The document discusses sheath bonding methods for underground high voltage (HV) cables, emphasizing the importance of grounding and minimizing losses due to induced voltages in the cable sheaths. It outlines various bonding options, including both ends bonding, single point bonding, and cross-bonding, detailing their advantages and disadvantages as well as their effects on cable ampacity and safety. The latter sections describe specific bonding implementations and the significance of maintaining balanced conditions to reduce circulating currents in the cable sheaths.

1. Sheath Bonding Method in Underground cables
Ahmed Adel - Project Manager (Brugg Cables)
Introduction
Now days, the underground cables became the fastest solution for electric
transmission in urban areas or crowded cities when the overhead transmission
line can’t be installed. In the 21 centauries, The HV cables industry in the world
wide had taken a lead in the commercial market offering a reasonable cable
prices with the suitable HV accessories and proper earthing methods. HV
companies had proven through years their ability to compete against each other
with a longer life XLPE cables and high quality cable accessories.
Before designing HV cable, many aspects should be taken into consideration
like: Cable voltage, short circuit calculation, cable ampacity many questions
should be asked like: cable laid in trench or buried in sand? Cable length? Is
there any cable sections? What is the earthing method used...?
Cable grounding is a very important aspect, without it, induced voltage will be
generated in the cable sheath causing over heat and leading to decrease the
cable ampacity. To overcome this issue, a lot of grounding methods had been
implemented just to choose the proper one to be compatible with the installed
cable system.

2. 1. Cable components
Fig (1)
Shown in Fig (1):
- The main conductor which is responsible for current transferring could be
stranded or segmented depending on the conductor cross section.
- The conductor screen is a semiconducting screen to achieve homogeneous
field within insulation.
- The insulation is XLPE (cross-linked poly ethylene) with dielectric properties
surrounding the cable conductor, the surface of the insulation should be clean
from any dust or voids which can cause partial discharge leading to complete
breakdown.
- The insulation screen is a semiconductor screen to achieve homogenous
electric field within insulation.
- The metallic screen is the moisture barrier and provides the main grounding for
the cable against short circuit current in case of faults or the capacitive charging
current.

3. Sheath type Moisture
Protection
Mechanical
protection
Corrosion
Protection
Diameter Costs
Lead Sheath Excellent Good Excellent + ==
Lead Sheath
& copper
wires
Excellent Good
Excellent
+ =
CU
corrugated
Sheath
good Excellent Good o =
AL
corrugated
Sheath
good Good Good o o
Cu wires &
laminated
Sheath
fair Fair Good ++ o
Al wires &
laminated
Sheath
fair Fair Good ++ +
Table (1)
- Outer protective jacket is the mechanical protection for the metallic sheath and
anticorrosion layer, usually it consist of polymeric material PE (Polyethylene) or
PVC (poly vinyl chloride).
2. Faradays law
According to the basic theory of faradays law in fig(2) that: if an AC current flow
in any wire it will produce magnetic field which rotates around the wire and the
rate of change of the magnetic field will induce voltage generating electric
current, if there is a path, flows in the opposite direction of the main current.

4. Fig (2)
In case of the high voltage cable in fig (3), the cable conductor are surrounded by
insulation and metallic sheath, when the current flow in the main conductor the
produced magnetic field will induce voltage on the metallic sheath and if the
sheath is grounded from both ends a circulating current will start to flow which is
will affect the cable ampacity and can cause harm to personal maintenances
Fig (3)

5. 3. Sheath losses
Applying faradays law on the high voltage cable, we will find that the sheath of
the cable acts as a secondary of a transformer; where the current in the
conductor induces voltage in the sheath.
The induced voltage depends on:
- The mutual inductance between core & sheath
- The conductor current
- The length of the cable
Assuming there is no proper grounding method for the cable, the induced e.m.f
will generate two types of losses: circulating current losses (λ1’) and eddy
current losses (λ1’’), so the total losses in cable metallic sheath:
λ 1 = λ 1’ + λ 1’’
3.1 The eddy current (λ 1’’):
Is generated on similar principle of skin and proximity effect; i.e. they are induced
by the conductor current, sheath circulating current and by current circulating in
close proximity current carrying conductor.
The induced voltage is maximum in the internal side of the sheath and minimum
in its external side. This situation induces the circulation of eddy currents in the
sheath as shown in fig (4).

6. Fig (4)
The eddy currents are generally of smaller magnitude when comparing with
circulating currents of solidly bonded cable sheaths and may be neglected in
case of large segmental conductors.
3.2 Circulating current (λ 1’):
Is generated when the cable sheath is forming a closed loop and grounded from
either ends or intermediate points along the cable route fig (5).

