EMTP® Cable Modelling

Sheath & Armour Grounding in EMTP® Cable Models

How you ground a cable’s metallic sheath and armour in the parameter routine is one of the most consequential modelling choices in a cable study. Marking a layer “grounded” inside Cable Constants quietly eliminates it from the matrices — faster, but you can no longer see its current or voltage. This note — the fourth in the cable series, after the model family, the cable workflow and designs & parameters — covers when to ground internally and when to keep a sheath or armour explicit, which parameters the transient is actually sensitive to, and the equivalent-conductor data conversion that comes first.

Reading time ≈ 24 min · EMTP® cable modelling guide

The grounding treatment of metallic sheaths and armours is one of the most consequential choices in an EMTP® cable study. A cable may carry several metallic layers — conductor, metallic screen, lead or aluminium sheath, copper-wire screen, armour, pipe — that can each carry current and develop voltage to earth. Whether a layer is included explicitly, or simply declared “grounded” and removed, changes the size of the model, the run time, and which quantities you can even observe. It should be decided against the study objective, before the network is built.

This is the fourth note in the cable series. The line/cable model family derives the per-unit-length \(Z'\) and \(Y'\) matrices and the five models; the cable workflow covers materials, bonding, semiconducting screens and validation; the designs & parameters note covers the matrix internals. This page uses those results and focuses on the grounding choice, on which cable parameters the transient is actually sensitive to, and on the equivalent-conductor data conversion that precedes a Cable Constants run — with the underlying physics linked rather than repeated.

Abbreviations used on this page

EMTP®Electromagnetic Transients Program

EMTElectromagnetic transient

GPRGround potential rise

SVLSheath voltage limiter

ECCEarth-continuity conductor

KronKron (matrix) reduction / elimination

\(R_{DC}\)DC conductor resistance

\(Z_0\)Zero-sequence impedance

\(\varepsilon_0\)Permittivity of free space (8.854 pF/m)

semiconSemiconducting screen

SC cableSingle-core cable

p.u.l.Per-unit-length

Key idea

Declaring a layer “grounded” in Cable Constants usually eliminates it from the matrices — faster, but its current and voltage can no longer be observed, and it forces \(V=0\) along the whole length.
Internal elimination is not the same as real bonding, which connects to earth only at discrete points. Keep a layer explicit whenever its voltage, current, cross-bonding, GPR or SVL duty is part of the answer.
For high-frequency core transients the core, insulation, semicon and sheath dominate; for zero-sequence and earth-fault studies the return path (soil, armour, pipe, sea, bonding) takes over.
Real cables must be converted to the routine’s simplified geometry — equivalent resistivity for DC resistance, effective permittivity for capacitance — and the conversion must preserve the behaviour the study depends on.

Key terms used on this page

01Internal grounding (elimination)

Flagging a layer “grounded” in Cable Constants: it is forced to \(V=0\) along the whole length and removed from the \(Z'\)/\(Y'\) matrices.

02Kron reduction

The matrix elimination that drops a conductor’s row and column, folding its mutual/return coupling into the conductors that remain.

03Explicit (manual) grounding

Keeping the layer as a conductor and earthing it externally at discrete points through a realistic bonding impedance, SVL or link box.

04Ground potential rise (GPR)

The rise of local earth potential during an earth fault — a key driver of sheath and oversheath stress.

05Circulating sheath current

Longitudinal current driven around a both-ends-bonded sheath loop; large even when the sheath standing voltage is small.

06Standing sheath voltage

The induced voltage along a sheath that is not bonded at both ends (single-point bonding), highest at the open end.

07Coaxial mode

The core–sheath travelling wave confined within the conductor–insulation–sheath structure; dominant at high frequency.

08Distributed conductance

Continuous leakage to a surrounding conductive medium (such as seawater) along the length, which holds a layer near earth potential.

09Mode conversion

Excitation of inter-sheath and sheath–ground modes at joints, terminations and discontinuities, where the earth is “seen” again.

10Equivalent tube

A solid tubular conductor that replaces a wire screen while preserving its total metallic cross-sectional area.

