📘 Protection Coordination – Time & Current Grading (Numerical Problems)
Protection coordination ensures that only the faulty section is isolated. Primary relay must operate first, backup relay operates after delay.
🔹 Problem 1: Time Grading
Two overcurrent relays R1 (near load) and R2 (upstream). Relay R1 operates in 0.4 sec. Coordination Time Interval (CTI) = 0.3 sec. Find operating time of R2.
Solution
Operating time of R2 = R1 time + CTI = 0.4 + 0.3 = 0.7 sec
Upstream relay must operate at 0.7 sec.
🔹 Problem 2: Plug Setting Calculation
CT ratio = 500/1 Full load current = 250 A Relay plug setting = 125% Find pickup current.
Step 1: Secondary Current at Full Load
Secondary current = 250 / 500 = 0.5 A
Step 2: Pickup Current
Pickup = 1.25 × 0.5 = 0.625 A
🔹 Problem 3: Plug Setting Multiplier (PSM)
Fault current = 2000 A CT ratio = 500/1 Pickup current (secondary) = 1 A Find PSM.
Step 1: Convert Fault to Secondary
Secondary fault current = 2000 / 500 = 4 A
Step 2: Calculate PSM
PSM = Fault current / Pickup current = 4 / 1 = 4
🔹 Problem 4: Inverse Time Relay Operation
Relay characteristic: T = 0.14 / (PSM^0.02 − 1) Given PSM = 5 Find operating time.
Solution
PSM^0.02 ≈ 1.032 T = 0.14 / (1.032 − 1) = 0.14 / 0.032 = 4.375 sec
🔹 Problem 5: Current Grading
Relay R1 pickup = 1 A Relay R2 pickup = 1.5 A Fault current = 4 A Check which operates first.
Solution
PSM1 = 4 / 1 = 4 PSM2 = 4 / 1.5 = 2.67
Higher PSM → Faster operation.
Relay R1 operates first (Primary protection).
🎯 Key Coordination Concepts
- CTI typically 0.2–0.5 sec
- Primary protection fastest
- Backup protection time delayed
- Plug setting multiplier decides relay speed
Protection Coordination = Selectivity + Reliability + Speed
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