EMTP® Cable Modelling

EMTP Modelling of Insulated Power Cables

An insulated cable is a tight coaxial structure in which millimetres of geometry, the metallic sheath and screen, the armour, the semiconducting layers and the bonding scheme decide the result — far less forgiving than an overhead line. This is the cable-specific companion to the Cable & Overhead Line Modelling in EMTP® guide: that page derives the line equations and the five models; this one focuses on turning real cable construction into accurate frequency-dependent series-impedance and shunt-admittance matrices — conductors, sheath, screen, armour, bonding, earth and sea return — and on the validation a cable model needs before it is used in a study.

Reading time ≈ 26 min · EMTP® cable modelling guide

Modelling an insulated power cable in an electromagnetic transient (EMT) study is more demanding than modelling an overhead line. The electromagnetic fields are shaped by small geometrical details, by metallic screens, sheaths and armour wires, by the sheath-bonding arrangement, by the soil or sea that provides the return path, and by the dielectric properties of the insulation. A small error in a cable radius, a screen thickness, a sheath diameter or the spacing between single-core cables can noticeably change the calculated capacitance, surge impedance, zero-sequence impedance, attenuation and travelling-wave behaviour.

This note is the cable-focused companion to the Cable & Overhead Line Modelling in EMTP® guide. That guide derives the distributed-parameter line equations, the per-unit-length \(Z'\) and \(Y'\) matrices, the propagation constant and characteristic impedance, and the five EMTP® models — constant-parameter (CP), frequency-dependent (FD), Wideband, Exact-PI and Nominal-PI. Rather than repeat that theory, this page concentrates on what makes cables hard: converting real construction into the matrices, and getting the conductors, sheath, screen, semiconducting layers, armour, bonding and earth/sea return right so that the computed model is physically meaningful.

Where this page sits

Read the line-equation derivation and the five-model overview on the general page first if you need them. Here we assume them and go deep on cable construction, materials, bonding and validation. Where a topic is already covered generally — the equations, the model family, basic soil return, the semiconducting-screen permittivity formula — we link to it rather than re-derive it.

Abbreviations used on this page

EMTP®Electromagnetic Transients Program

EMTElectromagnetic transient

SC cableSingle-core cable

XLPECross-linked polyethylene insulation

MI / MINDMass-impregnated (non-draining) insulation

semiconSemiconducting screen

SVLSheath voltage limiter

ECCEarth-continuity conductor

p.u.l.Per-unit-length (\(Z'\), \(Y'\) per metre)

tan δDielectric loss factor

\(Z_1\) / \(Z_0\)Positive- / zero-sequence impedance

\(R_{dc}\)DC conductor resistance

WB / FDWideband / Frequency-Dependent cable model

GISGas-insulated switchgear

Key idea

A cable model is only as good as its construction data — layer radii, materials, semiconducting screens, bonding and the surrounding medium — not just the conductor size and rated voltage.
The sheath-bonding arrangement often changes the zero-sequence impedance and sheath overvoltage more than a change in conductor size does. It must be modelled as installed.
Semiconducting screens, steel armour and the earth/sea return are the parts most often simplified incorrectly — and the parts that decide attenuation, velocity and zero-sequence behaviour.
Validate against measured capacitance and sequence impedance before trusting the model — a fit that the software accepts is not automatically a fit that is physically correct or passive.

Key cable terms used on this page

01Metallic sheath / screen

The earthed metallic layer over the insulation — lead sheath, corrugated-aluminium sheath or copper-wire screen. Electrically it is the cable’s second longitudinal conductor and return path.

02Semiconducting screen

Thin conductive-polymer layers either side of the insulation that grade the electric field. At power frequency they sit at electrode potential and are folded into the insulation in Cable Constants.

03Armour

Outer steel (or aluminium) wires or tape for mechanical protection. Magnetic steel armour can carry induced and zero-sequence current and adds frequency-dependent loss.

04Single-point bonding

Sheath earthed at one end only; the far end is open. No longitudinal circulating current flows, but a standing sheath voltage appears, highest at the open end.

05Sheath voltage limiter (SVL)

A metal-oxide limiter at link boxes and open sheath ends that protects the oversheath insulation against transient overvoltage during faults, switching and lightning.

