Ex-4: - Two transformer in parallel with calculations of source impedance for 3-phase and 1-phase fault.

Problem

Consider a S/S having two transformers of (a) 132/33kV 25 MVA having leakage reactance of 9.5% and (b) 132/33kV 50 MVA having leakage reactance of 12.5%. For this substation 132kV bus 3-phase and 1-phase fault level is 1700 MVA and 1400 MVA. Find out the 3-phase and 1-phase 33kV Bus fault current.

Solution

Consider 100 MVA as base MVA

Convert 25 MVA transformer leakage reactance to 100 MVA base

Hence X_T1-100MVA = X_T1-25MVA*(100/25) = 9.5*4 = 38% ----- (using formula – 2)

Convert 50 MVA transformer leakage reactance to 100 MVA base

X_T2-100MVA = X_T2-50MVA*(100/50) = 12.5*2 = 25% ---- (using formula – 2)

Find out POSITIVE SEQUENCE source % reactance for 100 MVA base for 132kV bus by reverse engineering.

1700 =  ---- (using formula – 3)

HENCE

Find equivalent reactance between source and fault point

X = X₁s + (X_T1||X_T2) = 5.88 + 38*25/(38+25) = 20.96%

Find 3-phase short circuit MVA (Base MVA = 100 MVA)

3-Ph short circuit MVA = 100x100/20.96% = 477 MVA ---- (using formula – 3)

For 33kV voltage 1 MVA = 17.5 Amp

Hence this current will be 17.5*477 = 8347 Amp.

Find out ZERO SEQUENCE source % reactance for 100 MVA base for 132kV bus by reverse engineering.

1400 =  ----- (using formula – 4)

HENCE

But as we have already calculated value for X_1s% as 5.88% and we know that X_1s = X_2s thus

X_0s = 9.67%

Find equivalent SEQUENCE reactance between source and fault point

X₁ = X₁s + (X_T1||X_T2) = 5.88 + 38*25/(38+25) = 20.96%

X₂ = X₁

AND as transformer zero sequence leakage reactance same as +Ve sequence

X₀ = X₀s + (X_T1||X_T2) = 9.67 + 38*25/(38+25) = 24.75%

Find 1-phase short circuit MVA (Base MVA = 100 MVA)

1-Ph short circuit MVA = 3*100x100/(20.96+20.96+24.75)_% = 449 MVA

For 33kV voltage 1 MVA = 17.5 Amp

Hence this current will be 17.5*449 = 7857 Amp.

Comments

We can calculate positive sequence and zero sequence source reactance by reverse engineering if source bus fault level for 3-phase and 1-phase fault is known. Generally up to 132kV bus; these fault levels are provided by Corporate Office. For remote stations 1-phase fault levels are less as compared to 3-phase owing to higher zero sequence reactance for the transmission line than its’ positive sequence reactance.