11Lay factor

The \(\approx 1/\cos(\text{lay angle})\) correction for the extra metallic length of helically wound screen or armour wires.

12Reference temperature

The temperature (often 20 °C) at which catalogue DC resistance is quoted; correct to the operating temperature if the study needs it.

Section 1

Why grounding is a modelling choice, not a wiring detail

In a Cable Constants routine the user is usually asked whether each metallic layer is grounded. That option is easy to tick and easy to misread. It does not just describe how the cable is earthed on site — it changes the mathematics of the model: the order of the series-impedance \(Z'\) and shunt-admittance \(Y'\) matrices, the number of conductors the simulation carries, and whether the sheath, armour or pipe is even available as a node to measure. A study of phase-conductor switching voltages can tolerate a heavily reduced model; a study of sheath overvoltage or SVL duty cannot. So the grounding treatment is part of the modelling decision, taken against the study objective, before the EMTP® network is assembled. The matrices, the propagation constant and the five line/cable models that consume them are covered on the general page; here we decide what goes into them.

Section 2

Internal “grounded” elimination: what it actually does

When a conductor is declared grounded inside Cable Constants, the program normally assumes it is at ground potential along the entire cable length and then eliminates it from the final impedance and admittance matrices — a Kron reduction that drops its row and column. The result is a smaller model with fewer conductors, lower matrix order and faster run time. The catch is that the eliminated conductor no longer exists as an independent node, so its current and voltage can no longer be observed.

Eliminated, but not deleted from the physics

The conductor is removed as a separately accessible conductor, but its electromagnetic influence is retained: the Kron reduction folds its mutual coupling and return-path effect into the conductors that remain. It is not deleted from the field problem — you simply lose access to its own current and voltage. (In some tools “grounded” and “eliminated” are separate flags, so a layer can be grounded yet retained; the common usage couples the two, which is why the elimination behaviour is the default to watch for.) And even a continuously, solidly bonded real sheath has a small but non-zero longitudinal voltage drop from its own impedance and earth return — so treating it as an ideal \(V=0\) conductor is an approximation: good for solid bonding, not exact.

Section 3

Continuous internal grounding vs discrete real bonding

In the software, internal grounding is a mathematical reduction; on site, bonding is a physical connection at selected locations. The most common mistake is to treat “grounded in Cable Constants” and “bonded to earth at the cable end” as the same thing. They are not. Internal elimination enforces \(V=0\) continuously, all along the cable — a distributed ground. Real bonding connects the sheath to earth only at discrete points: terminations, joints, link boxes. Between those points the sheath floats and can carry circulating current or develop a standing induced voltage.

Continuous internal grounding suppresses exactly those phenomena, so it misrepresents single-point and cross-bonded systems, whose whole behaviour is the sheath voltage and current that appear between bonds. It is physically valid only when the layer is genuinely, continuously solidly bonded (or its current and voltage are irrelevant). The bonding schemes themselves — both-ends, single-point, cross-bonding, SVLs, ECCs and link boxes — are described on the cable workflow page; the point here is that only continuous solid bonding maps onto internal elimination.

Section 4

Keeping the sheath or armour explicit — and grounding it properly

The alternative is to retain the sheath or armour as an explicit conductor in the reduced matrices and make the earth connections externally, in the EMTP® network. The sheath is then grounded only where it really is — at terminations, link boxes or bonding points — through a realistic bonding impedance, an SVL or arrester branch, or cross-bond transpositions between cable sections. This reproduces discrete-point bonding and lets the sheath/armour current, the standing voltage, the GPR contribution and the SVL energy duty all be monitored.

Two practical cautions

A “small resistance” is often used at the bond to avoid an ideal-short numerical singularity. For a slow study that may be a harmless numerical convenience; for fast-front studies the bonding impedance should reflect the real earth-electrode and bonding-lead impedance, not an arbitrarily tiny value, because the bonding-lead inductance can dominate the fast-front sheath voltage and SVL energy duty. And cross-bonding is more than a terminal earth connection: the line must be split into the correct minor sections with the sheaths transposed at the joints, exactly as installed.

