Two generators are connected in parallel to a 66 kV bus One

Two generators are connected in parallel to a 6.6 kV bus. One generator has a rating of 20 MVA and a reactance of 15% while the second generator is rated at 15 MVA and has a reactance of 12%. Calculate the pu reactance of a single equivalent generator on 50 MVA and 10 kV base. (answer is 0.083pu)

Solution

Let 20 MVA generator reactance be X1=15%=0.15 pu

Vbase=6.6kV Sbase=20 MVA

X1(real)=X1(pu)*Vbase^2/Sbase=0.15*6600*6600/20000000=0.32 ohms

X1(real)=0.32 ohms

Let 15 MVA generator reactance be X2=12%=0.12 pu

Vbase=6.6kV Sbase=15 MVA

X2(real)=X2(pu)*Vbase^2/Sbase=0.12*6600*6600/15000000=0.34 ohms

X2(real)=0.34 ohms

Now Equivalent reactance of single generatot=Xeq=X1 *X2(X1+X2)

Xeq=0.34*0.32/(0.34+0.32)

Xeq=0.16 ohms

Now per unit value

Sbase=50 MVA,Vbase=10 kV

Xeq(pu)=Xeq*Sbase/Vbase^2=0.16*50M/(10k)^2=0.083 pu

Xeq(pu)=0.083 pu