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We have introduced a new plot displaying calculated induced currents in earth continuous conductors. These currents are generally undesirable, making the abbreviation ICE an apt choice. Unlike their namesakes, however, induced currents in earth continuous conductors are not always unwelcome — they can in fact be beneficial, playing a role in controlling induced voltages in cable screens.
Posted 2026-04-06
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In high voltage cable installations, it is common to install parallel earth continuous conductors or short ECC. Magnetic coupling from the energized circuits induce a current in these cables or bars. This influences the induced voltage in the screen/sheath of the high voltage cables but they also produce additional ohmic losses which may reduce the cable rating if the ECC is positioned close to the cables.
With the new ICE plot feature in Cableizer, you can now generate a route-based visualization of this induced current in a parallel earth continuous conductor directly at the end of a rating calculation. Instead of naming this plot ECC we thought to give it a more fitting abbreviation ICE which stands for Induced Current in ECC – an abbreviation nowadays universally understood as being unwanted and disturbing. While the induced currents are an unwelcome nuisance in cable system design because it produces additional losses the ECC can help to control the induced voltage on open- and cross-bonded cable screens which is what we want to talk about.
The implementation is based on the work of Mikhail Dmitriev in his latest book 'High Voltage Cable Lines', excellent reading material for the engineer interested in cable technology.
High-voltage single-core cable systems at 50–550 kV carry three separate phase conductors, each wrapped in a metallic screen. Those screens must be grounded to be safe but how they are grounded determines whether the installation is practical.
The question engineers face on every medium-to-long HV cable project is: can we stay with single-end bonding, or do we have to cross-bond?
One way to extend the range of single-end bonding is to lay a highly conductive metal conductor alongside the cable route, grounded at both ends. In the literature this is known as an Earth Continuity Conductor (ECC).
The physics is straightforward. Without an ECC, single-phase fault return current flows through the earth at an effective depth $D_G$ typically hundreds of metres for typical soil resistivity. The large loop formed by the cable screen and that deep return path produces a large induced voltage.
When the ECC is installed close to the cables at distance $S_b \ll D_G$, fault current diverts into the ECC instead of the deep earth. The screen-ground loop area shrinks dramatically, and so does the induced voltage.
The ECC can take different physical forms depending on the installation environment.
Underground installations — the most common case — typically use a standard insulated low-voltage cable as the ECC, with all cores connected in parallel to achieve the required cross-section. The cable is routed either:
The insulation jacket serves a dual purpose: it prevents the ECC from making incidental contact with the surrounding soil or structures along its length, and it can be matched to the HV cable outer sheath to deter theft.
Above-ground installations — such as cable routes inside an energy tunnel — typically use a bare metal bar (steel, aluminium, or copper) mounted on insulators that isolate it from the tunnel structure and earth along the entire route. The bar is then connected to the grounding systems only at the two route ends.
The ECC is only useful during asymmetric faults — specifically, a single-phase short-circuit outside the cable line. In normal operating conditions and during three-phase faults (symmetric modes), the three core currents are balanced. The mutual couplings from the three phases nearly cancel, almost no current flows in the ECC, and the ECC has no effect on induced voltages.
This has a direct consequence for network voltage class:
| Network | Neutral | Design fault | ECC useful? |
|---|---|---|---|
| 50–550 kV | Solidly grounded | Single-phase short-circuit | Yes |
| 6–36 kV | Isolated / compensated / resistive | Three-phase short-circuit | No |
The ECC is therefore a tool exclusively for transmission-class HV systems.
A common civil engineering practice is to lay a bare copper conductor directly in the soil in parallel with the cable trench — for example as a combined lightning protection and grounding electrode. This configuration looks similar to an ECC but behaves fundamentally differently: the conductor is in electrical contact with the earth continuously along its entire length, not just at the two endpoints.
ICE does not cover this case. The calculation method implemented here assumes that the ECC is insulated from earth along the route and grounded only at both ends. When a conductor is continuously grounded through the soil, both the circuit equations and the physical behaviour change — the return current distribution, the effective impedance, and the resulting induced voltages must all be treated with a different model. Applying the ICE results to a continuously grounded conductor would give incorrect and non-conservative answers.
To compare ECC options quantitatively, the efficiency coefficient $K_b$ is defined as the ratio of the screen voltage with the ECC to the screen voltage without it:
$$K_b = \frac{U_s \text{ (with ECC)}}{U_s \text{ (without ECC)}}$$A value of $K_b = 1$ means the ECC does nothing. The lower $K_b$ falls below 1, the more the ECC reduces the induced voltage. For a given project, the required $K_b$ is simply:
$$K_b \leq \frac{U_s^{lim}}{U_s}$$where $U_s^{lim}$ is the permissible screen voltage (typically 7 000 V or 10 000 V depending on the standard applied) and $U_s$ is the voltage calculated without an ECC.
