The cable’s construction decides how it should be modelled. A single-core cable is nearly coaxial and easy to enter; three-phase, pipe-type, submarine and tunnel cables usually need an approximation that must still preserve the electrical behaviour the study depends on. This note is the third in the cable series — after the line/cable model family and the cable modelling workflow. It maps each cable design type to its EMTP® representation, then opens up the parameter calculation itself: how the series-impedance and shunt-admittance matrices are built from surface and transfer impedance, ground-return, and the spiral effect.
Reading time ≈ 24 min · EMTP® cable modelling guide
Cable design has a direct influence on how a cable should be represented in EMTP®. A cable is not only a phase conductor and insulation. It may carry semiconducting screens, metallic screens, lead or aluminium sheaths, copper-wire screens, armour wires, bedding layers, oversheaths, pipes, ducts, tunnel walls and bonding connections — and each of these can change the series impedance, shunt admittance, travelling-wave velocity, surge impedance, zero-sequence behaviour and transient attenuation. So the first step is not choosing the EMTP® line model; it is understanding the construction. Once the construction is understood, the modeller can decide how to enter the cable into the parameter routine (Cable Constants / Cable Data).
This is the third note in the cable series. The line/cable model family derives the distributed-parameter equations, the per-unit-length \(Z'\) and \(Y'\) matrices and the five models; the cable modelling workflow covers materials, semiconducting screens, bonding, validation and fitting. This page sits between them: it maps each design type to its EMTP® representation, and then opens up the parameter calculation — what actually goes into the series-impedance and shunt-admittance matrices. Throughout, the guiding rule is that an approximation is only acceptable if it preserves the electrical behaviour the study depends on: a simplification that is fine for positive-sequence impedance may be unacceptable for sheath overvoltage, cross-bonding, lightning surge or high-frequency transients.
\(Z'\) / \(Y'\)Per-unit-length series impedance / shunt admittance
\(Z_s\)Surface impedance
\(\delta\)Skin depth
SGGSaad–Gaba–Giroux ground-return approximation
tan δDielectric loss factor
\(Z_0\)Zero-sequence impedance
FEMFinite-element method
Key idea
Cable-parameter routines are strongest for coaxial geometry. Single-core cables fit naturally; three-phase, pipe-type, submarine and tunnel cables need an approximation — chosen for the study, not for convenience.
The two outputs are the series-impedance matrix (current flow, losses, magnetic coupling, damping) and the shunt-admittance matrix (capacitance, charging current, velocity, surge impedance). Both are frequency-dependent.
The internals are built from surface and transfer impedance, an inductive insulation-annulus term, the ground-return impedance (Pollaczek and its approximations) and the coaxial capacitance — with second-order effects such as the spiral of wire screens.
If the geometry cannot be represented with confidence, FEM or auxiliary methods are used — but they must still deliver frequency-dependent \(Z'\)/\(Y'\) or a fitted wideband model for the time domain.
Key terms used on this page
01Surface impedance, \(Z_s\)
The self-impedance of a conductor surface, \(Z_s=R_\text{ac}+j\omega L_\text{int}\). Its AC resistance rises with frequency while its internal inductance falls.
02Transfer impedance
The mutual term coupling current on one face of a tubular conductor (sheath, armour, hollow core) to the voltage on the other face.
03Skin depth, \(\delta\)
The depth to which current penetrates a conductor at a given frequency, \(\delta=\sqrt{2\rho/(\omega\mu)}\). Small in steel because of its high permeability.
04Complex penetration depth, \(p\)
\(p=1/\sqrt{j\omega\mu\sigma}\) for the earth or a metal — the length scale that governs how good a ground-return approximation is for a given geometry.
05Pollaczek integral
The rigorous earth-return impedance for buried conductors in a homogeneous half-space — accurate but numerically demanding, so it is usually approximated.
06Pipe-type formulation
The Cable Constants model for conductors inside a common conducting enclosure; the enclosure provides an internal return path and a partial electromagnetic shield.
