# Volt drop calculations for cables operating in fire conditions

When designing electrical installations within the scope of BS 7671 we perform cable calculations with consideration that the conductors are operating at their rated current i.e. 70 °C for thermoplastic and 90 °C for thermosetting sheathing where appropriate.

A rating factor, Ct, is also used for circumstances where the conductor will not be near the limited operating temperature during normal service. Examples of this may be where conductor sizing is increased due to the voltage drop of longer circuit lengths, therefore a lower design current is being applied relative to the cables current carrying capacities.

## What about circuits designed to maintain operation in fire conditions?

BS 8519:2020 titled "Selection and installation of fire-resistant power and control cable systems for life safety, fire-fighting and other critical applications" is a code of practice giving recommendations and guidance on the selection and installation of fire-resistant power control cable systems which need to maintain their circuit integrity for life safety and fire-fighting.

Primarily used for use in buildings which due to their size, height, form or use, require installation of life-safety and fire-fighting systems, e.g. sprinkler pumps, wet riser pumps, smoke control systems, fire-fighting and evacuation lifts or other circuits required by the fire engineered strategy.

Life safety systems include communication links to occupied, non evacuated areas as part of the fire strategy, for example intensive care wards in a hospital. BS 8519 addresses fire fighting systems of the type for fire fighters to take control of the fire.

During fire-fighting activities it is essential that the installations installed perform as intended and this includes consideration of the increase in volt-drop that will naturally occur as a conductors temperature increases whilst in operation.

Annex F of BS 8519:2020 includes correction factors for volt-drop adjustment with increase in temperatures.

In order to calculate volt-drop of the cable in a fire certain conditions need to be known or assumed as worst case:

1. total cable length (L)
2. current to be carried (Ib)
3. voltage drop per amp per metre of the cable at 90 °C
4. correction factor for the voltage drop from 90 °C to cable temperature in the fire
5. temperature of that part of the cable that is in the fire, and
6. length of that part of the cable that is in the fire.

Adjustment factors can be calculated using the temperature coefficient for copper conductors which is 0.00393 per °C (annealed copper), based on a room temperature of 20 °C.

These factors are calculated to consider the increase in voltage drop with increase in temperature from 90 °C to a number of temperatures that may be expected in fire-fighting conditions through assessment.

## Calculation for the rating factors

For a cable where the temperature is expected to reach a temperature of 650 °C in a fire:

${1 + 0.00393(650-20) \over 1 + 0.00393(90-20)}=2.7260$

Other factors include:

• 90 °C to 650 °C = 2.7260
• 90 °C to 750 °C = 3.0342
• 90 °C to 850 °C = 3.3424
• 90 °C to 950 °C = 3.6506

To use these factors we have insert them into the normal volt drop calculation in our design for the particular of the circuit which may be subjected to this fire condition.

Consider an installation with 2-core 2.5 mm2 cable for the supply to a 8 A load 30 m from the origin. Now consider three scenarios.

1. Where no fire takes place.

BS 7671, Table 4E2B states that a 90 °C multicore thermosetting 2.5 mm2 cable has a volt drop per amp per metre of 19 mV.

Therefore, 19 × 0.001 × 8 × 30 = 4.56 V.
2. Where a fire reaching a temperature of 850 °C takes place in one room for approximately 6 m of the route.

(19 × 0.001 × 8 × 24) + (19 × 0.001 × 3.3424 × 8 × 6) = 6.70 V.
3. Where a fire reaching a temperature of 850 °C takes place along the entire route.

(19 × 0.001 × 3.3424 × 8 × 30) = 15.24 V.

Consider an installation with 4-core 70 mm2 cable for the supply to a 200 A load 65 m from the origin. Consider the following scenarios.

1. Where no fire takes place.

BS 7671, Table 4E2B states that a 90 °C thermosetting 70 mm2 cable has a volt drop per amp per metre of 0.69 mV.

Therefore, 0.69 × 0.001 × 200 × 65 = 8.97 V.
2. Where a fire reaching a temperature of 650 °C takes place in one room for approximately 13 m of the route.

(0.69 × 0.001 × 200 × 52) + (0.69 × 0.001 × 2.7260 × 200 × 13) = 12.07 V.
3. Where a fire reaching a temperature of 650 °C takes place along the entire route.

(0.69 × 0.001 × 2.7260 × 200 × 65) = 24.45 V.

As can be seen from these examples, voltage drop will increase with increase in cable temperature in fire conditions. It is often considered to be unlikely that a fire would have a significant effect on most equipment being supplied by the cable.

It is in particular circumstances where the cable selection exercise selected the minimum cable size available and that this is combined with long runs of cables exposed to fire-survivals conditions that these cables may need to be increased in size for voltage drop considerations.

It should also be considered that some essential equipment may have volt-drop limitations and these will need to be taken into account in the design.