SLG Fault Calculation at Bus3 (High Side Start Grounded - 33kV) for three winding Aux Transformer (Hand Calculation)

[Rocky1991]

Can someone please help with solving Single Line to Ground fault current at the Bus3 (33kV) of the below single line diagram, single line parameters are as below:

Grid: 3Ph Fault current 50kA, X/R =14 1Ph Fault Current 50kA, X/R =14

TF1: 285/142.5/42.5 MVA, 330/33/33 kV, Yn0d1d1 Positive sequence impedance = Negative Sequence = Zps = 14%, Zpt = 14%, Zst = 28%, X/R =57 Zero Sequence is same as Positive sequence impedance.

TF2 (Aux TF datasheet and FAT attached): 33/0.436/0.114 kV, 0.5MVA, Ynyn0d1

Appreciate your help with hand calculation if possible.

 

[davidbeach]

Show your work. Some fault current but not much. Might not even make it to being effectively grounded.

 

[Rocky1991]

1. Base Values at 33kV:

Base MVA = 100 MVA

Base kV = 33 kV

Base Z = (33²)/100 = 10.89 Ω

Base I = 100MVA/(√3 × 33kV) = 1749.8 A


2. Positive & Negative Sequence from Grid + TF1 side:

Grid (referred to 33kV):

Z1g = Z2g = (33²)/(50000×√3) × (1/100) = 0.1258 Ω

X/R = 14

R = 0.1258/√(1+14²) = 0.00897 Ω

X = 0.1258×14/√(1+14²) = 0.1256 Ω

T1 (referred to 33kV):

Z1t = Z2t = 14% × (100/285) × 10.89 = 0.535 Ω

X/R = 57

R = 0.535/√(1+57²) = 0.00938 Ω

X = 0.535×57/√(1+57²) = 0.534 Ω

Total Grid + T1:

Z1 = Z2 = (0.00897 + j0.1256) + (0.00938 + j0.534)

= 0.01835 + j0.6596 = 0.6599∠88.41° Ω

In per unit = 0.6599/10.89 = 0.0606 pu


3. Positive & Negative Sequence from TF2 side:

Z1 = Z2 = 6% × (100/0.5) = 12 pu


4. Parallel combination of both sources for Z1 & Z2:

Z1 = Z2 = (0.0606 × 12)/(0.0606 + 12) = 0.0604 pu


5. Zero Sequence (only from TF2):

Z0(given) = 125.8 Ω/phase

Converting to per unit = 125.8/10.89 = 11.55 pu


6. Single Line to Ground Fault Current Calculation:

If(pu) = 3 × 1.0 / (Z1 + Z2 + Z0)

= 3 / (0.0604 + 0.0604 + 11.55)

= 3 / 11.67

= 0.257 pu

Actual fault current = 0.257 × 1749.8 A = 449.7 A

I am not sure if I have interpreted the FAT data of the Aux TF correctly but below is what I have come up with:

TF2 Zero sequence impedance is as follows:



Z12 = Zps = 125.8 ohms/phase

Z13 = Zpt = 141.1 ohms/phase

Z23 = Zst = 0.0097 ohms/phase