Calculating Cable Fault Ratings By Steven McFadyen on January 6th, 2014 When selecting a cable, the performance of the cable under fault conditions is an important consideration. It is important that calculations be carried out to ensure that any cable is able to withstand the effects of any potential fault or short circuit. circuit. This note looks at how to do this. The primary concern with cables under a fault condition is the heat generated, and any potential negative effect this may have on the cable insulation. Calculation of fault rating is based on o n the principle that the protective device will iso late the fault in a time limit such that the t he permitted temperature rise within the cable will not be excee ded. Contents [hide] 1. The adiabatic equation 2. Derivation - Adiabatic Adiabatic Equation and k 1. Obtaining Values of k 3. Non-adiabatic effects 4. Other Cable Fault Issues 5. References
The adiabatic equation When calculating the fault ratings of a cable, it is generally assumed that the duration so short enough that no heat is dissipated by the cable to the surrounding. Adopting this approach simplifies the calculation and errs on the safe side. The normally used equation is the so-called adiabatic equation. For a given fault fault of I , which lasts for time t , the minimum required cable cross sectional area is given by:
=
√
2
A - the nominal cross section area, mm
- the fault current in, A I - duration of fault current, s t k - a factor dependant on cable type (see below)
Alternatively, given the cable cross sect ion and fault current, the maximum time allowable for the protective device can be found from:
t=
The factor k is is dependent on o n the cable insulation, allowable temperature rise under fault conditions, conductor resistivity resistivity and heat capacity. capacity. Typical values values of k are: are:
Thermoplastic 70°C (PVC)
Value of k Temperature Conductor Material Initial °C]Final [°C] Copper AluminiumSteel Aluminium Steel 70 160/140 115/103 76/78 42/37
Thermoplastic 90°C (PVC) Thermosetting, 90°C (XLPE, EDR) Thermosetting, 60°C (rubber) Thermosetting, 85°C (rubber) Thermosetting, 185°C (silicone rubber)
90 90 60 85 180
160/140 100/86 250 143 200 141 220 134 350 132
66/57 94 93 89 87
36/31 52 51 48 47
2
*where two values; lower value applied to conductor CSA > 300 mm * these values are suitable for durations up to 5 seconds, source: BS 7671, IEC 60364-5-54 cat egorized, refer to our Cable Tip: for a better understanding of cable insulation and how it is categorized, Insulation Properties note. note. fault current of 13.6 kA and the protective protective device trips in 2.6 Example : Consider a maximum fault s. The minimum safe cable cross sectional area of a copper thermosetting thermosetting 90°C cable (k =143) =143) is:
S=
.
= 154mm2
Any selected cable larger than this will withstand the fault.
Derivation - Adiabatic Adiabatic Equation and k The term adiabatic applies applies to a process where there is no heat transfer. transfer. For cable faults, faults, we are assuming that all the heat generated during the fault is contained within the cable (and not transmitted away). Obviously this is not not fully true, but it is is on the safe side.
Q=cmΔT
From physics, the heat Q, required to rise a material ΔT material ΔT is is given by: Q - heat added, J
material, J.g-1.K -1 c - specific heat constant o f material, m - mass of the material, g
ΔT - temperature rise, K The energy into the cable during dur ing a fault is given by:
=
Rt
R - the resistance of the cable, Ω
From the physical cable properties we can calculate m and R as:
m= ρc Al and ρc - material density in g.mm
R =
⍴
-3
ρr - resistivity resistivity of o f the conductor, Ω.mm l - length of the cable, mm
I 2 Rt =cmΔT
Combining and substituting we have:
⍴ ⍴ t
r
A
=c A
and rearranging for A gives:
S=
by letting
k =
⍴
Note: ΔT Note: ΔT is the maximum allowable temperature temperature rise for the cable:
ΔT =θ f −θ −θ i θ f - final (maximum) cable insulation temperature, °C θ i - initial (operating) cable insulation temperature, °C 2
expressed in g (grams) and mm , as opposed to kg and m. m. This is widely adopted by Units: are expressed cable specifiers. The equations can easily be redone in kg and m if required.
Obtaining Values of k The constant k can can be calculated from the above equation. [1]
A more common approach for is to use the tabulated values for k , for example, from BS 7671 . [2]
IEC 60364-5-54 also allows a more direct calculation of k , using:
k=
Qc(
+
20
)
In(
+
+
)
-1
-3
Qc - volumetric heat capacity of conductor at 20°C, J.K .mm
β - reciprocal of temperature coefficient of resistivity at 0°C, °C ρ20 - resistivity resistivity of o f conductor as 20°C, Ω.mm θ i - initial conductor temperature, °C θ f - final conductor temperature, °C [°C] β [°C] Copper 234.5 Aluminium228 Steel 202
-1
-3
Q c [J.K .mm ] 20 [Ω.mm] -3 -6 3.45 x 10 17.241 x 10 -3 -6 2.5 x 10 28.267 x 10 3.8 x 10138 x 10-
Substituting the above values and rearranging the IEC equation slightly, gives:
k = 226 In(1+ I n(1+
k = 148 In(1+ I n(1+
k = 78 In(1+ I n(1+
.
)
-copper conductors
) -aluminum conduct
)-steel
Non-adiabatic Non-adiabatic effects As mentioned, the adiabatic equation assumes no heat is dissipated from the cable during a fault. While putting the calculation on the t he safe side, in some situations, situat ions, particularly for longer fault duration there is the potential potential to be able to get away with with a smaller cross section. In these instances, it is possible to do a more accurate calculation. Considering non-adiabatic effects is more more complex. Unless there is some driver, driver, using the adiabatic equations is just just easier. Software is available to consider non non adiabatic effects, however, there is a cost, time and complexity associated with this. The IEC also publish a standard which deals with non-adiabatic equations:
IEC 60949 "Calculation of o f thermally permissible permissible short-circuit sho rt-circuit current, taking into account non-adiabatic heating effects".
The method adopted by IEC 60949 is to use the adiabatic equation and apply a factor to cater for the non-adiabatic effects:
I =εI AD - permissible short circuit current, A (or kA) I circuit current, A (or kA) I AD - adiabatic calculated permissible short circuit ε - factor to allow for heat dissipation from cable The bulk of the IEC 60949 standard is concerned with w ith the calculation of ε.
Other Cable Fault Issues In addition to the direct heating effect e ffect of fault currents, other considerations include:
electro-mechanical stress and fault levels large enough to cause cable failure performance of joint and terminations under fault conditions
While in most cases the none heating effects are not serious, there may be situations where these could pose a risk to the cable or equipment/personnel in the vicinity.
References
[1]. BS 7671 - Requiremen Requirements ts for Electrical Electrical Installations Installations . 17th ed. United Kingdom: IEE; 2008. [2] IEC 60364-5-54 60364-5-54 Low-voltage Low-voltage electrical electrical installations installations - Part Part 5-54: Selection Selection and erection of electrical equipment - Earthing arrangements and protective conductors . 3rd ed. IEC; 2011.
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