A distance relays is said to under-reach when the impedance presented to it is greater than the apparent impedance to the fault. This may happen when two lines are connected in parallel and a faults occurs as shown in figure (27).
For the fault F with respect to distance relay R1, The expected Values of current, impedance, and voltage are as follows (Assuming one line, no parallel lines).
• Current = I1
• Impedance =Z1+Z2
• Volt (V) = I1(Z1+Z2)
Actually, due to the I2 feed
V = I1(Z1)+ Z2' (I1+I2)
Then, the effective reach of the distance relay is changed to be
Z1+Z2'
To overcome this problem, and due to the fact that V, and I1 are constants
I1(Z1+Z2) = I1(Z1) + Z2' (I1+I2)
Or
I1 Z2 = Z2' (I1+I2)
Then the setting must be increased by a factor equal to
( I1+I2)/(I1)
So, the Setting to be installed on the relay must be equal to
Z1+Z2 (( I1+I2)/(I1))