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[Selection Guide] How to choose the most economic size and type of cable?

Cable selection is about choosing the appropriate type of conductor and selecting a suitable size/cross-section area/ diameter of the conductor according to the application. First, there is a need to understand the significance of cable sizing and selection. Then selection criteria will be discussed keeping in mind all the derating factors that might reduce cable ampacity. A law named Kelvin's law plays a vital role in the economic sizing of conductors, so it will also be explained here. Other than the size of conductor, different types of the conductor will be studied. Also, the cable shielding and insulation will be discussed at the end.

Cable sizes are usually defined in terms of cross-sectional area, Kcmil (Kilo circular mils) or AWG (American Wire Gauge).

Standards available for the cable selection and size are:
  • IEC (International Electrotechnical Commission)
  • NEC (National Electrical Code)
  • BS (British Standards)

Significance of Selecting the Right Cable Size and Type:

​Selecting the right cable size and type is significant because of the following reasons:

  • If cable size is very small, when the current exceeds the cable ampacity, the cable will heat up and get damaged. So, there is a need to choose the cable size for which it is capable enough to withstand the full load current and the short circuit current that could flow through the cable.
  • Increasing the cross-section area of the cable will require more material to be used in its construction, causing it to become expensive. Therefore, it will be hard to maintain a good balance between the cable cost and its usage requirements. So, the cable's diameter is to be sized as per the requirements.
  • It must be ensured to provide a load with a suitable voltage i.e. with minimum voltage drop. Cable with a small diameter will have a higher resistance. Also, it will cause more voltage drop across the cable. That's why there is a need to select such cable a which causes no or less voltage drop.
  • There is a need to choose the best cable type according to the requirement of application as every type of conductor has its own resistance, thermal conductivity, etc.

Selection Criteria of Cables:

​Cable size is determined based on these factors:

Current Carrying Capacity: It is determined by evaluating the amount of current to be drawn by the equipment or load connected at the receiving end of the cable. The safety margin for overload current is also provided in it.

Voltage Drop: Due to resistance of the cable, power losses occur, causing the voltage to be dropped by some magnitude. In addition to it, voltage drop also varies with respect to temperature as temperature affects the resistance. If we know the values of resistance of cable and current flowing from cable, then we can determine the voltage drop across that cable by using the formula V=I*R.

Short Circuit Rating: It is the capability of a cable to withstand short circuit current for the specific duration of the fault before it has been cleared without any damage.

Derating Factors:

There are some external disturbances that affect the current rating of a cable i.e. cable ampacity. In such scenarios, current ratings are to be improved by applying some suitable factors known as derating factors. As we have more than one type of derating factor, so values of all of the derating factors are multiplied to get an average value. The following are the main derating factors that should be kept in consideration when selecting cable size.

Temperature Derating Factor (CT):Temperature derating factor (CT): Cables should be arranged in such a way so they get a minimum space to dissipate heat in their surroundings. This factor is used in calculations of cable sizing so as to consider the arrangement of cable for minimizing heat losses thus improving cable ampacity.

Conductor Grouping Factor (CG): Electromagnetic field around the conductors in a group is created when the current flows which causes the cable ampacity to decrease. For this reason, conductor grouping factor is considered.

Thermal Resistivity of Soil (CR): Standard temperature surrounding cables is 40°C. But if cables are to be buried in soil then temperature surrounding the cables rises up and cable ampacity gets affected. That's why a factor for thermal resistivity of soil is considered in calculations so as to compensate rise in temperature.

Burial Depth Derating Factor (CD): This factor depends on the depth of ground at which conductor is to be buried. Deeper in the ground cable will cause the derating factor to increase.

How to Calculate the Cable Size for a Given Load?

S =
P Power factor

Where,

         P = Real power(KW)
         S = Apparent power(KVA)
         VL = Line voltage
         IL = Line current or cable ampacity
S =
√3VLIL
IL =
S √3VL

Considering the derating factors:

IL* =
IL (CT.CG.CR.CD)

Now select cable size against above calculated current from standard tables of cable sizing e.g. 'IEC catalogues'.

Kelvin's Law for Economic Cable Sizing:

Kelvin's law states that:

The most economical size of a conductor is that for which annual interest and depreciation on the capital cost of the conductor is equal to the annual running cost

Let say,

         Size (cross sectional area) of conductor = a
         Annual interest and depreciation cost of conductor = P1
         Annual running cost of conductor = P2

As annual interest and depreciation cost of conductor is directly proportional to size of conductor (cause increase in size of conductor will increase its capital cost and so interest and depreciation cost) i.e.

P1 ∝ a

So, P1 = k1.a ------------------------ eq (i)

Also, annual running cost of conductor is inversely proportional to size of conductor (cause increase in size of conductor will decrease energy losses plus damage due to heat up and so operating cost) i.e.

