EMTP® Overhead Lines

Overhead Line Modelling in EMTP®

An overhead line should not be modelled the same way for every study. The right representation depends on the transient — a temporary overvoltage, a switching surge and a lightning stroke stress the line over different time scales, frequency ranges and parts of the structure. This guide is the overhead-line companion to the line and cable model family: how to match the model to the phenomenon, what the series-impedance and shunt-admittance matrices contain, and which physical elements — earth return, skin effect, bundling, shield wires, towers and corona — actually matter for each study.

Reading time ≈ 26 min · EMTP® overhead-line guide

The line model you choose shapes the answer. For an overhead line, the representation can strongly affect the calculated overvoltage, travelling-wave behaviour, insulation stress, lightning performance, secondary-arc behaviour and protection response. So the same line is not modelled the same way for every transient. The single most important decision is to match the line representation to the frequency content of the phenomenon: a temporary overvoltage, a switching surge and a lightning surge occupy different time scales and frequency ranges and stress different parts of the structure, and a model that is fine for one can be inadequate for another.

This page is the overhead-line companion to the cable series. It defers the shared model-family theory — the distributed-parameter equations, the propagation constant and the full model taxonomy — to the general line and cable modelling page, and concentrates on what is specific to overhead lines: how to choose the model for the study, what the series-impedance and shunt-admittance matrices contain, and how earth return, skin effect, bundling, shield wires, towers and corona enter the model.

Abbreviations used on this page

EMTP®Electromagnetic Transients Program

EMTElectromagnetic transient

TOVTemporary overvoltage

VFTVery-fast-front transient

CP / FDConstant-parameter / frequency-dependent line model

PILumped pi-section line model

ULMUniversal Line Model (FD phase-domain)

\(Z'\) / \(Y'\)Per-unit-length series impedance / shunt admittance

\(\delta\)Skin depth

GMRGeometric mean radius

ACSRAluminium-conductor steel-reinforced

EHVExtra-high voltage

quasi-TEMQuasi-transverse-electromagnetic field

Key idea

Match the line model to the frequency content of the transient, not to habit. A model that is fine for a temporary overvoltage can be wrong for a lightning surge.
The slower the transient, the more line (and adjacent network) you must include; the faster the front, the more local detail — towers, footing, flashover — you need. This is a rule of thumb driven by wave attenuation, not a strict law.
The two outputs are the series-impedance matrix \(Z'(\omega)\) (voltage drop, damping, magnetic coupling, earth return) and the shunt-admittance matrix \(Y'(\omega)\) (charging current, capacitance, surge impedance, velocity).
What controls the parameters is physical: conductor geometry, height and spacing, bundling/GMR, soil resistivity, skin effect, shield wires and corona. Get the geometry right before refining the model.

Key terms used on this page

01Distributed (Bergeron) model

A travelling-wave line representation with propagation delay and reflections; the constant-parameter form is evaluated at a single frequency.

02Frequency-dependent line model

A line whose \(R'\), \(L'\) and earth-return vary with frequency — either modal (J. Marti) or phase-domain (the Universal Line Model).

03Modal / Clarke transformation

A change of variables that decouples a multiconductor line into independent modes; the transformation matrix is constant for transposed lines, frequency-dependent otherwise.

04Carson earth return

The classical impedance of conductors above a homogeneous, lossy earth — the standard overhead-line earth-return formulation.

05Complex image method

A closed-form approximation to Carson that replaces the lossy ground by an image conductor at a complex depth below the surface.

06Skin depth, \(\delta\)

The depth to which current penetrates a conductor at a given frequency; smaller at high frequency and in magnetic (steel) material.

07Potential-coefficient matrix, \(P\)

Relates conductor charges to voltages; its inverse is the Maxwell capacitance matrix.

08Geometric mean radius (GMR)

An equivalent radius capturing a stranded conductor’s internal inductance or a bundle’s effective size.

