Relay Protection Device Current Calculation Formula

The current at which a relay operates, known as the pickup current, is calculated using the relay's pickup setting, CT ratio, and fault current, often expressed through the Plug Setting Multiplier (PSM).

Key Concepts

• Pickup Current (I_pickup): The minimum current required to actuate the relay, overcoming the controlling force of the relay coil ( ).
• Current Setting: Adjustment of the relay's pickup current, usually expressed as a percentage of the CT's rated secondary current ( ).
• Plug Setting Multiplier (PSM): Ratio of the actual fault current to the relay's pickup current, used to determine relay operation ( ).
• Time Multiplier Setting (TMS): Adjusts the relay operating time based on the PSM and the relay's time-current characteristic curve ( ).

Step-by-Step Calculation

1. Determine the CT Secondary Current: Identify the rated secondary current of the current transformer (CT) connected to the relay. For example, a CT may have a 1 A or 5 A secondary rating ( ).
2. Set the Relay Pickup Current: Decide the percentage of the CT secondary current at which the relay should operate. For instance, if the relay should trip at 125% of rated current, the pickup current is: $$I_{\text{pickup}}=1.25\times I_{\text{CT\_secondary}}(]\; (\; [^1^]).)$$
3. Calculate the Plug Setting Multiplier (PSM): The PSM is the ratio of the fault current seen by the relay to the relay's pickup current: $$\text{PSM}=\frac{I_{\text{fault}}}{I_{\text{pickup}}}(]\; (\; [^2^]\; [^3^]).)$$
4. Determine Relay Operating Time (if needed): Using the PSM and the relay's time-current characteristic (IEC 60255 curves: SI, VI, EI, LTI), calculate the operating time: $$t_{\text{operate}}=TMS\times f(\text{PSM})$$ where $f(\text{PSM})$ is the time-current curve function ( ).
5. Adjust for Coordination: Ensure that downstream relays operate before upstream relays by adjusting TMS and PSM to maintain selective fault clearing ( ).

Example

Suppose a relay is connected to a CT with a 5 A secondary rating, and you want it to trip at 150% of rated current:

• Pickup current: $$I_{\text{pickup}}=1.5\times 5\text{A}=7.5\text{A}$$
• If a fault current of 15 A flows through the relay: $$\text{PSM}=\frac{15}{7.5}=2$$
• Using the relay's time-current curve and a TMS of 0.5, the operating time can be read from the curve or calculated using the IEC 60255 formula ( ).

Additional Notes

• For short-circuit calculations, the secondary fault current seen by the relay is: $$I_{\text{secondary}}=\frac{I_{\text{fault}}}{\text{CT ratio}}(]\; (\; [^4^]).\; )$$
• Modern relay calculators can automate these calculations, including pickup current, PSM, TMS, and operating time ( ).
• Proper relay setting ensures selective protection, preventing unnecessary tripping of upstream devices while isolating the faulted section ( ). By following these steps, you can accurately calculate the current at which a relay protection device will operate and coordinate it with other protective devices in the system.