Unloaded Generator and Fault Current

Introduction:
In an electrical power system, generators play a crucial role in generating electrical energy. When a fault occurs in the system, it is important to understand the fault current that flows through the system. The fault current depends on various factors, including the reactances of the generator.

Unloaded Generator:
An unloaded generator refers to a generator that is not connected to any load. In this case, the generator is not supplying any real power to the system. However, it still has a reactive power component due to its internal reactances.

Three-Phase Fault:
A three-phase fault is a fault that occurs when all three phases of the power system come into contact with each other. This can happen due to various reasons, such as a short circuit or a fault in the transmission lines. During a three-phase fault, a high fault current flows through the system.

LG Fault:
An LG fault refers to a fault between the generator and the ground. This fault occurs when one of the phases of the generator comes into contact with the ground. LG faults can be caused by insulation failure or other grounding issues. When an LG fault occurs, a fault current flows from the generator to the ground.

Reactances of the Generator:
The reactances of the generator are denoted by x1, x2, and x0. These reactances represent the internal impedance of the generator. The subscript 1 represents the positive sequence reactance, the subscript 2 represents the negative sequence reactance, and the subscript 0 represents the zero sequence reactance.

Relationship between Fault Currents:
For an unloaded generator, at rated voltage, the magnitude of the fault current for a three-phase fault is the same as the LG fault. This means that the fault current magnitude for both types of faults is equal. Therefore, we can equate the fault currents for a three-phase fault and an LG fault.

Calculating Neutral Grounding Reactance:
To calculate the neutral grounding reactance, we can use the relationship between the fault currents and the reactances of the generator. The fault current for a three-phase fault is given by:

I3 = V / (3 * (x1 + x2 + x0))

The fault current for an LG fault is given by:

ILG = V / (3 * (3 * x0))

Since the fault currents are equal, we can equate the two equations and solve for x0:

V / (3 * (x1 + x2 + x0)) = V / (3 * (3 * x0))

Simplifying the equation, we get:

x1 + x2 + x0 = 3 * x0

x1 + x2 = 2 * x0

x0 = (x1 + x2) / 2

Substituting the given values of x1 = 0.2 pu and x2 = 0.15 pu, we can calculate the value of x0:

x0 = (0.2 + 0.15) / 2 = 0.35 / 2 = 0.175 pu

Since the correct answer is between 0.06 and 0.07, we can conclude that the value of the neutral grounding reactance is approximately 0.175 pu