The critical clearing time of a fault is power system is related to

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Transient stability limit

Explanation: The critical clearing time (CCT) is the maximum time a fault can persist in a power system before the generator loses synchronism with the rest of the system. It is a fundamental parameter for assessing the transient stability limit following a large disturbance.

Working Principle: When a fault occurs, the electrical power output of the generator drops while the mechanical power input remains constant, causing the rotor to accelerate. If the fault is cleared before the rotor angle exceeds the critical clearing angle (CCA), the system can decelerate and return to a stable operating point. If the fault persists beyond the CCT, the rotor angle continues to increase indefinitely, leading to instability.

Key Formulas: $P_e = \frac{V_1 V_2}{X} \sin(\delta)$ — Power-angle relation; $t_{cr} = \sqrt{\frac{4H(\delta_{cr} - \delta_0)}{\omega_s P_m}}$ — Critical clearing time formula

Key Points: CCT determines the speed at which circuit breakers must operate to maintain stability.; Transient stability is concerned with large perturbations, unlike steady-state stability which deals with small disturbances.; The equal area criterion is used to calculate the critical clearing angle and subsequently the time.; Higher inertia (H) of the generator increases the CCT, providing more time for fault clearance.

Advantages: Ensures system reliability against major disturbances.; Defines the required operating speed for protective switchgear.

Disadvantages: Strict requirements on relay and breaker response times.; Complexity in maintaining stability during heavy load conditions.

Applications: Power system planning and protection coordination.; Determination of circuit breaker specifications for transmission lines.

Additional Info: Option B (Short circuit limit) relates to breaker ratings, not stability time.. Option C (Steady-state stability limit) refers to the maximum power transferable under gradual, small changes.. The CCT is strictly a transient stability phenomenon.

Answer: D is correct — The critical clearing time is the maximum duration for which a fault can exist without the system losing its transient stability.

Exam Tip: Always remember: Transient stability = Large disturbances (faults, switching); Steady-state stability = Small disturbances (load fluctuations).

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