Ex-5: - Single transformer newly constructed substation.

Problem

Consider a S/S constructed newly having transformers of 132/33kV 25 MVA with leakage reactance of 9.5%. This substation being supplied from remote substation through a 132kV line of length 60 km. Positive and zero sequence reactance of the lines are 0.4 Ω / km and 1.2 Ω /km respectively. For remote 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 132kV line positive sequence and zero sequence reactance to 100 MVA base  

 ---- (using formula – 1)

 ---- (using formula – 1)

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

1700 =  ---- (using formula – 3)

HENCE

Find positive sequence equivalent reactance between source and fault point

X₁ = X₁s + X_1L + X_T = 5.88 + 13.77 + 38 = 57.65%

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

3-Ph short circuit MVA = 100x100/57.65% = 173 MVA ---- (using formula – 3)

For 33kV voltage 1 MVA = 17.5 Amp

Hence this current will be 17.5*173 = 3027 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_1L + X_T = 5.88 + 13.77 + 38 = 57.65%

X₂ = X₁

AND

X₀ = X₀s + X_T1 + X_0L = 9.67 + 41.32 + 38 = 88.99%

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

1-Ph short circuit MVA = 3*100x100/(57.65+57.65+88.99)_% = 147 MVA (using formula-4)

For 33kV voltage 1 MVA = 17.5 Amp

Hence this current will be 17.5*147 = 2572 Amp.

Comments

For remote substations fault current for earth fault is substantially less than 3-ph fault current due to presence of lengthy line. Hence it is customary to calculate it correctly i.e. without neglecting source impedances.