A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies

Olsen, R.G.; Willis, M.C.

doi:10.1109/61.489370

Cited by 77 publications

(29 citation statements)

References 15 publications

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“…The scattered electric field can be expressed in terms of the vector potential A and the scalar potential ϕ , and according to the thin wire approximation [7,8] only the axial component of the magnetic potential differs from zero and it can be written:…”

Section: The Generalized Telegrapher's Equations For a Horizontal Gromentioning

confidence: 99%

Boundary element modeling of horizontal grounding electrodes using the set of generalized telegrapher’s equations

Poljak

Drissi

Goić

2009

Mesh Reduction Methods

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The analysis of a horizontal grounding electrode has been carried out using the set of generalized telegrapher's equations. The integro-differential relationships arising from the full wave model are numerically handled via the GalerkinBubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the current and voltage induced along the horizontal electrode are given in the paper.

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Section: The Generalized Telegrapher's Equations For a Horizontal Gromentioning

confidence: 99%

Boundary element modeling of horizontal grounding electrodes using the set of generalized telegrapher’s equations

Poljak

Drissi

Goić

2009

Mesh Reduction Methods

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“…1. The wire is assumed to be perfectly conducting and the wire dimensions satisfy the well known thin wire approximation [4,7,8,11], so the current along the wire is z-directed only.…”

Section: Integral Equation For the Induced Current Along The Electrodementioning

confidence: 99%

“…This approach, however, suffers from too long computational time for the evaluation of broadband frequency spectrum, consesquently, the rigorous approach is often regarded as too complex for practical applications, especially for large grounding grids and it should be avoided wherever is possible [8]. A useful study on validity of quasistatic theory compared to full wave theory was presented in [8]. One possible way of avoiding the computation of Sommerfeld integral is the use of modified image theory (MIT) [5,9].…”

Section: Introductionmentioning

confidence: 99%

“…The analysis method presented in this paper is based on the Pocklington integro-differential equation formulation [4,7] arising from the antenna theory, and also proposes a simplified reflection coefficient approach for the treatment of the half-space problem (instead of analytically demanding and numerically time consuming Sommerfeld integral approach [4,5,[7][8][9][10][11]) is also proposed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wire Antenna Model for Transient Analysis of Simple Grounding Systems, Part I: The Vertical Grounding Electrode

Poljak¹,

Dorić²

2006

PIER

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Abstract-The paper deals with the transient impedance calculation for simple grounding systems. The mathematical modelmodel is based on the thin wire antenna theory. The formulation of the problem is posed in the frequency domain, while the corresponding transient response of the grounding system is obtained by means of the inverse Fourier transform. The current distribution induced along the grounding system due to an injected current is governed by the corresponding frequency domain Pocklington integro-differential equation. The influence of a dissipative half-space is taken into account via the reflection coefficient (RC) appearing within the integral equation kernel. The principal advantage of the RC approach versus rigorous Sommerfeld integral approach is simplicity of the formulation and significantly less computational cost.The Pocklington integral equation is solved by the Galerkin Bubnov indirect boundary element procedure thus providing the current distribution flowing along the grounding system. The outline of the Galerkin Bubnov indirect boundary element method is presented in Part II of this work.Expressing the electric field in terms of the current distribution along the electrodes the feed point voltage is obtained by integrating the normal field component from infinity to the electrode surface.The frequency dependent input impedance is then obtained as a ratio of feed-point voltage and the value of the injected lightning current. The frequency response of the grounding electrode is obtained multiplying the input impedance spectrum with Fourier transform of the injected current waveform.Finally, the transient impedance of the grounding system is calculated by means of the inverse Fourier transform. The vertical and horizontal grounding electrodes, as simple grounding systems, are analyzed in this work. The Part I of this work is related to the vertical 150 Poljak and Doric electrode, while Part II deals with a more demanding case of horizontal electrode.

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“…The antenna model of the grounding systems composed from straight conductors is based on the set of Pocklingtonʼs integro-differential equations for curved wires. The effect of a lossy ground is taken into account via the corresponding reflection coefficient [5] thus avoiding the rigorous approach based on the analytically demanding and numerically time consuming Sommerfeld integrals [8]. The set of Pocklington equations is numerically treated by means of the Galerkin-Bubnov scheme of the Boundary Element Method (GB-IBEM) with isoparametric elements [9].…”

Section: Introductionmentioning

confidence: 99%

Boundary element modeling of complex grounding systems: study on current distribution

Poljak

Cerdic

Dorić

et al. 2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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The assessment of current distribution induced along complex grounding systems has been undertaken using the corresponding antenna model and the set of Pocklington integro-differential equations for curved wires. The set of Pocklington equations is numerically handled via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM) featuring the isoparametric elements. Some illustrative numerical results for the current distribution are presented in the paper.

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A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies

Cited by 77 publications

References 15 publications

Boundary element modeling of horizontal grounding electrodes using the set of generalized telegrapher’s equations

Boundary element modeling of horizontal grounding electrodes using the set of generalized telegrapher’s equations

Wire Antenna Model for Transient Analysis of Simple Grounding Systems, Part I: The Vertical Grounding Electrode

Boundary element modeling of complex grounding systems: study on current distribution

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