7. Fig 5
The value of the circulating current can be determined by the magnitude of
current in cable conductor, frequency, mean diameter, the resistance of cable
sheath and the distance between single-core cables; i.e. the mutual inductance.
As a consequence the calculation of the circulating current and the induced
voltage is done by using specialized computer program (Power cable current
Analyzer).
4. Sheath losses effect
According to IEC 287, the permissible current of an AC cable is written as
Equation in buried cables where drying out of the soil does not occur on cables
installed in the air

8. - Δθ: permissible temperature rise of conductor above ambient temperature.
- Wd: dielectric losses per unit length per phase.
- n: number of conductors in a cable.
- λ1,λ2: ratio of the total losses in metallic sheaths and armour respectively to the
total conductor losses.
- R: alternating current resistance of conductor at its maximum operating
temperature.
- T1: thermal resistance per core between conductor and sheath.
- T2: thermal resistance of between conductor and cable armour.
- T3: thermal resistance of external serving
- T4: thermal resistance of surrounding medium.
By computing Δθ which is the conductor maximum temperature rises above the
ambient temperature:
Δθ = (I²R + ½ Wd) T1 + [I²R (1 + λ1) + Wd] nT2 + [I²R (1+ λ1 + λ2) +
Wd) n (T3 +T4)
However in the case of a simplified cable circuit consisting of single-core cables
(n=1) provided with metallic sheath and no metallic armour (λ2 = 0 and T2 =0) and
ignoring the environmental thermal resistance (T4) the temperature rise between
conductor and cable outer surface is given with the following equation:

9. Δθ = I²R [T1+ T3 (1 + λ1)] + Wd (½T1 +T3)
From the above relation its clear that λ1 (losses generated due to circulating
current) is increasing the temperature rise which will reduce the cable ampacity.
as shown in fig (6) the relation between sheath current and the temperature rise
affecting the cable permissible current.
Fig (6)
Therefore, the sheath circulating current must be reduced for the increment of
transmission capacity. In addition, the high sheath current has an effect on
individuals and may cause the fault by the breakdown of insulation.

10. 4. Sheath bonding methods
Various methods of bonding may be used for the purpose of minimizing sheath
losses. Formerly, where special bonding was employed for the prevention of
sheath losses on lead-sheathed cables without an insulating jacket, the sheaths
were subjected to ac voltages, and the bonding was designed to keep the
magnitude of the induced voltages within small limits so as to prevent the
possibility of sheath corrosion due to ac electrolysis.
Any sheath bonding or grounding method must perform the following functions:
(1) Reduce or eliminate the sheath losses
(2) Limit sheath voltages as required by the sheath sectionalizing joints.
(3) Maintain a continuous sheath circuit to permit fault-current return, and
adequate lighting and switching surge protection
4.1. Both ends bonding
- The metallic sheaths are grounded at least at the two extremes of the cable.
- This system doesn’t allow high values of the induced voltages in the metallic
sheaths. When dealing with both ends bonding cables, sheath circulating current
loss occurs because there is a closed circuit current.
- This type is applied for MV and LV cable system with short distance.

11. Fig (7)
Advantage:
- The two cable ends are directly connected to earth with no sheath voltage
limiter
- No need for parallel continuity earthing cable
- No stand voltage at the end of the cable
Fig (8)
Disadvantage:
- Establishing a closed circuit for the induced current causing over heat and
consequent reduction in the cable ampacity as discussed before.

12. Recommended:
In order to minimize the losses caused by both ends bonding, cables
should be laid in a trefoil formation and a proper balance of cable spacing for
good heat dissipation.
4.2. Single point bonding
- The simplest form of special bonding consists in arranging for the sheaths of the
three cables to be connected and grounded at one point only along their length.
- At all other points, a voltage will appear from sheath to ground that will be a
maximum at the farthest point from the ground bond. The sheaths must therefore
be adequately insulated from ground. Since there is no closed sheath circuit,
except through the sheath voltage limiter (if any), current does not normally flow
longitudinally along the sheaths and no sheath circulating current loss occurs
(sheath eddy loss will still be present) shown in fig (9).
Fig (9)

13. Types of single point bonding
- Types are divided according to cable length in fig (10), if the cable length is less
than 500 m or one drum length then one side bonding is applied, but if the cable
length is from 300m to 1000m long cable section then split bonded system is
applied.
Fig (10)
Advantage:
- The ampacity is higher compared with both sides bonding, as there are
practically no circulating current in cable sheath.
Disadvantage:
-
- As the screen is open, there are no circulating currents, but there is an induced
voltage appearing at the open cable screen, where sheath voltage limiters must
be installed in order to protect the cable outer jacket against transient
overvoltage.

