The cable engineering section contains a collection of topics related to using the application and cables in general.

Cable cross-section showing
insulation

Dielectrics (insulating materials for example) when subjected to a varying electric field, will have some energy loss.   The varying electric field causes a small realignment of weakly bonded molecules, which lead to the production of heat.  The amount of loss increases as the voltage level is increased.  For low voltage cables, the loss is usually insignificant and is generally ignored.  For higher voltage cables, the loss and heat generated can become important and needs to be taken into consideration.

Dielectric loss is measured using what is known as the loss tangent or tan delta (tan δ).  In simple terms, tan delta is the tangent of the angle between the alternating field vector and the loss component of the material.  The higher the value of tan δ the greater the dielectric loss will be.  For a list of tan δ values for different insulating material, please see the Cable Insulation Properties note.  

Note: in d.c. cables with a static electric field, there is no dielectric loss.  Hence the consideration of dielectric loss only applies to a.c. cables.

Cable Voltage

Dielectric loss only really becomes significant and needs to be taken into account at higher voltages.  IEC 60287 "Electric Cables - Calculation of the current rating", suggests that dielectric loss need only be considered for cables above the following voltage levels:

Cable Dielectric Loss

The economic optimisation of cables is the selection of cable sizing based on the overall cost of a cable installation, including consideration of the power losses throughout the life of the cable.  Typically an economic optimisation exercise suggests a cable which is larger than the minimum size required to meet sustained current capacity requirements.

Where economic optimisation of the cable results in a larger size, the supply and installation cost will be greater, but the cost of cable power losses during operation will be less.  The overall life cycle cost of the cable is reduced. With lower operating losses, the overall energy efficiency of the electrical cable system will increase.

IEC 60287-3-2

This section of the current rating standard gives a method for calculation of cable size based on the economic optimisation.  The total cost of cable is given by:

$CT=CI+CJ$

CT         - total cost of the installed length of cable, cu
CJ         - present value of the Joule losses over the life of the cable, cu

The costs are expressed in arbitrary currency units, cu.  The Joule losses consider the energy cost and the costs for the additional supply capacity to provide the losses.

Note: the standard goes into detail on the calculation CI and CJ.  As we move to implementing the calculation in myCableEngineering,  we will expand this section to illustrate the complete method.

BS 7671 18th. Edition

The new edition (18th) of the BS 7671 Wiring Regulations are due to be published in July 2018.  A key change is a new part, Section 8 on Energy Efficiency.  

It is likely that part 8 will recommend increasing the cable size based on accessing savings within a time scale to any additional cost of increasing the cable size. Currently, the draft standard is also suggesting, the calculation method found in IEC 60287-3-2.

myCableEngineering

The economic optimisation of cables has been on our to do list for a quite a while now.  Additionally, we already have already implemented many of the algorithms necessary to carry out an IEC 60287-3-2 calculation. With the future inclusion of this type of calculation in BS 7671, there is now, even more, of an impetus to complete our implementation of the analysis.  We do intend to have this up and running before the publication of the new 18th Edition. 

Estimating cable life is complex and will on give results within some statistical variance.  A key determinant in cable life is the temperature at which the insulation is operated. IEC standard 60216 gives guidance on estimating the thermal endurance of insulation based on measurements on test samples. For any particular cable, it is probably best to discuss with the manufacturer.  

Arrhenius Equation

The Arrhenius equation is often used to predict the lift span of insulation materials:

$k=A{e}^{E/RT}$

k - expected life in hours
A - pre-exponential factor
E - activation energy
R - Boltzmann constant
T - temperature in K

To put the equation in a more useful form, we can take the natural logarithm and rearrange the terms:

$\ln k=\ln A-\left(\frac{E}{R}\right)\times \left(\frac{1}{T}\right)$

Since A, E, and R are constants, this becomes a straight line with a negative slope of (E/R) plotted against the inverse of temperature (1/T). 

Rule of Thumb and Application Example

A sometimes adopted rule of thumb is that for every 10 °C rise in temperature, the life of insulation is halved.  Inversely a 10 °C decrease in temperature will double the life of the insulation. The Rule is based on the Arrhenius Equation of chemical reaction time vs temperature. 

The image below illustrates a typical cable performance as provided by the manufacturer:

From the Arrhenius equation, we know that relation ship is that of a log-linear straight line:

$\ln (y)=mx+b$

with the slope m, given by:  ( ln(20,000) - ln(5,000) ) / (125 - 145) = 0.0693

and the x-axis intercept, b by: ln(20,000) - m * 125 = 18.5678

giving:

$\ln (y)=-0.0693x+18.5678$

and, for example at 110 °C, the estimated life span would be:

$y=\exp (-0.0693\times 110+18.5678)=56,500\text{ (or 6}\text{.5 years)}$

Understanding the Differences: IEC 60502 vs. IEC 60840 Standards for Power Cables

Two crucial standards often come into play when specifying power cables: IEC 60502 and IEC 60840. Both are issued by the International Electrotechnical Commission (IEC) and provide comprehensive guidelines on power cables' construction, testing, and application. However, they cater to different voltage ranges and applications, making it essential to understand their distinctions.

