Thermal Capacity of Electrical Cables Calculator – IEC

Understanding the thermal capacity of electrical cables is crucial for ensuring safe and efficient power transmission. This calculation determines the maximum current a cable can carry without overheating.

This article explores the IEC standards for thermal capacity, providing formulas, tables, and practical examples for accurate cable sizing. Engineers and technicians will find comprehensive guidance here.

Artificial Intelligence (AI) Calculator for “Thermal Capacity of Electrical Cables Calculator – IEC”

• Calculate thermal capacity for a 4-core, 50 mm² copper cable in conduit.
• Determine maximum current for 3-core, 35 mm² aluminum cable buried underground.
• Find thermal capacity of a 1-core, 120 mm² copper cable in air.
• Evaluate cable rating for 5-core, 25 mm² copper cable in thermal insulation.

Comprehensive Tables for Thermal Capacity of Electrical Cables According to IEC

The following tables summarize typical thermal capacity values for common cable types, cross-sectional areas, installation methods, and conductor materials based on IEC 60287 and IEC 60364 standards.

These values are typical and should be adjusted based on ambient temperature, grouping factors, and cable construction.

Fundamental Formulas for Thermal Capacity Calculation According to IEC

IEC 60287 provides the methodology to calculate the continuous current rating (thermal capacity) of electrical cables by analyzing heat generation and dissipation.

The core formula for the thermal capacity (I) of a cable is derived from the steady-state heat balance:

• I: Thermal capacity or continuous current rating (A)
• Δθ: Allowable temperature rise of the conductor above ambient (°C)
• R_ca: Thermal resistance of the cable insulation and sheath (°C/W)
• R_cc: Thermal resistance of the conductor (°C/W)

The total thermal resistance is the sum of the conductor and cable insulation resistances, representing the cable’s ability to dissipate heat.

More detailed expressions for these resistances are:

• ρ₂₀: Resistivity of conductor at 20°C (Ω·m)
• α: Temperature coefficient of resistivity (1/°C)
• θ_c: Conductor temperature (°C)
• d: Diameter of conductor (m)
• l: Length of conductor (m)
• k_c: Thermal conductivity of conductor (W/m·°C)

However, for practical cable sizing, IEC 60287 simplifies the calculation by using tabulated thermal resistances and correction factors.

IEC 60287-1-1 Thermal Resistance Calculation

The thermal resistance of the cable insulation and sheath (R_ca) depends on the cable construction and installation method:

• r₁: Radius of conductor (m)
• r₂: Outer radius of cable insulation (m)
• λ: Thermal conductivity of insulation material (W/m·°C)
• l: Length of cable (m)

For installation in air, soil, or conduit, additional thermal resistances are added to account for heat transfer to the environment.

Correction Factors

IEC standards recommend applying correction factors to account for:

• Ambient temperature variations
• Grouping of cables (mutual heating)
• Soil thermal resistivity for buried cables
• Installation conditions such as thermal insulation or ventilation

These factors modify the allowable current rating as:

Where each k is a dimensionless correction factor less than or equal to 1.

Real-World Application Examples of Thermal Capacity Calculation

Example 1: Calculating Thermal Capacity for a 4-Core 50 mm² Copper Cable in Conduit

A 4-core copper cable with a cross-sectional area of 50 mm² is installed inside a conduit in an ambient temperature of 30°C. The allowable conductor temperature is 90°C. Calculate the thermal capacity (maximum continuous current) of the cable according to IEC 60287.

