There cannot be a real discussion about solving the world’s electric power requirements without seriously considering the ampacity of the power cables used in the transmission and distribution of the power from the sources (generator, solar, wind, plasma fusion, etc.) to the customer loads consuming power.

FEA solutions must be used for any case that is not covered by the standards and these are not limited to convective and radiative heat transfer problems. Power cable installation examples for which conductive heat transfer problems require FEA solutions include multiple duct banks, cooling/heating pipes around duct banks, and when the soil has several layers of different materials.

There are many cable installations that do not have a good standard. Here are a few examples but there are a lot more:

Cables in tunnels (differing size, carrying different loads, no standard)

Cables in trays (ladder, solid bottom, covered and uncovered)

Cables in riser poles (vented or not)

Cables in troughs

Cables in J tubes

Fire protected cables

Duct banks with large aspect ratios

Duct crossings

Multiple duct banks

Bentonite in ducts

Ducts in tunnels

Cable Joints

Cables with rain

Busbars

Longitudinal flow

There are many other things that are not considered in the standards correctly. In particular, the magnetic behavior is mostly wrong. Circuits are considered magnetically decoupled even when we know they are very coupled. This is well documented. Also, FEA can simulate 3D models of any type of power cable installation, while popular competitor template-based software is limited to standard 2D model installations.

The Ansys design tools include industry-based material libraries and multi-physics capability to allow designers to make guided technical decisions in the power cable design selection process.

Geometry

• Import into Ansys or create using Ansys CAD tools.
• Objects include cable and layers (single-core, trefoil, three-core, etc.), and may include ducts, tunnels, backfill, soil, etc.

Material Properties

• Determined from standards (NEC, IEEE, or IEC) or from manufacturer specification sheets.

Mesh

• Ozen engineers have substantial experience and knowledge to produce high quality meshes and have challenging CFD simulations to converge.
• Thermal boundary layers are computed, and meshing techniques are applied to increase mesh quality while minimizing the number of mesh elements.

Physics

• Heat sources are computed using standard equations (NEC, IEEE, or IEC) or using ac/dc ratios and loss distributions given by cable specification sheets.
• Ansys Maxwell is used to solve for electromagnetic losses and couple with CFD when standard heat source equations are not used.
• Conjugate Heat Transfer solvers are used when there is conductive and convective heat transfer in the model and CHTs are used on BCs.
• CFD is used when there is convective heat transfer in the model and fluid flow field is solved.
• Radiative Heat Transfer solvers are enabled when there is radiative heat transfer between surfaces.

Validation

• Designs are validated using data from manufacturer data sheets.

Ampacity of a power cable depends on the specific installation and operation conditions as described below:

Installation

• External thermal resistance (most important)
• Thermal properties between the cable surface and the ambient air (air or other fluid within cable enclosure, duct walls, tunnel walls, soil, backfill, ocean water, etc.).
• FEA models do not require using an equivalent (effective) external thermal resistance.
• FEA models can easily and realistically represent underground material (soil, backfill, etc.) with varying thermal properties.
• The sheath bonding type is the second most important parameter.
• Solid Bonding is always used in the USA. Other countries may use Solid Bonding, Cross Bonding, or Single Point Bonding.
• Ambient temperature.
• Depth (if buried).
• Conductor size and material.
• Cable layers and materials.
• Number of cables (loads) and proximity to between cables.
• Solar radiation.
• Enclosure clearances.
• Ventilated (forced convection) or non-ventilated (free convection)

Operation

• Operating time, load factor, varying load cycle, operating frequency (DC or AC).
• Emergency load transfers.

Determination of power cable ampacity is a multi-physics task. The heat source equations used in the standards were derived from electromagnetic theory and applied to heat transfer theory.

Electromagnetics: Maxwell’s equations are the governing equations to compute the losses due to the:

• Skin and proximity effect
• Dielectric (insulation)
• Sheath and armor
• Duct or pipe enclosing the cable.

Conservation of energy: The losses are applied in the conservation of energy so that power loss in the cable, heat generated via conduction, is equal to the heat transferred out of the cable.

The three modes of heat transfer are:

• Conduction: Heat generated in and transferred out of solid objects (cable and layers, enclosure walls).
• Convection: Heat transferred by fluid (air, water, oil, etc.).
• Radiation: Heat transferred by between surfaces (cables, enclosure walls, etc.).

Fluid Flow: The Navier-Stokes equations are the governing equations to determine fluid flow in convection heat transfer and these are solved using CFD.

Results may include:

• Temperature distribution plots of conductors and system
• Fluid flow plots of air around cables and system.
• Temperature transient plots of conductors and cable layers.
• Compare convective and radiative heat transfer values to determine the dominant mode.

Regarding optimization & robust design solutions there is a need for efficient optimization techniques which can offer data-driven exploration of the design space while utilizing multi-physics simulation:

• The power cable system design space is large with complex interactions.
• Use of OptiSLang enables:
  
• Class-leading multi-physics power cable system optimization.
• Traceability on design decisions and data-based trade-off analysis.
• Efficient multi-objective design optimization and fast response to changing requirements.
• Robust design insights.

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