Calculate IDMT over Current Relay Setting (50/51)

Calculate setting of IDMT over Current Relay for following Feeder and CT Detail
Feeder Detail: Feeder Load Current 384 Amp, Feeder Fault current Min11KA and Max 22KA.
CT Detail: CT installed on feeder is 600/1 Amp. Relay Error 7.5%, CT Error 10.0%, CT over shoot 0.05 Sec, CT interrupting Time is 0.17 Sec and Safety is 0.33 Sec.
IDMT Relay Detail:
IDMT Relay Low Current setting: Over Load Current setting is 125%, Plug setting of Relay is 0.8 Amp and Time Delay (TMS) is 0.125 Sec, Relay Curve is selected as Normal Inverse Type.
IDMT Relay High Current setting :Plug setting of Relay is 2.5 Amp and Time Delay (TMS) is 0.100 Sec, Relay Curve is selected as Normal Inverse Type

Calculation of Over Current Relay Setting:

Over Load Current (In) = Feeder Load Current X Relay setting = 384 X 125% =480 Amp
Required Over Load Relay Plug Setting= Over Load Current (In) / CT Primary Current
Required Over Load Relay Plug Setting = 480 / 600 = 0.8
Pick up Setting of Over Current Relay (PMS) (I>)= CT Secondary Current X Relay Plug Setting
Pick up Setting of Over Current Relay (PMS) (I>)= 1 X 0.8 = 0.8 Amp
Plug Setting Multiplier (PSM) = Min. Feeder Fault Current / (PMS X (CT Pri. Current / CT Sec. Current))
Plug Setting Multiplier (PSM) = 11000 / (0.8 X (600 / 1)) = 22.92
Operation Time of Relay as per it’s Curve
Operating Time of Relay for Very Inverse Curve (t) =13.5 / ((PSM)-1).
Operating Time of Relay for Extreme Inverse Curve (t) =80/ ((PSM)2 -1).
Operating Time of Relay for Long Time Inverse Curve (t) =120 / ((PSM) -1).
Operating Time of Relay for Normal Inverse Curve (t) =0.14 / ((PSM) 0.02 -1).
Operating Time of Relay for Normal Inverse Curve (t)=0.14 / ( (22.92)0.02-1) = 2.17 Amp
Here Time Delay of Relay (TMS) is 0.125 Sec so
Actual operating Time of Relay (t>) = Operating Time of Relay X TMS =2.17 X 0.125 =0.271 Sec
Grading Time of Relay = [((2XRelay Error)+CT Error)XTMS]+ Over shoot+ CB Interrupting Time+ Safety
Total Grading Time of Relay=[((2X7.5)+10)X0.125]+0.05+0.17+0.33 = 0.58 Sec
Operating Time of Previous upstream Relay = Actual operating Time of Relay+ Total Grading TimeOperating Time of Previous up Stream Relay = 0.271 + 0.58 = 0.85 Sec

Pick up Setting of Over Current Relay (PMS) (I>>)= CT Secondary Current X Relay Plug Setting
Pick up Setting of Over Current Relay (PMS) (I>)= 1 X 2.5 = 2.5 Amp
Plug Setting Multiplier (PSM) = Min. Feeder Fault Current / (PMS X (CT Pri. Current / CT Sec. Current))
Plug Setting Multiplier (PSM) = 11000 / (2.5 X (600 / 1)) = 7.33
Operation Time of Relay as per it’s Curve
Operating Time of Relay for Very Inverse Curve (t) =13.5 / ((PSM)-1).
Operating Time of Relay for Extreme Inverse Curve (t) =80/ ((PSM)2 -1).
Operating Time of Relay for Long Time Inverse Curve (t) =120 / ((PSM) -1).
Operating Time of Relay for Normal Inverse Curve (t) =0.14 / ((PSM) 0.02 -1).
Operating Time of Relay for Normal Inverse Curve (t)=0.14 / ( (7.33)0.02-1) = 3.44 Amp
Here Time Delay of Relay (TMS) is 0.100 Sec so
Actual operating Time of Relay (t>) = Operating Time of Relay X TMS =3.44 X 0.100 =0.34 Sec
Grading Time of Relay = [((2XRelay Error)+CT Error)XTMS]+ Over shoot+ CB Interrupting Time+ Safety
Total Grading Time of Relay=[((2X7.5)+10)X0.100]+0.05+0.17+0.33 = 0.58 Sec
Operating Time of Previous upstream Relay = Actual operating Time of Relay+ Total Grading Time.
Operating Time of Previous up Stream Relay = 0.34 + 0.58 = 0.85 Sec

Pickup Setting of over current Relay (PMS) (I>) should be satisfied following Two Condition.
(1) Pickup Setting of over current Relay (PMS)(I>) >= Over Load Current (In) / CT Primary Current
(2) TMS <= Minimum Fault Current / CT Primary Current
For Condition (1) 0.8 > =(480/600) = 0.8 >= 0.8, Which found OK
For Condition (2) 0.125 <= 11000/600 = 0.125 <= 18.33, Which found OK
Here Condition (1) and (2) are satisfied so
Pickup Setting of Over Current Relay = OK
Low Over Current Relay Setting: (I>) = 0.8A X In Amp
Actual operating Time of Relay (t>) = 0.271 Sec
High Over Current Relay Setting: (I>>) = 2.5A X In Amp
Actual operating Time of Relay (t>>) = 0.34 Sec