A relay is connected to a 400/5 current transformer. For a fault current of 2.4 kA and relay setting of 150%, the PSM is:

Explanation:

Numerical Solution: Protective System Multiplier (PSM)

The given problem involves calculating the Protective System Multiplier (PSM) for a relay connected to a current transformer (CT) with a given fault current and relay setting percentage. Below is the detailed solution:

Step 1: Understanding Protective System Multiplier (PSM):

The Protective System Multiplier (PSM) is defined as the ratio of the fault current (secondary current of the CT during a fault) to the relay pickup current. It is mathematically expressed as:

PSM = (Fault Current in CT Secondary) ÷ (Relay Pickup Current)

Where:

• Fault Current in CT Secondary: This is the current flowing through the secondary winding of the current transformer during a fault condition.
• Relay Pickup Current: This is the threshold current at which the relay starts to operate. It is calculated using the relay setting percentage.

Step 2: Given Data:

• Current Transformer Ratio: 400/5
• Fault Current (Primary Side): 2.4 kA = 2400 A
• Relay Setting: 150%

Step 3: Calculate Fault Current in CT Secondary:

The fault current in the secondary winding of the CT can be calculated using the CT ratio:

Fault Current in CT Secondary = (Fault Current in Primary Side × CT Secondary Rating) ÷ CT Primary Rating

Substituting the values:

Fault Current in CT Secondary = (2400 × 5) ÷ 400

Fault Current in CT Secondary = 30 A

Step 4: Calculate Relay Pickup Current:

The relay pickup current is determined using the relay setting percentage. Relay setting is given as 150%, which means:

Relay Pickup Current = (Relay Setting × CT Secondary Rating) ÷ 100

Substituting the values:

Relay Pickup Current = (150 × 5) ÷ 100

Relay Pickup Current = 7.5 A

Step 5: Calculate PSM:

Now, the PSM can be calculated using the formula:

PSM = (Fault Current in CT Secondary) ÷ (Relay Pickup Current)

Substituting the values:

PSM = 30 ÷ 7.5

PSM = 4

Step 6: Final Answer:

The Protective System Multiplier (PSM) is 4. Therefore, the correct answer is Option 3