07Insulation-annulus term
The inductive series contribution of the magnetic field in the gap between two metallic layers, \(\tfrac{j\omega\mu_0}{2\pi}\ln(d/c)\) — not a loss term.
08Spiral effect
The extra inductance from the helical current path in wire screens / spiral sheaths, set by the helix pitch-circle diameter and the winding pitch.
09Self / mutual ground-return
The earth-return impedance of one conductor (self) and the coupling between two conductors through the earth (mutual).
10Equivalent pipe
A circular pipe used to approximate a non-circular tunnel or trench so a pipe-type routine can represent it.
11Potential-coefficient matrix
A matrix relating conductor charges to voltages; inverted to obtain capacitance for bare conductors inside an enclosure or for overhead/buried bundles.
12Conductor subdivision
Splitting a conductor into many filaments so proximity effect and non-uniform current can be computed where analytic formulas fall short.
Section 1
From cable construction to the \(Z'(\omega)\) and \(Y'(\omega)\) matrices
The purpose of cable-parameter calculation is to convert the physical construction into the two matrices the EMTP® cable model needs. The series-impedance matrix \(Z'(\omega)\) describes the voltage drop along the cable from conductor resistance, internal and external magnetic fields, and sheath, armour, pipe and earth-return currents. The shunt-admittance matrix \(Y'(\omega)\) describes the charging current through the insulation system between conductors, screens, sheaths, armour and the outer reference. In short: \(Z'\) controls current flow, losses, magnetic coupling and damping; \(Y'\) controls capacitance, charging current, wave velocity and surge impedance. Both are frequency-dependent — a cable does not have one impedance for all transients; its behaviour at 50 Hz is not its behaviour at 10 kHz, 100 kHz or 1 MHz.
What this page assumes
The general guide derives \(Z'=R'+sL'\) and \(Y'=G'+sC'\), the propagation constant, characteristic impedance and the five models these matrices feed; the cable workflow covers input data, materials, bonding and validation. This page is about what the matrices contain for each cable design — not how to enter the data or which model to pick.
Section 2
Single-core cable systems: three coaxial cables in earth
A single-core cable system is normally three separate single-core cables, one per phase. Each is approximately coaxial: a central conductor (copper or aluminium — solid, stranded, compacted, segmental or Milliken, and occasionally hollow in fluid-filled designs) surrounded by the main insulation, the semiconducting screens, and a metallic sheath or screen of lead, corrugated aluminium, copper wires or tape. Submarine or high-strength cables add steel armour. This concentric form is exactly what most Cable Constants routines are built for, so single-core cables are the easiest design to model.
Two points keep the model honest. First, the semiconducting screens are not modelled as conductors: what matters here is not their material chemistry but how their presence changes the effective geometry the routine uses — it folds them into the dielectric, adjusting the insulation to an effective permittivity so the modelled core–sheath capacitance matches the real geometry (the cable workflow covers the material side). The metallic conductors are therefore the core, the sheath and (where present) the armour. Second, the cable being coaxial does not make the system simple: three single-core cables may be in trefoil, flat, separate ducts, a tunnel or direct burial, and their sheaths may be both-ends, single-point or cross-bonded. The inter-cable coupling is then carried almost entirely by the ground-return mutual terms in the series matrix — which is why the phase spacing and the common return path must be in the model (Sections 8–9), and why the bonding arrangement matters as much as the cable itself.
Section 3
Three-phase self-contained cables: metallic vs insulating enclosure
Three-phase self-contained cables carry the three cores inside one common body. Each core may resemble a single-core cable, but the shared layers make the cross-section non-coaxial, and most Cable Constants routines are limited in the cross-sections they accept. The decisive question is whether the common outer enclosure is metallic or insulating.
If the enclosure is metallic — a common sheath, pipe or armour around three individually sheathed cores — it can be represented with the pipe-type formulation (Section 4). The metallic enclosure is not just mechanical: it is an internal electromagnetic return path that affects zero-sequence impedance, attenuation and the sheath/pipe current distribution, and that partly isolates the inner conductors from external earth at frequencies where current does not penetrate the wall. (At lower frequency, or with a thin or high-resistivity wall, current does penetrate and external earth-return reappears, so it is not a perfect shield.)