Section 5

A decision view: eliminate or keep explicit?

The choice reduces to a simple rule: if the conductor’s voltage or current is a study output, keep it explicit; if it is genuinely at continuous earth potential and its own behaviour is not required, internal grounding may be acceptable. The table makes that call concrete.

Table 1 — When to internally ground (eliminate) a layer, and when to keep it explicit.

Internally Ground (Eliminate)	Keep Explicit
Continuously, solidly bonded layer whose own current/voltage is not needed	Sheath standing voltage, or single-point open-end voltage
Phase-conductor voltage study where the \(V=0\) approximation is acceptable	Sheath/armour/bonding current, or circulating-current heating
An armour you do not need to monitor and that stays near earth	Cross-bonded systems (section voltages and link-box behaviour)
—	Ground potential rise, induced joint voltages, SVL energy duty

Two refinements keep this honest. First, “low sheath voltage” is not the same as “negligible sheath effect”: solid both-ends bonding gives a low standing voltage but a large circulating current, so if that current, its losses or its heating affect the result, the sheath cannot simply be eliminated. Second, even with both-ends bonding the sheath still influences the core’s surge impedance and propagation velocity through mutual coupling, so fully eliminating it can shift even phase-quantity results at fast fronts — approximating the sheath as grounded at the terminations is not the same as deleting it from the EMT formulation.

The validation that matters for this decision is specific: not just that the phase voltage looks reasonable, but that the sheath and armour voltage and current are physically meaningful whenever those quantities are part of the study — and an eliminated conductor cannot be checked at all.

Section 6

Armour and submarine cables: when “near ground” holds, and when it fails

Armour is often the layer that can reasonably be treated as near earth potential — but the justification is specific. For wet-design submarine cables the steel armour is in distributed contact with low-resistivity seawater (around 0.2–0.3 Ω·m), so it has a large distributed conductance to a near-earth medium and stays close to earth potential along its length — in a quasi-steady, power-frequency sense, and provided it is also bonded at the terminations. (The mechanism is the large distributed conductance to a low-resistivity medium that reaches the bedding and serving, not literal water penetration between every armour wire.) During fast transients and high-GPR earth faults, bonding-lead inductance and finite distributed contact resistance can still lift the armour locally, so “grounded” is not universal.

\[ \delta=\sqrt{\frac{2}{\omega\mu\sigma}} \]

\(\delta\): penetration (skin) depth, m
\(\omega\): angular frequency, rad/s
\(\mu\): magnetic permeability of the material, H/m
\(\sigma\): electrical conductivity, S/m

An approximate guide for a homogeneous conductor. Steel armour is more complex — its permeability is nonlinear and frequency-dependent — so treat it as an order-of-magnitude indicator. The fuller treatment, and why steel differs from copper, is on the parameter page.

Shielded is not the same as grounded

At high frequency the skin depth in steel armour is very small (its permeability \(\mu_r\gg1\) shrinks it further), so the field is largely confined and the armour acts as a shield and return boundary. But a well-shielding armour can still float at significant potential at a fast front unless it is actually earthed — high-frequency shielding justifies treating the armour as an electromagnetic return boundary, not collapsing it to a \(0\,\text{V}\) node. Steel makes the shielding non-ideal anyway: magnetic saturation, frequency-dependent permeability, and the wire lay/twist (helical and proximity effects, semi-transparency between wires) mean accurate lightning and fast-front studies usually still need an explicit, frequency-dependent armour.

So armour should be kept explicit when it can carry significant zero-sequence current, when armour losses matter, for earth-fault studies, for complex or magnetic armour construction, or when the armour current or voltage is itself a study output. “Treat the armour as grounded” is a study- and construction-specific approximation, not a general rule.

The armour rule

Armour may be eliminated (internally grounded) only when it is genuinely bonded or effectively held near earth potential across the study frequency range, and when its own voltage and current are not required. Otherwise it should remain explicit.

