ME5507 - Electrical Services

11 Overload and volt drop

11.1 Overload protection

Note: In = rating of fuse or circuit breaker

It = capacity of cable under standard, tabulated conditions
Iz = capacity of cable as installed
Ib = circuit design current, i.e. maximum demand under healthy conditions

If overload protection is provided by HRC fuses (but not motor circuit fuses) or MCBs
complying with BS EN 60898 then we can ensure overload protection if: In ≤ Iz, as we
might expect.
Both In and Iz need to be greater than the design current Ib.
The installed current-carrying capacity of cable can be calculated by consulting
published data for standard installation conditions (see BS7671 Appendix 4), and
then using rating factors for the true conditions, e.g.
Iz = It × Cg × Ca × Ci
where: Ca is rating factor for ambient temperature
Cg is rating factor for grouping (with other cables)
Ci is rating factor for thermal insulation

The tabulated capacity is for an ambient temperature no more than 30 °C, cable
installed alone and with no thermal insulation.
We need Iz ≥ In so from the equation above we can say: It × Cg × Ca × Ci ≥ In
In
or, more usefully: It ≥
C g × Ca × C i

If the cable is buried we have to divide by another rating factor, Cc, for "installation
condition". This factor has a value of 0.9.

Further rating factors may need to be used according to the details: Cd according to
depth of burial; and Cs according to soil thermal resistivity.
There are alternative, less demanding formulae that can be used for groups of
circuits not liable to simultaneous overload. See Appendix 4 of BS 7671.
Finally, note from BS 7671 Reg 435.1 that if we have provided overload protection to
conductors with devices of sufficient breaking capacity, then fault current protection
can be assumed.

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11.2 Volt Drop

BS 7671 requires that we consider the extent to which the voltage supplied to
equipment is reduced as a result of cable impedances. This ‘volt drop’ must not
cause a hazard. It would be laborious to check the performance at reduced voltage
of all of the electrical equipment. Instead an installation is deemed to comply if the
volt drop from the origin to each point of connection of equipment does not exceed:
3% for lighting, or 5% for other uses.
For supplies provided at hv, or, if privately-fed, other criteria apply [5, Appx 12].
The voltage drop is calculated for the normal design current. BS7671 lists volt drop
data for various cables (see Appendix 4), in units mV/A/m. Note the provision of
separate data for single-phase and three-phase circuits, and the assumptions implicit
in this:
• Single-phase circuits are expected to suffer volt drop in phase and neutral, so
quoted mV/A/m are double the conductor mΩ/m.
• Three-phase circuits are assumed to be balanced with negligible neutral
current, so they are expected to suffer volt drop in phase conductors only.
However, volt drop is calculated relative to line voltage, so quoted mV/Am are
√3 times conductor mΩ/m.
The data assume the worst case, i.e. that the conductors are operating at their
maximum permitted temperature. If they are not, i.e. the circuit is not fully loaded,
then a correction factor Ct can be applied to the resistive part of the volt drop for
cables above ground, i.e.
I b2
230 + t p − (Ca2Cg2 − )(t p − 30)
I t2
Ct =
230 + t p

where tp is the maximum conductor operating temperature (e.g. 70°C for pvc-
insulated cables).
Compare this with the temperature correction formula in section 9.3.3.

Additionally, a correction to the tabulated volt drop data is permissible if the load
power factor is different from the resistance/impedance ratio of the cable.
Approximately, design mV/A/m becomes:
cos φ × tabulated (mV/A/m)r + sin φ × tabulated (mV/A/m)x
Compare this with the equation for transformer voltage regulation in section 3.3.
In practice these corrections provide only small improvements and are only resorted
to if the choice of cable size is marginal.

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Tutorial Questions

Volt drop

11.1 An XLPE-insulated cable is installed to provide a single-phase supply to a

remote distribution board carrying a design load of 55 A, from a 230 V source.
The cable route length is 40 m.
The cable live conductors have the following characteristics at 20 °C:
resistance per unit length = 1.15 mΩ/m;
reactance is negligible
temperature coefficient of resistance = 0.004 per °C
Calculate the percentage volt drop at the distribution board. [2.8%]

11.2 A particular three-phase electrical load of 40 A is to be fed from a supply at

400 V, 50 Hz by a final circuit of uncertain route length. The load does not
include lighting. The designer has to choose between two cables having
installed current-carrying capacities of 40 A. Data for the two cables are given
below:

Maximum conductor Conductor Conductor resistance

Cable type
operating temperature size per unit length at 20 °C
PVC/SWA/PVC 70 °C 6 mm2 3.08 mΩ/m
XLPE/SWA/PVC 90 °C 4 mm2 4.61 mΩ/m

The temperature coefficient of resistance of the conductors is 0.004 per °C at

20 °C, and the cables have negligible reactance.
Calculate the maximum permitted route length for each of the two choices of
cable, assuming that this is determined by the volt drop alone. [78 m, 49 m]

Mixed

11.3 A single-phase ring final circuit feeding socket outlets is to be installed. The
source of supply is 230 V, 50 Hz, TN with a declared value of external earth
fault loop impedance, Ze, of 0.8 Ω. The circuit will use cable with the following
characteristics at the maximum conductor operating temperature:-
phase conductor resistance, R1 = 8.9 mΩ/m
circuit protective conductor resistance, R2 = 14.5 mΩ/m
volt drop per amp per metre = 18 mV/A/m
The circuit will be protected using a 32 A HRC fuse and a 30 mA RCD that
operates within 40 ms at 150 mA.
Calculate the maximum length of the circuit measured around the ring. [80 m]

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11.4 A building takes a three-phase supply at 400 V with a declared prospective
short circuit current of 30 kA at the intake switchboard. The cable installed
between the intake switchboard and a remote distribution board has a circuit
length of 100 m. The cable is PVC-insulated and has the following
characteristics at 20 °C:
Phase conductor resistance = 0.095 mΩ/m
Phase conductor reactance = 0.075 mΩ/m
Conductor temperature coefficient of resistance = 0.004 per °C
Connected to the remote distribution board is a balanced three-phase load of
250 kVA, non-distorting, but with a power factor of 0.8. Calculate:
(a) the percentage volt drop at the remote distribution board; and
(b) the minimum breaking capacity for the protective devices installed in
the remote distribution board. [2.1%, 12.8 kA]

11.5 A 400V three-phase 10 kW induction motor has a power factor of 0.85 and an
efficiency of 90%. The motor is provided with a star-delta motor starter
incorporating motor overload protection. The supply cables to the starter and
between the starter and the motor comprise single-cores in a conduit.
(a) Calculate by what proportion the starting current is reduced compared
to starting direct-on-line. [1/3]
(b) Given that the ambient temperature does not exceed 30 °C, and the
grouping rating factors shown in Table 1, calculate the tabulated
current-carrying capacity (It) required of the cables installed between
the supply and the starter; and between the starter and the motor.
[18.9 A, 13.6 A]

Table 1. Grouping Rating Factor (Cg)

Number
2 3 4 5 6 7 8
of circuits
Cg 0.80 0.70 0.65 0.60 0.57 0.54 0.52

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