Calculation of Relay Protection Correct Operating Rate

The operating rate of a relay is determined using the formula: Relay Operating Time = (PSM × Rated Current) × TMS, where PSM is the Plug Setting Multiplier and TMS is the Time Multiplier Setting.

Key Components of Relay Operation

1. Plug Setting Multiplier (PSM): This is the ratio of the fault current to the relay's pickup current. It defines how sensitive the relay is to overcurrent conditions. The pickup current on the primary side can be calculated as: Relay Pickup Current (Primary) = PSM × Rated CT Primary Current .

2. Time Multiplier Setting (TMS): This adjusts the relay's operating time. A higher TMS increases the delay before the relay trips, while a lower TMS reduces the operating time .

3. Rated Current: The nominal current of the system or the current transformer (CT) secondary rating used for relay coordination.

Formula for Relay Operating Time

For overcurrent relays, the correct operating time can be calculated as: Operating Time = TMS × f(PSM) Where f(PSM) is the time obtained from the relay's time-current characteristic curve corresponding to the selected PSM .

For practical calculations, a simplified formula often used is: Relay Setting = (PSM × Rated Current) / TDS Here, TDS (Time Dial Setting) is equivalent to TMS in some relay types and controls the delay in tripping .

Example Calculation

Suppose a relay has:

• Rated Current = 1250 A
• PSM = 150% (1.5)
• TMS = 0.25

The relay operating time can be calculated as: Operating Time = 1.5 × 1250 × 0.25 = 468.75 units (depending on the time curve units used) This ensures the relay trips correctly for the fault current while maintaining coordination with upstream and downstream relays .

Additional Considerations

• Inverse Time Relays: For inverse time relays, the operating time decreases as fault current increases, and the formula incorporates the inverse time characteristic curve.
• Selectivity and Grading: Proper relay coordination requires grading times between relays to ensure the relay closest to the fault operates first, minimizing system disruption .
• CT Changes: When changing current transformers, the PSM must be recalculated to maintain the same pickup current, using: New PSM = (Old CT Primary × Old PSM) / New CT Primary .

By applying these formulas and settings, the correct operating rate of relay protection can be accurately determined, ensuring reliable fault detection and system stability.