Cable (or conductor) sizing is the process of selecting appropriate sizes for electrical power cable conductors. 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:
Cable sizing methods do differ across international standards (e.g. IEC, NEC, BS, etc) and some standards emphasise certain things over others. However the general principles that underpin all cable sizing calculation do not change. When sizing a cable, the following general process is typically followed:
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:
(2) Load data - the characteristics of the load that the cable will supply, which includes:
(3) Cable installation - how the cable will be installed, which includes:
Current flowing through a cable generates heat through the resistive losses in the conductors, dielectric losses through the insulation and resistive losses from current flowing through any cable screens / shields and armouring.
A cable's constituent parts (particularly the insulation) must be capable of withstanding the temperature rise and heat emanating from the cable. The ampacity of a cable is the maximum current that can flow continuously through a cable without damaging the insulation. It is sometimes also referred 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 mm^{2} (or 6 AWG) cable will have a higher ampacity than a 4 mm^{2} (or 12 AWG) cable.
International standards and manufacturers of cables will quote base ampacities for specific types of cable constructions (e.g. copper conductor, PVC insulated, 0.6/1kV voltage grade, etc) and a base set of installation conditions (e.g. ambient temperature of 40°C, installation in conduit / raceways, etc). It is important to note that these ampacities are only valid for the quoted types of cables and base installation conditions.
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 manufacturers will provide derating factors for a range of installation conditions, for example ambient / soil temperature, grouping or bunching of cables, soil thermal resistivity, etc. The installed current rating is calculated by multiplying the base current rating with each of the derating factors, i.e.
where I_{c} is the installed / derated ampacity of the cable (A)
I_{b} is the base cable ampacity (A)
k_{d} are the product of all the derating factors
For example, suppose a cable had an ambient temperature derating factor of k_{amb} = 0.94 and a grouping derating factor of k_{g} = 0.85, then the overall derating factor k_{d} = 0.94x0.85 = 0.799. For a cable with a base ampacity of 42A, the installed / derated ampacity would be I_{c} = 0.799x42 = 33.6A.
A cable's conductor can be seen as an impedance and as a result, whenever current flows through a cable, there will be a voltage drop across it, derived by Ohm's Law (i.e. V = IZ). The voltage drop will depend on two things:
The impedance of the cable is a function of the cable size (cross-sectional area) and the length of the cable. Most cable manufacturers will quote a cable's resistance and reactance in Ohms/km or Ohms/ft.
For AC systems, the method of calculating voltage drops based on load power factor is commonly used. Full load currents are normally used, but if the load has high startup currents (e.g. motors), then voltage drops based on starting current (and power factor if applicable) should also be calculated.
For a three phase 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)
R_{c} is the ac resistance of the cable (Ohms/km or Ohms/ft)
X_{c} is the ac reactance of the cable (Ohms/km or Ohms/ft)
\cos\phi is the load power factor (pu)
L is the length of the cable (m or ft)
When sizing cables for voltage drop, a maximum voltage drop is specified, and then the smallest cable size that meets the voltage drop constraint is selected. For example, suppose a 5% maximum voltage drop is specified. 16mm^{2}, 25mm^{2} and 35mm^{2} cables have calculated voltage drops of 6.4%, 4.6% and 3.2% respectively. The 25mm^{2} cable is selected as it is the smallest cable that fulfils the maximum voltage drop criteria of 5%.
Maximum voltage drops are typically specified because load consumers (e.g. appliances) will have an input voltage tolerance range. This means that if the voltage at the appliance is lower than its rated minimum voltage, then the appliance may not operate correctly.
In general, most electrical equipment will operate normally at a voltage as low as 80% nominal voltage. For example, if 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% at full load.
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 surge in current flow causes a temperature rise within the cable. High temperatures can trigger unwanted reactions in the cable insulation, sheath materials and other components, which can prematurely degrade the condition of the cable. As the cross-sectional area of the cable increases, it can dissipate higher fault currents for a given temperature rise. Therefore, cables should be sized to withstand the largest short circuit that it is expected to see.
The minimum cable size due to short circuit temperature rise is typically calculated with an equation of the form:
Where A is the minimum cross-sectional area of the cable (mm^{2})
i is the prospective short circuit current (A)
t is the duration of the short 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 the initial and final conductor temperatures. IEC 60364-5-54 calculates it as follows:
For copper cables:
For aluminium cables:
Where \theta_{i} and \theta_{f} are the initial and final conductor temperatures respectively.
As a rough guide, the following temperatures are common for the different insulation materials:
Material | Max Operating Temperature ^{o}C | Limiting Temperature ^{o}C |
---|---|---|
PVC | 75 | 160 |
EPR | 90 | 250 |
XLPE | 90 | 250 |