Insulating enclosure — mind the phantom conductor
If the common enclosure is insulating, the pipe-type formulation does not strictly apply, because it requires a conducting return enclosure. A common trick is to place a very thin conducting layer on the inner surface of the insulating pipe so the pipe-type code can be reused — but this introduces a spurious conductor. If that layer is electrically continuous and grounded, it can carry circulating current and short out the very sheath-to-sheath coupling you are trying to study. It is acceptable only as a pure geometric trick, with the layer made highly resistive or left floating so it does not alter currents. More commonly the insulating enclosure is handled by placing the three single-core cables directly in earth, or better by modifying the earth-return geometry — not by adding a phantom conductor.
Either approximation is reasonable when the sheaths are solidly bonded at both ends — the sheath potentials are then pinned and the general impedance and travelling-wave behaviour are not very sensitive to the missing enclosure. They are not adequate for induced sheath overvoltage, sheath-voltage-limiter duty, open-end (single-point bonded) sheath voltage rise or high-frequency sheath transients, where the enclosure geometry and the sheath return path change the field and voltage distribution. The space between cores and enclosure (bedding, fillers, oil, gas or polymer) is usually entered as one homogeneous material; this is rarely the dominant factor, because the main field is already controlled by each core–sheath insulation, but it should be reviewed for high-frequency or special studies.
Section 4
Pipe-type cables: three cores cradled inside a steel pipe
Pipe-type cables (high-pressure fluid- or gas-filled, HPFF/HPGF) carry three insulated, individually sheathed cores inside a steel pipe filled with oil or gas. The cores are not concentric with the pipe — they sit asymmetrically, usually cradled at the bottom, and the sheaths may be close enough to touch. The steel pipe is both the mechanical enclosure and an electrical return path, and it strongly influences the impedance of the system, so most Cable Constants routines provide a dedicated pipe-type template.
Why the pipe matters: it provides a return path for magnetic fields and currents, changes each phase’s series impedance, modifies or reduces the external ground-return effect, influences zero-sequence impedance, adds losses, affects travelling-wave behaviour and damping, and — being steel — may magnetically saturate under high current. At power frequency the skin depth in steel is small (its high, though nonlinear, permeability outweighs its higher resistivity), often less than the pipe wall thickness, so the return current is largely confined inside the pipe and external earth-return contributes comparatively little. That same skin effect makes the pipe a significant series-loss element, so the pipe is the dominant return path but not a lossless shield.
Modelling the pipe
Define each core’s position inside the pipe, the pipe radius and thickness, the pipe resistivity and — if steel — its magnetic permeability, which is an important and nonlinear parameter. Standard routines use linear material properties, so for high fault current the steel pipe’s saturation is not captured and the result is an approximation. A standard pipe-type model is usually sufficient for general switching transients; detailed fault-current, zero-sequence, loss or high-frequency studies need the pipe assumptions reviewed.
Section 5
Cables in tunnels and trenches: the equivalent-pipe approximation
Many installations are neither directly buried in uniform soil nor inside a circular metallic pipe: cables run in tunnels, trenches, concrete troughs, galleries, basements, shafts or on bridges. These cross-sections are usually rectangular or irregular, while Cable Constants routines expect circular or coaxial geometry. The practical approximation is to represent the tunnel or trench as an equivalent circular pipe, with its resistivity set to the wall material (reduced if the wall is steel-reinforced, to represent the extra metallic paths). This is a geometrical and electromagnetic approximation — a way to preserve the approximate spacing between the cable and the surrounding wall — not a full model of the tunnel and everything in it.
