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Calculating The Short-Circuit Heating Of Busbars

Calculating The Short-Circuit Heating Of Busbars (photo credit: teknomega.com)

Short-Circuit EffectsLike all electrical circuits, busbars need to be protected against the effects of short-circuit currents. The openconstruction of busbars increases the risk of faults, e.g. by the ingress of foreign bodies into air gaps, and the riskof consequent damage is high due to their high normal operating currents and the amount of energy available.

Very high currents lead to rapid and extreme overheating of the bars with consequent softening of the materialand damage to the support structure. At the same time, the electromagnetic forces generated will distort thesoftened conductors which may break free from their supports.

Resonance effects may make the situation worse.

Heating Caused By Short-CircuitThe maximum potential short-circuit current depends on the source impedance of the supply and reduces alongthe length of the bar as the impedance increases. For the purpose of ensuring the safety and integrity of the bar,the short circuit current should be initially calculated close to the feed end of the bar, making no allowance for bar

impedance, to establish the worst case.

When a fault occurs, the short-circuit current will be many times the normal operating current and willflow until the protective device operates.

Because the time duration is small a few seconds at most it is usual to assume adiabatic heating, in otherwords, that, over the time scale of interest, there is no significant cooling effect and that all the heat generatedby the current flow is retained in the bar.

Therefore it is assumed that the temperature rise of the bar is simply linear this simplifies the calculationsignificantly and yields a conservative result (A similar simplification is made in determining cable behaviourunder fault conditions.)

The amount of heat energy required to raise the temperature of a unit mass of material by one degree Centigradeis called the specific heat. For copper, at room temperature, the value is 385 Joule/kg/K.

Knowing the mass of the bar and the energy produced by the short circuit current, the temperature rise can becalculated:

where:

Q is the amount of heat added to the bar (Joule)S is the specific heat of the bar material (J/kg/K)m is the mass of the bar (kg)tr is the temperature rise.

The amount of energy dissipated in the bar is:

where:

P is the power dissipated in the bar (W)T is the time for which the power is dissipated (seconds).

Therefore,

where tr is the rate of temperature rise in degrees C per second. The power dissipated in the baris given by:

where:

R is the resistance of the bar ()r is the resistivity of the bar material (m) l is the length of the bar (m)A is the cross-sectional area of the bar (m2).

Substituting for W and M gives:

where:

D is density (kg/m3).

Two of the physical constants, specific heat and resistivity, varyconsiderably with temperature so it is not obvious which valuesshould be used. Resistivity increases with temperature (by afactor of 1.6 from 20C to 300C) so increasing the energy dissipated as the temperature increases, whilespecific heat falls by around 8% over the same range.

Using room temperature values, and adjusting to use convenient units, gives the initial rate oftemperature rise as:

where:

I is current in kAA is the cross-sectional area in mm2.

At higher temperatures in other words, as the fault current continues to flow until the protective deviceoperates the rate of temperature rise will increase as the resistance of the bar increases.

The worst case rate of rise at the feed end of the bar is approximately:

However, if the short circuit is at some distance from the feed end, the fault currentmagnitude will be lower due to the resistance of the bar and will reduce further as the bartemperature rises.

Practice TipsIn practice, what is important is that the final temperature of the bar remains lower than the limiting designtemperature throughout the short circuit event. The limiting temperature for copper busbars is determined by thetemperature resistance of the support materials but, in any case, should not exceed ~ 200C. The maximumcircuit breaker tripping time is 200/tr seconds.

Busbars that have been subject to short circuit should be allowed to cool and inspected before being returned toservice to ensure that all joints remain tight and that the mountings are secure.

Note that, although the heating time the duration of the fault is quite short, the bar will remain at hightemperature for a considerable length of time. Also, because of the very high thermal conductivity ofcopper, parts of the bar beyond the fault will also have become hot.

Reference // Guidance for Design and Installation David Chapman & Professor Toby Norris

Calculating The Short-Circuit Heating Of BusbarsShort-Circuit EffectsHeating Caused By Short-CircuitPractice Tips