Dielectric Loss Formula

The dielectric losses in a cable are calculated using the following formula:

• w = C × U₀² × ω × tanδ

Where:

• w: Dielectric losses per unit length (W/km)
  
• C: Capacitance of the cable (µF/km)
  
• U₀: Applied voltage between the conductor and the metal screen (kV)
  
• ω: Angular frequency (rad/s), defined as:
     
  • ω = 2 × π × f
  where f is the frequency (Hz)
  
• tanδ: Loss angle of the dielectric material (dimensionless), typically:
     
  • tanδ = 0.001 (for XLPE insulation, from IEC 60287)

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Key Parameters and Notes

• Dielectric Losses (w): Represent the energy lost as heat in the dielectric material of the cable.
  
• Capacitance (C): Determines the amount of charge stored in the cable insulation.
  
• Loss Angle (tanδ): Indicates the efficiency of the insulation material. A lower value means less dielectric loss.
  
• Frequency (f): Dielectric losses increase with operating frequency, which is 50 Hz or 60 Hz in most systems.
  

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Standards Reference

The calculation for dielectric losses is typically covered in the following standards:

• IEC 60287 - Electric Cables - Calculation of the Current Rating
     - This standard defines how to calculate power losses in cables, including dielectric losses.
     - Provides guidelines for determining insulation performance and power dissipation in high-voltage cables.
  
• IEC 60840 - Power Cables with Extruded Insulation for Rated Voltages Above 30 kV
     - Includes specifications for XLPE insulation and loss angles (tanδ values).
  
• IEEE 442 - Guide for Thermal Considerations in Cable Systems
     - Explains heat generation due to dielectric losses and their impact on cable performance.
  

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Example Calculation

**Given Data:**

• C = 0.15 µF/km
  
• U₀ = 20 kV
  
• f = 50 Hz
  
• tanδ = 0.001
  

**Steps:**

• Calculate the angular frequency:

ω = 2 × π × f = 2 × 3.1416 × 50 = 314.16 rad/s

• Substitute into the formula:

w = C × U₀² × ω × tanδ
   w = 0.15 × 20² × 314.16 × 0.001
   w = 0.15 × 400 × 314.16 × 0.001
   w = 18.85 W/km
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**Result:** The dielectric loss is approximately **18.85 W/km**.

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Conclusion

Dielectric loss calculations are crucial for designing high-voltage cables to ensure energy efficiency and thermal stability. These calculations are detailed in standards such as **IEC 60287** and **IEC 60840**, which guide the proper design and operation of power cables.