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IDMT grading: R1, R2 with 1000/5 CTs
Short answer
Relay current = 25 A. R1 PSM=5 gives 4 s at TMS=1, so t1=0.3×4=1.2 s. R2 pick-up=6.25 A, PSM=4 gives 5 s at TMS=1. Required t2=1.2+0.5=1.7 s, so TMS=1.7/5=0.34. R1 operates in 1.2 s, R2 in 1.7 s, TMS of R2 is 0.34.
Two relays R1 and R2 are connected in two sections of a feeder as shown in figure. CTs are of ratio 1000/5 A. The plug setting of relay R1 is 100% and R2 is 125%. The operating time characteristic of the relays is given below. The time multiplier setting of the relay R1 is 0.3. The time grading scheme has a discriminative time margin of 0.5 s between relays. A three phase short circuit at F results in a fault current of 5000 A. Find the actual operating times of R1 and R2. What is the time multiplier setting (TMS) of R2?
| Plug setting multiplier | 2 | 4 | 5 | 8 | 10 | 15 | 20 |
|---|---|---|---|---|---|---|---|
| Time in seconds for a time multiplier of 1 | 10 | 5 | 4 | 3 | 2.8 | 2.6 | 2.4 |
[Figure: Bus A – CB – CT 1000/5 with relay R2 – bus B – CB – CT 1000/5 with relay R1 – fault F (5000 A) – bus C.]
Each relay's operating time is found from its plug setting multiplier (PSM) using the given curve, then multiplied by the time multiplier setting (TMS). R2 (upstream) must operate 0.5 s after R1.
Data: CT ratio 1000/5 (ratio 200); relay rated current 5 A; fault current = 5000 A; R1: PS = 100%, TMS = 0.3; R2: PS = 125%; discrimination margin = 0.5 s.
Relay current
Both relays see the same fault current (the fault is beyond R1 and fed through R2):
Relay current = 5000 / 200 = 25 A (secondary)
Relay R1
Pick-up current = 100% × 5 = 5 A
PSM = 25 / 5 = 5
Time at TMS = 1 (from table, PSM 5) = 4 s
Actual time t₁ = 0.3 × 4 = 1.2 s
Relay R2
Pick-up current = 125% × 5 = 6.25 A
PSM = 25 / 6.25 = 4
Time at TMS = 1 (from table, PSM 4) = 5 s
Required time t₂ = t₁ + 0.5 = 1.2 + 0.5 = 1.7 s
TMS of R2 = 1.7 / 5 = 0.34
Results
| Relay | PS | PSM | t (TMS=1) | TMS | Operating time |
|---|---|---|---|---|---|
| R1 | 100% | 5 | 4 s | 0.3 | 1.2 s |
| R2 | 125% | 4 | 5 s | 0.34 | 1.7 s |
Answer: R1 operates in 1.2 s, R2 operates in 1.7 s, and the TMS of R2 is 0.34.
✓ Answer checked by Claude Opus 5.5 (high effort)
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