09Surge impedance

\(Z_0=\sqrt{L'/C'}\) — the ratio of voltage to current for a travelling wave on the line.

10Corona

Partial discharge at the conductor surface above inception; adds nonlinear capacitance and loss and attenuates steep fronts.

11Tower footing impedance

The transient impedance of the tower-to-earth connection; current-dependent through soil ionisation.

12Backflashover

Insulator flashover from tower to phase caused by the tower-top voltage rise after a stroke to the tower or shield wire.

Section 1

Match the model to the phenomenon

Because the line model affects the calculated overvoltage, travelling-wave behaviour, insulation stress, lightning performance, secondary-arc behaviour and protection response, the phenomenon — not habit — should set the representation. A temporary overvoltage, a switching surge and a lightning surge do not stress the line in the same way, so a model that is acceptable for a low-frequency overvoltage may be inadequate for a lightning study, and each stress also drives a different design decision.

Each stress drives a different design decision

In overhead-line design the main voltage stresses are power-frequency voltage (especially under contamination), temporary overvoltages (faults, load rejection, ferroresonance), slow-front overvoltages (switching and disconnector operations) and fast-front overvoltages (mainly lightning). Each controls a different design parameter: lightning performance influences shield-wire position, tower footing resistance and backflashover; temporary overvoltages influence arrester rating and insulation withstand; contamination influences creepage distance; switching and lightning overvoltages influence strike distance and insulator-string length. For EHV transmission, switching surges often control air clearance while contamination controls creepage; for distribution lines, lightning is usually the dominant stress.

The purpose of EMTP® modelling, then, is not simply to build a line model — it is to build the line model that is appropriate for the phenomenon being studied. The frequency bands overlap rather than being sharply bounded; CIGRE and IEC 60071-4 group them as low-frequency, slow-front, fast-front and very-fast-front.

Section 2

Lumped, distributed and frequency-dependent models

Overhead-line models fall into two broad families. A lumped-parameter model represents the line with discrete \(R\), \(L\), \(G\) and \(C\) — the nominal-PI section is the common form — and suits steady-state and low-frequency transients on electrically short lines. A distributed-parameter model represents the line as a travelling-wave system with propagation delay and reflections, and is required when the line is electrically long for the transient of interest.

\[ \lambda=\frac{v}{f} \]

\(\lambda\): wavelength, m
\(v\): wave propagation velocity (close to \(c\), slightly lower with earth-return effects), m/s
\(f\): frequency, Hz

A line is “electrically short” only when its length is a small fraction of the wavelength at the highest frequency of interest — a common rule of thumb is below about \(\lambda/10\). Equivalently, compare the line’s one-way travel time with the rise time of the transient and with the EMTP® time-step.

Within the distributed family, EMTP®-type programs offer a constant-parameter (Bergeron) model, evaluated at a single frequency, and frequency-dependent models. The frequency-dependent modal model (J. Marti) fits the line in modal coordinates with a constant transformation matrix; the frequency-dependent phase-domain model — the Universal Line Model of Morched, Gustavsen and Tartibi, with related auto-regressive moving-average (ARMA) fitting by Noda — works directly in phase quantities and handles untransposed and asymmetrical lines that defeat a constant modal transformation. The general taxonomy of these models is developed on the line and cable family page; here the point is to pick the family that matches the study.

Cascaded PI is not a free distributed model

A chain of nominal-PI sections can approximate travelling-wave behaviour, but it is inefficient and introduces spurious numerical oscillations at the section frequencies. When the line travel time is comparable to the transient front, prefer a true distributed (Bergeron) or frequency-dependent model rather than stacking PI sections.

