6.1 Cable Sizing & Correction Factors

Cable Sizing Principles in BS 7671

Designing an electrical installation requires strict adherence to BS 7671 (The IET Wiring Regulations, 18th Edition Amendment 2). One of the most critical aspects of electrical design is ensuring that cables are appropriately sized to carry the required load without overheating, while also being adequately protected by overcurrent devices against overloads and short circuits. This requires a systematic approach following standardized mathematical relationships.

The Fundamental Relationship

The core of cable sizing revolves around a vital inequality that must be satisfied for every circuit:

Ib ≤ In ≤ Iz

Where:

• Ib = Design current of the circuit (the actual current the load will draw under normal operating conditions).
• In = Rated current or current setting of the protective device (e.g., the MCB rating or fuse rating).
• Iz = Continuous current-carrying capacity of the cable in its specific installed environment.

The design current (Ib) is calculated by dividing the active power (P in Watts) by the supply voltage (U = 230V for single-phase AC, or U = 400V for three-phase AC), accounting for power factor (cos φ) and efficiency where applicable. Once Ib is determined, a standard protective device rating (In) is selected such that In ≥ Ib. Finally, the cable must be selected so that its effective thermal capacity (Iz) in its installed state is equal to or greater than the protective device rating (In).

Understanding Tabulated Capacity (It)

Appendix 4 of BS 7671 provides comprehensive reference tables detailing the tabulated current-carrying capacity of various cable types (e.g., thermoplastic PVC, thermosetting XLPE, mineral insulated) under standard reference installation conditions (e.g., ambient temperature of 30°C, un-grouped, clipped direct). This standard capacity is denoted as It.

Because physical installations rarely mirror standard laboratory reference conditions, the electrician must derate the cable using correction factors. The formula to calculate the minimum required tabulated current-carrying capacity (It) is:

It ≥ In / (Ca × Cg × Ci × Cf × Cc)

Correction Factors Detailed

Correction factors are dimensionless multipliers (typically ≤ 1.0) applied to compensate for environmental and installation conditions that impair the cable's ability to dissipate heat:

Ca - Ambient Temperature Factor

BS 7671 tables assume an ambient air temperature of 30°C (or ground temperature of 20°C for buried cables). If the ambient temperature is higher, heat dissipation is hindered, raising conductor operating temperature. Table 4B1 provides Ca values (e.g., Ca = 0.87 for 40°C PVC). If temperature exceeds standard levels, Ca reduces allowable current.

Cg - Grouping Factor

When multiple power carrying cables are installed in close physical contact (such as enclosed together in conduit, trunking, or bundled on a cable tray), mutual thermal radiation occurs. Table 4C1 provides Cg values based on the number of grouped circuits. For example, grouping 4 single-phase circuits in trunking yields a Cg factor of 0.65, meaning each cable's effective capacity is reduced by 35%.

Ci - Thermal Insulation Factor

Thermal insulation installed in modern energy-efficient buildings severely restricts heat loss from cables. Under BS 7671 Regulation 523.9:

• If a cable is totally surrounded by thermal insulation for a length of 0.5m or more, a derating factor of Ci = 0.50 must be applied (halving its current capacity).
• If surrounded for shorter lengths (e.g., 100mm to 400mm), specific derating factors from Table 52.2 apply.

Cf and Cc - Device and Direct Burial Factors

• Cf = Semi-enclosed (rewirable) fuse factor to BS 3036. Rewirable fuses have a high fusing factor (1.45), so Cf is fixed at 0.725 to protect against prolonged overloads.
• Cc = Direct burial factor. Fixed at 0.9 for cables buried directly in soil or ducting to account for soil thermal resistivity.

Protective Devices: MCB Tripping Characteristics

Miniature Circuit Breakers (MCBs) manufactured to BS EN 60898 provide overload and short-circuit protection. They are categorized by magnetic tripping characteristics that specify the instantaneous trip threshold required to clear high fault currents:

• Type B: Trips instantaneously at 3 to 5 times rated current (3-5In). Designed for domestic and light commercial resistive loads (heating, standard domestic socket and lighting final circuits) where switching surges are minimal.
• Type C: Trips instantaneously at 5 to 10 times rated current (5-10In). Designed for commercial and industrial installations containing moderate inductive loads, such as small electric motors, fluorescent lighting arrays, and transformer power supplies with moderate inrush currents.
• Type D: Trips instantaneously at 10 to 20 times rated current (10-20In). Reserved for industrial applications with very high transient inrush currents, such as large industrial motors, arc welders, X-ray machines, and site transformers.

Selecting the correct MCB type ensures robust fault protection while preventing frustrating operational nuisance tripping.