3) The impedance for a 120 km, 230-kV line is given as j 0.9 ohm/km and
j 0.6 ohm/km for self and mutual terms respectively; resistance is neglected. The mho
characteristic for the line’s distance protection is set to reach 100 km at the line’s
characteristic impedance angle. Assume that a line-to-ground fault occurs at a distance “x”
from the relay by contact with a tree branch, where the tree presents an impedance of 30
ohms to the flow of fault current.
(a) What is the impedance seen by the relay, expressed as a function of x?
(b) What is the relay reach (in km) for this fault condition (i.e. at what distance from the relay
is the fault on the verge of going undetected)?