Efficient thermal dissipation in electrical cables is critical for system reliability and safety. Calculating heat loss ensures cables operate within safe temperature limits.
This article explores the IEC standards for thermal dissipation calculations, providing formulas, tables, and practical examples. Learn how to optimize cable performance and prevent overheating.
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- Calculate thermal dissipation for a 3-core 50 mm² copper cable in conduit.
- Determine heat loss for a 4-core XLPE insulated cable buried underground.
- Estimate cable temperature rise for a 95 mm² aluminum cable in air.
- Find thermal dissipation for a 3-core cable with PVC insulation in duct.
Comprehensive Tables for Thermal Dissipation Parameters According to IEC
| Parameter | Typical Values | Units | Notes |
|---|---|---|---|
| Thermal Resistivity of Soil (ρ) | 0.8 – 1.2 | K·m/W | Varies with soil moisture and composition |
| Thermal Conductivity of Cable Insulation (k) | 0.2 – 0.4 | W/m·K | Depends on insulation type (PVC, XLPE, EPR) |
| Ambient Temperature (Ta) | 20 – 40 | °C | Typical environmental temperature range |
| Maximum Cable Operating Temperature (Tc) | 70 – 90 | °C | Depends on insulation rating |
| Thermal Resistance of Cable Sheath (Rsh) | 0.05 – 0.15 | K/W | Influences heat transfer from conductor to environment |
| Conductor Cross-Sectional Area (A) | 1.5 – 300 | mm² | Standard cable sizes per IEC 60228 |
| Current Load (I) | 1 – 1000 | A | Depends on application and cable rating |
| Resistivity of Conductor (ρc) | 1.68 × 10⁻⁸ (Cu), 2.82 × 10⁻⁸ (Al) | Ω·m | At 20°C; varies with temperature |
| Cable Type | Insulation Material | Thermal Conductivity (k) | Max Operating Temp. | Typical Application |
|---|---|---|---|---|
| PVC Insulated | PVC | 0.19 – 0.22 W/m·K | 70°C | General wiring, low voltage |
| XLPE Insulated | Cross-linked Polyethylene | 0.35 – 0.40 W/m·K | 90°C | Power distribution, medium voltage |
| EPR Insulated | Ethylene Propylene Rubber | 0.30 – 0.35 W/m·K | 90°C | Industrial power cables |
| Paper Insulated | Oil-impregnated Paper | 0.15 – 0.20 W/m·K | 70°C | High voltage, legacy systems |
Fundamental Formulas for Thermal Dissipation in Electrical Cables (IEC)
Thermal dissipation in electrical cables is primarily governed by the heat generated due to electrical resistance and the heat transfer mechanisms to the environment. The IEC standards provide a framework to calculate these parameters accurately.
1. Heat Generated by the Conductor (Joule Heating)
Where:
I = Current through the conductor (A)
R = Resistance of the conductor (Ω)
The resistance R depends on the conductor material, length, and temperature:
Where:
ρc = Resistivity of conductor material at reference temperature (Ω·m)
L = Length of the cable (m)
A = Cross-sectional area of the conductor (m²)
Note: Resistivity varies with temperature, typically adjusted by:
Where:
ρ20 = Resistivity at 20°C (Ω·m)
α = Temperature coefficient of resistivity (Copper ≈ 0.00393 /°C)
T = Operating temperature (°C)
2. Thermal Resistance Network
Heat dissipation from the conductor to the ambient environment can be modeled as a series of thermal resistances:
Where:
R_cond = Thermal resistance of the conductor
R_ins = Thermal resistance of insulation
R_sheath = Thermal resistance of cable sheath
R_env = Thermal resistance of environment (soil, air, duct)
Each resistance is calculated by:
Where:
r1 = Inner radius (m)
r2 = Outer radius (m)
k = Thermal conductivity of the material (W/m·K)
L = Length of cable (m)
3. Temperature Rise Calculation
The temperature rise of the cable conductor above ambient is given by:
Where:
ΔT = Temperature rise (K or °C)
P = Heat generated (W)
R_total = Total thermal resistance (K/W)
The operating temperature of the cable conductor is then:
Where:
Tc = Conductor temperature (°C)
Ta = Ambient temperature (°C)
4. IEC Standard Correction Factors
IEC 60287 and IEC 60502 provide correction factors for installation conditions:
- Grouping Factor (Fg): Accounts for multiple cables installed together, increasing heat dissipation challenges.
