7. Cable Sizing and Derating

Principle: Cable sizing ensures that conductors have sufficient cross-sectional area to carry the expected current without overheating or excessive voltage drop. The “ampacity” (permissible current) of a cable depends on installation conditions, insulation type, ambient temperature, grouping with other cables, soil thermal resistivity (if buried), etc. Derating factors are applied to the base current capacity to account for these conditions. The general approach is: Required Cable Current Capacity = Design current ÷ (product of applicable derating factors). The chosen cable size must then have a rated capacity (from standards) at least equal to that required capacity.

Key Factors Affecting Cable Current Rating

Ambient Temperature (factor C_a): Cables are typically rated at a reference ambient (e.g., 30°C for air). If the actual ambient is higher, capacity reduces. For example, at 40°C a PVC cable might only carry ~0.87 of its 30°C rating.
Thermal Insulation (factor C_i or C_t): When a cable is surrounded by insulation or located in a hot conduit, it cannot dissipate heat effectively, so its current capacity must be reduced. For example, BS 7671 gives a factor of ~0.5 if a cable is fully surrounded by insulation for more than 0.5 m.
Grouping (factor C_g): When multiple cables run together (in a conduit, tray, or bundle), they heat each other. Standards provide grouping factors depending on the number of circuits and spacing; more cables result in a lower factor (e.g., 3 touching cables might have C_g ≈ 0.7).
Cable Arrangement: The installation method—whether in trays with air, buried in the ground, or in ducts—affects the base rating and may require additional factors (e.g., C_c or C_d for depth).
Conductor Material and Insulation: Different conductor materials (copper vs. aluminum) and insulation types have varying properties. For example, PVC insulation typically has a maximum temperature of 70°C, whereas XLPE can operate at 90°C or 110°C, allowing a higher current rating for the same size.
Altitude: At higher altitudes, the thinner air reduces cooling efficiency, which can lower a cable's ampacity.
Harmonic Currents: Non-linear loads may cause increased heating due to harmonics. In three-phase systems with triplen harmonics, the neutral can carry up to 1.73× the phase current, sometimes necessitating a larger neutral conductor.

Cable Sizing Process

Determine the design current I_b: For example, calculate from the load power divided by voltage and power factor.
Choose a tentative cable type and route: For instance, selecting a multicore PVC cable in a conduit on a wall.
Obtain the base rating I_base: Use standard tables for the chosen cable size and installation method at reference conditions.
Identify all relevant derating factors: Such as C_a (ambient), C_g (grouping), C_i (thermal insulation), etc.
Calculate the required minimum rating: I_req = I_b / (C_a × C_g × C_i ...).
Select a cable size: Ensure that its base rating I_base meets or exceeds I_req.
Verify voltage drop: Check that the selected cable size maintains an acceptable voltage drop, and adjust if necessary.
Verify short-circuit withstand: Use the adiabatic check (see section 13) to ensure the cable can handle short-circuit conditions.

For example, suppose a 50 A load is to be served in an environment at 40°C (with C_a = 0.91), with two circuits bunched together (C_g = 0.85), using 90°C XLPE cable. Then:

I_req = 50 / (0.91 × 0.85) ≈ 64.5 A.

You would select a cable whose rating at reference conditions (30°C, single circuit) is at least ~65 A. For instance, a 10 mm² XLPE cable (clipped direct) might be rated for ~70 A, which could suffice. Next, you would check the voltage drop; if the run is 50 m long and the drop is too high, a larger cable such as 16 mm² might be needed.

Niche and Less Common Applications

High Ambient or Industrial Plants: In environments such as steel mills at 50°C, cables are often upsized significantly.
Cables on Roofs: Exposure to direct sunlight may require additional derating for solar heating.
Underground Cables: Variations in soil thermal resistivity and the presence of multiple circuits in one trench may require advanced calculations or finite element simulations.
Enclosed in Conduit vs. Free Air: A cable in free air benefits from better convection cooling compared to one in a tight conduit.
Fire-Protected Cables: Cables in fire-proof wraps or filled ducts dissipate heat less effectively, necessitating heavy derating.
Submarine Cables: Although water cooling is advantageous, these cables are often continuously loaded, requiring unique thermal considerations.
Busways or Cable Bus Systems: While they have their own sizing methodologies, the basic principle of applying a base rating and derating factors remains the same.

Industry Relevance and Standards

Proper cable sizing is critical to prevent overheating, insulation breakdown, fires, and excessive voltage drop. Undersized cables can lead to hazardous conditions, while oversized cables increase costs and complicate terminations. Consequently, codes such as BS 7671 and NEC provide extensive tables and guidelines.

BS 7671 Appendix 4: Offers tables for current-carrying capacities under various installation methods (e.g., in conduit, clipped direct) along with derating factor tables for ambient temperature, grouping, and insulation.
IEC 60364-5-52: Provides the international framework for presenting ampacity, which is then adapted by national standards.
NEC (NFPA 70): Articles 310 and associated tables present ampacity for different insulation ratings and installation conditions, including corrections for ambient temperature and conductor bundling.
IEEE/ICEA Standards: These standards offer methodologies for calculating cable ampacities, with considerations for buried cables and varying environmental conditions.

Software Tools

Cable Sizing Programs: Tools such as ETAP and SKM include modules that, given load current, route details, ambient conditions, and more, recommend the proper cable size.
Manufacturer Tools: Calculators from companies like Nexans or Prysmian allow you to enter installation parameters and output the required cable size.
Spreadsheets: Many engineers use in-house Excel models that incorporate standard tables and derating factors (often referencing BS 7671 or NEC tables).
Online Calculators: Numerous electrical engineering portals offer quick cable sizing calculators based on insulation type, installation method, and bundling.
Thermal Simulation Software: For large or critical installations, finite element analysis tools (e.g., CYMCAP) can model cable heating under various conditions.

Although cable sizing might seem routine, it is a critical task in electrical design. By following standards and using appropriate tools, engineers ensure safe, efficient, and cost-effective cable selections that prevent overheating, minimize voltage drop, and comply with safety regulations.