06Link box

The underground box at a joint where sheath sections are earthed, transposed (cross-bonded) or connected to SVLs. Its leads add inductance for fast transients.

07Earth-continuity conductor (ECC)

A parallel earth conductor laid with single-point-bonded sections to carry fault current that the open sheath cannot.

08Equivalent solid conductor

A stranded, compacted, segmental or Milliken conductor entered as a solid tube whose resistivity is raised so the calculated DC resistance matches the datasheet.

09Effective permittivity

The permittivity raised in the model so the geometric insulation (taken over the semicons) reproduces the measured capacitance per unit length.

10Sequence impedance (\(Z_1\) / \(Z_0\))

Positive- and zero-sequence per-length impedance. \(Z_0\) is strongly sensitive to bonding, soil/sea resistivity, sheath and armour.

11Cable surge impedance

\(Z_c\approx\sqrt{L'/C'}\) for the coaxial mode — much lower than an overhead line (tens of ohms) because cable capacitance is high.

12Trefoil / flat formation

The laying arrangement of three single-core cables (touching triangle vs spaced flat) — it sets the mutual coupling and the induced sheath voltages.

Section 1

Why cables are unusually sensitive to modelling detail

An insulated cable is a compact electromagnetic structure. The conductor, insulation, screen, sheath and oversheath are separated by millimetres or centimetres, the electric field is almost entirely confined inside the insulation, and the magnetic field links the conductor, sheath, armour, neighbouring phases, ducts, pipes, bonding leads and the earth. An overhead line, by contrast, has metres of air between phases and a low shunt capacitance. The same modelling tool serves both, but the cable demands construction-accurate data because so much of its behaviour is decided by geometry that is small and by metal that is close.

This produces several distinct sensitivities:

The capacitance is set by the insulation permittivity and the ratio of conductor radius to the inner radius of the screen. A modest error in insulation thickness or screen diameter moves it directly — and capacitance sets the surge impedance and the resonances a long cable introduces.
The series impedance is set by conductor resistance and skin effect, by sheath, screen and armour currents, by proximity between adjacent cables, and by the earth return. In trefoil or flat formations the mutual coupling between phases matters.
The zero-sequence impedance is especially sensitive to the sheath-bonding arrangement, soil or seabed resistivity, burial depth, armour design and any parallel metallic return path.
The transient response depends on surge impedance, propagation velocity, losses, and reflections at terminations, joints, cross-bonding points, bonding leads, surge arresters, transformers, reactors and converter stations.
The high-frequency attenuation depends not only on conductor losses but on the semiconducting screens, the insulation loss, the armour behaviour and the accuracy of the high-frequency parameter calculation.

Takeaway

A cable model can look physically detailed and still be electrically wrong if the bonding arrangement, the screen and sheath treatment, or the material data are incorrect. Because cable capacitance is high, the cable is frequently the element that decides energisation, resonance, sheath-voltage and HVDC results — so the input data deserve the same scrutiny as the study itself.

Section 2

From construction to \(Z'(\omega)\) and \(Y'(\omega)\): the Cable Constants workflow

A transient cable model is not the rated voltage, conductor size and positive-sequence impedance. It is a distributed-parameter electromagnetic model that represents how waves propagate and attenuate, how the screens and sheaths carry induced current, and how the earth or sea returns the zero-sequence and common-mode current. EMTP-type programs build it with a dedicated parameter routine — Cable Constants, Cable Data or Line/Cable Data — that converts the physical construction and installation into the per-unit-length matrices the line/cable model needs:

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

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

These are the same telegrapher’s-equation quantities derived on the general page. Here they are matrices, not single values.

The size of the matrix is the point most often misread. Its order equals the number of longitudinal, current-carrying conductors actually represented — not a count of layer names. A single-core cable usually contributes a \(2\times2\) block (core + metallic sheath/screen) or a \(3\times3\) block (core + sheath + armour); a three-phase circuit assembles these blocks into the full matrix, together with any pipe or parallel earth/ECC conductor. “Metallic screen”, “lead sheath” and “copper-wire screen” are different names for the same single sheath conductor of a given cable, not extra conductors; and a layer that carries no current — or a semiconducting screen — adds nothing to the order.

