The following diagram shows the negative sequence network of a system with one synchronous
generator and two induction motors:
3.
XL13 = 0.1
??? = 0.3
2
XL12 = 0.1
XL23 = 0.15
??3 = 0.14
Xc1 = 0.15
XM2 = 0.18
An arcing double-line-to-ground fault with impedance ZF = j0.007 pu occurs at bus 3. The
Thevenin equivalents of the positive and zero sequence networks as viewed from bus 3 are:
V = 1.00?0°
+
Z? = j0.095
Positive
V
Z = j0.08
+
Zero
Vo
?
a) (12 points) Reduce the negative sequence network to its Thevenin equivalent as viewed
from bus 3.
b) (10 points) Use the Thevenin equivalents of the sequence networks to calculate the p.u.
sequence components of the fault current.
Note: if you cannot solve part (a), use Z2 = j0.085 for the Thevenin impedance of
the negative sequence network. This is not the correct value of the Thevenin
impedance from part (a), but you can use this value to solve the rest of the problem.
c) (3 points) Write down the matrix equation for solving for the p.u. phase components of the
fault current. You do not need to find the values of the phase currents. Include the entries
of each matrix, as opposed to writing something in symbolic form.
d) (10 points) Calculate the p.u. sequence components of the fault voltage.
