Lightning arresters are critical devices designed to protect electrical systems from transient overvoltages caused by lightning strikes. Calculating the correct arrester specifications ensures optimal surge protection and system reliability.
This article explores lightning arrester calculations based on IEC and IEEE standards, providing formulas, tables, and real-world examples. Engineers will gain comprehensive insights into selecting and sizing arresters effectively.
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- Calculate arrester energy absorption for a 10 kA surge current at 8/20 µs waveform.
- Determine maximum continuous operating voltage (MCOV) for a 33 kV distribution line.
- Estimate residual voltage for a 20 kA lightning impulse current on a 11 kV system.
- Compute protective level voltage for a 145 kV transmission line arrester.
Common Values for Lightning Arrester Parameters According to IEC and IEEE Standards
| Parameter | Typical Values | Units | IEC Reference | IEEE Reference |
|---|---|---|---|---|
| Maximum Continuous Operating Voltage (MCOV) | 1.05 to 1.15 × system voltage | kV | IEC 60099-4 | IEEE C62.11 |
| Nominal Discharge Current (In) | 5, 10, 20, 30, 40 | kA (8/20 µs) | IEC 60099-4 | IEEE C62.11 |
| Maximum Lightning Impulse Current (Iimp) | 10, 20, 30, 40, 50 | kA (10/350 µs) | IEC 60099-4 | IEEE C62.11 |
| Protective Level Voltage (Up) | 1.5 to 3.0 × system voltage | kV | IEC 60099-4 | IEEE C62.11 |
| Energy Discharge Capability (W/R) | 10 to 100 kJ/kΩ | kJ/kΩ | IEC 60099-4 | IEEE C62.11 |
| Residual Voltage at In | 1.8 to 2.5 × MCOV | kV | IEC 60099-4 | IEEE C62.11 |
| System Voltage Level | MCOV (kV) | Nominal Discharge Current (kA) | Maximum Impulse Current (kA) | Typical Protective Level (kV) |
|---|---|---|---|---|
| 11 kV | 12.7 | 10 | 20 | 20 – 25 |
| 33 kV | 38 | 20 | 40 | 60 – 70 |
| 66 kV | 76 | 30 | 50 | 120 – 140 |
| 145 kV | 145 | 40 | 60 | 280 – 320 |
Fundamental Formulas for Lightning Arrester Calculations
1. Maximum Continuous Operating Voltage (MCOV)
The MCOV is the highest RMS voltage that the arrester can continuously withstand without degradation.
- Vsystem: Rated system voltage (RMS line-to-ground voltage), in kV.
- IEC and IEEE recommend MCOV to be slightly above system voltage to avoid nuisance tripping.
2. Residual Voltage (Ures)
Residual voltage is the voltage across the arrester terminals during surge current flow.
- Ures: Residual voltage (kV)
- k: Voltage-current characteristic constant (kV/kA), depends on arrester design
- Ip: Peak surge current (kA)
Typical values of k range from 1.8 to 2.5 kV/kA depending on arrester type and system voltage.
3. Energy Discharge Capability (W/R)
Energy absorbed by the arrester during surge events is critical for sizing and longevity.
- W/R: Energy per unit resistance (kJ/kΩ)
- In: Nominal discharge current (kA)
- t: Duration of surge current (seconds), typically 8/20 µs waveform
IEC 60099-4 defines energy capability based on standard surge waveforms.
4. Protective Level Voltage (Up)
The protective level voltage is the maximum voltage that appears across the arrester terminals during a surge.
- Up: Protective level voltage (kV)
- Ures: Residual voltage (kV)
- Usystem: System voltage (kV)
- Safety factor accounts for system tolerances and transient conditions, typically 1.1 to 1.3
5. Coordination of Arrester with Insulation Level
To ensure proper protection, the arrester’s protective level voltage must be below the insulation withstand voltage.
- Uinsulation: Insulation withstand voltage (kV), defined by IEC 60071 or IEEE standards
Detailed Real-World Examples of Lightning Arrester Calculations
Example 1: Selecting a Lightning Arrester for a 33 kV Distribution System
A 33 kV distribution line requires a lightning arrester to protect equipment from surges. The system voltage is 33 kV (line-to-line), and the line-to-ground voltage is approximately 19 kV (33/√3). The arrester must handle a nominal discharge current of 20 kA (8/20 µs) and a lightning impulse current of 40 kA (10/350 µs).
- Step 1: Calculate MCOV
MCOV = 1.1 × Vsystem (line-to-ground) = 1.1 × 19 kV = 20.9 kV
- Step 2: Determine residual voltage at nominal discharge current
Assuming k = 2.0 kV/kA (typical for 33 kV arresters),
Ures = k × In = 2.0 × 20 = 40 kV
- Step 3: Calculate protective level voltage
Assuming safety factor = 1.2,
Up = Ures + (Vsystem × safety factor) = 40 + (19 × 1.2) = 40 + 22.8 = 62.8 kV
- Step 4: Verify coordination with insulation level
Typical insulation withstand voltage for 33 kV system is about 75 kV (lightning impulse withstand). Since 62.8 kV < 75 kV, the arrester is suitable.
Result: Select a 33 kV arrester with MCOV ≈ 21 kV, nominal discharge current 20 kA, and protective level voltage below 75 kV.
Example 2: Energy Absorption Calculation for a 145 kV Transmission Line Arrester
A 145 kV transmission line arrester must absorb energy from a 40 kA surge current with an 8/20 µs waveform. Calculate the energy discharge capability (W/R) to ensure the arrester can withstand the surge.
- Step 1: Identify nominal discharge current (In) = 40 kA
- Step 2: Use standard duration t = 20 µs = 20 × 10-6 s
Using formula:
Calculate:
W/R = 1.5 × (40)2 × 20 × 10-6 = 1.5 × 1600 × 0.00002 = 0.048 kJ/Ω
Since this value seems low, note that IEC defines energy in kJ/kΩ for standard waveforms, and the actual energy rating is often provided by manufacturers based on test data. The calculation here is a simplified estimate.
- Step 3: Compare with manufacturer’s energy rating
If the arrester’s energy rating is ≥ 50 kJ/kΩ, it is sufficient for the application.
Result: Confirm arrester energy rating from datasheet; select arrester with energy rating ≥ 50 kJ/kΩ for 145 kV system.
Additional Technical Considerations for Lightning Arrester Calculations
- Surge Current Waveforms: IEC 60099-4 defines standard waveforms such as 8/20 µs for nominal discharge current and 10/350 µs for lightning impulse current. These waveforms affect arrester sizing and energy absorption.
- Temperature Effects: Arrester performance varies with ambient temperature; derating may be necessary in extreme conditions.
- Multiple Arresters in Series: For high voltage systems, multiple arrester units may be connected in series to achieve required voltage ratings.
- Residual Voltage vs. System Insulation: Protective level voltage must always be below the insulation withstand voltage to prevent equipment damage.
- Standards Compliance: Always verify arrester selection against IEC 60099-4 and IEEE C62.11 for compliance and safety.
Authoritative External Resources
- IEC 60099-4: Surge Arresters – Part 4: Metal-oxide Surge Arresters Without Gaps for AC Systems
- IEEE C62.11-2012 – IEEE Standard for Metal-Oxide Surge Arresters for AC Power Circuits
- NEMA Surge Arrester Standards and Guidelines
Understanding and applying these calculations ensures the correct selection and application of lightning arresters, safeguarding electrical infrastructure from damaging surges.