The frequency dependence is essential. At power frequency, current uses most of the conductor cross-section. As frequency rises, skin effect crowds it toward the surfaces, and the return-current distribution in the sheath, armour, pipe, soil or sea also changes. So the effective resistance and inductance are not constant — they vary with frequency and strongly shape the damping and the front of a transient overvoltage. The conversion runs in five steps:

Collect the manufacturer’s construction data — every relevant diameter and material property.
Convert it to the simplified geometry the routine accepts: stranded conductors as equivalent solid tubes, wire screens as equivalent tubular screens, armour wires as an equivalent cylindrical layer, semiconducting screens folded into the insulation.
Compute the frequency-dependent \(Z'\) and \(Y'\) matrices over a frequency range that covers the phenomena of interest.
Select the model — constant-parameter, frequency-dependent modal, frequency-dependent phase-domain or wideband (see the model overview and Section 10).
Connect the sections into the network with the correct bonding, cross-bonding, SVLs, link boxes, terminations, grounding, and connected plant — then validate (Section 11).
Design & internals. For how each cable design type maps to its representation and what the parameter matrices contain — surface/transfer impedance, ground-return and the spiral effect — see the companion note.

The conversion is the weakest step

Datasheets often give nominal layer thicknesses rather than as-designed radii, and quote DC/AC resistance, capacitance, inductance and sequence impedance without stating the bonding, formation, soil resistivity, temperature or armour assumptions behind them. Those numbers are for validation, not for copying blindly into the model. Get the conversion wrong and a geometrically tidy model is still electrically wrong.

Section 3

The construction and installation data the model actually needs

A reliable model starts with reliable input data, normally divided into geometry, material properties, installation and bonding. The table below groups the minimum information and shows what each group controls in the resulting matrices.

Table 1 — Cable input data and what each group controls.

Input Group	What to Obtain	What It Mainly Controls
Geometry	Conductor radius and construction; insulation thickness; inner/outer semicon dimensions; screen/sheath dimensions; armour dimensions; oversheath; laying arrangement, phase spacing, burial depth, duct/tunnel layout; position of parallel circuits	Capacitance, surge impedance, inductance, mutual coupling
Materials	Resistivity and relative permeability of conductor, screen, sheath, armour, pipe and surrounding medium	Series resistance, skin/proximity effect, armour loss
Insulation	Relative permittivity and loss factor (tan δ) of the dielectric	Capacitance, propagation velocity, dielectric loss
Installation	Buried / duct / tunnel / seabed / pipe; soil, sea-water and seabed resistivity; thermal backfill; nearby metallic infrastructure	Earth-return impedance, zero-sequence, common-mode behaviour
Bonding	Solid / single-point / cross-bonded / both-ends; SVLs; link boxes; section lengths; local earth electrodes	Sheath current, sheath voltage, zero-sequence impedance

Copper and aluminium can be treated as non-magnetic (relative permeability close to unity). Steel armour, steel pipes and other ferromagnetic structures need more care: their permeability is nonlinear, frequency-dependent and direction-dependent. XLPE and PE insulation have low dielectric loss over a wide frequency range; oil-paper, mass-impregnated and fluid-filled insulation can have more significant, frequency-dependent dielectric loss, which matters when the transient under study contains high-frequency content — lightning, restrikes, very fast switching or converter-generated steep fronts. The bonding configuration is not a minor detail: in many cable studies it influences the zero-sequence impedance and the sheath overvoltage more than small changes in conductor size do.

Nominal data are not always the real dimensions

Datasheets often quote nominal or minimum-specification thicknesses, and the as-built insulation, semiconducting screens and oversheath can be thicker than stated. Because the core-to-sheath geometry sets the capacitance and surge impedance, building the model from nominal radii alone can bias them — typically a surge impedance that is too low, and (where it leaves the effective permittivity under-estimated) a wave velocity that is too high — shifting reflection timing and resonance. Treat datasheet dimensions with care: prefer measured specimen dimensions where available, and anchor the model to the manufacturer capacitance rather than to nominal geometry alone.

