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📘 Plug Setting Multiplier (PSM) – Advanced Numerical Problems

PSM = Fault Current (Secondary) / Pickup Current

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🔹 Problem 1: Basic PSM

CT ratio = 1000/1 Fault current = 5000 A Relay plug setting = 1 A Find PSM.

Solution

Secondary fault current = 5000 / 1000 = 5 A PSM = 5 / 1 = 5

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🔹 Problem 2: With Percentage Plug Setting

CT ratio = 800/1 Full load current = 400 A Plug setting = 125% Fault current = 3200 A Find PSM.

Step 1: Full Load Secondary

FL secondary = 400 / 800 = 0.5 A

Step 2: Pickup Current

Pickup = 1.25 × 0.5 = 0.625 A

Step 3: Fault Secondary

Fault secondary = 3200 / 800 = 4 A

Step 4: PSM

PSM = 4 / 0.625 = 6.4

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🔹 Problem 3: Operating Time Using PSM

Relay equation (Standard Inverse): T = 0.14 / (PSM^0.02 − 1) PSM = 8 Find operating time.

Solution

8^0.02 ≈ 1.041 T = 0.14 / (1.041 − 1) = 0.14 / 0.041 = 3.41 sec

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🔹 Problem 4: Compare Two Relays

Relay R1: Pickup = 1 A Relay R2: Pickup = 1.5 A Fault secondary current = 6 A Which operates faster?

Solution

PSM1 = 6 / 1 = 6 PSM2 = 6 / 1.5 = 4

Higher PSM → Lower operating time.

Relay R1 operates faster.

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🔹 Problem 5: Required Plug Setting

Fault secondary current = 5 A Desired PSM = 4 Find pickup current.

Solution

PSM = Fault / Pickup Pickup = Fault / PSM = 5 / 4 = 1.25 A

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🎯 Important Observations

• Higher PSM → Faster relay operation
• PSM < 1 → Relay does not operate
• PSM determines relay time using characteristic curve
• Used in coordination studies

PSM Controls Relay Speed & Coordination