Section 3

Matching the model extent to the transient

How much of the line to include depends on the transient. For power-frequency and temporary-overvoltage studies the whole line is usually included, but the frequency range is low, so a multiphase PI or constant-parameter line is often enough; phase-conductor asymmetry can matter, while shield wires, towers and footing impedance are usually omitted unless they bear on the study. For switching-overvoltage studies the whole line should normally be a distributed multiphase model — switching surges are travelling waves, so a lumped PI is rarely adequate for long lines — and frequency-dependent parameters may be needed where the earth-return mode affects the result. For lightning studies only a few spans around the strike point are modelled, but in much more detail: phase conductors, shield wires, towers, tower-footing impedance, insulator flashover and the relevant clearances, with conductor asymmetry, distributed parameters and sometimes corona. For very-fast-front studies only the local part near the disturbance is needed, but its high-frequency behaviour must be right.

A rule of thumb, not a law

The lower the frequency, the longer the line section to include; the faster the transient, the more local detail it needs. Treat this as a rule of thumb. The real driver is wave attenuation: steep, high-frequency surges attenuate quickly and produce local stress, so a short but detailed section suffices; slow, low-frequency surges propagate with little attenuation over the whole line, so the full line and the adjacent network must be represented.

Section 4

What to model — and what to leave out

An overhead line is more than its phase conductors. Depending on the study, the model may need phase conductors and their bundled subconductors, shield (earth) wires, towers and tower-footing impedances, insulator strings and flashover paths, tower geometry and clearances, corona, the earth-return path, transposition or asymmetry, and the terminal equipment, surge arresters and substation connections that set the reflections.

For low-frequency and switching studies the phase conductors dominate, and shield wires and towers can often be omitted. For lightning studies the shield wires, towers, footing impedance and insulator flashover become essential — a lightning surge does not only travel along the phase conductor; it may strike a shield wire or tower, raise the tower voltage, reflect from the footing impedance and cause backflashover across the insulator. A line model built for switching studies should not be reused blindly for lightning.

Section 5

Series impedance and shunt admittance

The electrical behaviour of phase conductors and shield wires is captured by two per-unit-length quantities. The series impedance is the longitudinal voltage drop — conductor resistance, internal inductance, the external magnetic field and earth return. The shunt admittance is the transverse current path between conductors and earth — mainly capacitance; the leakage conductance is small and usually neglected except for polluted or wet insulators, or corona.

\[ Z'(\omega)=R'(\omega)+j\omega L'(\omega) \qquad Y'(\omega)=G'+j\omega C' \]

\(Z'\): per-unit-length series-impedance matrix of the line, normally Ω/km or Ω/m
\(Y'\): per-unit-length shunt-admittance matrix, normally S/km or S/m
\(R',\ L'\): resistance and inductance per unit length
\(G',\ C'\): conductance and capacitance per unit length
\(\omega\): angular frequency, rad/s

\(R'\) and \(L'\) are frequency-dependent — through conductor skin effect and through the earth-return term. The air-geometry (external) inductance is essentially frequency-independent, so the low-frequency variation of \(L'\) comes mainly from the earth-return (Carson) contribution and the conductor’s internal inductance. \(C'\) is treated as frequency-independent over the overhead-line design range, and \(G'\) is neglected unless leakage or corona matters. Because these are per-unit-length quantities, the line length must use the same length basis: line constants in per km require the line length in km, and constants in per metre require it in metres — a mismatched basis is a common source of wrong EMTP® line parameters.

Section 6

The line equations in the time domain

The line equations describe how voltage and current change along the line: the change of voltage is set by the series resistance and inductance, and the change of current by the shunt conductance and capacitance. For a multiconductor line, voltage and current become vectors and the parameters become matrices, because the phase conductors and shield wires are electromagnetically coupled — a current in one phase affects the voltage in the others (mutual inductance), and a voltage on one conductor affects the charging current of the others (mutual capacitance). The line cannot, in general, be treated as independent single-phase circuits.