\(D_\text{eq}=D_1+D_2\) is a first guess, not the method
A common rule replaces the tunnel by a circle of diameter \(D_\text{eq}\approx D_1+D_2\), where \(D_1\) and \(D_2\) are the distances from the cable centre to the near and far walls. Treat this as a crude first estimate only. It is geometry-dependent: \(D_1+D_2\) is a meaningful diameter only when the cable lies on the line joining the two walls, and it ignores the other transverse dimension of a rectangular tunnel and the cable’s eccentricity — both of which strongly affect the result. A more defensible equivalent uses an area- or perimeter-equivalent circle, places the cable eccentrically, and includes a sensitivity check. Note too that dry concrete is a poor conductor, so its resistivity makes the equivalent pipe a lossy, partly transparent return — very different from a steel pipe.
The equivalent pipe is meant to capture the electromagnetic relationship between the cable and the surrounding wall — roughly, the surge impedance between the outer cable conductor and the wall. It does not capture irregular geometry, reinforcement layout, cable-tray bonding, parallel metallic services, multiple circuits, earthing conductors, ventilation ducts, water pipes, asymmetric wall materials or local bonding points. For high-frequency studies, induced-voltage studies, or installations crowded with metallic objects, a more detailed method — finite-element analysis or a validated equivalent network — may be required (Section 13).
Section 6
Surface and transfer impedance of solid and tubular conductors
The series impedance is assembled from how current flows in each metallic layer and how the magnetic field links the conductors. Two building blocks do most of the work: surface impedance and transfer impedance.
Surface impedance \(Z_s\) is the self-impedance of a conductor surface: a resistance plus an internal inductance, \(Z_s=R_\text{ac}+j\omega L_\text{int}\). As frequency rises, skin effect concentrates current near the surface, so the AC resistance increases; at the same time the internal inductance falls (internal flux is progressively excluded, \(L_\text{int}\to0\)). The overall magnitude grows roughly as \(\sqrt{f}\) — for a thick conductor \(Z_s\propto\sqrt{j\omega\mu\rho}\). It is the resistance and the magnitude that rise with frequency, not the inductive term.
Transfer impedance represents the electromagnetic coupling between the inner and outer surfaces of a hollow conductor — a sheath, armour or hollow core. Current on one face influences the field and current on the other; the coupling falls rapidly once the wall is many skin depths thick, because the two surfaces then decouple. A tubular conductor therefore needs three terms — inner-surface impedance, outer-surface impedance and the transfer impedance between them — while a solid conductor reduces to a single outer-surface term (the usual case for cable cores, except hollow fluid-filled designs).
Section 7
Skin depth and why steel behaves differently
Skin effect is the reason the series resistance and inductance change with frequency. At low frequency current uses most of the cross-section; at high frequency it crowds near the surface. The characteristic length is the skin depth:
\(\delta\) scales as \(1/\sqrt{f}\) and \(1/\sqrt{\mu}\), and increases with resistivity.
This explains why steel behaves differently from copper or aluminium. Steel’s relative permeability is large (hundreds to over a thousand), and that outweighs its higher resistivity, so its skin depth is far smaller — often only a few millimetres at power frequency. That is why a steel pipe or steel armour confines return current near its inner surface and dominates the return path (Sections 4 and 9). The catch is that steel permeability is nonlinear and saturable, so “high \(\mu\)” is a current-dependent statement, and the same small skin depth that confines the current also makes the steel a significant series-loss element.
Section 8
Assembling the series-impedance matrix
For a coaxial cable with core, sheath and armour, the routine combines the surface and transfer impedances of each metallic layer with the inductive contribution of the insulation gaps between them. The magnetic field exists in the insulation region, so each annulus between two metallic layers adds an inductive series term:
permeability of free space (insulation is non-magnetic, \(\mu_r=1\))
This is a purely inductive (magnetic-field) term. Insulation series losses are neglected; dielectric loss is not ignored — it appears in the shunt admittance \(Y'\) (Section 10), not here.