Section 4

Representing conductors, sheaths and the equivalent-solid assumption

The main conductive materials are copper and aluminium (phase conductors and metallic screens), lead (sheaths in some HV and submarine cables) and steel (armour, pipes, mechanical protection). The DC resistivity should come from manufacturer data wherever project-specific values exist — especially for large, Milliken, compacted, segmented and submarine conductors — rather than a generic table, and it should be corrected to the relevant operating temperature:

\[ \rho_T=\rho_{20}\,\bigl[\,1+\alpha\,(T-20)\,\bigr] \]

\(\rho_T\): resistivity at operating temperature \(T\) (°C)
\(\rho_{20}\): resistivity at 20 °C
\(\alpha\): temperature coefficient of resistance (≈ 0.0039 K\(^{-1}\) for Cu, ≈ 0.0040 K\(^{-1}\) for Al)

Transient studies often need the cable at normal operating temperature, not at 20 °C — the difference in conductor resistance changes the damping.

Stranded, compacted, segmental and Milliken conductors are normally entered as equivalent solid tubes of the same outer radius. Because the geometric area of that tube exceeds the real metallic area (there are gaps between strands), the effective resistivity must be raised by a fill/lay factor so the calculated DC resistance matches the manufacturer value:

\[ \rho_\text{eff}=\rho_T\,\frac{A_\text{geom}}{A_\text{metal}} \qquad\text{so that}\qquad R_{dc}=\frac{\rho_\text{eff}}{A_\text{geom}}=\frac{\rho_T}{A_\text{metal}} \]

\(A_\text{geom}\): geometric cross-section of the equivalent solid tube
\(A_\text{metal}\): true metallic cross-section of the real conductor

It matches \(R_{dc}\) only — not AC resistance or internal inductance

Raising the resistivity reproduces the DC resistance (the IEC 60228 / datasheet value). It does not reproduce the real AC skin-effect resistance or the internal inductance of a stranded or segmental conductor. Milliken conductors are designed specifically to suppress skin effect; the equivalent solid tube has no such suppression and therefore overstates the skin effect and AC resistance at high frequency. Treat it as an equivalent-DC-resistance representation, and be cautious when the study leans on high-frequency conductor loss.

Steel armour needs particular care. Its magnetic permeability is not a fixed universal value: it depends on grade, magnetic field strength, wire shape, lay angle, frequency and on whether the field is longitudinal, radial or circumferential. In three-core submarine cables the armour can be a significant return path for induced and zero-sequence current (Section 9). Ignoring it, or giving it an unrealistic permeability, leads to incorrect impedance and loss.

Section 5

Insulation permittivity, tan δ and how dielectric loss is represented

The main insulation sets the shunt capacitance and the propagation velocity of travelling waves. For the idealised coaxial mode of a single-core cable the wave velocity is approximately

\[ v\;\approx\;\frac{c}{\sqrt{\varepsilon_r}} \]

\(c\): speed of light in vacuum
\(\varepsilon_r\): relative permittivity of the insulation (≈ 2.3 for XLPE; higher for mass-impregnated and fluid-filled insulation)

This relation is exact only for a lossless, homogeneous coaxial line with a perfect conductor and \(\mu_r=1\); in a real cable model it is an approximation. Three caveats matter: folding the semiconducting screens into the insulation raises the effective permittivity and lowers the coaxial velocity (Section 6), so \(\varepsilon_r\) is tuned to match the measured capacitance rather than taken from a textbook; conductor and sheath losses with skin and proximity effect make the velocity frequency-dependent (there is no single velocity); and the earth/ground-return modes propagate well below this coaxial value. So XLPE and paper-oil cables have different velocities, but quote them as mode- and frequency-dependent quantities, not one number for the whole cable.

Dielectric loss is usually represented through the loss factor tan δ. In the simplified representation:

\[ G'\;\approx\;\omega\,C'\,\tan\delta \]

\(G'\): shunt conductance per unit length
\(\tan\delta\): dielectric loss factor (low and nearly constant for XLPE; larger and frequency-dependent for oil-paper)

In practice the shunt is often modelled lossless

Standard EMTP cable models (CP, FD/J. Marti, WB) most often treat the shunt admittance as a frequency-independent, lossless capacitance and neglect dielectric loss unless the user explicitly enables it. For low-loss XLPE this is usually acceptable for switching-transient studies. For oil-paper cables, or studies with very high-frequency content, dielectric loss can be frequency-dependent and may need measured frequency-dependent data or a fitted wideband admittance. The numerical risks of a naive constant tan δ are discussed in Section 10.

