Power Losses Calculation for High Voltage Underground Cables

How Calculate the Losses in Power Cables?

You will find mainly two kinds of power losses in high voltage or medium voltages power cables. The occurred losses in cable would be-

1. Voltage-dependent power loss; &
2. Current-dependent power losses.

Voltage-dependent power losses

Voltage-dependent power losses are caused by polarization effects within the main insulation.

Cross-linked polyethylene (XLPE) has low dielectric permittivity, loss factor, good dimensional stability and solvent resistance. Because of these inherent and desirable properties XLPE cables are extensively used in power distribution applications. Dielectric properties of polymers may change irreversibly with continued electric stress because of injection of electrical charges and their subsequent localization. As a result the polymer may suffer electrical degradation and studies of dielectric relaxation behavior over a wide frequency range and determination of polarization distribution by laser intensity modulation method (LIMM) are useful to detect ageing.

The calculation of voltage dependent power losses to:
P_d=U_o².ω.C_b.tanδ   (W/Km)
Where,
U_o= Operating voltage (kV)
ω = Angular frequency (1/s)
C_b= Operating capacity (µF/km)
Dielectric power loss factors tanδ for typical cable insulations are:

• XLPE      (1.5 to 3.5)10^b4
• EPR         (10 to 30)10^b4
• Oil cable  (18 to 30)10^b4

Current-dependent power losses

The current-dependent losses consist of the following components:

- Ohmic conductor losses;

- Losses through skin effect;

- Losses through proximity effect;

- Losses in the metal sheath.

Ohmic conductor losses

Ohmic losses are due to ionic, electronic, and contact resistances, which occur in the electrodes and electrolyte, current collectors, contact resistance, and interconnects because every material has instinct resistance to charge flow. It indicates the losses of FC performance.

The ohmic losses depend on material and temperature. For the calculation of the ohmic losses RI², the conductor resistance stated for 20^oC(R_o) must be converted to the operating temperature θ of the cable:

R=R_o[1+α(θ-20^oC)]  [Ohm/km]
Where,

• α = 0.0393 for Copper;
• α= 0.0403 for Aluminum

The conductor cross-section and admissible DC resistances at 20^oC(R_o) correspond to the standards series pursuant to IEC 60228.

Losses through skin effect

The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current.

The losses caused by the skin effect, meaning the  displacement of the current against the conductor surface, rise approximately quadratic with the frequency. This effect can be reduced with suitable conductor constructions, e.g. segmented conductors.

Losses through proximity effect

The proximity effect detects the additional losses caused by magnet fields of parallel conductors through eddy currents and current displacement effects in the conductor and cable sheath. In practice, their influence is of less importance, because three-conductor cables are only installed up to medium cross-sections and single-conductor cables with large cross-sections with sufficient axis space. The resistance increase through proximity effects relating to the conductor resistance is therefore mainly below 10%.

Losses in the metal sheath

High voltage cables are equipped with metal sheaths or screens that must be earthed adequately.

Sheath losses occur through:

• Circulating currents in the system
• Eddy currents in the cable sheath (only applicable for tubular types)
• Resulting sheath currents caused by induced sheath voltage (in unbalanced earting systems)

The sheath losses, especially high circulating currents, may substantially reduce the current load capacity under certain circumstances. They can be lowered significantly through special earthing methods.