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Principles of Cable Sizing

1. Introduction

Cable (or conductor) sizing is the process of selecting appropriate sizes for electrical power cableconductors. Cable sizes are typically decribed in terms of cross-sectional area, American Wire Gauge(AWG) or kcmil, depending on geographic region.

The proper sizing of cables is important to ensure that the cable can:

Operatecontinuously under full load without being damagedProvide the load with a suitable voltage (and avoid excessive voltage drops)Withstand the worst short circuits currents flowing through the cable

Cablesizing methods do dif fer across international standards (e.g. IEC, NEC, BS, etc) and somestandards emphasise certain things over others. However the general principles that underpin all cablesizing calculation do not change. When sizing a cable, the following general process is typicallyfollowed:

Gather data about the cable, its installation conditions, the load that i t will carry, etcDetermine the minimum cable size based on ampacity (continuous current carrying capacity)Determine the minimum cablesize based on voltage drop considerations

Determine the minimum cablesize based on short circuit temperature riseSelect the cable based on the highest of the sizes calculated in the steps above

2. Data Gathering

The first step is to collate the relevant information that is required to perform the sizing calculation.Typically, you will need to obtain the following data:

(1) Basic cable data - the basic characteristics of the cable's physical construction, which includes:

Conductor material - e.g. copper or aluminium

Insulation or cable type- e.g. PVC, XLPE, EPR (for IEC cables), TW, THHW, XHH, etc (forNEC cables)Number of cores - single core or multicore (e.g. 2C, 3C or 4C)

(2) Load data - thecharacteristics of the load that the cable will supply, which includes:

Number of phases, e.g. three phase or singlephaseSystem / source voltageFull load current (A) - or calculate this if the load is defined in terms of power (kW)

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Full load power factor (pu)Distance / length of cable run from source to load - this length should be as close as possible tothe actual route of the cableand include enough contingency for vertical drops / rises andtermination of the cable tails

(3) Cable installation - how the cable will be installed, which includes:

Installation method - e.g. cable tray / ladder, in conduit / raceways, against a wall, in air,directly buried, etcAmbient or soil temperature at the installation siteCable grouping, i.e. the number of other cables that are bunched together or installed in thesame areaCable spacing, i.e. whether cables are installed touching or spacedSoil thermal resistivity (for underground cables)For single core three-phasecables, are the cables installed in trefoil or laid flat?

3. Cable Selection Based on Ampacity

Current flowing through a cable generatesheat through the resistive losses in the conductors,dielectric losses through the insulation and resistive losses from current flowing through any cablescreens / shields and armouring.

A cable's consti tuent parts (particularly the insulation) must be capable of withstanding thetemperature rise and heat emanating from the cable. The ampacity of a cable is the maximum currentthat can flow continuously through a cable without damaging the insulation. It is sometimes alsoreferred to as the continuous current rating or current carrying capacity of a cable.

Cables with larger conductor cross-sectional areas (i.e. more copper or aluminium) have lower

resistive losses and are able to dissipate the heat better than smaller cables. Therefore a 16 mm2 (or 6

AWG) cable will have a higher ampacity than a 4 mm2 (or 12 AWG) cable.

3.1 Base Ampacities

International standards and manufacturers of cables will quote base ampacities for specific types ofcableconstructions (e.g. copper conductor, PVC insulated, 0.6/1kV voltage grade, etc) and a base setof installation conditions (e.g. ambient temperature of 40C, installation in conduit / raceways, etc). Itis important to note that theseampacities are only valid for the quoted types of cables and baseinstallation conditions.

3.2 Installed / Derated Ampacities

When the proposed installation conditions differ from the base conditions, derating (or correction)factors can be applied to the base ampacities to obtain the actual installed current ratings.

International standards and cable manufacturerswi ll provide derating factors for a range ofinstallation conditions, for example ambient / soil temperature, grouping or bunching of cables, soilthermal resistivity, etc. The installed current rating is calculated by multiplying thebase current ratingwith each of the derating factors, i.e.