IEC 60502 at a Glance

IEC 60502, "Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1.2 kV) up to 30 kV (Um = 36 kV)," primarily addresses the needs of medium voltage distribution networks. This standard details requirements for materials, construction, and testing of cables for up to 30 kV voltages. It encompasses various aspects, including:

• Conductor materials and sizes
• Insulation and sheathing materials
• Construction details ensuring operational reliability
• Testing methodologies to verify safety and performance

IEC 60502 is a comprehensive guide for engineers and consultants in designing and implementing medium voltage distribution networks, ensuring that the selected cables meet the required operational and safety standards.

IEC 60840: For Higher Voltages

IEC 60840, titled "Power cables with extruded insulation and their accessories for rated voltages above 30 kV (Um = 36 kV) up to 150 kV (Um = 170 kV)," steps into the domain of high-voltage transmission. This standard is tailored for applications requiring electrical power transmission over longer distances at higher voltages. Key areas covered include:

• Advanced material specifications to handle high voltages
• Construction requirements focused on managing electrical stresses
• Rigorous testing protocols, including partial discharge tests, to ensure long-term reliability
• Specifications for accessories and jointing techniques suitable for high-voltage environments

Deciphering the Key Differences

While both standards share the common goal of ensuring cable quality and safety, they diverge significantly in their scope and application:

• Voltage Range: IEC 60502 covers up to 30 kV, making it suitable for medium-voltage applications. In contrast, IEC 60840 caters to the 30 kV to 150 kV range, aimed at higher voltage transmission needs.
• Application Specificity: The choice between IEC 60502 and IEC 60840 is dictated by the application's voltage requirements—distribution vs. transmission networks.
• Technical Rigor: Given the higher operational voltages, IEC 60840 demands more stringent construction and testing requirements, mainly focusing on insulation integrity and electrical stress control.

In Summary

Selecting the correct power cable is not merely a technical decision but a strategic one that impacts electrical infrastructure's overall reliability and safety. Understanding the nuances between IEC 60502 and IEC 60840 allows engineers and consultants to make informed decisions, ensuring that the infrastructure not only meets current needs but is also poised for future challenges. Whether designing a robust medium-voltage distribution network or a high-voltage transmission line, knowing these standards is indispensable for the project's success.

When metallic cable sheaths or armour of three-phase single core cables are unbonded or bonded at only one end, a voltage is induced at the unbonded ends. Should both ends be bonded, a circulating current flows in the sheath or armour as a result of the induced voltage.

This note presents a method to calculate the induced voltage and circulating currents. While presented for cable sheaths, the method is equally applicable to armouring.

INDUCED VOLTAGE

The inductive voltage induced per unit length in the sheath of a single core cable is given by:

with and

For a three phase set of cables this is expanded to[2]:

, ,

with and

and

CIRCULATING CURRENTS

Circulating current is made up of two components:

1. Capacitive - the conductor and sheath, coupled with the insulation (dielectric), act as a capacitor. Capacitive current flows from the conductor into the sheath and to the ground.
2. Inductive - sheaths bonded at both ends, transformer coupling between the sheath and conductor results in a sheath current flow.

CAPACITIVE CURRENT

For a single core cable, the capacitance is given by:

Leakage current in the insulation can be ignored and the capacitive current for each phase per unit length is given by:

, ,

For sheaths bonded to ground at one end only, the total capacitive current is given by multiplying the above by the total cable length.

For sheaths bonded to ground at both ends the, the capacitive current can flow in two directions towards the ground. For simplicity, it can be assumed that the current divides equally (Is1/2 for example). This can be added (or subtracted) to the inductive current to give an estimate of maximum sheath circulating current.

INDUCTIVE CURRENT

For sheaths bonded at only one end, no inductive current can flow. The inductive circulating current for sheaths bonded at both ends is given by dividing the induced sheath voltage by the impedance:

The sheath resistance can be estimated from:

with

The sheath reactance Xs, for cables bonded at both ends, depends on the configuration and can be approximated by[3]:

trefoil -

flat, no transposition -

flat, regular transposition -

Note: the calculation of sheath voltage and currents is complex and is affected by the conductor current, the physical construction of the cable, installation arrangements and deliberate or accidental parallel current paths. Given, this complexity the results obtained by the calculation method presented, should be considered as indicative of magnitude rather than a measurable value.

CROSS BONDING AND TRANSPOSITION

To reduce sheath induced voltages and circulating current, cables are often cross bonded and transposed. Figure 1 illustrates the cross bonding and transposition of cables.

