Calculation formula for relay protection
Relay protection calculations involve determining pickup current, plug setting multiplier (PSM), time multiplier setting (TMS), and operating time to ensure selective and reliable fault isolation.
Key Parameters and Formulas
1. Pickup Current (Ip): The pickup current is the minimum current at which the relay begins to operate. It is usually set as a percentage of the CT secondary rated current: Ip = Current Setting × CT Secondary Rating For example, if the CT secondary rating is 1 A and the relay is set to operate at 125% of rated current, then Ip = 1 × 1.25 = 1.25 A . 2. Plug Setting Multiplier (PSM): PSM represents how many times the actual fault current exceeds the relay pickup current: PSM = Fault Current / Pickup Current This is critical for inverse time relays, as it determines the operating time from the relay's characteristic curve . 3. Time Multiplier Setting (TMS): TMS scales the base operating time obtained from the relay's inverse time-current characteristic: Operating Time (t) = TMS × Base Time from IDMT Curve The TMS allows coordination between upstream and downstream relays, ensuring selectivity . 4. Operating Time (t): For an inverse definite minimum time (IDMT) relay, the operating time can be calculated using standard IEC 60255 formulas:
- Standard Inverse: t = TMS × 0.14 / (PSM^0.02 - 1)
- Very Inverse: t = TMS × 13.5 / (PSM - 1)
- Extremely Inverse: t = TMS × 80 / (PSM^2 - 1) These formulas vary depending on the relay type and curve selected . 5. Coordination Time Interval (CTI): CTI is the intentional time difference between the operation of downstream and upstream relays to ensure selectivity: CTI = t(upstream) - t(downstream) A typical CTI margin is 0.2–0.5 seconds for industrial systems .
Practical Steps for Relay Setting
- Determine the full load current and fault current at the relay location.
- Select the pickup current as a percentage of the CT secondary rating.
- Calculate PSM using the expected fault current.
- Choose the TMS to achieve the desired operating time and coordination with other relays.
- Verify operating time using the relay's IDMT curve and ensure proper CTI with upstream relays. By following these calculations, relays can trip only the faulted section, protect equipment, and maintain system stability without unnecessary outages .
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