The short-circuits hidden story

Welcome to our new release on the short-circuit hidden story.

This is the first edition of a long series on power system protection.

1??Introduction

Even the best-design electrical system will experience a short circuit.

This makes it paramount to:

①Properly specify the equipment (Switchgears, circuit breakers)

②Properly apply overcurrent protection devices.

Applying these two directives will not only minimize damage to the electrical apparatus but also minimize service interruption.

For that, it is important to determine the magnitude of the voltages and currents that the system will produce under various short-circuit conditions. Of the two later, short-circuits are the most complicated to derive and even understand.

2??Short-circuit characteristics

The good news is, even the short-circuit current follow the fundamental principle of Ohm’s law.??

The short-circuit current is nothing but the ratio of the system voltage divided by the sum of impedances from the source to the short circuit location.

The picture below illustrates the power system conditions during normal and short-circuits conditions

The load impedance is usually the largest of all and is predominantly resistive. Because of that, it is the main determinant of the load current, and this later tends to be in phase with the driving voltage.??

The line and source impedance are usually very small and are predominantly inductive. For that reason, short-circuits current are usually far greater than the load current and they lag the driving voltage by an angle approaching the theoretical maximum of 90?.??

Perhaps the main point we are trying to make in this article, the impedance of the circuit from the source up to the short-circuit location is what determines the short-circuit current value and characteristic.

We learned that impedance is predominately inductive (cable and generator windings).

The change in state from normal to short-circuit current conditions occurs rapidly. Fundamental physics demonstrates that the magnitude of current in an inductor cannot change instantaneously. This con?ict can be resolved by considering the short-circuit current to consist of two components:

?Asymmetrical ac current with the higher magnitude of the short-circuit current. The mathematical expression of this current is given by:

?An offsetting dc transient with an initial magnitude that is equal to the initial value of the ac current, but which decays rapidly. The mathematical expression of this current is given by:

The combined resultant asymmetrical short circuit current can be expressed as:

From formula 3, we can see that a t=0, the instantaneous asymmetrical current is zero which means that the transient dc component has the same absolute value as the symmetrical component of the short-circuit.

From formula 1, we can also see that at t =0, the symmetrical component of the short circuit is at its minimum value.????

So, assuming the symmetrical component of the short circuit is 1pu RMS, the transient dc component of the short circuit will be equal to 1.414 pu.( 1pu x sqrt(2)).????

The dc component of the short-circuit declines exponentially from the initial value, with a time constant that is determined by the values of the circuit reactance (X) and resistance (R)

ANSI/IEEE and the IEC standards, the time constant of dc decay is standardized at 45 ms, which corresponds to an X/R ratio of 17 for a 60 Hz system.

The figure below illustrates different facts about asymmetrical short-circuit and its components:

Important industry Short-circuit terms

For what follows, we assume that the short-circuit rating is 1 pu.

Short-circuit (interrupting) rating

This is the symmetrical ac component of the short circuit. It is assumed to remain constant. In our illustration above, the short-circuit rating has an RMS value of 1 pu and a peak value of 1.414 pu.

Closing and latching current (for circuit breakers) or peak withstand current (for switchgear) (in peak amperes)

This is the first peak of the (total instantaneous) asymmetrical short circuit current. This value is 2.6 pu and is measured at ? cycle (180?). This current produces the most severe mechanical forces between conductors. It is the critical mechanical current value for bus bars and supports design.

Momentary current (in RMS amperes)

This is the RMS value corresponding to the peak withstand current discussed above. In the illustration, the RMS value of the asymmetrical current is represented by the S-factor curve. The momentary current is equal to the S-factor at ? cycle or 1.55pu.

%dc component

This is the percentage of the transient dc component in the total instantaneous current

At t= 0, %dc component is equal to 100% and it declines exponentially, approaching zero around 10 cycles. At ? cycle, %dc component is equal to 83%.

The %dc component and the S-factor express the same concept and are related by the following expression:

The formula can be illustrated by the figure below:

I hope this article helped you understand the origin of some terms used by industry standards about short-circuits.

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Author: Yves Zomebot, PE

Source: Siemens, IEEE Buff, and Red books, ANSI/IEEE C37.20.2, ANSI/IEEE C37.04

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