6.2 Voltage Drop Limits & Protection Selection

Voltage Drop Limits and Disconnection Time Verification in BS 7671

Correct cable selection in accordance with BS 7671 (18th Edition Amendment 2) extends beyond ensuring current-carrying capacity (Iz ≥ In). A candidate in the AM2 assessment must demonstrate full competence in verifying two further statutory criteria: ensuring that cumulative voltage drop does not impair equipment functionality and confirming that automatic disconnection of supply (ADS) occurs within prescribed time limits under earth fault conditions.

Fundamentals of Voltage Drop and Ohm's Law

Every electrical conductor possesses finite internal electrical resistance proportional to its length, cross-sectional area, and material resistivity. As load current flows through a conductor, energy is dissipated as heat, resulting in a potential difference (voltage drop) between the supply origin and the load terminals in accordance with Ohm's Law (V = I × R). If the voltage drop along a final circuit is excessive, the actual terminal voltage available at connected appliances will fall below safe operational thresholds, impairing efficiency and longevity.

Regulatory Voltage Drop Limits (BS 7671 Regulation 525)

Regulation 525.101 and Appendix 4 of BS 7671 set out strict upper boundaries for allowable voltage drop from the origin of an installation (typically the consumer unit or main distribution board) to the furthest point of any final circuit. These limits are expressed as percentages of the nominal single-phase supply voltage (U0 = 230V AC) or nominal three-phase supply voltage (U = 400V AC).

For standard installations connected to the public distribution network, a single-phase 230V lighting circuit must experience no more than 6.9V drop across its full run (ensuring a minimum terminal voltage of 223.1V). A single-phase 230V power circuit (such as a 32A ring final circuit or 20A radial socket circuit) is permitted up to 11.5V drop, guaranteeing at least 218.5V at the socket outlet under full design load.

Calculation Methodology for Voltage Drop

To calculate the voltage drop for a single-phase AC circuit, BS 7671 provides tabulated millivolt per ampere per metre (mV/A/m) values in Appendix 4 for each cable type and conductor size. The basic single-phase voltage drop formula is:

Vdrop = ( (mV/A/m) × Ib × L ) / 1000

Where:

• mV/A/m = Tabulated voltage drop value from BS 7671 Appendix 4 tables.
• Ib = Circuit design current in Amperes (A). Crucially, voltage drop is calculated using Ib (actual expected load current) rather than the protective device rating In, because voltage drop is a physical load-dependent parameter.
• L = Total circuit route length in metres (m).
• Division by 1000 converts the calculated figure from millivolts (mV) to Volts (V).

For three-phase balanced circuits, the tabulated mV/A/m value already incorporates the √3 multiplier for line-to-line voltage drop, yielding the three-phase formula: Vdrop_3 phase = ( (mV/A/m)_3p × Ib × L ) / 1000.

Temperature Correction Factor (Ct)

Tabulated mV/A/m figures in BS 7671 assume the conductor is operating at its maximum rated operating temperature (70°C for thermoplastic PVC, 90°C for thermosetting XLPE). When a cable is oversized or operating below its maximum thermal capacity (Ib < Iz), its actual operating temperature will be lower, resulting in lower conductor resistance. Where precise calculation is required, a temperature correction factor Ct (BS 7671 Appendix 4 Section 2.3) can be applied to derate the tabulated mV/A/m value, avoiding unnecessary cable oversizing.

Operational Consequences of Excessive Voltage Drop

Failing to limit voltage drop produces severe operational detriments:

• Luminaires: Light output drops non-linearly; LED drivers may flicker, drop out, or suffer driver overheating.
• Electric Motors: Induction motors suffer a reduction in starting and running torque proportional to the square of voltage (Torque ∝ V²). Under voltage causes motors to stall, draw excessive running current, and trip thermal overload relays.
• Heating Appliances: Power output drops with the square of voltage (P = V² / R), causing slow heating cycles.
• Electronic Control Gear: Sensitive microprocessors, contactors, and digital control circuits may experience random dropouts or relay chatter.