Modal versus phase-domain

EMTP® solves these coupled equations by decoupling them into modes — the modal (Clarke-type) transformation turns the matrices into nearly independent modes, each with its own velocity and attenuation. For ideal, transposed or reasonably symmetrical lines, modal-domain frequency-dependent models (such as J. Marti) are often adequate; for untransposed, multicircuit or strongly asymmetrical lines — where the modal transformation changes significantly with frequency — phase-domain models (such as the Universal Line Model) are usually more robust. The practical message is simply that coupled phase conductors and shield wires are solved with modal or phase-domain line models, and the choice follows the line’s symmetry; the line-equation solution page develops the propagation constant, characteristic admittance, modal and phase-domain fitting, passivity and Line Constants output in full.

Section 7

Series impedance: external and internal

The series impedance is conventionally split into an external and an internal part:

\[ Z' = Z'_{\text{ext}} + Z'_{\text{int}} \]

\(Z'_{\text{ext}}\): external impedance — magnetic field outside the conductor (air geometry plus the earth-return path)
\(Z'_{\text{int}}\): internal impedance — current distribution inside the conductor (resistance and internal inductance)

The split is useful because different physics controls each: the external part depends on conductor geometry, height, spacing and earth-return behaviour; the internal part depends on conductor material, radius, conductivity, permeability and frequency. For inductance the external part dominates; for resistance and frequency-dependent damping the internal part is important. The earth-return contribution sits in \(Z'_{\text{ext}}\) and is itself frequency-dependent — so frequency dependence is not confined to the internal term.

Section 8

Ground return: Carson and the complex image

The earth is part of the return path for overhead-line currents, especially for zero-sequence, ground-mode and unbalanced transients, so the earth-return impedance is an essential part of \(Z'\). The return current does not flow in a perfect ground plane: it spreads through the soil, and its distribution depends on frequency and soil resistivity through the complex penetration depth.

How deep the return current goes

\(p=\sqrt{\rho/(j\omega\mu)}\) is the complex earth-return penetration depth, where \(\rho\) is the soil resistivity (\(\Omega\cdot\text{m}\)), \(\omega\) the angular frequency (rad/s), \(\mu\) the magnetic permeability (H/m) and \(j\) the imaginary unit. At higher frequencies \(p\) is small and the return current concentrates near the line; at lower frequencies, and for higher soil resistivity \(\rho\), it spreads deeper and wider — and the ground-return impedance rises. Earth return mainly affects the zero-sequence and ground-mode behaviour; the positive- and negative-sequence parameters are set by the conductor geometry, so ground return is less critical there. This is the engineering meaning behind the complex-image method; the detailed Carson or complex-image formula is normally handled by the Line Constants routine.

The classical overhead earth-return formulation is Carson’s (1926): the self and mutual impedances of conductors above a homogeneous, lossy half-space. Because Carson’s correction is an infinite series, EMTP®-type programs commonly use the complex-image method (Deri, Tévan, Semlyen and Castanheira, 1981), which replaces the lossy ground by an image conductor at a complex depth and reproduces Carson in closed form. Carson assumes a homogeneous earth and a quasi-TEM field, so its accuracy degrades at very high frequencies; the complex-image form is likewise accurate across the usual EMT band for homogeneous soil, while stratified or multilayer ground may need a more detailed model. Sunde’s formulas are also used, particularly where overhead and buried/grounding returns must be treated consistently.

Not the buried-cable methods

These are the overhead earth-return methods. The buried-cable counterpart is the Pollaczek integral and its Saad–Gaba–Giroux and Wedepohl–Wilcox approximations, covered on the cable designs & parameters page — do not mix the two. The ground-return model becomes decisive when shield wires, towers, faults to earth, induced voltages or common-mode transients are part of the study.

