Selection of short circuit currents for temperature rise calculations

Some cable sizing standards require that cables are sized to withstand short circuit temperature rises (which are assumed to be adiabatic). The idea is that a short circuit can cause high currents to flow in the cable, which leads to a rise in conductor temperature. A high enough conductor temperature, even for a short duration, can trigger unwanted chemical reactions in the cable insulation (e.g. oxidation, decomposition, evaporation of the plasticizer, etc). Obviously, the short circuit temperature limit depends on the insulation material (e.g. PVC, EPR, XLPE, etc).

A larger-sized cable requires more energy to raise the conductor temperature. Therefore, given the short circuit current, fault duration, conductor operating temperature before the fault and type of insulation, we can calculate a minimum cable size (cross-sectional area) from the familiar short circuit temperature rise equation:

SC_Temp_Rise

The constant K is calculated based on the type of insulation and conductor operating temperature.

This all seems quite straightforward doesn’t it? Sure, applying the formula is simple, but the selection of the prospective short circuit current is not so clear cut. The right answer will largely depend on the operating philosophy of the system and your company’s (or your own) level of conservativeness. In this post, we will look at a few approaches for selecting the short circuit current and discuss some of the pros and cons of each approach.

Three Approaches:

  1. Use the short circuit current at the upstream bus
  2. Use the short circuit current at the downstream bus / load
  3. Use the let-through energy of the fuse (for fuse protected cables)

Approach 1: Short circuit current at upstream bus

Using the short circuit current at the upstream bus or switchboard has at least two advantages – it is very conservative and easy to calculate (i.e. from a short circuit study). The rationale with this approach is that the cable can withstand the temperature rise from a fault anywhere along its length (since the short circuit current for a fault on the cable will be less than that of a fault on the upstream bus).

However, the question is whether or it is necessary for the cable to withstand such a temperature rise. After all, if there’s a fault on the cable, then it is almost certainly damaged in some way. Therefore, if the cable is already damaged, does it matter if it can withstand the short circuit temperature rise?

The answer to this comes down to the philosophy in fixing faulted cables – will the cable be replaced or will it be repaired, e.g. with joints? If the standard procedure is to replace faulted cables, then it would be unnecessary to withstand the short circuit temperature rise for a cable fault because the cable will be replaced anyway. But if the philosophy is to repair damaged sections of the cable, then it may be crucial to maintain the integrity of the rest of the cable.

Sometimes the fault rating of the upstream switchgear is used (e.g. 50kA, 63kA, etc). The justification for doing this is that it allows for growth in fault levels over time and represents the absolute worst case. Of course, this could potentially lead to very large cables should the fault rating of the board be very high.

Approach 2: Short circuit current at downstream bus / load

In this approach, the cable only has to withstand temperature rises due to through faults, e.g. a fault at the load / downstream end. The cable therefore cannot withstand temperature rises associated with faults on the cable itself. This would be an appropriate approach if the philosophy is to replace faulted cables rather than repairing them.

The key advantage over Approach 1 is a smaller minimum conductor size, although potentially at the expense of being able to withstand faults on the cable.

Approach 3: Let-through energy of fuse

The let-through energy (i2t) is the amount of energy a fuse will allow before it blows. Thus for fuse protected cables, the let-through energy of the fuse can be used as the maximum i2t value that the cable will need to withstand. Fuse let-through energy data is often available from manufacturer data sheets (for example, the let-through energies in the figure below).

Fuse_i2t

The main advantage is that the minimum conductor sizes will be smaller than Approach 1, while still being able to withstand faults on the cable. The disadvantage is that this approach is really only applicable for cables protected by current-limiting fuses.

DC cable sizing feature released for NEC module

You can now size DC cables to NEC standards!

Simply select “DC” in the number of phases selection box:

No_phases_dc

And size the cable as normal. Obviously, the full load power factor will be ignored in the load calculations. Another change is the inclusion of conductor operating temperature in the voltage drop calculation:

volt_drop_updates

This has been done to account for the temperature dependency of the DC resistance, which can lead to higher resistances at high conductor operating temperatures. The voltage drop is therefore calculated as follows:

dc_volt_drop

Where:

  • I is the DC load current (A)
  • Rc is the DC resistance of the cable at 68°F (Ohms / 1000ft)
  • L is the cable length (ft)
  • T is the conductor operating temperature (°F)
  • α is the temperature coefficient of resistance, which is 0.00218333 Ω/°F for copper and 0.00227778 Ω/°F for aluminum.