Three phase power cables represent the basis of electrical distribution systems.

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Understanding the purpose of these cables particularly regarding sheath current and charging effects is essential for:

• Preventing excessive heating and insulation degradation,
• Ensuring the stability of power transmission systems,
• Optimizing the power factor (PF) for efficient energy utilization and
• Reducing reactive power charges from the utility providers.

Cable Capacitance Fundamentals

Every power cable acts as a distributed capacitor. 

The capacitance exists between the conductor and the grounded cable sheath with the insulation serving as the dielectric material. 

This capacitive effect has 2 important implications.

Charging Current

When voltage is applied across the cable a charging current flows to develop the electric field. 

This current is independent of the load current.

Sheath Current

The combination of the charging current and load current that creates the total sheath current that should be properly managed to avoid safety hazards and equipment damage.

Formulas & Calculations

Total Capacitance

Formula: C = Capacitance per km x Cable Length

The total capacitance is calculated by multiplying the specific capacitance that is (typically 0.2-0.3 µF/km for standard power cables) by the total length of the power cable. 

This value represents the cumulative capacitive reactance effect of the complete cable run.

Example: A 10 km cable with 0.25 µF/km capacitance / km = 2.5 µF total capacitance

Capacitive Reactance

Formula: X_c = 1 / (2π x f x C)

Where

f – System frequency (50 Hz / 60 Hz)

C – Total capacitance in Farads

Capacitive reactance is inversely proportional to frequency. 

Higher frequencies result in lower reactance which is allowing more charging current to flow.

Charging Current

Formula: I_c = V / X_c

Where

V – Voltage to earth (phase-to-ground voltage)

X_c – Capacitive reactance

The charging current increases with voltage & cable length. 

This is a pure reactive current that leads the voltage by 90⁰.

Load Current

Formula: I_L = P / (√3 × V × cos φ)

Where

P – Active power (W – Watts)

V – Line-to-Line voltage (V – Volts)

cos φ – power factor (0 to 1)

The load current is determined by the actual electrical load that is being supplied via the cable. 

This current is in phase with the voltage for resistive loads and lags the voltage for the inductive loads.

Sheath Current

Formula: I_s = √(I_c² + I_L²)

The sheath current is calculated as the vector sum of charging current and load current. 

As these currents are randomly perpendicular (different phases) they combine vectorially rather than arithmetically.

Power Factor Correction

The calculator determines the needed capacitor bank size to bring the power factor to a desired value (typically 0.95). 

The reactive power that should be supplied by the capacitor bank is calculated as

Q_CAP = Q_Current – Q_Desired

Where 

Q- Reactive power in (kVAR) kilovars

This ensures an efficient power utilization and reduces the penalties from utility companies.

Input Parameters 

Cable Parameters

Parameter	Description	Unit
Voltage to Earth	Phase-to-ground voltage in the power system	V (Volts)
Cable Length	Total length of the power cable run	km
Capacitance per km	Specific capacitance of the cable type (typically 0.2-0.35)	µF/km
Power Frequency	System frequency (usually 50 Hz/60 Hz)	Hz

Electrical Load Parameters

Parameter	Description	Unit
Voltage (Line-to-Line)	Rated voltage of the 3 phase system	V
Active Power	Real power being consumed by load	kW
Current Power Factor	Cosine of phase angle between voltage & current	cos φ

Advanced Settings

Desired Power Factor

Target power factor after the capacitor installation (typically 0.95).

Temperature Derating

Temperature derating accounts for the 10% reduction in the current carrying capacity due to ambient temperature.

Harmonics Factor

Multiplier of 1.2x applied to the charging current to account for the harmonic distortion in modern power systems.

Step by Step Calculation

Data Collection

Step-1: Gather the cable specifications from manufacturer data sheets.

Step-2: Identify the system voltage & frequency.

Step-3: Determine the current & desired power factors.

Step-4: Verify cable length & routing.

Calculator Input

Step-5: Enter voltage to earth value (typically phase voltage for the system).

Step-6: Enter the cable length in kilometers (km).

Step-7: Specify the required capacitance per km (µF/km) from cable specifications.

Step-8: Enter the system frequency (usually 50 / 60 Hz).

Step-9: Select the appropriate line-to-line voltage.

Step-10: Input active power in kilowatts (kw).

Step-11: Enter the current power factor (PF).

Results

Step-12: Review the calculated sheath current & compare to cable rating.

Step-13: Note the required capacitor bank size in (kVAR).

Step-14: Verify that corrected power factor that meets utility requirements.

Step-15: Document the results for design and procurement.

Output Results

Calculated Parameters

Output	Significance	Unit
Total Capacitance	Total capacitive effect of the complete cable.	µF
Charging Current	Pure capacitive current flowing due to cable capacitance.	A
Load Current	Three phase current that is carrying the active power.	A
Sheath Current	Total current flow via cable sheath (essential parameter).	A
Capacitive Reactance	Opposition to capacitive current at system frequency.	Ω
Capacitor Bank Size	Rating of capacitor bank needed for the power factor correction (PFC).	kVAR
Corrected Power Factor	Power factor (PF) after capacitor bank is installed.	cos φ

Applications of Sheath Current in Cables

Power Factor Correction

One of the major primary applications is determining the correct size of capacitor banks. 

Poor power factor results in:

• Higher energy bills (utility penalties for PF < 0.95).
• Increased cable heating.
• Reduced transmission capacity.
• Greater voltage drop along the line.

Cable Sizing

The sheath current value is essential for selecting the appropriate cable cross sections. 

The calculated sheath current ensures that the cable cross section has adequate capacity to manage not just the load current but also the additional thermal stress from the capacitive charging.

System Protection

Understanding the sheath current is essential for:

• Setting protective relay thresholds.
• Preventing nuisance trips during the normal operation.
• Ensuring the proper fault detection.

Reference

Standard Cable Capacitance Values

Cable Type	Capacitance (µF/km)
Single core, XLPE, Cu conductor	0.18 – 0.24
Single core, PVC, Cu conductor	0.22 – 0.28
3-core cable, XLPE	0.25 – 0.35
Medium voltage (11kV – 33kV)	0.15 – 0.20

Common System Voltages

System Type	Voltage (V)	Region
Low Voltage	380-400	Europe/Asia
Low Voltage	480	North America
Medium Voltage	3300-6600	Industrial
High Voltage	11000-33000	Transmission

Recommended Power Factor Values

• Industrial: 0.95 – 0.98
• Commercial: 0.90 – 0.95
• Utility Standard: ≥ 0.95