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An Overview Of Short Circuit Current (part 1)

An Overview Of Short Circuit Current (part 1)

Basic conceptThere are essentially four types of faults: three-phase, single line-to-ground, double line-to-ground, and line-to-line.

Each of these types of faults can result in different magnitudes of fault current.

In all types, however, there is a common element: an abnormally low-impedance path or shorted path for current toflow, hence the name short circuit current. Such a condition can lead to extremely high currents.

By Ohms Law, voltage equals current times impedance (resistance) . Therefore, when the impedance becomesvery low and the voltage does not change, the current becomes very high. Large electrical currents produce a lot ofheat transfer, which increases the temperature of cables, transformers, etc.

The increase in temperature can cause insulation damage. These currents also produce high magnetic forces,which can actually bend buses in switchgear.

High fault currents cause magnetic forces that are proportional to the square of the fault current.

RL circuit as a simplified equivalent of the circuits inelectricity-distribution networks

Mathematical background, X/R ratio and type of fault currentThe treatment of electrical faults should be carried out as a function of time, from the start of the event at time t = 0+until stable conditions are reached, and therefore it is necessary to use differential equations when calculating thesecurrents.

In order to illustrate the transient nature of the current, consider an RL circuit as a simplified equivalent of thecircuits in electricity distribution networks.

This simplification is important because all the system equipment must be modeled in some way in order to quantifythe transient values which can occur during the fault condition.

For the circuit shown in Figure, the mathematical expression which defines the behavior of the current is:

e(t) = L di + Ri(t)

This is a differential equation with constant coefficients, of whichthe solution is in two parts:

ia (t): ih (t) + ip(t)

Where:

ih(t) is the solution of the homogeneous equation corresponding to thetransient period.ip(t) is the solution to the particular equation corresponding to the steady-state period.

By the use of differential equation theory, the complete solution can bedetermined and expressed in the following form:

Where:

the closing angle which defines the point onthe source sinusoidal voltage when the faultoccurs

= tan-1(L/R) or = tan-1(X/R)

The second term in the equation for fault current isrecognized as the DC component of the current, and has an initial maximum value when:

- = / 2, and zero value when = .

Notes:Here we introduce the concept of X/R ratio. We can very well see that since L = XL or simply X hence DCcomponent of fault current to large extent depends upon = tan-1(X/R) or simply X/R ratio.The X/R ratio is important because it determines the peak asymmetrical fault current .In X/R ratio when X equals zero, there is only symmetrical current with no DC component. With R equalszero, the DC component would never decay. One can say there will always be both resistance and reactivecomponents in the system.

The resistance and reactance of a circuit establishes a power factor.The power factor (p.f.) is given by the following equation: p.f. = cos(tan-1(X/R)) this equation means that thepower factor and X/R ratio are related.Therefore, system power factor and system X/R ratio are different ways of saying the same thing.Please note that as power factor decreases, the X/R ratio increases.

It is impossible to predict a that is at what point the fault will be applied or take place on the sinusoidal cycle andtherefore it is not possible to determine exactly what magnitude the DC component will reach.

Symmetrical fault currentIf in a circuit mainly containing reactance a short circuit occurs at the peak of the voltage wave, the short-circuitcurrent would start at zero and trace a sine wave which would be symmetrical about the zero axis.

This is known as a symmetrical short circuit current.

Asymmetrical fault currentRight after a fault occurs, the current waveform is no longer a sine wave.

Instead, it can be represented by the sum of a sine wave and a decaying exponential . Figure below illustrates thisphenomenon. Please note that the decaying exponential added to the sine wave causes the current to reach a muchlarger value than that of the sine wave alone.

The waveform that equals the sum of the sine wave and the decaying exponential is called the asymmetrical currentbecause the waveform does not have symmetry above and below the time axis.

The sine wave alone is called the symmetrical current because it does have symmetry above and below the time axis.

Sine wave, decaying exponential and their sum

Hence we can define asymmetrical fault current in the following way: If, in a circuit containing only reactance, theshort circuit occurs at any point at the peak of the voltage wave, there will be some offset of the current.

The amount of offset depends upon the point on the voltage wave at which the short circuit occurs.

This is known as asymmetrical short circuit current. Maximum asymmetry occurs when short circuit takes placewhen voltage is zero.

Asymmetrical fault remains only for few cycles after which it becomes symmetrical fault . Decay of asymmetricalcomponent depends on the value of X/R. More the value of R, faster is the decay of asymmetrical fault current.

Magnitude of asymmetrical fault current is more than that of symmetrical fault current.

If the short circuit current does not include DC component it is called symmetrical short circuit current. If the shortcircuit current contains DC component it is called as asymmetrical component.

Figure above represents the short circuit current with and without DC component.

Will be continued soon

An Overview Of Short Circuit Current (part 1)Basic conceptMathematical background, X/R ratio and type of fault currentNotes:Symmetrical fault currentAsymmetrical fault current