The core, sheath and armour are electromagnetically coupled, so the voltage drop in one conductor depends on its own current and on the currents in the other metallic layers. That is why the output is a matrix, not a single value: a single number cannot describe the interaction of core, sheath, armour and earth return. For three single-core cables, each with core, sheath and armour, this gives a \(9\times9\) series-impedance matrix (and a \(9\times9\) shunt-admittance matrix) before any sheath/armour elimination from the bonding, or modal/Clarke reduction, is applied for the line model.
Modelling message
If the sheath, armour or pipe can carry current, it should be represented as an electrical conductor whenever the study needs accurate sheath current, fault current, zero-sequence impedance or high-frequency transient behaviour. The matrix is reduced only afterwards, once the real bonding is imposed — and which layers stay in the matrix depends on that bonding. The internal-grounding versus explicit-bonding decision itself is covered in the sheath & armour grounding note, not repeated here.
Section 9
Ground-return impedance: Pollaczek and its approximations
Not all return current flows in metallic sheaths, armour or pipes. For underground cables — especially for zero-sequence and common-mode currents — part of the return path is the surrounding earth, so the earth-return impedance is an essential part of \(Z'\). It depends on frequency, soil conductivity, burial depth and the spacing between conductors, and a distinction must be drawn between self ground-return (one conductor returning through earth) and mutual ground-return (the coupling between two conductors through earth). A three-phase system therefore cannot be modelled by treating each phase independently.
The rigorous formulation for a buried conductor in a homogeneous half-space is the Pollaczek integral — accurate but a slowly converging improper integral that is numerically demanding, which is why closed-form approximations are used. The common ones for buried cables are the Saad–Gaba–Giroux (a closed-form, complex-image approximation of the Pollaczek integral), the Wedepohl–Wilcox formula, and Pollaczek’s own asymptotic forms; an “infinite-earth” assumption (an infinitely deep homogeneous half-space) is a further simplification rather than a named formula. Carson’s series is the dual problem for overhead conductors with earth return — it is covered on the general page and should not be confused with the buried-cable methods here.
How accurate is an approximation?
Compare it against a more accurate reference and quote the relative error:
Accuracy is not simply a function of frequency. It depends on a dimensionless ratio of the geometry (spacing, depth) to the complex penetration depth \(p=1/\sqrt{j\omega\mu\sigma}\); an approximation can degrade at low frequency or large spacing as well as at high frequency. Because the impedance \(Z\) here is complex, a single scalar error can hide large errors in resistance or reactance separately, so the real and imaginary parts are often checked individually. The practical rule: the approximation must stay accurate over the frequency range that dominates the transient — modest accuracy may do for power-frequency impedance, but lightning, restrike, harmonic-resonance and zero-sequence/common-mode studies are far more demanding.
What actually depends on it
Where the earth-return approximation bites depends on the quantity. The directly energised core’s series impedance is dominated by its own conductor and coaxial-annulus terms, so it is comparatively — not completely — insensitive to which earth-return formula is used. The induced voltages on adjacent cables, sheaths, pipelines and other metallic systems are not: they are governed by the mutual earth-return coupling, so the choice between Pollaczek, Saad–Gaba–Giroux and Wedepohl–Wilcox shows up most in those quantities, and in zero-sequence and common-mode current. Check the approximation against the induced or mutual quantity the study needs, not against the energised core alone.
Section 10
Shunt admittance and capacitive coupling between cables
The shunt-admittance matrix represents the capacitive and dielectric current between the conductors and metallic layers. In a coaxial cable the dominant capacitance is between the core and its sheath. For a coaxial insulation layer:
\[ C'=\frac{2\pi\varepsilon}{\ln(d/c)} \qquad Y'=G'+j\omega C' \qquad G'\approx\omega C'\tan\delta \]
\(C'\)
capacitance per unit length
\(Y'\)
shunt admittance per unit length
\(\varepsilon\)
permittivity of the insulation
\(c,\ d\)
inner and outer radii of the insulation region
\(G',\ \tan\delta\)
shunt conductance and dielectric loss factor
\(\omega\)
angular frequency, rad/s
If dielectric loss is neglected, \(Y'=j\omega C'\). This is where dielectric loss enters the model — in the shunt admittance, not the series impedance. The cable workflow covers permittivity and tan δ in detail. The \(\delta\) in \(\tan\delta\) is the dielectric loss angle, not the skin depth \(\delta\) used in the skin-effect section.