The efficiency coefficient depends on three ECC parameters:
Proximity matters as much as material. A copper ECC at 1.0 m may underperform a steel ECC at 0.3 m.
Summary
The ECC is a cost-effective way to keep single-end screen bonding viable on HV cable routes that would otherwise require cross-bonding. Its effectiveness is governed by ECC material, cross-section, and placement — and it is exclusively useful in 50–550 kV solidly grounded networks where single-phase faults are the design case.
The ICE tool automates the impedance-matrix calculation described in Chapter 4.1 for insulated ECCs grounded only at both ends — the configuration used in the vast majority of underground and tunnel installations. Engineers can quickly screen ECC options, compare materials, and confirm that the chosen specification brings $K_b$ below the project-specific threshold before any cables or ECCs are ordered.
ICE (ECC Induced Current Solver) implements this multi-conductor impedance-matrix method in Python. It is designed to handle the full range of screen bonding configurations encountered in practice:
with one (or more) insulated ECCs bonded at both route ends.
The full calculation solves a system of steady-state voltage-drop equations written simultaneously for the three cable screens and the ECC, accounting for:
The boundary conditions encode the bonding scheme. For single-end screen bonding with a both-end bonded ECC: screen currents are zero ($\dot{I}_{sA} = \dot{I}_{sB} = \dot{I}_{sC} = 0$) and the ECC has no longitudinal voltage drop ($\Delta\dot{U}_b = 0$).
For a single-phase fault on phase A — with the non-faulted phase currents set to zero as a conservative approximation — the ECC current becomes:
$$\dot{I}_b = \frac{\dot{Z}_{bA}}{\dot{Z}_b + \dot{Z}_{gr1} + \dot{Z}_{gr2}} \cdot \dot{I}_{cA}$$and the induced voltage on phase A's screen simplifies to:
$$\Delta\dot{U}_{sA} = \left(\dot{Z}_{cs} - \dot{Z}_{bA} \cdot \frac{\dot{Z}_{bA} + \dot{Z}_{gr1}}{\dot{Z}_b + \dot{Z}_{gr1} + \dot{Z}_{gr2}}\right) \cdot \dot{I}_{cA}$$With ideal grounding ($Z_{gr1}, Z_{gr2} \rightarrow 0$), the efficiency coefficient reduces to a clean form that is independent of route length $l_{cl}$:
$$K_b = 1 - \frac{(\dot{Z}_{bA}^*)^2}{\dot{Z}_{cs}^* \cdot \dot{Z}_b^*}$$This is the working formula for ECC selection. The asterisk (*) denotes per-unit-length impedances.
After completing the rating calculation, Cableizer provides a modal window titled "Induced current in earth continuity conductor". In this window you select which system is treated as the victim — the ECC whose induced current you want to evaluate — and trigger the calculation for that system. You can repeat the process by selecting a different victim.
The ICE inputs are split into two groups: a small set of global parameters entered once at the top of the modal, and a per-system table that mirrors the structure already familiar from the EMF and WRK modal windows.
Global Parameters
| Parameter | Meaning | Typical input guidance |
|---|---|---|
rho_E [Ω·m] |
Electrical resistivity of the soil surrounding the cable route. Used to compute the effective earth-return depth $D_G$. | Use a site-measured value where available. In the absence of measurements, national standards or conservative estimates (e.g. 100 Ω·m for moist soil, 1 000 Ω·m for dry sand) are commonly applied. |
U_k [V] |
Permissible induced voltage on the cable screen — the limit against which results are assessed. | Use the value agreed for the project. For continuous operation typically 50 V or 65 V are used depending on the legal requirements. If you consider a high short circuit current by modifying the cable current then set a typical value for the induced voltage which is still permissible depending on screen insulation rating and the applicable standard. |
Per-System Parameters
The following inputs are defined for each cable system present in the project.
