For a fault at terminals of the synchronous generator, the fault current is maximum for a:  

Explanation:

Fault Current in Synchronous Generators:

Definition: When a fault occurs at the terminals of a synchronous generator, the generator's response to the fault depends on the type of fault. Fault current is the current that flows during a fault condition, which is significantly higher than the normal operating current. The magnitude of the fault current depends on the type of fault and the impedance of the system.

Correct Option Analysis:

The correct option is:

Option 1: Three-phase fault.

Among all types of faults that can occur in a power system, a three-phase fault generates the highest fault current. This is because a three-phase fault involves all three phases of the system, creating a condition where the impedance of the fault path is minimum. As a result, the current during a three-phase fault is maximum compared to other types of faults.

Why Three-Phase Fault Produces Maximum Fault Current:

• Symmetrical Nature: A three-phase fault is a balanced fault, meaning all three phases are equally affected. This symmetry ensures that the fault current magnitude is uniform across all three phases, leading to the highest possible current flow.
• Minimum Fault Impedance: During a three-phase fault, the impedance of the fault path is at its lowest, as all three phases are directly short-circuited. Lower impedance results in higher current flow as per Ohm's Law (I = V/Z, where I is current, V is voltage, and Z is impedance).
• Generator's Response: Synchronous generators are designed to supply balanced three-phase power. When a three-phase fault occurs, the generator supplies maximum current to the fault because the fault aligns with the generator's natural three-phase configuration.

Implications of Three-Phase Fault:

• It is the most severe type of fault in terms of current magnitude and system impact.
• Protection systems, such as circuit breakers and relays, are designed to detect and isolate three-phase faults quickly to prevent damage to equipment and ensure safety.
• System studies and fault analysis prioritize three-phase fault scenarios to design robust protection schemes and ensure system stability.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Double line to ground fault.

A double line to ground fault involves two phases and the ground. While this type of fault results in a higher fault current than single line to ground or line-to-line faults, it does not exceed the fault current produced by a three-phase fault. The presence of ground in the fault path increases impedance compared to a three-phase fault, reducing the current magnitude.

Option 3: Line to line fault.

A line-to-line fault involves a short circuit between two phases. The fault current in this scenario is lower than that of a three-phase fault because only two phases are involved, and the impedance in the fault path is higher. Line-to-line faults are less severe than three-phase faults in terms of current magnitude and system impact.

Option 4: Line to ground fault.

A line-to-ground fault occurs when one phase is short-circuited to the ground. This type of fault has the highest impedance among all fault types, resulting in the lowest fault current. While line-to-ground faults are common in power systems, their impact is less severe compared to other faults.

Conclusion:

Among all types of faults, a three-phase fault produces the maximum fault current due to its symmetrical nature and minimum fault impedance. This makes it the most severe fault type in terms of system impact, requiring robust protection systems to mitigate its effects. Understanding the characteristics of different fault types is essential for designing effective power system protection schemes and ensuring system stability.