White Paper By the Author John Horak of Basler Electric

A. One’s
imagination should be used to fill in the blanks. An inspection of Fig. 1 shows
that we have 3 current loops, but 4 currents are shown on the diagram. This
means we can actually only set up 3 voltage drop equations, and we will need to
take advantage of IG = IA + IB + IC to remove IG from directly being part of
the voltage drop equations.

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Abstract -
This paper reviews the basic equations for the sequence impedance of
transmission lines, including ground loop current flow, how neutral wires are
included in the equations, and how this impedance is transformed from an ABC
domain impedance to the 012 domain impedance. A side benefit of the approach taken
is that the paper shows how one calculates the sequence impedances of
untransposed power lines, including calculation of the off-diagonal (mutual)
elements of the sequence component 012 domain impedances. The paper also
addresses the calculation of mutual impedances between two parallel lines.

I.
INTRODUCTION

The paper
begins by analyzing system impedances in the ABC (physical or phase) domain,
first without any overhead ground wires, and then shows how the overhead ground
conductors are incorporated into the analysis. Then the paper shows the
translation of these ABC domain impedances to the 012 (sequence) domain, which
provides the zero sequence impedances, and other sequence impedances.
Thereafter, the paper discusses the calculation of mutual impedance coupling between
two parallel lines.

II. BASIC
ABC DOMAIN IMPEDANCE CONCEPTS

In Fig. 1
there are three phase current loops, A, B, and C, each passing through a common
neutral/ground. For this initial investigation, there is no independent
metallic neutral/ground conductor, so the phase currents sum together and
return through the earth in the current named IG. The phase A loop is shown as
a dotted line.

Each phase loop
in Fig. 1 has different impedance; each loop is defined by a different current
path, a different loop cross section area and, when magnetic core material is
involved, a different permeability of the material through which the flux
passes. To keep the drawing from becoming exceedingly complex, only the main
representative flux loops are shown and only for phase

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