• Conductor resistivity at 20°C, ρ₂₀ = 1.68 × 10^-8 Ω·m
• Temperature coefficient, α = 0.00393 /°C
• Thermal conductivity of copper, k_c = 385 W/m·°C
• Thermal conductivity of insulation, λ = 0.3 W/m·°C
• Radius of conductor, r₁ = 4.0 mm = 0.004 m
• Outer radius of insulation, r₂ = 7.0 mm = 0.007 m

Step 1: Calculate allowable temperature rise (Δθ)

Δθ = θ_c – θ_ambient = 90°C – 30°C = 60°C

Step 2: Calculate thermal resistance of insulation (R_ca)

Step 3: Calculate thermal resistance of conductor (R_cc)

Assuming unit length (1 m) for calculation:

Diameter d = 2 × r₁ = 0.008 m

Calculate numerator:

ρ₂₀ × (1 + α × 70) = 1.68 × 10^-8 × (1 + 0.00393 × 70) = 1.68 × 10^-8 × 1.2751 ≈ 2.143 × 10^-8

Calculate denominator:

π × d × k_c = 3.1416 × 0.008 × 385 ≈ 9.67

Therefore:

This value is negligible compared to R_ca, so total thermal resistance R ≈ 0.297 °C/W.

Step 4: Calculate thermal capacity (I)

This value seems low because the simplified calculation assumes 1 m length and does not consider cable construction factors. Using IEC tabulated data, the thermal capacity for this cable is approximately 192 A (see table above), which accounts for real installation conditions and correction factors.

Example 2: Determining Thermal Capacity for a 3-Core 35 mm² Aluminum Cable Buried Underground

A 3-core aluminum cable with 35 mm² cross-section is buried underground in soil with thermal resistivity of 1.2 K·m/W. Ambient soil temperature is 25°C, and maximum conductor temperature is 90°C. Calculate the thermal capacity according to IEC 60287.

• Thermal resistivity of soil, ρ_soil = 1.2 K·m/W
• Thermal conductivity of soil, λ_soil = 1 / ρ_soil = 0.833 W/m·K
• Thermal resistance of soil layer, R_soil = ln(r_soil/r_cable) / (2 × π × λ_soil × l)
• Radius of cable, r_cable = 10 mm = 0.01 m
• Radius of soil cylinder, r_soil = 0.3 m

Step 1: Calculate allowable temperature rise (Δθ)

Δθ = 90°C – 25°C = 65°C

Step 2: Calculate thermal resistance of soil (R_soil)

Step 3: Use tabulated thermal resistance of cable insulation and conductor (R_ca)

From IEC tables, typical R_ca for 35 mm² aluminum cable insulation is approximately 0.3 °C/W.

Step 4: Calculate total thermal resistance (R_total)

R_total = R_ca + R_soil = 0.3 + 0.649 = 0.949 °C/W

Step 5: Calculate thermal capacity (I)

This simplified calculation again underestimates the current rating due to assumptions and unit length. Using IEC 60287 and correction factors, the actual thermal capacity is closer to 105 A (see table above), which accounts for real installation conditions and soil thermal properties.

Additional Technical Considerations for Thermal Capacity Calculations

• Grouping Effects: Multiple cables installed together increase mutual heating, reducing thermal capacity. IEC 60364-5-52 provides grouping correction factors.
• Ambient Temperature: Higher ambient temperatures reduce cable current rating. Correction factors adjust for this effect.
• Soil Thermal Resistivity: Soil composition and moisture content significantly affect heat dissipation for buried cables.
• Installation Method: Cables in air, conduit, or buried have different heat dissipation characteristics, influencing thermal resistance.
• Conductor Material: Copper has lower resistivity and higher thermal conductivity than aluminum, affecting thermal capacity.
• Insulation Type: Different insulation materials have varying thermal conductivities and maximum operating temperatures.

For precise cable sizing, engineers should always refer to the latest IEC standards, manufacturer datasheets, and consider site-specific conditions.

Authoritative References and Further Reading

• IEC 60287 – Electric cables – Calculation of the current rating
• IEC 60364 – Electrical Installations of Buildings
• NEMA – National Electrical Manufacturers Association
• CIGRE – International Council on Large Electric Systems

By integrating these standards and methodologies, professionals can ensure safe, efficient, and compliant electrical cable installations with optimized thermal capacity.