- Soil Thermal Resistivity Correction (Fs): Adjusts for soil moisture and composition.
- Ambient Temperature Correction (Fa): Adjusts for ambient temperature deviations from standard 30°C.
Corrected current rating I_corr is calculated by:
Where I_rated is the nominal current rating from cable datasheets.
Real-World Application Examples of Thermal Dissipation Calculations
Example 1: Thermal Dissipation for a 3-Core 50 mm² Copper Cable in Conduit
A 3-core copper cable with 50 mm² cross-sectional area is installed in a conduit. The cable length is 100 meters, ambient temperature is 30°C, and the cable carries 150 A current. The insulation is XLPE with thermal conductivity 0.35 W/m·K. Calculate the temperature rise and verify if the cable operates within the 90°C limit.
Step 1: Calculate Resistance of the Conductor
Resistivity of copper at 20°C, ρ20 = 1.68 × 10⁻⁸ Ω·m
Length, L = 100 m
Cross-sectional area, A = 50 mm² = 50 × 10⁻⁶ m²
Step 2: Calculate Heat Generated (P)
Step 3: Calculate Thermal Resistances
Assuming cable radius r1 = 0.01 m (conductor radius), r2 = 0.015 m (insulation outer radius), length L = 100 m, and thermal conductivity k = 0.35 W/m·K.
Assuming sheath and environment thermal resistances combined R_sheath + R_env = 0.05 K/W (typical value for conduit installation).
Step 4: Calculate Temperature Rise (ΔT)
Step 5: Calculate Operating Temperature (Tc)
The operating temperature is 68.3°C, which is below the XLPE insulation limit of 90°C, indicating safe operation.
Example 2: Thermal Dissipation for a 4-Core 95 mm² Aluminum Cable Buried Underground
A 4-core aluminum cable with 95 mm² cross-sectional area is buried underground at 0.7 m depth. Soil thermal resistivity is 1.0 K·m/W, ambient temperature is 25°C, and the cable carries 200 A. The insulation is PVC with thermal conductivity 0.22 W/m·K. Calculate the temperature rise and verify compliance with the 70°C insulation limit.
Step 1: Calculate Resistance of the Conductor
Resistivity of aluminum at 20°C, ρ20 = 2.82 × 10⁻⁸ Ω·m
Length, L = 100 m (assumed)
Cross-sectional area, A = 95 mm² = 95 × 10⁻⁶ m²
Step 2: Calculate Heat Generated (P)
Step 3: Calculate Thermal Resistance of Soil
Using the IEC formula for soil thermal resistance:
Where:
ρ = Soil thermal resistivity = 1.0 K·m/W
D = Burial depth = 0.7 m
d = Cable diameter ≈ 0.02 m (assumed)
L = 100 m
Calculate ln term:
Calculate R_soil:
Step 4: Calculate Thermal Resistance of Insulation
Assuming cable radius r1 = 0.01 m, r2 = 0.015 m, k = 0.22 W/m·K:
Step 5: Total Thermal Resistance
Assuming sheath resistance R_sheath = 0.02 K/W:
Step 6: Calculate Temperature Rise (ΔT)
Step 7: Calculate Operating Temperature (Tc)
The operating temperature is 58.05°C, safely below the PVC insulation limit of 70°C.
Additional Technical Considerations for Thermal Dissipation Calculations
- Impact of Cable Grouping: Multiple cables installed together reduce heat dissipation efficiency, requiring correction factors.
- Effect of Installation Environment: Air, soil, ducts, or water immersion significantly affect thermal resistance values.
- Temperature Coefficient Variations: Resistivity and thermal conductivity change with temperature, influencing calculations.
- IEC Standards Compliance: IEC 60287 and IEC 60502 provide detailed methodologies and correction factors for accurate thermal calculations.
- Dynamic Load Conditions: Transient thermal effects during load changes may require time-dependent analysis.
For further reading and official guidelines, consult the IEC 60287 standard documentation available at IEC Webstore.