P ∝
1 a
So, P2 =
k2  a
------------------------ eq (ii)

Here k1 and k2 are constants.

Total annual cost of conductor (let say P) can be obtained by adding eq (i) and eq (ii):

P = P1 + P2
P = k1.a +
k2 a

For total cost to be minimum, differential of 'P' with respect to 'a' should be zero:

dP da
=
d da(k1.a + k2a )
0 = k1 + k2 (- 1a2)
0 = k1 - (k2a2)
k2a2 = k1
k2a = k1.a
P2 = P1

Economic conductor size (at which annual interest and depreciation cost is equal to the annual running cost of the conductor) can be calculated from the above derivation:

k2a2 = k1
a = k1k2
a = √ ( k1k2 )

Example:
Consider 1 km long cable with cable ampacity of 150A throughout a year (8760 hours). Installation cost of cable is $ 0.1a / meter, where a is size of conductor in cm2. Energy cost is $ 0.001 / kWh and 12% are interest & depreciation charges. Resistivity of conductor is 1.91 µΩ.cm, so determine economical size of conductor.

long-cable

By EagleRJOCC BY-SA 4.0, Link

 

Resistance of conductor =
ρL a
=
(1.91x10-6)(105) a Ω
R =
0.191 a
Energy lost annum
=
2I2Rt 1000kWh
Energy lost annum
=
2x(150)2x(0.191a)(8760) 1000
Energy lost annum
= (
75292.2 a
) kWh
Annual running charges =
Cost kWh
x
Energy lost annum
Annual running charges = 0.1 x (
75292.2 a
)
Annual running charges = $ (
75292.2 a
)
Capital cost = $
16a meter

For 1 km,

Capital cost = $16a × 1000 = $16000a

Annual fixed charges = Interest & depreciation on capital cost

Annual fixed charges = 12% of $16000a = $1920a

According to Kelvin's law,​

Annual running charges = Annual fixed charges
7529.22 a
= 1920a
a2 =
7529.22 1920
a = 3.92 cm2
So, the economical size of conductor is 3.92 cm2.

Limitations:

  • Accurate interest and depreciation on capital cost can't be determined.
  • Some factors like cable ampacity, corona effect, etc. are not considered in this law.
  • There may be an excessive voltage drop in the size of the conductor evaluated by Kelvin's law.
ACSR and ACCC
Dave Bryant / CC BY-SA

Types of Conductor:

Based on physical structure, conductors are either stranded (multiple thin wires) or solid (solid metal wire). Cable types (conductors) which are used in transmission lines are:

ACSR (Aluminum Conductor, Steel Reinforced): It consists of steel strands surrounded by aluminum strands. It is the most recommended conductor for transmission lines and used for longer spans.

ACAR (Aluminum Conductor, Alloy Reinforced): It consists of aluminum-magnesium silicon alloy surrounded by the aluminum conductor. It has high mechanical strength and conductivity than ACSR, so it can be used for distribution and transmission on a large scale, but it is more expensive.

AAC (All Aluminum Conductor): It is also known as ASC (Aluminum Stranded Conductor) and has a conductivity of 61% IACS. Though it has good conductivity, still it is limited in its applications cause of low strength.

AAAC (All Aluminum Alloy Conductor): It is made up of aluminum-magnesium-silicon alloy and has a conductivity of 52.5% IACS. Because of better strength, it can be used for distribution but not suggested for transmission. It is suitable to be used in areas with high moisture content.

⁘ IACS (International Annealed Copper Standard) is a standard introduced by US.
It is a standard against which conductivity of any conductor is compared.
It is value of conductivity of commercially available copper.

Cable Shielding and Insulation:

There are different layers of various materials which are to be laid over conductor so as to provide cable insulation and shield for the purpose of protection of conductor. Each of the layer has its own specific function and its requirement depends on the application of cables. For example, for overhead lines we don't need to have any insulation or shielding as bare conductors are used there, but for underground cables they must be insulated and shielded.

Insulation: Cable insulation is done by means of any dielectric like PVC so as to prevent leakage of current from a conductor.

Sheath: Cable is provided with the sheath for the purpose of the safety of cable from moisture. It should be some non-magnetic material like lead alloy.

Bedding:  Purpose of bedding is to protect the sheath of cable from any damage caused by armouring.

Armouring: Armouring is another layer of galvanized steel over the cable so as to protect it from any kind of mechanical damage.

Serving: It adds to the mechanical strength of the cable. It provides overall protection against moisture, dust, etc. 

Cable cross-sectional diagram

Summing-Up:

The electrical power transmission system can be made efficient and economical by following the proper methodology of cable sizing and selection. Selection criteria, derating factors, type of conductor, proper insulation and shielding, etc. Must be in our mind at the time of cable installation. This is how we can achieve efficient, safe and cost-efficient transmission of electricity.

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