Section 6

Semiconducting screens: effective permittivity, velocity and HF attenuation

High-voltage extruded cables include an inner semiconducting screen between conductor and insulation, and an outer semiconducting screen between insulation and metallic screen. These layers smooth the electric field and prevent local stress enhancement. They are also a classic modelling trap, because most Cable Constants routines do not represent them as distributed lossy dielectric layers with their own frequency-dependent properties — they must be folded into the insulation.

In practice the semiconducting screens are not entered as longitudinal conductors; they are absorbed into an effective insulation representation. Because they are conductive at power frequency they sit at conductor and sheath potential and act as field-smoothing parts of the electrodes. The effective insulation radius and relative permittivity are then chosen so that the calculated core–sheath capacitance matches the manufacturer’s value — the standard fix keeps the true radii (over the screens, out to the outer radius of the main insulation) and raises the permittivity to an effective value, a permittivity scaling rather than a literal thinning of the insulation. The general guide gives the effective-permittivity correction in full. This preserves the main shunt-capacitance behaviour, although it does not represent the high-frequency attenuation that the semiconducting material introduces.

Why it matters beyond capacitance

If the semicons are ignored and the bare insulation radii are used, the model under-estimates the capacitance, over-estimates the velocity and surge impedance, and mis-times reflections. Folding them in correctly fixes the electrostatic (shunt) behaviour. But the semicons are neither perfect conductors nor perfect insulators, so at high frequency they add series resistance and extra attenuation that the permittivity scaling does not capture.

The first validation of the semicon treatment is to compare the calculated capacitance with the manufacturer’s stated capacitance; if they do not agree within tolerance, the geometry or effective-insulation boundary should be reviewed before the model is used. But capacitance matching validates only the shunt representation. Because the screens also introduce high-frequency attenuation, a complete check — for lightning, restrike or VFT studies — also compares high-frequency attenuation and propagation against measurement or against a model that represents the semicons explicitly.

Section 7

Sheath bonding, cross-bonding and link boxes in the model

The cable is only one part of the model; the bonding network is equally important. The three standard schemes change the sheath current, the sheath voltage and the sequence impedance in different ways.

Table 2 — Sheath-bonding schemes and what they do.

Scheme	Circulating Sheath Current	Sheath Standing Voltage	EMTP Modelling Need
Both-ends bonded	Flows — raises losses, affects \(Z_0\)	Low	Bond sheath to earth at both ends
Single-point bonded	None (far end open)	Rises with distance; highest at the open end	Open the far sheath; add SVL and ECC
Cross-bonded	Largely cancels over a major section	Controlled by transposition	Model link boxes & minor-section lengths explicitly

Both-ends bonding earths the sheath at both ends: it reduces sheath overvoltage but allows a circulating sheath current that increases losses and influences the sequence impedance. Single-point bonding earths the sheath at one end only and leaves the far end open — so there is no longitudinal circulating current at all (not merely a reduced one). A standing sheath voltage instead rises with distance from the bonded end and is highest at the open end. That power-frequency standing voltage is kept within limits by limiting the section length; the SVL’s job is to protect the open sheath end and the oversheath insulation against transient overvoltages during faults, switching and lightning, not to control the standing voltage. A parallel earth-continuity conductor is normally run with single-point sections to carry fault current.

Cross-bonding splits the route into minor and major sections and transposes the sheaths so the induced voltages tend to cancel over a complete major section — reducing circulating current while controlling sheath voltage. In EMTP this should be represented explicitly: treating a cross-bonded cable as a single equivalent cable, without the link boxes and section lengths, removes important transient behaviour. The general page offers convenient cross-bonded averaging options for steady-state and slow-front work; for fast-front, sheath-voltage and SVL-duty studies, model the sections explicitly.

Watch the bonding leads

Long bonding leads and link-box connections add inductance. During fast-front surges, restrikes or lightning, that inductance can significantly affect sheath voltage and arrester (SVL) duty. For high-frequency studies, do not represent every bonding point as an ideal zero-impedance connection unless the simplification is justified.

Whether each sheath, screen, armour or pipe is retained as an explicit conductor or eliminated (internally grounded) in the parameter routine is a related modelling decision — and it depends on whether that conductor’s own voltage and current are part of the study. The sheath & armour grounding note covers that internal-versus-explicit choice, and the parameter sensitivities it drives, in full.