14. - The length of one section is limited as the magnitude of the induced voltage is
increasing with length.
Recommended
- During a ground fault on the power system, the zero-sequence current carried by
the cable conductors could return by whatever external paths are available. A
ground fault in the immediate vicinity of the cable can cause a large difference in
ground potential rise between the two ends of the cable system, posing hazards
to personnel and equipment.
- For this reason, single-point bonded cable installations need a parallel ground
conductor, grounded at both ends of the cable route and installed very close to
the cable conductors, to carry the fault current during ground faults and to limit
the voltage rise of the sheath during ground faults to an acceptable level.
Fig (11)

15. - The parallel ground continuity conductor (PGCC) is usually insulated to avoid
corrosion and transposed, if the cables are not transposed, to avoid circulating
currents and losses during normal operating conditions.
- The sheath voltage reduction rate of transposed PGCC is compared with no
transposed PGCC. As shown in Fig. 11, the effect of transposed PGCC is better
than no transposed PGCC. The average reduction rate in the sheath voltage of
transposed PGCC is 70.8 %, about 8.7 % better than no transposed PGCC.
Consequently, the difference is not big compared with duct formation or directly
buried formation because the spacing between phase conductors is closer than
duct or directly buried formation fig (12).
Fig (12)

16. 5. Cross-bonding method
- For underground circuits, longer than 1 km, the losses on the metallic sheaths
can be minimized making in each joint a cross bonding of the cable shields.
- The most basic form of cross bonding consists of sectionalizing the cable into
three minor sections of equal length and cross connecting the sheaths between
each two-minor section. Three minor cable sections form a major section fig (13).
- The natural points to establish the crossings are the joints, where appropriate
cross bonding boxes connected to the sheaths, these boxes include SVL. This
method provides balanced induced voltages at a vectorial angle of 120°of no
resultant circulating current when phasorial summation was applied.
Fig (13)

17. 5.1. Laying formation:
5.1.1 Flat formation
a) Un Transposed:
If the single-core cables are installed in flat formation un transposed the
voltages induced in the cable sheaths of outer cables are higher than the
induced voltage in the middle cable and the vectorial (phasor) summation is
not zero fig (14). As a consequence, it is not possible to eliminate the
circulating currents in a cable circuit where only the cable sheaths are cross-
bonded. The imbalanced phasorial voltage is generating a residual voltage
which, in return would generate circulating currents.
Ub (smaller induced voltage leading to imbalance)
Uc
Ua
Fig (14)

18. b) Transposed:
When the cable sheaths of transposed cables occupying the same position in
circuit configuration are straight connected, the vectorial summation of
induced voltage would be zero if the system would be of balanced
parameters: currents, spacing and length.
Fig (15)
- By connecting in series the cable sheath of the three phases (120° phasor
displacement) the circulating currents could be eliminated; the phasor sum of
induced voltages could be zero if the geometrical data of cable circuit is uniform
along the three cable sections as fig (16).
Uc Ub
Ua
Fig (16)

19. - So, it is obvious that in order to significantly reduce or to eliminate the circulating
current losses the cable and cable sheaths must be transposed at every joint bay
position and the sheaths cross-connected with phase rotation in opposition to
that of cable transposition.
- The maximum induced voltage in respect to earth depends on the position of
each minor transposition section within the major transposition section. At the
ends of major transposition sections the cable sheaths are at earth potential as
shown in fig (17) ,while at all other points along the cable the voltage is
proportional to cable length in respect to earthing points or, for the median (2nd)
minor section, of measuring point in respect to the other two minor sections.
Fig (17)
5.1.2.Trefoil formation
- When the cables are laid in trefoil formation, the induced voltage in the sheath of
the three cables is similar so the cross-bonding method will be applied like the
flat type system with transposition. As in fig (17).

20. 5.2. CROSS BONDING COMPONENTS
To a cross bonding system implementation the following equipments are applied:
a) Cross bonding boxes to execute the crossing of the sheaths. These boxes
include SVL and each box should have an earth electrode itself for create an
earth return circuit in each divided section of the line. These boxes should be
watertight and capable of containing the effects of the thermal or electrical
failures of any element inside the box, including a possible internal short circuit.
To facilitate its maintenance, these boxes should be installed in joints boxes with
easy access (for example through the placement of manholes) and they should
not be at more than one meter below the ground level [3].
b) Direct bonding boxes to connect the sheath directly to earth. These boxes
include earth electrode but, unlike cross bonding boxes, they do not include SVL.
c) Kits for shield interruption: it is necessary for each phase joint to introduce an
additional kit to remove the shield outside the respective box and to connect a
concentric cable.
d) Cables to the sheaths connection to cross bonding boxes: should be coaxial
cables insulated with XLPE (cross linked polyethylene) or flexible monopole
conductors. The section of these cables is determined by the maximum value of
short circuit current of the power line. Thus, the monopole conductors are directly
connected to the cross bonding boxes. The sheaths connections should be
designed to minimize the cable length, which should not exceed the 10 meters
5.3. Un balanced Conditions
In cross-bonded cable system, there are so many unbalanced conditions. These
unbalanced condition cause circulating current along the metallic sheath. Various
unbalanced conditions are considered:
- Length of minor sections
- Mixed cable arrangement in same major section
- Multiple circuits
- earthing resistance
- etc