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Ic = Ib . kd

where Ic is the installed / derated ampacity of the cable (A)

Ib is the base cable ampacity (A)

kd are the product of all the derating factors

For example, suppose a cable had an ambient temperature derating factor of kamb = 0.94 and agrouping derating factor of kg = 0.85, then the overall derating factor kd = 0.94x0.85 = 0.799. For acable wi th a base ampacity of 42A, the installed / derated ampacity would be Ic = 0.799x42 = 33.6A.

4. Cable Selection Based on VoltageDrop

A cable's conductor can be seen as an impedance and as a result, whenever current f lows through acable, there will be a voltage drop across it, derived by Ohm's Law (i.e. V = IZ). The voltage drop willdepend on two things:

Current flow through the cable - thehigher the current flow, the higher the voltage dropImpedance of theconductor - the larger the impedance, the higher the voltagedrop

The impedance of the cable is a function of the cable size (cross-sectional area) and the length of thecable. Most cable manufacturers wi ll quote a cable's resistance and reactance in Ohms/km or Ohms/f t.

For AC systems, the method of calculating voltage drops based on load power factor is commonlyused. Full load currents are normally used, but i f the load has high startup currents (e.g. motors), thenvoltage drops based on starting current (and power factor if applicable) should also be calculated.

For a threephase system:

For a single phase system:

Where V is the three phase or single phase voltage drop (V)

I is the nominal full load or starting current as applicable (A)

Rc is the ac resistance of the cable (Ohms/km or Ohms/ft)

Xc is the ac reactance of the cable (Ohms/km or Ohms/f t)

\cos\phi is the load power factor (pu)

L is the length of the cable (m or ft)




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When sizing cables for voltagedrop, a maximum voltage drop is specified, and then the smallestcable size that meets the voltage drop constraint is selected. For example, suppose a 5% maximum

voltage drop is specified. 16mm2, 25mm2 and 35mm2 cables have calculated voltage drops of 6.4%,

4.6% and 3.2%respectively. The 25mm2 cable is selected as it is the smallest cable that fulfils themaximum voltage drop criteria of 5%.

Maximum voltagedrops are typically specified because load consumers (e.g. appliances) will have aninput voltage tolerance range. This means that if the voltage at theappliance is lower than its ratedminimum voltage, then the appliance may not operate correctly.

In general, most electrical equipment will operatenormally at a voltage as low as 80% nominalvoltage. For example, i f the nominal voltage is 230VAC, then most appliances will run at >184VAC.Cables are typically sized for a more conservative maximum voltage drop, in the range of 5 to 10% atfull load.

5. Cable Selection Based on Short Circuit Temperature Rise

Note that short circuit temperature rise is not required for cable sizing to NEC standards.

During a short circuit, a high amount of current can flow through a cable for a short time. This surgein current flow causes a temperature rise within the cable. High temperatures can trigger unwantedreactions in the cable insulation, sheath materials and other components, which can prematurelydegrade the condition of the cable. As the cross-sectional area of the cable increases, it can dissipatehigher fault currents for a given temperature rise. Therefore, cables should be sized to wi thstand thelargest short circuit that it is expected to see.

The minimum cable size due to short circuit temperature rise is typically calculated with an equationof the form:

Where A is theminimum cross-sectional area of the cable (mm2)

i is the prospective short circuit current (A)

t is the duration of theshort circuit (s)

k is a short circuit temperature rise constant

The temperature rise constant is calculated based on the material properties of the conductor and theinitial and final conductor temperatures. IEC 60364-5-54 calculates it as follows:

For copper cables:

For aluminium cables:




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Where \thetai and \thetaf are theinitial and final conductor temperatures respectively.

As a rough guide, the following temperatures are common for the different insulation materials:

Material

Max OperatingTemperature

oC

LimitingTemperature

oC

PVC 75 160

EPR 90 250

XLPE 90 250

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