Explanation:
When a fault occurs in a power system, it can be categorized into different types based on the nature of the fault and the fault path. These fault types include three-phase fault, line to ground fault, line to line fault, and double line to ground fault. In this case, if all the sequence voltages at the fault point are equal, then the fault is a double line to ground fault.

Sequence Voltages:
In a power system, sequence voltages are used to analyze and study the behavior of the system during a fault. Sequence voltages are the positive, negative, and zero sequence components of the fault voltages. Positive sequence voltages have the same phase sequence as the normal system voltages, negative sequence voltages have reverse phase sequence, and zero sequence voltages have the same phase for all three phases.

Double Line to Ground Fault:
A double line to ground fault occurs when two phases of a power system come into contact with the ground simultaneously. This fault can be caused by a variety of reasons such as insulation failure, equipment malfunction, or external factors. In this fault, two phases are shorted to the ground, resulting in a flow of fault current through the fault path.

Equal Sequence Voltages:
When a double line to ground fault occurs, the fault current flows through the faulted phases and the ground. This fault current creates voltage drops across the impedances in the fault path, resulting in different sequence voltages at the fault point. However, if all the sequence voltages at the fault point are equal, it indicates that the fault is a double line to ground fault.

Reasoning:
The reason behind this is that during a double line to ground fault, the fault current flows through both the faulted phases and the ground, creating a parallel path for the fault current. This parallel path results in equal sequence voltages at the fault point. On the other hand, in other fault types such as three-phase fault, line to ground fault, or line to line fault, the fault current follows a different path, resulting in different sequence voltages at the fault point.

Conclusion:
Therefore, if all the sequence voltages at the fault point in a power system are equal, it indicates a double line to ground fault. By analyzing the sequence voltages, engineers can identify the type and nature of the fault and take appropriate measures to protect the power system and ensure its reliable operation.