Section 9

Skin effect and internal impedance

Skin effect is why the series resistance and internal inductance change with frequency. At low frequency the current uses most of the cross-section; at high frequency it crowds toward the surface, within a skin depth:

\[ \delta=\sqrt{\frac{2}{\omega\mu\sigma}} \qquad R'_{\text{dc}}=\frac{1}{\pi r^{2}\sigma} \]

\(\delta\): skin depth, m
\(\omega\): angular frequency, rad/s
\(\mu=\mu_0\mu_r\): magnetic permeability, H/m
\(\sigma\): conductivity, S/m
\(R'_{\text{dc}}\): DC resistance per unit length, Ω/m
\(r\): conductor radius, m

As frequency rises, \(\delta\) falls, the effective area falls and the AC resistance rises, while the internal inductance falls as flux is excluded from the conductor interior. For non-magnetic aluminium or copper \(\mu_r\approx1\); a steel ACSR core has \(\mu_r\gg1\), so its skin depth is far smaller. The DC formula is a sanity check only — real conductors are stranded or ACSR, and for ACSR the aluminium area (not the steel) governs the DC resistance — so take conductor resistance from manufacturer or line-design data. EMTP® line-constants routines compute the frequency-dependent internal impedance automatically.

Section 10

Shunt capacitance and bundled conductors

The shunt capacitance is controlled almost entirely by geometry — conductor radius, height above ground, spacing between conductors and the presence of shield wires. It is found from a potential-coefficient matrix:

\[ C' = P^{-1} \]

\(C'\): capacitance matrix per unit length
\(P\): potential-coefficient matrix (relates conductor charges to voltages)

\(P\) maps charges to voltages; its inverse is the Maxwell capacitance matrix, whose off-diagonal terms are negative — so the matrix entries are not the physical conductor-to-conductor capacitances directly; those are obtained from it by the standard transformation. Practically: raising conductor height reduces capacitance to ground; reducing phase spacing increases inter-phase coupling; shield wires reshape the electrostatic field and the matrix. Check the geometry entered into the software — errors in height, spacing or shield-wire position feed straight into the capacitance and the surge behaviour.

Thin-wire approximation

Most line-constants formulas assume the conductor radius is small compared with its height and spacing — the thin-wire approximation — so the field can be found without modelling the conductor surface in detail. This is valid for ordinary overhead conductors, but should be reviewed for compact lines, very low clearances, bundles or conductors close to grounded metal.

Bundled conductors and GMR

A bundle of subconductors is normally represented by an equivalent radius or geometric mean radius (GMR) rather than every subconductor. Bundling increases the effective radius, lowers the surface field, raises capacitance and lowers surge impedance (less inductance), and improves corona and radio-interference performance. The equivalent representation is adequate for most studies; detailed high-frequency work may need the subconductors and spacers represented explicitly.

Section 11

Frequency-dependent parameters

An overhead line does not have one resistance and inductance at all frequencies — skin effect changes the conductor internal impedance and the earth-return term changes with frequency. For slow transients a constant-parameter model, evaluated at a single representative frequency, may be adequate; for switching surges, lightning and any study involving the ground mode, a frequency-dependent model is usually more appropriate. The ground-return (zero-sequence) mode is the dominant source of frequency dependence, through earth skin effect, which is exactly what a constant-parameter model misrepresents.

What gets it wrong

Frequency-dependent resistance sets the attenuation; frequency-dependent inductance sets the velocity and modal behaviour; a constant-parameter model can under- or over-damp the transient, and a model fitted over the wrong frequency range will mislead. Match the fitted range to the phenomenon — there is no benefit in a wideband model for a low-frequency study, and real risk in a low-frequency model for a fast-front study.

Section 12

Corona

Corona adds a nonlinear, voltage-dependent capacitance and loss once the conductor-surface field exceeds inception, slowing and rounding travelling surges and attenuating their high-frequency content. It matters mainly for lightning, incoming surges to substations and severe long-line switching overvoltages; for temporary overvoltages and most switching it is a secondary effect.