Section 7

Which parameters the transient is actually sensitive to

Cable transients are not equally sensitive to every layer; the dominant sensitivities depend on the frequency range and the type of study. For high-frequency transients in single-core cables the dominant wave is the coaxial (core–sheath) mode, confined within the conductor–insulation–sheath structure. The parameters that matter most are then the core, the main insulation, the semiconducting screens and the metallic sheath; the soil, armour and pipe matter less if the sheath shields well. This does not extend to low-frequency, zero-sequence or common-mode behaviour, where the external return path becomes important (Sections 8–9).

For the grounding decision the consequence is what matters: when the metallic sheath shields the core–sheath mode well, the soil, armour and pipe have little influence on the energised-core transient, so those external conductors can often be eliminated; when the study is zero-sequence, earth-fault, cross-bonding or sheath-overvoltage, the external return path dominates and they must stay explicit. The underlying parameter sensitivities — conductor resistivity and attenuation, insulation permittivity and velocity, and the semiconducting-screen permittivity correction (which is chosen to preserve the velocity and surge impedance, not change them) — are detailed on the parameter page.

Section 8

Earth-return sensitivity: depth, spacing, resistivity, frequency

Ground-return impedance depends on burial depth, horizontal spacing, ground resistivity and frequency — quantities that are usually known only approximately, since soil resistivity varies along a route and depth is rarely constant. That makes a sensitivity sweep worthwhile. The earth-return formulations (Pollaczek and its Saad–Gaba–Giroux and Wedepohl–Wilcox approximations) are on the parameter page; here the question is how much each input moves the answer.

For the grounding decision the headline is simple: this earth-return sensitivity is mild for a well-shielded high-frequency core–sheath mode — so the soil and external conductors can often be eliminated — but important for zero-sequence, common-mode, induced-voltage and earth-fault studies, where they must stay explicit and the soil or seabed model is chosen with care. Within that, burial depth mainly shifts the inductive part (the earth-return resistance is nearly depth-independent), horizontal spacing the mutual coupling, and soil resistivity the magnitude — all frequency-dependent, so sweep the band that matters and treat any single percentage figure as example-specific.

Section 9

Zero-sequence, earth-fault and common-mode: the ground path takes over

The mild-earth-influence picture of Section 7 holds specifically for the coaxial mode of an ideal, continuous, solidly bonded single-core cable, where high-frequency sheath skin effect confines the return current to the inner sheath surface and decouples the core loop from earth. It is not a blanket statement. With single-point or cross-bonding the sheath does not carry the full return current at the section scale, and even with both-ends bonding the inter-sheath and sheath–ground modes are excited at joints, terminations and discontinuities (mode conversion) — and those modes do see the earth.

For earth-fault, zero-sequence and common-mode studies the return path moves to centre stage. Significant zero-sequence current flows through the sheath, armour, pipe, earth or sea water, and at power frequency the sheath may not fully shield the external flux, so the armour or pipe can strongly affect the zero-sequence impedance \(Z_0\). That impedance governs the earth-fault current, the sheath and armour currents, the induced voltages, the ground potential rise and the protection performance — so a positive-sequence-only cable model is inadequate for earth-fault work, and a cross-bonded or single-point sheath cannot be treated as continuously grounded. The medium choice — multi-layer soil, sea and seabed — is covered on the cable workflow page.

Direct vs induced response — a model can be right for one and wrong for the other

Separate the direct response — the voltage or current on the energised core, usually controlled by the core–sheath coaxial mode and so sensitive to the core, insulation, semicon and sheath — from the induced response on a neighbouring cable, sheath, pipe or parallel structure, which is driven by the external field, the soil-return path, the spacing and the mutual impedance. A model can predict the energised core voltage accurately yet be unreliable for induced voltages. So the ground-return approximation may barely affect the directly energised core, while it can noticeably change induced voltages in nearby conductors — an effect that grows with spacing, making pipeline- and parallel-cable-induction studies the ones that most demand care with the ground-return method.

Section 10

Data conversion — and how it shapes the grounding decision

Why this sits on the grounding page: getting the core, sheath or screen conversion wrong shifts the calculated sheath and armour impedance and current — which can lead the modeller to eliminate a conductor that should have stayed explicit, or to trust a sheath voltage that is wrong. The conversions below therefore underpin the grounding decision rather than stand apart from it.

