A short circuit occurs in a transmission line (neglect line capacitance) when the voltage wave is going throug

Question

A short circuit occurs in a transmission line (neglect line capacitance) when the voltage wave is going through zero, the maximum possible momentary short circuit current corresponding to

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Option A: Twice the maximum of symmetrical short circuit current

Explanation & Concepts:
When a short circuit occurs in an inductive circuit at the instant of voltage zero, the DC transient component reaches its maximum value. This results in the total momentary short-circuit current reaching a peak of twice the maximum value of the symmetrical steady-state short-circuit current.

Working Principle: In a purely inductive circuit, the current lags the voltage by $90^\circ$. If a fault occurs at voltage zero, the steady-state current should be at its negative peak. To satisfy the circuit's natural response (where current cannot change instantaneously), a DC offset current equal and opposite to the steady-state value is introduced at $t=0$. This DC component decays over time, causing the total current to reach an initial peak of $2 	imes I_{max(sym)}$.

Key Formulas: $i(t) = I_{max}[\sin(\omega t + \alpha - \phi) - \sin(\alpha - \phi)e^{-Rt/L}]$ — total short circuit current equation; $I_{momentary} = 2 	imes I_{max(sym)}$ — peak current under worst-case condition

Key Points: The DC transient component magnitude depends on the fault initiation angle.; Maximum momentary current occurs when the voltage is zero, leading to the largest DC offset.; The DC component is maximum when the circuit is purely inductive ($R \approx 0$).; As $t 	o \infty$, the DC component decays to zero, leaving only the symmetrical AC component.

Applications: Switchgear rating selection; Circuit breaker mechanical stress design

Additional Info: This phenomenon is often referred to as the 'doubling effect'.. Option B is incorrect as it ignores the contribution of the DC transient component.. Options C and D are mathematically incorrect based on the circuit dynamics.

Answer: A is correct — The momentary current reaches twice the maximum of the symmetrical short-circuit current due to the maximum DC offset transient when a fault occurs at voltage zero.

Exam Tip: Always remember that in inductive power systems, the worst-case mechanical stress on conductors and circuit breakers occurs at the first peak of the fault current, which is influenced by the fault initiation timing.

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Option B: Maximum of short circuit current

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Option C: Thrice the maximum of symmetrical short circuit current

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Option D: Four times the maximum symmetrical short circuit current

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