If a sudden short circuit occurs on a power system (considered as R-L series circuit), the current wave-form c

Question

If a sudden short circuit occurs on a power system (considered as R-L series circuit), the current wave-form consists of

1 · Decaying AC current

2 · Decaying DC current

Let the alternator reactance be X and the power system resistance R · Which one of the following is correct?

Examoogle · Accepted Answer

Option A: The decay in (1) is caused by the increase in X but in (2) is caused by R

Explanation & Concepts:
A short-circuit current in an R-L power system comprises a symmetrical AC component and a DC offset component. The AC component decays because the effective reactance of the alternator increases as the magnetic flux adjusts from sub-transient to transient and finally to steady-state, while the DC component decays purely due to the circuit resistance R dissipating the trapped energy.

Working Principle: Immediately after a fault, the alternator's internal reactance is minimal (sub-transient reactance $X_d''$), leading to high initial current. As time progresses, armature reaction and field flux changes increase the effective reactance to $X_d'$ and then $X_d$, causing the AC component to decay. The DC offset current $i_{dc} = I_{max} e^{-Rt/L}$ exists to satisfy the continuity of flux linkage at the instant of the fault and is attenuated strictly by the ohmic resistance $R$ of the system.

Key Formulas: $i(t) = \sqrt{2}I_{rms} [\sin(\omega t + \alpha - \phi) - e^{\frac{-Rt}{L}} \sin(\alpha - \phi)]$; $i_{dc}(t) = I_{max} e^{\frac{-Rt}{L}}$

Key Points: The sub-transient period is characterized by the lowest reactance $X_d''$.; The DC offset depends on the point-on-wave at which the short circuit occurs.; The transient period is governed by the transient reactance $X_d'$.; Resistance $R$ is the only parameter responsible for the dissipation of the DC offset.

Advantages: Allows for calculation of momentary duty for circuit breakers.; Essential for sizing protective relay settings.

Disadvantages: High sub-transient currents can cause severe mechanical stress on windings.; The DC offset increases the required breaking capacity of switchgear.

Applications: Power system stability studies.; Design of short-circuit protection schemes.; Selection of circuit breakers.

Additional Info: The AC component decays through three stages: Sub-transient, Transient, and Steady-state.. Option B is incorrect because resistance does not govern the decay of the AC waveform amplitude; it is purely inductive reactance variation.

Answer: A is correct — The AC current decay is dictated by the change in the generator's internal reactance (from sub-transient to steady-state), while the DC current decay is governed by the $L/R$ time constant of the circuit.

Exam Tip: Always remember that in an inductive circuit, the DC component is associated with the storage of magnetic energy and its subsequent dissipation through resistive loss, whereas the AC component's magnitude is limited by the system impedance (primarily reactance).

Examoogle · Answer

Option B: The decay in (1) is caused by R but in (2) is caused by increase in X

Examoogle · Answer

Option C: The decay in both (1) and (2) is caused by R

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Option D: The decay in both (1) and (2) is caused by the increase in X

Feature	AC	DC
Current Component	ACComponent	DCComponent
Primary Cause of Decay	Increase in X	Ohmic Resistance R

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