21. 5.3.1 Correlation of the sheath current and length imbalance
We consider unified burying formation, which is constructed by the same
formation as trefoil or duct. When the cables in each minor section have the
same length, the cables are referred to balance and the length imbalance rate is
zero. In trefoil and duct formation like Fig 18. Supposing the normal length of the
cable is 300 meters, and the lengths of the cables in the first minor section are
changing, then the imbalance rate of the system and the sheath circulating
currents are indicated in Fig 19.
Fig 19

22. Fig 20
The current marked with square represent the cable in trefoil formation and the
other is the duct formation:
- Its obvious that the circulating current are nearly the same in the both formation.
- The circulating current reaches Zero when all the minor sections are equal in
length which means balanced system.
- The change in length of the minor section affect the circulating current leading to
un balanced conditions.
5.4 Scenarios of Cross-bonding:
The basic form of the cross-bonding system is each major section consists of
3 minor section equal in length, and between the three minors sections the
sheath is connected to a sheath voltage limiter and earthed at the beginning
and at the end of the major section.
It is not generally possible to divide the route length into exactly matched
minor section lengths, nor is it always possible to maintain a constant spacing
of the cables throughout the route, Due to the different site situations, other
scenarios had been applied to the cross-bonding achieving the same results,
and reducing the induced sheath voltage as well.

23. 5.4.1 Modified Cross-bonding:
In this modified version of the sectionalized cross-bonding system, it is not
necessary to have the number of minor sections exactly divisible by three.
Balanced voltage conditions within a given major section consisting of four minor
sections can be achieved by subdividing one minor section into two subsections,
as follows:
(1) One short length (or subsection) followed by two equal lengths (or
minor sections) with another short length (or subsection)
completing the major section; the combined length of the two
subsections should be equal to the length of one minor section as
shown
Fig 21
(2) One short length (or subsection) followed by one longer length
(or minor section) then another short length (or subsection)
followed by one longer length (or minor section) to complete the
major section; the two longer lengths (or minor sections) should be
equal and the combined length of the two subsections should be
equal to the length of one minor section as shown on Fig 22. In this
case, the first cross bonding must be reversed

24. Fig 22
5.4.2 Continuous Cross Bonding.
In this system the sheaths are cross bonded at the end of each minor section
throughout the whole cable route. The three sheaths are bonded and grounded
at the two ends of the route only, as shown in Fig 23. It is again generally
desirable that the cables are transposed so that each conductor occupies each of
the three positions for one third of the total length. The number of matched minor
sections should preferably be exactly divisible by three, but this becomes less
important as the total number of minor sections increases.
Its preferable to apply this system when there is large number of minor sections
with unequal lengths.

25. 5.4.3 Mixed Systems.
When the number of minor sections is not exactly divisible by three, the system
may consist of a mixture of (regular or modified) cross-bonded system and
single-point bonded lengths. When necessary, on account of a large number of
minor sections having unequal lengths, the cross bonding may be of the
continuous type. Figure 24 shows the arrangement of a final single point bonded
length at the end of a cross-bonded system.
Fig 24
References:
[1] IEC 287-1-1: “Electric cables-calculation of the current rating, part 1: current rating equations (100%
load factor) and calculation of losses, section 1: general”. IEC publication 287, 1994.
[2] ANSI/IEEE Std 575-1 988, IEEE Guide for the Application of Sheath-Bonding Methods for Single
Conductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths.
[3] J.S. Barrett, G.J.Anders. “Circulating current and hysteresis losses in screens, sheaths and armour of
electric power cables-mathematical models and comparison with IEC Standard 287”. IEE Proc.-Sei.
Meas. Technol., Vol. 144, No. 3, pp. 101-110, May 1997
[4] Peter Graneau. “Underground power transmission. The science, technology & economics of high
voltage cables”. Ed. John Wiley & Sons, 1979.
[5] Manuel Llorente Antón. “Cables eléctricos aislados. Descripción y aplicaciones practices”. Editorial
Paraninfo, 1994..

26. [6] Víctor Sierra Madrigal, Alfonso Sansores Escalante. “Manual técnico de cables de energía”. Ed. Mc
Graw Hill, 2ª Edición, 1984
[7] Enrique Ras. “Teoría de líneas eléctricas”. Ed. Marcombo 1986
[8] Jordi-Roger Riba, Xavier Alabern. “Experimental behavior of a magneticfield shield for an underground
power line”. Internacional Conference on Renewable Energy and Power Quality. Zaragoza, 2005.