Section 8

Earth-return, sea-water and the surrounding medium

The surrounding medium is part of the electromagnetic system. For underground cables the earth-return impedance depends on soil resistivity, burial depth, frequency and any parallel metallic paths. For submarine cables, sea water and the seabed layers create a return path very different from a land installation. The general guide covers the basic soil-return treatment; the cable-specific points are these.

A single uniform soil resistivity is a simplification. It is often adequate, but it can be inaccurate where the route crosses different soil layers, tunnels, ducts, sea transitions, shore crossings or areas dense with metallic infrastructure. Modern line/cable parameter methods increasingly use multi-layer earth and more complete earth-return formulations. For zero-sequence studies, earth faults, sheath-voltage and induced-voltage studies, and common-mode transients, the surrounding medium must be chosen with care: a model calibrated only for positive-sequence behaviour may be unreliable for zero-sequence or common-mode behaviour, which is sensitive to bonding, soil, sheath, armour and the return path.

Section 9

Steel armour, three-core and submarine cables

Three-core submarine cables add complexity. The three cores sit close together inside fillers, bedding, armour wires and serving layers. The armour is often magnetic steel and may carry induced current, influencing impedance, losses, the magnetic-field distribution and transient damping.

The behaviour is strongly mode-dependent. For positive-sequence currents the three phase currents are balanced and the external magnetic field partly cancels. For zero-sequence or unbalanced conditions the return path can involve the armour, the sheaths, the sea water, the seabed and the grounding systems. The same cable therefore behaves very differently under balanced operation, earth faults, resonance and common-mode transients — which is exactly why a positive-sequence-only calibration is not enough.

Check how the tool represents armour

When modelling armoured submarine cables, check whether the Cable Constants routine represents the armour as a continuous tubular layer, as individual wires, or as an approximate equivalent conductor — and whether it captures the wire lay angle. If only a simplified representation is available, state the limitation in the study report, especially where zero-sequence impedance, sheath/armour current, losses or high-frequency damping are important.

Section 10

Frequency range, modal vs phase-domain choice and passivity

The frequency range for parameter calculation follows the study objective: a cable energisation study focuses on low and medium frequencies; a lightning or restrike study needs a much wider range; a harmonic-resonance study needs accuracy around the characteristic harmonics and possible resonance bands; a converter-interaction study needs accuracy around the control, switching and resonance frequencies. A common mistake is to compute parameters over a narrow range and then use the model for a much faster transient; another is to extend the range without checking that the material models, semicon approximation, armour representation and dielectric loss remain physically meaningful across it.

The model choice is covered generally on the companion page; the cable-specific consequences are:

The Constant-Parameter (CP) model is a single-frequency distributed-parameter travelling-wave model. It is not a “short cable” model — it is fine for long cables in steady-state or narrow-band studies near its fitting frequency. Its real limitation is that it ignores frequency dependence (and often uses a constant, near-DC resistance), so it is inadequate for broadband transients regardless of length.
Of the four per-unit-length quantities, the strongly frequency-dependent ones are the series \(R'\) and \(L'\) (skin, proximity and earth-return effects). The shunt \(C'\) is essentially constant and \(G'\) is usually negligible or only weakly frequency-dependent — so “all of R, L, G, C vary with frequency” overstates the case.
The classic frequency-dependent modal model (e.g. J. Marti) assumes a constant, real modal transformation matrix. For cables that matrix is itself frequency-dependent and complex — especially in unbalanced or cross-bonded systems — so modal-domain models may become less accurate than phase-domain / wideband models. Frequency-dependent phase-domain / wideband models (such as the Universal Line Model) fit the propagation and characteristic admittance directly in phase coordinates and are the recommended choice for cables and for cross-bonded or unbalanced systems.

Fitting and passivity

Frequency-dependent cable models use rational (vector) fitting to build a time-domain model. The fit should be checked for stability and passivity: a non-passive model can generate artificial energy and cause unrealistic oscillations or numerical instability. The genuine fitting pitfalls are less “a constant tan δ is unrealistic” (a roughly constant tan δ is physically reasonable) and more: a shunt conductance \(G'=\omega C'\tan\delta\) that rises without bound at high frequency when extrapolated, a shunt modelled as a constant capacitance with no causal frequency-dependent \(C'(\omega)\), and data extrapolated outside the fitted band. If the software offers passivity checking or fitting-error plots, review them before accepting the model.

