A distance relay is said to under reach when the impedance seen by relay due to fault is more than the relay setting value even though the fault point is within the protected zone of line. This means that reach of relay has decreased from the setting value.

Therefore, percentage under reach can be defined as

(ZR – ZF)x100/ZR

where ZR = Relay Reach Setting and ZF = Effective Reach

Under Reach can be best illustrated by the figure below. Figure shows an uncompensated transmission line having an impedance of Z and a distance relay.


A line to ground fault take place at point F. The impedance measured by distance relay is ZF and the setting of relay is Z (say). In some cases, it may happen that line impedance ZF measured by relay due to fault at F may exceed the setting value Z i.e. ZF > Z. What will happen then? The relay will not actuate to clear the fault even though point F is within the protected zone. This scenario is called under reach of relay. Why it is called under reach?

Reach of distance relay is defined as line protection covered by relay in terms of line length or impedance. In the example, the reach of relay is Z as it is expected to protect the entire line. But due to absence of residual compensation, the relay is not only able to protect the whole line rather it is protecting only a part of line say 90% of line. This means the effective reach of relay has decreased. This is why; we say relay is under reaching.

Cause of Under Reach

Under Reach of distance relay is observed due to remote infeed. What is meant by remote infeed? 

Remote infeed means, the fault is being fed through different circuit other than the protected line. As a transmission line connects two substations, therefore it may happen in double circuit line that fault may be fed by other circuit. To understand the under reach and remote infeed, let us consider the figure below.

under reach distance protection

A & B are two substations connected by two lines 1 and 2. A third line 3 is connected from substation B & C. Suppose,

Impedance of line 1 = Z1

Impedance of line 2 = Z2

Impedance of line 3 = ZL

Relay impedance setting or reach = Z1+ZL

As the relay setting is assumed (Z1+ZL) therefore the reach of relay is (Z1+ZL). A fault occurs at point F on line 3 at a distance x from B. This fault will be fed by line 1 as well as line 2. Notice that line 2 is also feeding the fault. This is called remote infeed.

Let us now calculate the reach of relay by calculating the impedance seen by the distance relay 21.

Current flowing through relay = I1

Voltage seen by relay = I1Z1 + Z’ (I1+I2)

Z’ is impedance of line 3 up to point of fault F. Let Z’ = µZL where 0<µ<1.

Voltage seen by relay = I1Z1 + µZL(I1+I2)

Therefore the impedance Zm measured by distance relay,

Zm = Voltage seen by relay / current through relay

     = [I1Z1 + µZL(I1+I2)] / I1

     = Z1 + µZL(1+ I2/I1)  ………..(1)

Thus the relay reach = Z1 + µZL(1+ I2/I1) < Actual reach (Z1+ZL). Confused?

Let us make it more clear by assuming that fault point F is very close to C. As point F is close to C, therefore µ = 1 and Z’ = ZL.

Now, the impedance measured by relay Zm = Z1 + ZL(1+ I2/I1)

Carefully observe that, this measured impedance Zm is more than setting (Z1+ZL) and hence relay will not actuate even though it is supposed to actuate. This why relay is said to under reach.

How to Eliminate Under Reach?

As clear from discussion, to overcome this problem we need to increase the reach i.e. impedance setting of distance relay. Since the reach of relay Zm is less than setting (Z1+ZL), therefore the setting of relay shall be increased to Z1 + ZL(1+ I2/I1).

Hope you fully understand the concept of under reach. Please comment. Thank you!

2 thoughts on “Under Reach of Distance Relay

  1. jagan says:

    Very clear sir.
    Thanq very much

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