GATE Electrical Engineering - Complete Master Library

 

📘 Overcurrent Relay – Numerical Problems with Detailed Solutions

Overcurrent relays operate when current exceeds preset value. Very important for feeder protection and coordination problems in GATE.

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🔹 Basic Formula (IEC Standard Inverse)

Operating Time T = TMS × (0.14 / (PSM^0.02 − 1))

Where:

• TMS = Time Multiplier Setting
• PSM = Plug Setting Multiplier = Fault Current / Pickup Current

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🔹 Problem 1: Calculate Operating Time

Pickup current = 5 A Fault current = 20 A TMS = 0.2

Step 1: Calculate PSM

PSM = Fault Current / Pickup Current = 20 / 5 = 4

Step 2: Substitute in Formula

T = 0.2 × (0.14 / (4^0.02 − 1))

Calculate: 4^0.02 ≈ 1.028

T = 0.2 × (0.14 / (0.028)) = 0.2 × 5 = 1 second

Operating Time ≈ 1 second

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🔹 Problem 2: Relay Coordination

Relay A operates in 0.6 sec. Coordination time interval required = 0.3 sec. Find operating time of upstream Relay B.

Solution

Relay B Time = Relay A Time + Coordination Interval = 0.6 + 0.3 = 0.9 sec

Relay B must operate at 0.9 sec

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🔹 Problem 3: Pickup Current Setting

CT ratio = 400/5 Plug setting = 125% Find pickup current on primary side.

Step 1: Secondary Pickup Current

Pickup = 1.25 × 5 A = 6.25 A

Step 2: Convert to Primary Side

Primary Pickup = 6.25 × (400/5) = 6.25 × 80 = 500 A

Primary Pickup Current = 500 A

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🎯 GATE Important Points

• PSM = Fault Current / Pickup Current
• Time depends on TMS
• Coordination requires time grading
• Upstream relay must operate slower

Proper Relay Coordination = Selective & Reliable Protection