Underground System Design

TADP 547

Basic Cable

Design I

Presentation 4.1

Instructor: Frank Frentzas

Basic Cable Design

Power cable design involves designing a system that has

the required current capacity, and sufficient insulation to

withstand both normal and surge voltage levels that will be

experienced during operation. In addition, the cable system

must be able to withstand the installation and operation

environment.

Fundamental design criteria include insulation voltage

withstand, along with normal and emergency allowable

conductor temperatures.

In addition to the above criteria, other design aspects that

need to be considered include the following:

System Design Criteria

Conduit-to-cable size ratio for single conductor

cables or pipe-to-cable ratio for pipe type systems.

Grounding design of sheaths to minimize standing

voltage and circulating currents, thus maximizing

system current carrying capacity.

For oil filled cables the control of hydraulic pressure

to avoid cable sheath rupture and high pressure on

accessories during thermal expansion, and low

pressure during cable cooling cycles.

System Design Criteria (cont.)

Thermomechanical forces generated during thermal

expansion of the cable conductor means joints and

terminations must be designed to withstand these

forces. (A typical cable with a copper conductor can

produce several thousand pounds of thrust - larger

conductors produce larger forces.)

Design of supports and cable clamps to withstand

both thermal expansion forces and short circuit

forces.

System Design Criteria (cont.)

Size of manholes or joint bay to accommodate

joints during installation and normal operation.

For pipe type and metallic sheath cables with a

corrosion protection system must be considered.

Soil, cable depth, and other cable crossings or

heat sources in the cable environment.

Length of cable circuit must be considered since it

will affect the capacitance, inductance and surge

impedance of the system.

Electrical Field Stress

Defined as the maximum voltage insulation can

withstand before electrical breakdown or failure.

If voltage stress is not controlled it can lead to the

overall breakdown of cable insulation.

Cables should be designed to operate with a safe

electrical field stress based on operating voltage.

Higher operating voltages generally result in high

electrical field stress levels.

Allowable Electrical Stress

Semi-conductive shields are used to reduce field

stress levels in the conductor insulation.

AEIC standards provide recommend stress levels

for cables at various voltages and insulation types.

For 138 kV cable, allowable field stress is 8 kV/mm

at conductor or inner shield and 4 kV/mm at the

insulation or outer shield.

Allowable stress for 345 kV system is 12 kV/mm at

conductor and 6 kV/mm at insulation shield.

Maximum Internal Stress

Provided by industry standards such as AEIC, ICEA, IEEE,

and IEC, as shown in Table 4-2 from ICEA S108-720 below:

Allowable Stress

Table 2.3 – 1 Allowable field stress for nominal internal and external

stress (from AEIC CS9)

Rated

Voltage

kV

Conductor

Size kcmil

Conductor

Size mm2

Max.

Insulation

Eccentricity %

Nominal Internal

AC Stress Limit

V/mil (kV/mm)

Nominal

External AC

Stress Limit

V/mil (kV/mm)

69 wet 500-4000 240-2000 12 100 (4.0) 50 (2.0)

69 dry 500-4000 240-2000 12 150 (6.0) 75 (3.0)

115 750-4000 400-2000 12 200 (8.0) 100 (4.0)

138 750-4000 400-2000 12 200 (8.0) 100 (4.0)

161 750-4000 400-2000 10 225 (9.0) 100 (4.0)

230 1000-5000 500-2500 10 275 (11.0) 125 (5.0)

345 1000-5000 500-2500 10 350 (14.0) 150 (6.0)

Table 2.3 - 1 Rated Voltage, Conductor Size Range, Insulation Eccentricity Limits,

Nominal Internal AC Stress Limits and Nominal External AC Stress Limits

Design Stress Calculations

Electrical field stress can be calculated using the

following:

and

Where,

V = rated voltage line to ground

Einner = electrical stress at inner insulation surface

Eouter = electrical stress at outer insulation surface

R = insulation radius

r = conductor radius

Cable Diagram

Electrical Stress - Accessories

Field stress can have a significant effect on

accessories (splices and terminations) since cables

can withstand higher stress levels.

Splices and terminations are designed for a smooth

transition of field stress between the cable and

accessories.

If not controlled by joint design or termination

stress cone, a high electrical stress will eventually

cause a breakdown and failure at the interface

between cable and joint or termination.

Typical Electrical Stress on a Splice

Cable Capacitance

A cable can be viewed as a large capacitor in which

conductor and outer sheath are two parallel plates

separated by insulation.

The actual capacitance will depend upon the cable’s

geometry and type of insulation used.

Capacitance for a single conductor cable can be

calculated using the following equation:

Capacitance Calculation

Where,

C – capacitance

– dielectric constant

T – insulation thickness

d – diameter over conductor shield

Charging Current

Is the current that flows when voltage is applied

to a cable conductor.

Charging current is caused by the cable’s

capacitive reactance and decreases

exponentially with time.

As a rule of thumb, a typical cable can draw 1

amp per 1000 feet.

Charging Current (cont.)

Charging current can be calculated using:

Where,

Ic – charging current per 1000 feet

f – frequency

C – capacitance

V – line-to-ground voltage

Dielectric Loss

When voltage is applied to a perfect dielectric

no power loss occurs since the capacitance

current (Ic) leads the applied voltage by 90°.

For practical dielectric materials there is always

a small current (Iv) in phase with the applied

voltage.

Summing the above two vectors results in a

current (I) that leads the voltage by less than

90°, as shown in the following diagram:

Dielectric Loss Diagram

Iv

Iv

Ic I

V

Fd

d = 900 - Fd

Dielectric Power Factor

The parameter cos Fd is known as the power factor and it

provides a useful measure of the cable’s dielectric quality.

The power factor is also referred to as tan d, and should not

be confused with the supply power factor.

Under normal operating conditions cos Fd should be kept

very small, otherwise the resulting power loss can cause the

insulation to increase in temperature.

An increase in material temperature can cause more power

loss, which contributes to a further temperature increase.

Should the cable continue to operate under this condition the

temperature will continue rising until the insulation breaks

down or fails.

Typical Values (tan d)

Typical tan d values for cable insulation are listed

below:

XLPE – 0.00015 to 0.00035

Oil – 0.0018 to 0.003

EPR – 0.001 to 0.003

Skin Effect

For DC circuits, current flows uniformly throughout

the conductor cross section.

For AC circuits, as frequency increases the non-

uniformity of current density becomes large.

Current flows more densely towards the outer

conductor surface than at the center.

The phenomenon that causes this non-uniform

current distribution is known as Skin Effect.

Skin Effect Losses

Skin effect occurs because magnetic flux linkage

of current near conductor center is greater than

that of current flowing at outer conductor surface.

Skin effect is a function of frequency, conductor

size, and relative resistance of conductor material.

Skin Effect increases as conductor size and

frequency increase.

Skin effect decreases as the conductors relative

resistance decreases.

Skin Effect Reduction

Skin effect can be reduced with suitable conductor

construction - such as conductor stranding and

use of segmented conductors.

In some underground cable designs the center

strand is omitted and replaced with a non-

conductive core since the center stand only carries

a very small current.

Proximity Effect

Proximity effect is similar to the skin effect.

Proximity effect is the additional losses caused by

magnetic fields from parallel conductors - through

eddy currents and current displacement effects in

conductors and cable sheaths.

Since three conductor cables are only used for

medium cross sections, and single conductor

cables with large cross sections have sufficient

axial spacing, these losses have less influence in

cable installations.