Fault Current Calculation in Synchronous Machine

Introduction:
In power systems, fault current calculations are essential to determine the maximum fault current that can occur in the system during a fault. These calculations help in designing protective devices and equipment for the system. In this question, we are required to determine the fault current in each phase following a double line to ground fault in a star connected synchronous machine.

Given Data:
Open circuit voltage of the synchronous machine = 1.0 pu
Positive sequence reactance of the generator (X1) = j0.35
Negative sequence reactance of the generator (X2) = j0.25
Zero sequence reactance of the generator (X0) = j0.20
Star point of the generator is isolated from ground.

Solution:
To determine the fault current, we need to follow these steps:

Step 1: Determine the fault impedance
During a double line to ground fault, the fault impedance can be represented as a balanced three-phase fault with a fault impedance of Zf = 3Z1. Therefore, the fault impedance can be calculated as:
Zf = 3 × X1 = 3j0.35 = j1.05 pu

Step 2: Determine the fault current
The fault current can be calculated using the following equation:
If = Vp / Zf
where, If is the fault current, Vp is the open circuit voltage of the generator, and Zf is the fault impedance.

Substituting the given values, we get:
If = 1.0 / j1.05 = -0.95 ∠ -90° pu

Step 3: Determine the fault current in each phase
The fault current in each phase can be determined using symmetrical component analysis. The positive, negative, and zero sequence currents can be calculated using the following equations:

I1 = (2Ia - Ib - Ic) / 3
I2 = (Ib - Ic) / √3
I0 = (Ia + Ib + Ic) / 3

where, Ia, Ib, and Ic are the phase currents.

Substituting the values, we get:
I1 = (2 x (-0.95) - 0 + 0) / 3 = -1.27 ∠ -60° pu
I2 = (0 - 0) / √3 = 0 pu
I0 = (-0.95 - 0 - 0.95) / 3 = -0.63 ∠ -180° pu

Therefore, the fault current in phase A is -1.27 ∠ -60° pu, the fault current in phase B is 0 pu, and the fault current in phase C is -1.27 ∠ 60° pu.

Conclusion:
In conclusion, the fault current in each phase following a double line to ground fault in a star connected synchronous machine can be determined using symmetrical component analysis. The fault current in each phase depends on the fault impedance and the sequence reactance of the generator. The fault current can be used to design protective devices and equipment for the system.