Section 11

Validating a cable model before you trust it

A cable model should not be accepted simply because the software generated it. The following engineering checks are recommended, in roughly increasing difficulty.

Capacitance against the manufacturer’s stated value — the best single check of insulation geometry, permittivity and the semicon treatment (validates the shunt).
Conductor resistance against the datasheet, at the correct temperature.
Positive-sequence impedance at 50/60 Hz against manufacturer or project data where available.
Zero-sequence impedance — reviewed carefully, because it depends strongly on bonding, soil/sea, sheath, armour and return-path assumptions. Check it separately from \(Z_1\); a positive-sequence-only calibration is not a zero-sequence validation.
Sheath currents for bonded and cross-bonded systems — unrealistic sheath current usually signals an incorrect bonding representation.
High-frequency attenuation and surge impedance / velocity — especially for travelling-wave, lightning and switching studies, where the semicon and series losses dominate the answer and capacitance matching alone is not sufficient.
A simple energisation or open-end wave-propagation test before embedding the cable in a large network — it exposes unrealistic reflections, excessive attenuation, unstable fitting or incorrect phase/sheath connections.
Initial inrush against the surge impedance — a fast voltage step draws an initial current set by the surge impedance, \(I_\text{initial}\approx V/Z_c\). If a field energisation or discharge record exists, a wrong initial current points to a wrong \(Z_c\), and a wrong first-arrival time points to a wrong propagation velocity.

Where field measurements exist — impedance, capacitance, sheath current, induced voltage or frequency-response data — use them. Measured data significantly improves confidence and is often the only way to confirm the high-frequency behaviour that datasheets do not state.

Section 12

Practical guidance and common cable-modelling mistakes

Match the model to the job. For short MV connections, transformer-energisation studies and approximate switching studies where the cable is not the dominant element, a simplified frequency-dependent model may be enough. For long HVAC export cables, offshore-wind projects, long underground transmission, harmonic-resonance and cable–transformer interaction studies, use a frequency-dependent or wideband model. For cross-bonded systems, represent the physical section lengths and bonding points rather than a single averaged equivalent. For submarine cables, review armour and sea-return assumptions whenever zero-sequence current, sheath/armour current, resonance or common-mode behaviour is involved. For very fast transients — lightning, restrikes, GIS/cable interaction, steep-front converter disturbances — give extra attention to bonding-lead inductance, SVLs, terminations, semiconducting screens and dielectric loss. And for harmonic-resonance or converter-interaction work, check the model in the frequency domain first: cable capacitance shifts network resonances to lower frequencies, and long cable systems create lightly damped resonance modes.

Common mistakes

Treating the cable as a simple positive-sequence impedance — fine for load flow, not for EMT analysis.
Ignoring the sheath, screen or armour return paths, or earthing them differently from how they are installed.
Trusting datasheet sequence impedance without checking the formation, bonding, soil and temperature it assumes.
Failing to match the calculated capacitance and resistance to the manufacturer’s data.
Using the model outside the frequency range it was fitted for.

Key takeaway

A reliable EMTP cable model converts the physical construction, materials, installation and bonding into frequency-dependent series-impedance and shunt-admittance matrices — and the skill is not drawing the geometry but representing the conductor, insulation, screen, sheath, armour, earth/sea return and bonding correctly over the frequency range the transient demands. A constant-parameter model may do for simple studies; for switching surges, energisation, resonance, lightning, restrikes, long HVAC cables, HVDC links, offshore export systems and cross-bonded transmission cables, a frequency-dependent or wideband model is the normal choice. Always validate it against manufacturer capacitance, calculated sequence impedance, sheath-current behaviour and, where possible, measurements — not against positive-sequence data alone.

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.
A. Ametani, “A general formulation of impedance and admittance of cables,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-99, no. 3, pp. 902–910, May/Jun. 1980.
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.
B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 1052–1061, Jul. 1999.
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.
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.

Part 2 Reading now

EMTP® Modelling of Insulated Power Cables

The cable-specific workflow — Cable Constants conversion, conductors, insulation, semiconducting screens, bonding and earth/sea return.

Series progress 2 of 16

Part 3

Cable Designs & Parameter Calculation

Cable construction and geometry, and the series-impedance and shunt-admittance parameters needed for the model.