Electrical cable losses critically affect power system efficiency, thermal performance, and overall reliability, requiring precise calculations. IEEE and IEC standards guide engineers in calculating conductor, dielectric, sheath, screen, and armour losses accurately.

Electrical Cable Losses Calculator — IEEE / IEC Friendly

Estimate conductor resistance, I²R losses, voltage drop and power loss.

Conductor material Copper (Cu)Aluminium (Al) Units / selection mm² (area)AWG Conductor area (mm²) Select AWG 14 AWG (2.08 mm²)12 AWG (3.31 mm²)10 AWG (5.26 mm²)8 AWG (8.37 mm²)6 AWG (13.3 mm²)4 AWG (21.2 mm²)2 AWG (33.6 mm²)1/0 AWG (53.5 mm²)2/0 AWG (67.4 mm²)3/0 AWG (85.0 mm²)4/0 AWG (107.2 mm²) Conductor length one-way (m) Electrical system Single-phase (L–N)Three-phase (L–L)DC circuit Nominal voltage (V) Load current (A) — OR enter power below Load power (kW) — optional Power factor (0–1) Operating temperature (°C)

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Common Values for Electrical Cable Losses

The following table presents typical values for various parameters used in cable loss calculations, based on IEEE and IEC standards:

Parameter	Typical Value Range	Unit	Notes
Conductor Resistance (R₀)	0.01 – 0.10	Ω/km	Depends on conductor material and cross-sectional area
Dielectric Loss Factor (tanδ)	0.0002 – 0.002	–	Affected by insulation material and operating voltage
Sheath Resistance (Rₛ)	0.02 – 0.10	Ω/km	Influenced by sheath material and construction
Armour Resistance (Rₐ)	0.01 – 0.05	Ω/km	Varies with armour type and construction
Mutual Inductance (Xₘ)	0.1 – 1.0	μH/m	Affected by cable configuration and spacing
Skin Effect Factor (kₛ)	1.0 – 1.5	–	Increases with frequency and conductor size
Operating Frequency (f)	50 – 60	Hz	Standard power system frequency
Load Current (I)	10 – 1000	A	Varies based on application and cable rating
Cable Length (L)	10 – 1000	m	Affects voltage drop and loss calculations

Formulas for Cable Loss Calculations

1. Conductor Losses (Joule Losses)

The primary source of losses in cables is the resistance of the conductors. The power loss due to the resistance is given by:

P₁ = I² × R₀

Where:

• P₁ = Power loss in the conductor (W)
• I = Load current (A)
• R₀ = Conductor resistance per unit length (Ω/km)

2. Dielectric Losses

Dielectric losses occur due to the insulation material between the conductor and the sheath. These losses are frequency-dependent and are calculated as:

P₂ = I² × tanδ × C × V² × f

Where:

• P₂ = Dielectric power loss (W)
• tanδ = Dielectric loss factor (dimensionless)
• C = Capacitance per unit length (F/km)
• V = Voltage (V)
• f = Frequency (Hz)

3. Sheath Losses

Sheath losses arise due to circulating currents in the metallic sheath, especially in multi-core cables. These losses can be calculated using:

P₃ = I² × Rₛ × (1 + Yₛ)²

Where:

• P₃ = Sheath power loss (W)
• Rₛ = Sheath resistance per unit length (Ω/km)
• Yₛ = Sheath circulating current factor (dimensionless)

4. Armour Losses

For cables with metallic armour, losses occur due to eddy currents induced in the armour. These losses are calculated as:

P₄ = I² × Rₐ × (1 + Yₐ)²

Where:

• P₄ = Armour power loss (W)
• Rₐ = Armour resistance per unit length (Ω/km)
• Yₐ = Armour circulating current factor (dimensionless)

5. Total Power Loss

The total power loss in a cable is the sum of all individual losses:

P_total = P₁ + P₂ + P₃ + P₄

Detailed Explanation of Variables

• Conductor Resistance (R₀): This is the DC resistance of the conductor, which depends on the material (e.g., copper or aluminum) and the cross-sectional area.
• Dielectric Loss Factor (tanδ): Represents the energy dissipation in the insulating material. Higher values indicate greater losses.
• Sheath Resistance (Rₛ): The resistance of the metallic sheath, which can be influenced by its material and construction.
• Armour Resistance (Rₐ): The resistance of the armour layer, which also depends on the material and design.
• Mutual Inductance (Xₘ): Indicates the magnetic coupling between conductors, affecting circulating currents.
• Skin Effect Factor (kₛ): Describes the tendency of alternating current to flow near the surface of the conductor, increasing effective resistance at higher frequencies.
• Operating Frequency (f): The frequency of the AC supply, influencing inductive and capacitive reactances.
• Load Current (I): The current drawn by the load, directly affecting the losses.
• Cable Length (L): The distance the current travels through the cable, impacting voltage drop and losses.

Real-World Application Examples

Example 1: Industrial Power Distribution

In an industrial setting, a 3-phase 11kV power cable is used to supply a motor with a rated current of 200 A. The cable has the following characteristics:

• Conductor resistance (R₀) = 0.05 Ω/km
• Sheath resistance (Rₛ) = 0.03 Ω/km
• Armour resistance (Rₐ) = 0.02 Ω/km
• Dielectric loss factor (tanδ) = 0.0005
• Capacitance (C) = 0.2 μF/km
• Operating frequency (f) = 50 Hz
• Cable length (L) = 1000 m

Calculations:

1. Conductor Losses: P₁ = (200 A)² × 0.05 Ω/km = 2000 W
2. Dielectric Losses: P₂ = (200 A)² × 0.0005 × 0.2 μF/km × (11kV)² × 50 Hz = 2200 W
3. Sheath Losses: P₃ = (200 A)² × 0.03 Ω/km × (1 + 0.5)² = 2400 W
4. Armour Losses: P₄ = (200 A)² × 0.02 Ω/km × (1 + 0.3)² = 2080 W

Total Power Loss:

P_total = 2000 W + 2200 W + 2400 W + 2080 W = 8680 W

This calculation helps in determining the heat generation and selecting appropriate cable sizes and insulation materials.

Example 2: Residential Cable Sizing

In a residential building, a 3-phase 415V cable is used to supply a lighting circuit with a total load of 50 A. The cable has the following characteristics:

• Conductor resistance (R₀) = 0.1 Ω/km
• Sheath resistance (Rₛ) = 0.05 Ω/km
• Armour resistance (Rₐ) = 0.03 Ω/km
• Dielectric loss factor (tanδ) = 0.0003
• Capacitance (C) = 0.1 μF/km
• Operating frequency (f) = 50 Hz
• Cable length (L) = 100 m