By cross bonding as shown, over three sections the induced voltage in each section is 120° phase shifted. Summation of the phase shifted voltages reduces the overall induced voltage and circulating currents.

Figure 1. Cross Bonding and Transposition of cables

For balanced cables in a trefoil, the induced sheath currents are symmetrical, and cross bonding only of the sheaths is required. For flat formation, the induced voltages vary across phases and to balance out the induced voltages it is necessary to transpose (rearrange) the cables.

The calculation of induced voltages and sheath currents described can be extended to cover differing arrangements of cross bonding and transposing of cables.

REFERENCES AND SYMBOLS

REFERENCES

[1] Moore G. Electric cables handbook/BICCCables. Oxford: BSCI; 2000.
[2] Chen, Wu, Cheng, Yan. Sheath circulating current calculations and measurements of underground power cables. Xi'an Jiaotong University;
[3] IEC 60287-1. Electric cables - calculation of the current rating, part 1-1: current rating equations (100% load factor) and calculation of losses - general, IEC; 2006

SYMBOLS

As - cross-sectional area of sheath, m²
C - capacitance, F.m^-1
d_c - diameter of the conductor, m
d_s - inside diameter of the sheath, m
f - frequency, Hz
I - cable conductor current, A​
I₁, I₂, I₃ - conductor phase current of L1, L2 and L3, A
I_s1, I_s2, I_s3 - sheath phase current of L1, L2 and L3, A
L_s - inductance of sheath, H.m^-1
R_s - resistance of the sheath, Ω.m^-1
S - distance between cable centres, m
S₁₂ - distance of cable centres between L1 and L2, m
S₂₃ - distance of cable centres between L2 and L3, m
S₃₁ - distance of cable centres between L3 and L1, m
t_s - the thickness of sheath, m
X₁, X₃, X_a, X_b - reactance formulas; sheath induced voltage, Ω.m^-1
X_m - mutual reactance between conductor and sheath, Ω/unit length
X_s - sheath reactance, Ω.m^-1
U_s - sheath voltage, V
U₁, U₂, U₃ - phase voltage of L1, L2 and L3, V
U_s1, U_s2, U_s3 - sheath inductive phase voltage of L1, L2 and L3, V
ɑ_s - temperature coefficient of resistivity, per °C
η - sheath/conductor temperature ratio (typically 0.7-0.8)
ϵ_o - permittivity of freespace = 8.854187819x10^-12 F/m
ϵ_r - relative permittivity of a dielectric
θ - service temperature of conductor, °C
ρ_s - resistivity of sheath, Ω.m
ω - angular frequency = 2πf, s^-1

This is a blog post by Steven McFadyen, which first appeared on myElectrical.com, July 25th, 2011

A recurring theme I encounter is cable sizing.  Now many installations are unique and require special consideration.  However,  a lot of the time cable selection is a repeated activity.  When looking at low voltage power cables I generally always start with the same basic strategy. 

1. Default to using XLPE - why bother with other insulations (PVC, rubber, etc.).  XLPE is well established, cost competitive and doesn't have any of the degradation or fire related issues of other insulations.  You will also end up with a smaller cross sectional area.  Only in special circumstances would you need to look at other installation types.
    
2. Use armoured - buried cable mechanical protection is essential.  For indoor cables, the use of armouring is not necessary. However, even indoors you have the benefit of using the armouring for the CPC.  On indoor cables, choose armoured or not dependant on local practice.
    
3. Use LSZH (low smoke zero halogen) sheath - smoke and toxic fumes in a fire situation are not good.  Why not just avoid the issue.
         
4. Calculate the current rating using an acceptable method.  I tend to use the method given in BS 7671 as this is applicable where I work.  Calculate the rating taking into account both the design current and protective device rating and apply the necessary derating factors.
    
5. Calculate the voltage drop - again you can use BS 7671 and check it complies with local regulations.  The voltage drop needs to be the sum of all cables in a circuit (from source to end load).
    
6. Ensure the cable can take the fault level - for most larger cables this tends not to be a problem, but for smaller cables, it can be an issue.
    
7. Use myCableEnginering to carry out the calculations - it makes life easier.  
    
8. Be practical - make sure your cable size is reasonable.  If you end up with a 50 mm² cable on a 2 A load due to meeting voltage drops or fault levels, start to look a the system design concept itself.

while you cannot say "once you have selected one cable you have selected all cables',  you may be able to get away with saying "once you have selected a few cables you have selected most cables"

Finally, we need a disclaimer here.  While the above is suitable for most situations (low voltage power), it does not cover every case.  There are situations which are different, unique or require some special consideration.   To evaluate these situations, one of the best things is to understand fully the characteristics of the load the cable will be supplying, the environment it is being installed in and be aware of other overriding issues.  If you can do this,  any necessary adjustments to the eight point plan often become apparent.