| Parameter | Meaning | Typical input guidance |
|---|---|---|
system |
Cable system identifier shown as the system label together with the configuration summary (number of circuits × cores per cable × cable type). | Review the description to ensure you are selecting the correct circuit, especially in projects with multiple similar cable types. Select the system you want to treat as the victim ECC using the corresponding Go button. |
I_c [A] |
Load current magnitude of the system. | For inducing systems, use the expected operating current for the scenario of interest (normal load, contingency, fault level, etc.). For the victim ECC, this value is typically not critical since the ECC carries no load current of its own. |
f [Hz] |
System frequency used for coupling evaluation. | Enter the actual operating frequency of each system. This matters when multiple systems operate at different frequencies, as the phase relationship changes over time. |
α_f [°] |
Phase shift of the system current relative to a reference. | Use 0 to represent "in phase" with the reference. For different-frequency systems, any value from 0° to 360° may be used. Keep values consistent across scenarios. |
loadflow [1 / −1 / 0] |
Load flow direction and activation state: 1 = positive direction, -1 = negative direction, 0 = deactivated (excluded from induction). |
Set 0 for systems that should not contribute to induction in the considered scenario. At least one system must be set to 1 or -1, otherwise there is no energised source and no induced current can be computed. Use the correct direction when studying cancellation or reinforcement effects between circuits. |
start / end [m] |
Route position limits of each system along a common reference coordinate. Only sections where an inducing system runs in parallel with the victim ECC contribute to the induced current. | Use the same stationing reference for all systems from the same route origin. Check that victim and inducing systems overlap where they physically run in parallel. Partial overlap contributes only over the overlapping segment. |
Calc. (Go) |
Runs the ICE calculation for the selected victim system and generates the result plot. | Click Go on the row of the system you want to treat as the victim. Repeat for other systems if needed. |
Parameters Taken Directly from the Project
The following quantities are not entered in the modal — they are read automatically from the cable system definitions already set up in the project:
| Parameter | Source |
|---|---|
| Cable type and cross-section | Cable library selection |
| Screen dimensions and resistivity | Cable construction data |
| Phase arrangement (trefoil / flat) and cable spacing | Installation geometry |
| ECC material, cross-section, and position relative to cables | ECC definition in the installation |
| Route length | Derived from start / end positions |
This means the modal stays compact: the engineer only needs to provide the scenario-specific electrical quantities (currents, frequencies, phase shifts, load flow directions, and route extents). All geometry and conductor properties flow in automatically.
Note: At least one cable system must have a load flow of 1 or −1. If all systems are set to 0, there is no energised source and no induced current can be computed.
Consider a 110 kV cable line, 800/240 mm² (copper core, copper screen), cables in a closed triangle arrangement, single-end screen bonding. The cables are installed in an urban area where ground return depth is conservatively taken as $D_G = 10$ m (a site-specific expert estimate rather than the formula-derived 1,127 m).
A single-phase fault in the external network produces a screen voltage of $U_s = 8 820$ V without an ECC. The permissible limit is $U_s^{lim} = 7 000$ V. The required efficiency is:
$$K_b \leq \frac{7 000}{8 820} \approx 0.80$$Running ICE for an ECC placed at $S_b = 0.3$ m from the cables shows the following minimum cross-sections that meet $K_b \leq 0.80$:
| ECC material | Minimum $F_b$ |
|---|---|
| Steel (Fe) | 270 mm² |
| Aluminium (Al) | 90 mm² |
| Copper (Cu) | 50 mm² |
All three options achieve the same electrical outcome — $U_s$ drops to at most 7 000 V. The final choice is a cost comparison. At a distance of $S_b = 1.0$ m, none of these cross-sections are sufficient; the ECC must be installed close to the cables.
The arrangement consists of two systems of 2500mm2 Cu cables in ducts in flat arrangement one above the other in a backfill. In additional two ducts we have installed an ECC each. We will run the calculations for system C which is at the top and its ECC which is inside the left pipe.
| Arrangement | Induced voltage in screen (for information) |
|---|---|
 |
 |
The induced voltage is shown for information purposes.
The ambient temperature $\theta_a$ is 15°C, the thermal resistivity of the soil is $\rho_4$ is 1.0 K.m/W. We consider a specific electrical resistivity of the soil of $\rho_E$ = 100 Ω.m and want to check the efficiency of the ECC for a max permissible induced voltage under normal operation of $U_{lim}$ = 50 V.
The calculation was done for different cases to show the capabilites of the tool and the impact of some parameters:
The resulting plots with the induced current is shown for the four cases:
| Case 1 | Case 2 |
|---|---|
 |
 |
| Case 3 | Case 4 |
|---|---|
 |
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High Voltage Cable Lines by Mikhail Dmitriev. Porto, Portugal, 2024. 690 p.
This book explores the design, construction and operation of alternating current cable lines rated from 6 to 500 kV, consisting of single-core or three-core cables with XLPE insulation. It is intended for employees of design organizations and power grid companies, as well as university students.