedance) could be used in the case of a symmetrical multipoint grounding system. We show also that the experimental evaluation of the impedance of a grounding system using a single injection point is a conservative engineering practice, since the obtained impedance might be overestimated at high frequencies.

On the evaluation of input impedance and transient impedance for grounding electrodes using antenna theory

Purpose – The purpose of this paper is to propose a fast, accurate and efficient algorithm for assessment of input impedance and consequently the evaluation of transient impedance of the grounding electrode. Design/methodology/approach – The mathematical model is based on the thin wire antenna theory and related Pocklington integro-differential equation in the frequency domain, which is numerically treated via Galerkin-Bubnov variant of the indirect boundary element method (GB-IBEM). Two different approaches, scattered voltage method (ScVM) and induced electromotive force – boundary element method (IEMF-BEM), for input and transient impedance are discussed in detail. Extensive numerical experiments have been undertaken to analyze numerical sensitivity of the methods. Findings – Although it was widely used so far, the ScVM, was shown to be unsuitable for the grounding impedance assessment because results are dependent on the number of elements used in the numerical solution. On the other hand, the other me...

Modeling of Tesla’s transmitter using the wire antenna theory with ground effects included

According Teslapsilas idea his magnifying transmitter has been designed not only to efficiently emit Hertzian waves, but also to transmit power at large distances. Analysis of Teslapsilas transmitter by using the wire antenna theory and reflection coefficient approximation is carried out in this work. The radiating part of the Teslapsilas transmitter is represented by an equivalent monopole antenna driven by an ideal current source thus replacing the Teslapsilas transformer. The frequency domain formulation is based on a homogeneous Pocklington integro-differential equation. The ground effects are taken into account via the corresponding reflection coefficient appearing within the integral equation kernel. Solving the Pocklington equation via the Galerkin Bubnov variant of the Indirect Boundary Element Method (GB-IBEM) the current distribution along the monopole antenna is assessed. Knowing the current distribution along the vertical monopole the radiated electric field is obtained by integrating the induced current. Numerical results for the monopole current and the related irradiated field are presented in the paper. The case studies of free space, perfect ground and imperfectly conducting half-space have been considered. This paper should be regarded as an extension of the previous work on the subject.