Neglecting corona may be conservative for some propagated-surge studies because it can overestimate peak and steepness, but this should not be treated as a blanket rule — the effect depends on the waveform, line length, voltage level, weather, conductor geometry and corona model. If the result is close to the insulation limit, state whether corona is included. The dedicated corona modelling page covers the charge–voltage (\(q\)–\(V\)) curve, Peek inception, static and dynamic (Suliciu) models, distributed corona branches and field-test validation.

Section 13

Line asymmetry and transposition

Overhead lines are usually geometrically asymmetrical — the phases are not in identical positions, and shield wires, tower geometry and earth return add to the asymmetry. For low-frequency and switching studies this affects phase coupling, sequence quantities and unbalanced behaviour: a transposed line can sometimes be represented by its average over the line, while an untransposed or partially transposed line may need the actual section geometry. For lightning, asymmetry matters when a detailed multiphase response is required and can be relaxed when the study is simplified to a single struck phase.

Do not assume symmetry

Do not assume a line is symmetrical unless the objective justifies it. For phase-to-phase overvoltages, unbalanced switching and coupling studies, asymmetry matters; for statistical screening an averaged representation may be acceptable. Asymmetry is also the reason frequency-dependent phase-domain models are preferred over modal models for untransposed lines (Section 6).

Section 14

Shield wires, towers and footing impedance

Shield (earth) wires are installed above the phase conductors to intercept lightning and reduce direct strikes. In lightning studies they are essential: a stroke to a shield wire or tower drives current through the shield wire, the tower and the footing impedance, and the resulting tower-top voltage rise can cause backflashover across the insulator string. For switching and temporary-overvoltage studies shield wires are often omitted unless they affect the phenomenon. Include them when lightning performance, tower voltage rise, backflashover, induced shield-wire voltages or ground-mode propagation is being studied — not mechanically.

For lightning the tower and its footing impedance are often as important as the conductors. When lightning current enters the tower, the tower-top voltage depends on the tower surge impedance, the footing impedance and the reflections along the tower and line. Include tower and footing models whenever tower voltage or backflashover is part of the study; the dedicated tower modelling for lightning page covers tower surge impedance, equivalent radius, travel time and the variable-impedance and multistorey tower models.

Footing impedance and what it controls

A high footing impedance raises the tower voltage and the backflashover risk; a low footing impedance drains the current to earth and reduces the insulator stress — but that benefit applies to backflashover (strokes to the tower or shield wire). For a shielding failure (a direct stroke to the phase conductor) the footing impedance usually has much less direct influence on the initial phase-conductor stress than it has for backflashover, although it may still affect later reflections and the wider network response. Footing impedance is also not a fixed number: it varies with frequency-dependent soil response and, in some high-current cases, can be reduced by soil ionisation — though simplified ionisation reduction should not be used as a default favourable correction; if investigated at all, treat it only as a clearly labelled, validated sensitivity case, because its ionisation/de-ionisation time lag can make it non-conservative for backflashover (see the HIFREQ soil and footing page). Model enough spans around the strike to capture the relevant reflections — the full line is not needed, because fast-front transients are local.

Section 15

Insulators and flashover

Insulators are not included in ordinary low-frequency line models unless flashover is being simulated. For lightning and insulation-coordination studies the insulator string is represented by a flashover model — a voltage–time withstand, a voltage-controlled switch or a leader-progression model. The detail should match the purpose: a simple withstand comparison if the aim is peak phase voltage without flashover; an explicit flashover path for backflashover or shielding-failure studies; an arc and post-fault representation for secondary-arc or reclosing studies. Keep the conductor model and the insulation model consistent — a very detailed line with an oversimplified flashover representation does not improve reliability. The flashover models themselves — voltage–time withstand, the voltage-controlled switch and leader progression — are developed on the air-gap and insulator flashover modelling page.

