Accurate tripping time calculation is critical for reliable electrical protection and system stability. It ensures timely fault clearance, minimizing equipment damage and outages.
This article explores tripping time calculations based on IEC and IEEE standards, providing formulas, tables, and practical examples. Learn how to optimize protection settings effectively.
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- Calculate tripping time for a 100 A fault current using IEC inverse time characteristics.
- Determine IEEE standard tripping time for a relay with plug setting multiplier of 2.5.
- Find tripping time for a 500 A fault current with IEC standard long-time inverse curve.
- Compute tripping time for an overcurrent relay with time dial setting 0.1 and fault current 300 A.
Common Tripping Time Values for Electrical Protection – IEC and IEEE Standards
| Relay Type | Characteristic Curve | Typical Time Dial Setting (TDS) | Plug Setting Multiplier (PSM) | Typical Tripping Time Range (seconds) | Standard Reference |
|---|---|---|---|---|---|
| Overcurrent Relay | Standard Inverse (SI) | 0.05 – 1.0 | 1.0 – 20.0 | 0.1 – 30 | IEC 60255-151 |
| Overcurrent Relay | Very Inverse (VI) | 0.05 – 1.0 | 1.0 – 20.0 | 0.05 – 20 | IEC 60255-151 |
| Overcurrent Relay | Extremely Inverse (EI) | 0.05 – 1.0 | 1.0 – 20.0 | 0.02 – 15 | IEC 60255-151 |
| Overcurrent Relay | Long Time Inverse (LTI) | 0.1 – 1.0 | 1.0 – 20.0 | 0.5 – 40 | IEEE C37.112 |
| Overcurrent Relay | Moderate Inverse (MI) | 0.1 – 1.0 | 1.0 – 20.0 | 0.3 – 25 | IEEE C37.112 |
| Instantaneous Relay | Instantaneous | N/A | Set at pickup current | 0 – 0.05 | IEC 60255-151, IEEE C37.90 |
Fundamental Formulas for Tripping Time Calculation in Electrical Protection
Tripping time calculation depends on the relay characteristic curve, time dial setting, and fault current magnitude. The most common formula for inverse time overcurrent relays is based on IEC and IEEE standards.
IEC Standard Inverse Time Overcurrent Relay Formula
The IEC 60255-151 standard defines the tripping time (t) as:
- t = Tripping time in seconds
- TDS = Time Dial Setting (dimensionless, typically 0.05 to 1.0)
- PSM = Plug Setting Multiplier = Fault Current / Pickup Current (dimensionless)
This formula applies to the Standard Inverse (SI) curve. For other curves, constants differ.
IEC Very Inverse and Extremely Inverse Curves
The IEC standard provides formulas for different inverse characteristics:
- Very Inverse (VI): t = TDS × (13.5 / (PSM – 1))
- Extremely Inverse (EI): t = TDS × (80 / (PSM^2 – 1))
Where variables are as defined above.
IEEE Standard Inverse Time Overcurrent Relay Formula
IEEE C37.112 defines the tripping time for different inverse curves as:
- Long Time Inverse (LTI): t = TDS × (0.0515 / (PSM – 1)^0.02)
- Moderate Inverse (MI): t = TDS × (0.114 / (PSM – 1)^0.02)
- Very Inverse (VI): t = TDS × (13.5 / (PSM – 1))
Note: The exponents and constants vary slightly from IEC values.
Instantaneous Relay Tripping Time
Instantaneous relays operate without intentional time delay:
Tripping occurs immediately when fault current exceeds the pickup setting.
Detailed Explanation of Variables
- Time Dial Setting (TDS): A multiplier that adjusts the relay operating time. Lower TDS means faster tripping.
- Plug Setting Multiplier (PSM): Ratio of actual fault current to relay pickup current. Higher PSM results in faster tripping.
- Pickup Current (Ip): Minimum current at which the relay starts timing. Set according to system protection coordination.
- Fault Current (If): The current flowing during a fault condition, typically measured or calculated from system parameters.
Real-World Application Examples
Example 1: Calculating Tripping Time Using IEC Standard Inverse Curve
A feeder is protected by an overcurrent relay with the following parameters:
- Pickup current, Ip = 100 A
- Fault current, If = 300 A
- Time Dial Setting, TDS = 0.2
- Characteristic curve: Standard Inverse (SI)
Calculate the tripping time.
Step 1: Calculate Plug Setting Multiplier (PSM)
Step 2: Apply IEC SI formula
Calculate PSM^0.02:
Calculate denominator:
Calculate tripping time:
Result: The relay will trip in approximately 1.27 seconds.
Example 2: IEEE Long Time Inverse Curve Tripping Time Calculation
An overcurrent relay is set with the following parameters:
- Pickup current, Ip = 150 A
- Fault current, If = 450 A
- Time Dial Setting, TDS = 0.3
- Characteristic curve: Long Time Inverse (LTI)
Calculate the tripping time according to IEEE C37.112.
Step 1: Calculate Plug Setting Multiplier (PSM)
Step 2: Apply IEEE LTI formula
Calculate denominator:
Calculate tripping time:
Result: The relay will trip in approximately 0.015 seconds, indicating a very fast response.
Additional Technical Considerations for Tripping Time Calculations
- Coordination with Upstream and Downstream Devices: Tripping times must be coordinated to ensure selectivity, preventing unnecessary outages.
- Impact of CT Accuracy: Current transformer accuracy affects fault current measurement, influencing PSM and tripping time.
- Relay Operating Time Tolerances: Manufacturing tolerances and relay aging can cause deviations in actual tripping times.
- Environmental Factors: Temperature and humidity can affect relay performance and timing.
- Digital vs. Electromechanical Relays: Digital relays may have programmable curves and more precise timing compared to electromechanical types.
Summary of IEC and IEEE Standard References
- IEC 60255-151: Electrical relays – Part 151: Measuring relays and protection equipment – Overcurrent and earth-fault protection
- IEEE C37.112-1996: Standard Inverse-Time Characteristic Equations for Overcurrent Relays
- IEEE C37.90: Standard for Relays and Relay Systems Associated with Electric Power Apparatus
Understanding and applying these standards ensures protection systems operate reliably and safely under fault conditions.