Real cables rarely match the cylindrical, homogeneous geometry a Cable Constants routine expects, so the construction must first be converted into an equivalent form that preserves the important electrical behaviour. Where insulation losses and frequency-dependent permittivity are neglected — common for low-loss XLPE — the routine effectively uses a frequency-dependent series impedance and a lossless shunt:

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

\(Z'\) / \(Y'\): per-unit-length series impedance / shunt admittance matrices
\(R',\ L',\ C'\): resistance, inductance and capacitance per unit length
\(\omega\): angular frequency, rad/s

Series impedance stays frequency-dependent (skin effect and earth return); the shunt is essentially capacitance, with dielectric conductance \(G'\) neglected. Acceptable for XLPE; less so for paper-oil or fluid-filled cables, or where dielectric loss and HF attenuation matter (see the cable workflow).

A stranded, compacted or segmental core entered as an equivalent solid conductor of radius \(r_1\) needs its resistivity adjusted so the equivalent solid reproduces the correct DC resistance — the geometric area \(\pi r_1^2\) exceeds the true metallic area \(A_c\):

\[ \rho_c=\rho'_c\,\frac{\pi r_1^{2}}{A_c} \qquad\text{or, from the DC resistance:}\qquad \rho_c=R_{DC}\,\frac{\pi r_1^{2}}{\ell} \]

\(\rho'_c\): true material resistivity; \(A_c\) the metallic cross-section
\(R_{DC},\ \ell\): DC resistance over length \(\ell\)

This reproduces the DC (low-frequency) resistance only. The inflated radius \(r_1\) alters the internal inductance and the HF AC resistance — a solid rod overstates skin effect versus a stranded conductor, and segmental/Milliken designs deliberately suppress it. Use \(R_{DC}\) at the reference temperature (catalogue values are usually 20 °C) and temperature-correct if the study differs.

Semiconducting screens are folded into the insulation by raising the permittivity to preserve the measured capacitance (Section 7). When the manufacturer gives the capacitance \(C'\), invert the coaxial-capacitance relation for the effective permittivity:

\[ \varepsilon_r=\frac{C'\,\ln(r_2/r_1)}{2\pi\varepsilon_0} \qquad\text{or, with no capacitance given:}\qquad \varepsilon_{r,\text{equiv}}=\varepsilon_{r,\text{ins}}\,\frac{\ln(r_2/r_1)}{\ln(b/a)} \]

\(r_1,\ r_2\): effective core radius and inner sheath radius in the simplified model
\(a,\ b\): true inner and outer radii of the main insulation
\(\varepsilon_0\): permittivity of free space, \(8.854\times10^{-12}\) F/m

The first form lumps the whole core-to-sheath shunt (main insulation, semicons, tapes and bedding between \(r_1\) and \(r_2\)) into one homogeneous effective \(\varepsilon_r\), which therefore exceeds the true insulation value. XLPE is typically \(\varepsilon_r\approx2.3\)–2.5 — representative, not a fixed constant; the underlying treatment is on the cable workflow page.

Section 11

Wire screens and segmental conductors: equivalent-tube limits

When the metallic screen is made of wires rather than a continuous tube, it is usually represented as an equivalent tubular conductor with the same total metallic area. For total wire area \(A_s\) sitting on inner radius \(r_2\), the equivalent outer radius is:

\[ r_3=\sqrt{\,r_2^{2}+\frac{A_s}{\pi}\,} \]

\(A_s\): total metallic cross-section of the wires
\(r_2,\ r_3\): inner and outer radii of the equivalent tube

Area preservation gives a reasonable current-carrying representation, but a solid tube is not a wire screen. The dominant EMT errors are that the solid tube under-estimates the screen’s AC/series resistance and mis-states its skin-effect frequency dependence — a thin tube carries current quite differently from discrete wires — and that it removes the lay/transposition behaviour. To match the catalogue DC resistance, the tube resistivity should be scaled by the lay factor (\(\approx1/\cos(\text{lay angle})\)), because the helical wires’ metallic length per axial metre exceeds the cable length; area preservation alone slightly under-states the resistance. The helical path also adds the spiral inductance discussed on the parameter page, which matters for high-frequency travelling waves.