Section 16

Practical model selection and pre-run checks

For day-to-day work, choose the model in order. Identify the transient — temporary overvoltage, switching surge, lightning, power-quality, protection, secondary arc or very-fast-front. Set the frequency range and time scale: slow phenomena need more network length, fast phenomena need more local detail. Decide which physical parts matter — phase conductors may suffice for switching, while lightning needs shield wires, towers, footing impedance and flashover paths. Then choose the model type: PI for low-frequency or short lines, distributed where propagation and reflection matter, frequency-dependent where damping or the ground mode matters. For switching-overvoltage distributions, use a statistical multiple-run (Monte-Carlo) study with realistic circuit-breaker and surge-arrester models, and represent the terminations and sources (Thévenin or frequency-dependent network equivalents) with enough detail to give correct reflections; interpreting the resulting overvoltage distribution against the insulation strength (the statistical withstand check) belongs on the switching-surge dielectric strength page, not here. Finally, respect the numerical limits — the time-step must resolve the travel time of the shortest line section (the Courant condition).

Before running an overhead-line study, confirm:

The line length suits the transient type, and the model type suits the highest relevant frequency.
The line length uses the same length basis as the per-unit-length line constants (km with per-km constants, metres with per-metre).
The conductor geometry, phase coordinates, sequence and bundle data are correct.
Shield wires are included when lightning, tower voltage or backflashover is in scope.
The soil resistivity is reasonable, and frequency-dependent parameters are used where the ground mode or high-frequency behaviour matters.
Transposition — or the real untransposed geometry — is represented correctly.
Corona is considered where overvoltages may exceed inception.
Tower and footing models, and insulator flashover, are included for lightning and backflashover / shielding-failure studies.
The terminal network gives realistic reflections, and the time-step satisfies the Courant / travel-time limit.
The output is physically reasonable in propagation time, damping and reflection.

Section 17

Choosing the right overhead-line model

Overhead-line EMTP® modelling should be driven by the transient, not by a default model. Temporary-overvoltage studies need much of the line and network but a relatively simple conductor model; switching studies need a distributed multiphase model of the whole line; lightning studies need a detailed local model with shield wires, towers, footing impedance and insulator flashover.

Main takeaway

The two quantities that matter are the per-unit-length series-impedance matrix \(Z'\) (voltage drop, damping, magnetic coupling and earth return) and the shunt-admittance matrix \(Y'\) (charging current, capacitance and travelling-wave propagation). You do not need to reproduce every parameter formula by hand, but you must know what controls them — conductor geometry, height, spacing, bundling, soil resistivity, skin effect, shield wires and corona. A good overhead-line model is not the most complicated one; it is the one that includes the correct physical elements for the transient, uses a valid frequency range, and produces propagation, reflection and damping behaviour consistent with what is expected.

References

The standards, technical brochures, key papers and reference works behind this page.

J. A. Martinez-Velasco, Ed., Power System Transients: Parameter Determination. Boca Raton, FL, USA: CRC Press, 2010.
H. W. Dommel, Electromagnetic Transients Program Reference Manual: EMTP Theory Book. Portland, OR, USA: Bonneville Power Administration, 1986.
J. R. Marti, “Accurate modelling of frequency-dependent transmission lines in electromagnetic transient simulations,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-101, no. 1, pp. 147–157, Jan. 1982.
A. Morched, B. Gustavsen, and M. Tartibi, “A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables,” IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 1032–1038, Jul. 1999.
IEEE Std 1243-1997, IEEE Guide for Improving the Lightning Performance of Transmission Lines. New York, NY, USA: IEEE, 1997.
CIGRE Working Group C4.23, Procedures for Estimating the Lightning Performance of Transmission Lines – New Aspects, Technical Brochure 839. Paris, France: CIGRE, 2021.

Part 5 Reading now

Overhead Line Modelling in EMTP®

Choosing the line model for the transient — series impedance, earth return, skin effect, corona and transposition.

Series progress 5 of 16

Part 6

Overhead Line Equations & Solution

The line equations, modal and phase-domain solution, and frequency-dependent line fitting.