When a conductor carries a current it creates a magnetic field which interacts with any other magnetic field present to produce a force. When the currents flowing in two adjacent conductors are in the same direction the force is one of attraction, and when the currents are in opposite directions a repulsive force is produced.
In most busbar systems the current-carrying conductors are usually straight and parallel to one another.
Normally in most busbar systems the forces are very small and can be neglected, but under short-circuit conditions, they become large and must be taken into account together with the conductor material fibre stresses when designing the conductor insulator and its associated supports to ensure adequate safety factors.
The factors to be taken into account may be summarised as follows:
- Stresses due to direct lateral attractive and repulsive forces.
- Vibrational stresses.
- Longitudinal stresses resulting from lateral deflection.
- Twisting moments due to lateral deflection.
In most cases the forces due to short-circuits are applied very suddenly. Direct currents give rise to unidirectional forces while alternating currents produce vibrational forces.
When a busbar system is running normally the interphase forces are normally very small with the static weight of the busbars being the dominant component.
Under short-circuit conditions this is very often not the case as the current rises to a peak of some thirty times its normal value, falling after a few cycles to ten times its initial value.
These high transitory currents create large mechanical forces not only in the busbars themselves but also in their supporting system.
The peak or fully asymmetrical short circuit current is dependent on the power factor (cos φ) of the busbar system and its associated connected electrical plant. The value is obtained by multiplying the r.m.s. symmetrical current by the appropriate factor given in Balanced three-phase short-circuit stresses.
If the power factor of the system is not known then a factor of 2.55 will normally be close to the actual system value especially where generation is concerned. Note that the theoretical maximum for this factor is 2√2 or 2.828 where cos φ = 0. These peak values reduce exponentially and after approximately 10 cycles the factor falls to 1.0, i.e., the symmetrical r.m.s. short circuit current.
The peak forces therefore normally occur in the first two cycles (0.04 s) as shown in Figure 1 below.
In the case of a completely asymmetrical current wave, the forces will be applied with a frequency equal to that of the supply frequency and with a double frequency as the wave becomes symmetrical. Therefore in the case of a 50 Hz supply these forces have frequencies of 50 or 100 Hz.
The maximum stresses to which a bus structure is likely to be subjected would occur during a short-circuit on a single-phase busbar system in which the line short-circuit currents are displaced by 180°.
In a balanced three-phase short-circuit, the resultant forces on any one of the three phases is less than in the single-phase case and is dependent on the relative physical positions of the three phases.
In the case of a single-phase short-circuit, the forces produced are unidirectional and are therefore more severe than those due to a three-phase short-circuit, which alternate in direction. The short-circuit forces have to be absorbed first by the conductor. The conductor therefore must have an adequate proof strength to carry these forces without permanent distortion.
Copper satisfies this requirement as it has high strength compared with other conductor materials (Table 2 below).
Table 2 – Typical relative properties of copper and aluminium
|Properties of Cu and Al||Copper(CW004A)||Aluminium (1350)||Units|
|Electrical conductivity (annealed)||101||61||% IACS|
|Electrical resistivity (annealed)||1.72||2.83||μΩ cm|
|Temperature coefficient of resistance(annealed)||0.0039||0.004||/° C|
|Thermal conductivity at 20°C||397||230||W/mK|
|Coefficient of expansion||17 x 10–6||23 x 10–6||/° C|
|Tensile strength (annealed)||200 – 250||50 – 60||N/mm2|
|Tensile strength (half–hard)||260 – 300||85 – 100||N/mm2|
|0.2% proof stress (annealed)||50 – 55||20 – 30||N/mm2|
|0.2% proof stress (half–hard)||170 – 200||60 – 65||N/mm2|
|Elastic modulu||116 – 130||70||kN/mm2|
|Specific heat||385||900||J/kg K|
Because of the high strength of copper, the insulators can be more widely spaced than is possible with lower-strength materials.
Methods of reducing conductor stresses
In cases where there is a likelihood of vibration at normal currents or when subjected to short- circuit forces causing damage to the conductor, the following can he used to reduce or eliminate the effect:
a) Reduce the span between insulator supports.
This method can be used to reduce the effects of both continuous vibration and that due to short-circuit forces.
b) Increase the span between insulator supports.
This method can only be used to reduce the effects of vibration resulting from a continuous current. It will increase the stresses due to a short-circuit current.
c) Increase or decrease the flexibility of the conductor supports.
This method will reduce the effects of vibration due to continuous current but has very little effect on that due to short-circuit forces.
d) Increase the conductor flexibility.
This can only be used to reduce the effects of vibration due to a continuous current. The short-circuit effect is increased.
e) Decrease the conductor flexibility.
This method will reduce the effects of vibration due to either a continuous current or a short-circuit.
It will be noted that in carrying out the various suggestions above, changes can only be made within the overall design requirements of the busbar system.
Reference: Fundamentals of Power System Protection