The same spirit applies to the core: the equivalent-solid assumption for a stranded or Milliken conductor reproduces the DC resistance but overstates the high-frequency skin effect, so it is a low-frequency-accurate, not an exact, representation. In every case the conversion is judged by whether it preserves the quantity the study needs — capacitance, DC resistance, sequence impedance, surge impedance — over the relevant frequency range.

Section 12

Choosing your grounding model — and sanity-checking it

Grounding choices in Cable Constants directly shape the final EMTP® model. Internally grounding a sheath or armour removes it from the model, cutting run time but also preventing any monitoring of its voltage and current — acceptable only when the layer can genuinely be treated as continuously at earth potential and its behaviour is not part of the study. Cable transients are most sensitive to the core, insulation, semicon and sheath for high-frequency core–sheath propagation; at lower frequencies, and especially for zero-sequence and earth-fault studies, the armour, pipe and ground-return path become decisive.

Common mistakes

Reading “grounded in Cable Constants” as “bonded at the cable end” — one is a continuous ground, the other is discrete.
Eliminating the sheath of a single-point or cross-bonded system, removing the very voltages and currents under study.
Assuming low sheath standing voltage means negligible sheath effect — solid bonding still gives large circulating current.
Treating a high-frequency-shielding armour as a \(0\,\text{V}\) node when it can float at a fast front unless earthed.
Writing that semiconducting screens lower the velocity or raise the surge impedance — the permittivity correction preserves both.
Trusting an equivalent-solid core or equivalent-tube screen at high frequency without the skin-effect and lay-factor caveats.
Quoting an earth-return depth sensitivity as a universal bound rather than an example-specific figure.

Main takeaway

A good EMTP® cable model is not made by entering every dimension blindly. Match the grounding representation to the study — eliminate a layer only when it is continuously bonded and its own behaviour is not the answer; keep it explicit whenever sheath, armour or earth behaviour is the answer. Feed it consistent converted data — equivalent resistivity that reproduces the DC resistance, effective permittivity that reproduces the capacitance — sweep the uncertain earth and frequency parameters, and validate the result against DC and high-frequency limits and against measurement before you trust it.

References

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

IEEE Std 575-2014, IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV Through 500 kV. New York, NY, USA: IEEE, 2014.
CIGRE Working Group B1.18, Special Bonding of High Voltage Power Cables, Technical Brochure 283. Paris, France: CIGRE, 2005.
CIGRE Working Group B1.50, Sheath Bonding Systems of AC Transmission Cables: Design, Testing and Maintenance, Technical Brochure 797. Paris, France: CIGRE, 2020.
IEC 60287-1-2:2023, Electric Cables – Calculation of the Current Rating – Part 1-2: Sheath Eddy Current Loss Factors for Two Circuits in Flat Formation. Geneva, Switzerland: International Electrotechnical Commission, 2023.
IEC 60840:2020+AMD1:2023, Power Cables with Extruded Insulation and Their Accessories for Rated Voltages above 30 kV (U_m = 36 kV) up to 150 kV (U_m = 170 kV) – Test Methods and Requirements. Geneva, Switzerland: International Electrotechnical Commission, 2023.
IEC 62067:2022, Power Cables with Extruded Insulation and Their Accessories for Rated Voltages above 150 kV (U_m = 170 kV) up to 500 kV (U_m = 550 kV) – Test Methods and Requirements. Geneva, Switzerland: International Electrotechnical Commission, 2022.
J. A. Martinez-Velasco, Ed., Power System Transients: Parameter Determination. Boca Raton, FL, USA: CRC Press, 2010.

Part 4 Reading now

Cable Sheath & Armour Grounding

Single-point, both-ends and cross-bonding — circulating currents, induced sheath voltage and losses.

Series progress 4 of 16

Part 5

Overhead Line Modelling in EMTP®

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