Automatic Disconnection of Supply (ADS) Requirements

Automatic Disconnection of Supply (ADS) is the primary protective measure against electric shock under fault conditions (BS 7671 Chapter 41). ADS requires that if an earth fault occurs (line conductor contacting exposed metallic structural parts or CPC), the protective device must disconnect the supply rapidly enough to prevent dangerous touch voltages from persisting and causing fatal ventricular fibrillation.

Maximum Permitted Disconnection Times (BS 7671 Regulation 411.3.2)

For final circuits operating at nominal AC voltage U0 = 230V to earth, Regulation 411.3.2 specifies maximum allowable disconnection times based on the earthing system arrangement:

• TN Systems (TN-S and TN-C-S / PME):

  • Final circuits supplying socket-outlets and fixed equipment not exceeding 32A: Maximum disconnection time is 0.4 seconds.
  • Final circuits exceeding 32A and all distribution/sub-main circuits: Maximum disconnection time is 5.0 seconds.

• TT Systems (Earth Electrode Supply):

  • Final circuits supplying socket-outlets and fixed equipment not exceeding 32A: Maximum disconnection time is 0.2 seconds.
  • Final circuits exceeding 32A and all distribution/sub-main circuits: Maximum disconnection time is 1.0 second.

The shorter disconnection time mandated for TT systems (0.2s vs 0.4s) reflects the higher shock risk associated with high earth electrode resistance and potential elevation of earth voltage during faults.

Earth Fault Loop Impedance (Zs) Verification

To achieve the required disconnection time, the total earth fault loop impedance (Zs) of the circuit must be low enough to allow sufficient earth fault current (If) to flow and instantly trip the protective device.

The total earth fault loop impedance equation is:

Zs = Ze + (R1 + R2)

Where:

• Ze = External earth fault loop impedance outside the installation (supplied by DNO or earth electrode).
• R1 = Resistance of the line conductor from origin to fault location.
• R2 = Resistance of the circuit protective conductor (CPC) from origin to fault location.

BS 7671 Tables 41.2, 41.3, and 41.4 provide maximum tabulated Zs values (Zs(max)) for Type B, C, and D circuit breakers and BS 88 / BS 3036 fuses to ensure disconnection within 0.4s or 0.2s.

The 80% Rule of Thumb (0.8 Temperature Correction Factor)

Tabulated Zs values in BS 7671 are calculated assuming conductors are at their maximum operating temperature (70°C). However, initial verification testing on an unenergized site is performed at ambient room temperature (typically 10°C to 20°C). Because copper resistance increases with temperature (alpha = 0.004 per °C), cold-measured Zs values will rise when the circuit is loaded.

Therefore, electricians must apply the 80% Rule of Thumb (BS 7671 Appendix 14): measured ambient Zs must not exceed 80% of the tabulated Zs(max):

Zs(measured) ≤ 0.8 × Zs(max)

If measured Zs exceeds 0.8 × Zs(max), detailed ambient temperature correction calculations must be conducted to verify compliance.

Worked Numerical Example

Consider a single-phase 230V radial socket circuit supplying a 20A design current load (Ib = 20A) over a route length of 30 metres using 2.5mm² / 1.5mm² Twin and Earth PVC cable (mV/A/m = 18). The protective device is a 20A Type B MCB (In = 20A). Supply is TN-C-S with Ze = 0.20 Ω.

1. Voltage Drop Check:

   • Vdrop = (18 mV/A/m × 20A × 30m) / 1000 = 10.8V.
   • Maximum allowed for power circuit = 5% of 230V = 11.5V.
   • Since 10.8V ≤ 11.5V, voltage drop complies.

2. Disconnection Time & Zs Check:

   • Maximum tabulated Zs for a 20A Type B MCB (0.4s disconnection) = 2.19 Ω (Table 41.3).
   • 80% limit = 0.8 × 2.19 = 1.75 Ω.
   • From On-Site Guide tables, combined R1+R2 resistance for 2.5/1.5mm² cable at 20°C = 19.51 mΩ/m.
   • R1+R2 for 30m = (19.51 × 30) / 1000 = 0.585 Ω.
   • Total expected Zs = Ze + (R1+R2) = 0.20 + 0.585 = 0.785 Ω.
   • Since 0.785 Ω ≤ 1.75 Ω, ADS disconnection within 0.4s is fully verified.