The capacitance is sensitive to geometry: if the insulation thickness or the effective insulation radius (after folding in the semiconducting screens) is slightly wrong, \(C'\) changes — which is why matching the calculated capacitance to the manufacturer value is the best single validation check.
Why separate single-core cables decouple capacitively
When each core is enclosed by a continuous (closed, tubular) metallic sheath that is grounded (or bonded), the sheath is an equipotential held at reference, so the core’s own field terminates on the sheath and, outside it, that core contributes essentially no field. The direct core-to-core capacitive coupling between separate single-core cables is then normally negligible, and the shunt-admittance matrix is near-block-diagonal (separate phase blocks). This holds for a closed, continuous sheath acting as an ideal equipotential at reference; it should not be assumed for discontinuous or open wire screens, damaged or interrupted sheaths, isolated or floating sheaths, special terminations, or very high-frequency cases where the screen is not an ideal equipotential surface. The inter-cable shunt coupling that does exist is between the sheaths, through the shared outer (earth, pipe or air) dielectric. This capacitive decoupling does not make the cables independent: magnetic and ground-return coupling remain important in the series-impedance matrix (Sections 8–9).
Section 11
Pipe-type series impedance and shunt admittance
Pipe-type cables need special treatment because the three cores share a common pipe that carries return current. The series impedance calculation includes the core impedance, each core’s sheath impedance, the core–sheath insulation term, the sheath/armour-to-pipe term, the inner-surface impedance of the pipe, and the mutual impedance between cores through the pipe. Because the cores are not concentric with the pipe, the offset of each core from the centre and its angular position both matter — they change the mutual coupling. The modeller does not derive these by hand when the software has a pipe-type routine, but should treat the pipe as part of the electrical model, not a passive mechanical detail.
The shunt admittance of a pipe-type cable is built from the capacitances of each coaxial region — core-to-sheath and sheath-to-pipe-inner-wall — using the same coaxial formula \(C=2\pi\varepsilon/\ln(r_o/r_i)\). Each continuous sheath acts as an electrostatic shield, so the inner conductor’s field terminates on its own sheath and the pipe is the outer reference only for the sheath-to-pipe capacitances. For this simplified closed-sheath representation, with grounded, continuous sheaths, the dominant capacitances can be assembled from the coaxial regions through a connection (incidence) matrix rather than by inverting a full Maxwell potential-coefficient matrix. This coaxial reduction is exact only where each core/sheath assembly is concentric within the pipe; any residual sheath-to-sheath or sheath-to-pipe coupling inside the enclosure is still handled through potential coefficients. Some formulations express the same problem through potential coefficients throughout, especially where conductors are treated as bare inside a common enclosure (the method also used for overhead/buried bundles). The key modelling point is that the pipe is an electrical reference and return path, not only a mechanical enclosure — so a pipe-type cable should normally be modelled with the dedicated pipe-type input rather than as three independent single-core cables.
Section 12
The spiral effect of wire screens and helical sheaths
Some cables use copper or aluminium wires, or spiral metallic tapes, as the screen or sheath. The sheath current then does not flow straight along the axis — it follows a helical path. That helix adds inductance between the core and the sheath, and the effect grows with the lay angle (a longer helical path per unit length). It can be represented by an added series inductance per unit length:
mean (pitch-circle) diameter of the helical wire screen
\(p\)
winding pitch (axial length of one turn)
\(\mu_0\)
permeability of free space
\(\omega\)
angular frequency, rad/s
The factor \(\pi d_{sm}/p\) is a turns-density term (turns per unit length × helix circumference). This is an additional, purely inductive series term — it adds in series with the sheath surface impedance; it does not replace the surface impedance or its resistance. Treat it as an order-of-magnitude estimate; some formulations add a geometric/coupling coefficient.
