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Edvard

Electromagnetic Stresses On Busbar System

Electromagnetic Stresses On Busbar System (photo credit: teknomega.com)

IntroductionWhen a conductor carries a current it creates a magnetic field which interacts with any other magnetic fieldpresent to produce a force. When the currents flowing in two adjacent conductors are in the same direction theforce 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.

The force produced by the two conductors is proportional to the products of their currents.

Normally in most busbar systems the forces are very small and can be neglected, but under short-circuitconditions, they become large and must be taken into account together with the conductor material fibre stresseswhen 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:

1. Stresses due to direct lateral attractive and repulsive forces.2. Vibrational stresses.3. Longitudinal stresses resulting from lateral deflection.

Figure 1 Short-circuit current waveform

4. Twisting moments due to lateral deflection.

In most cases the forces due to short-circuits are applied very suddenly. Direct currents give rise to unidirectionalforces while alternating currents produce vibrational forces.

Maximum stressesWhen a busbar system is running normally the interphase forces are normally very small with the static weight ofthe 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 thirtytimes 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 theirsupporting system.

This means that the support insulators and their associated steelwork must be designed to withstand these highloads as well as their normal structural requirements such as wind, ice, seismic and static loads.

The peak or fully asymmetrical short circuit current is dependent on the power factor (cos ) of the busbar systemand its associated connected electrical plant. The value is obtained by multiplying the r.m.s. symmetrical currentby 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 systemvalue especially where generation is concerned. Note that the theoretical maximum for this factor is 22 or 2.828where cos = 0. These peak values reduce exponentially and after approximately 10 cycles the factor falls to1.0, 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 completelyasymmetrical current wave, the forceswill be applied with a frequency equalto that of the supply frequency andwith a double frequency as the wavebecomes symmetrical. Therefore inthe case of a 50 Hz supply theseforces have frequencies of 50 or 100Hz.

The maximum stresses to which abus structure is likely to be subjectedwould occur during a short-circuit on asingle-phase busbar system in whichthe line short-circuit currents aredisplaced by 180.

In a three-phase system a short-circuit between two phases is almostidentical to the single- phase case andalthough the phase currents arenormally displaced by 120, under short-circuit conditions the phase currents of the two phases are almost 180out of phase. The effect of the third phase can be neglected.

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 severethan those due to a three-phase short-circuit, which alternate in direction. The short-circuit forces have to beabsorbed first by the conductor. The conductor therefore must have an adequate proof strength to carry theseforces 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) UnitsElectrical conductivity (annealed) 101 61 % IACSElectrical resistivity (annealed) 1.72 2.83 cmTemperature coefficient of resistance(annealed) 0.0039 0.004 / CThermal conductivity at 20C 397 230 W/mKCoefficient of expansion 17 x 106 23 x 106 / C

Tensile strength (annealed) 200 250 50 60 N/mm2

Tensile strength (halfhard) 260 300 85 100 N/mm2

0.2% proof stress (annealed) 50 55 20 30 N/mm2

0.2% proof stress (halfhard) 170 200 60 65 N/mm2

Elastic modulu 116 130 70 kN/mm2

Specific heat 385 900 J/kg KDensity 8.91 2.70 g/cm3

Melting point 1083 660 C

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 stressesIn cases where there is a likelihood of vibration at normal currents or when subjected to short- circuit forcescausing 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 increasethe 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 toshort-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 isincreased.

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 theoverall design requirements of the busbar system.

Reference: Fundamentals of Power System Protection

Edvard - Electrical engineer, programmer and founder of EEP. Highly specialized for design ofLV high power busbar trunking (