A larger helix diameter or a shorter pitch (more turns per unit length) increases the term. If the spiral effect is ignored, the calculated surge impedance and propagation velocity can be inaccurate; measurements have shown that adding the spiral inductance improves agreement with measured travelling-wave behaviour. It is most relevant where high-frequency propagation matters — lightning surges, restrikes, steep-front energisation, travelling-wave protection, surge-arrester coordination and cable-terminal overvoltages — and less significant, though still worth considering, at low frequency.
Section 13
Limits of analytic Cable Constants — and when FEM is needed
A general Cable Constants routine cannot represent every cross-section. Real systems include complex geometry, multiple circuits, non-circular ducts, steel reinforcement, armour wires, corrugated sheaths, screens with gaps, segmented conductors and nearby metallic infrastructure — and effects such as steel-pipe saturation that linear routines do not capture. Where the geometry cannot be represented with confidence, auxiliary methods are used:
Finite-element electromagnetic analysis — especially where proximity effect, complex armour geometry, steel saturation, tunnel reinforcement or non-standard installation geometry dominates.
Conductor subdivision — splitting conductors into filaments to compute proximity effect and non-uniform current.
Manufacturer or measured data — impedance, capacitance, sequence impedance or frequency-response measurements.
Validated equivalent circuits and specialist cable-parameter software.
Whatever the method, the result must end up in a form the time-domain simulation can use: frequency-dependent \(Z'\) and \(Y'\) data, or a validated wideband model. The cable workflow covers the fitting and passivity checks that this final step needs.
Section 14
Choosing the right cable representation
The cable design determines the modelling approach. Single-core cables suit coaxial modelling, but their sheath bonding and installation must be represented carefully. Three-phase self-contained cables need an approximation chosen by whether the common enclosure is metallic (pipe-type) or insulating (cables in earth, avoiding a phantom conductor). Pipe-type cables should use the dedicated pipe-type representation because the steel pipe is part of the electromagnetic return path. Tunnels and trenches can be approximated by an equivalent pipe when the study does not need detailed field modelling.
Design approximation limits
Do not trust a pipe-type or coaxial approximation for induced sheath voltage, cross-bonding or SVL duty without checking it against that quantity — not just the positive-sequence impedance.
Do not treat a wire screen or spiral sheath as a perfect continuous tube for high-frequency or travelling-wave studies without accounting for the lay/spiral effect.
Do not assume a ground-return approximation that is fine at 50 Hz is harmless for induced-voltage, zero-sequence or wideband studies.
Main takeaway
A good cable model is not the one with the most complicated input — it is the one that correctly represents the conductors, sheaths, armour, pipe, insulation, earth return and bonding over the frequency range the transient demands. Match the design type to the formulation, know which physical effect each matrix term captures and where it is approximate, and validate the internals — capacitance, sequence impedance, sheath current — before feeding \(Z'\) and \(Y'\) into the line/cable model. The detailed mathematics (surface and transfer impedance, ground-return, potential coefficients, numerical approximations) need not be reproduced by hand, but the modeller must understand what each part represents physically.
References
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.
IEC 60287-1-1:2023, Electric Cables – Calculation of the Current Rating – Part 1-1: Current Rating Equations (100% Load Factor) and Calculation of Losses – General. 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 (Um = 36 kV) up to 150 kV (Um = 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 (Um = 170 kV) up to 500 kV (Um = 550 kV) – Test Methods and Requirements. Geneva, Switzerland: International Electrotechnical Commission, 2022.
CIGRE, A Guide for Rating Calculations of Insulated Cables, Technical Brochure 640. Paris, France: CIGRE, 2015.
Sixteen-Part Technical Series
EMTP® Line, Cable & Lightning Modelling
A sixteen-part guide spanning line and cable modelling, overhead-line physics, lightning, and the dielectric strength of external insulation.
03
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Cable Designs & Parameter Calculation
Cable construction and geometry, and the series-impedance and shunt-admittance parameters needed for the model.
