Mechanical forces in large cross section cables systems

669
Mechanical forces in large cross section
cables systems
Working Group
B1.34
December 2016

Application guide for extruded land cables
Members
J. KAUMANNS, Convenor DE
M. BACCHINI IT
G. GEHLIN SE
B. GREGORY UK
D. JOHNSON US
T. KURATA JP
H-P. MAY DE
F. PEURTON (repl. by J. SAMUEL) FR
R. REINOSO ES
J. TARNOWSKI CA
R. VAN DEN THILLART NL
M. A. VILHELMSEN DK
D. WALD CH
Invited Expert
C. PYE IR
WG B1.34
Copyright © 2016
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MECHANICAL FORCES IN LARGE
CROSS SECTION CABLES SYSTEMS
ISBN : 978-2-85873-372-9

MECHANICAL FORCES IN LARGE CROSS SECTION CABLES SYSTEMS
IMPORTANT FOREWORD
This TB is the final issue of the report published by WG B1.34.
After completion of the task by the Working Group, this document has been circulated within SC B1 and has
received tens of comments from the SC Members which have been for most of them rejected by the WG
Convener. The rejected comments were mostly coming from one National Committee while there was a
member nominated by this National Committee in the Working Group B1.34.
During the progress of the Working Group, in compliance with CIGRE Rules, this member expressed the
opinion of his Country as confirmed by the experts of the National Committee.
As there was no possible consensus within the Working Group, this final document cannot be considered as
official CIGRE recommendations for updating TB 194, published by WG 21.17 in 2001.
During their 2016 plenary Annual Meeting (August 23rd 2016), the members of SCB1, upon proposal of the
Strategic Advisory Group, unanimously decided to launch a new Working Group, titled WG B1.61 ( Installation
of HV Cable Systems) to update the TB 194, taking into account the work of following Working Groups/Task
Force:
·WG B1.35: Guide for Cable Rating Calculations
·WG B1.41: Long Term performance of soil and backfill of cable systems
·WG B1.48: Trenchless Technologies
·TF B1.53: Installation Related Cable Damages
This TB published by WG B1.34 will be considered as input data for the updating of TB 194 which remains
the only reference document of SC B1 regarding Installation of Extruded and SCFF HV Cable systems.
Anyhow, the reader might take this TB as summary of methods given by various experts and guidance to
analyze and understand thermo-mechanical forces effects with large conductor cross section XLPE cable
systems.
ISBN : 978-2-85873-372-9

Mechanical Forces in Large Cross Section Cable Systems
Page 2
Mechanical Forces in Large
Cross Section Cable Systems
A P P L I C A T I O N G U I D E F O R E X T R U D E D L A N D C A B L E S
Table of Contents
EXECUTIVE SUMMARY……………………………………………………………………………….. 7
1 Scope and Definitions ................................................................................................. 7
2 Introduction.................................................................................................................. 8
2.1 Findings of the Working Group 9
2.2 Categories and Principles of Types of Thermo-mech. Installations 11
2.3 Input Factors and Effects on Large Conductor Cable Systems 12
3 Rigid Installations: Theory and Practice ................................................................. 13
3.1 Forces.......................................................................................................................... 13
3.1.1 Calculation ................................................................................................................... 13
3.1.2 Forces Measured on Cables........................................................................................ 14
Example 1.................................................................................................................... 18
Example 2.................................................................................................................... 18
Example 3.................................................................................................................... 18
3.1.3 Cable Fixing................................................................................................................. 19
3.2 Practical Examples for Rigid Applications ................................................................... 20
4 Flexible Installations: Theory and Practice............................................................. 24
4.1 Flexible Systems (Western Approach) ........................................................................ 24
4.2 Flexible Installations (Japanese Approach)................................................................. 30
4.3 Practices of Flexible Installations in Tunnels............................................................... 35
5 Transitions between Rigid and Flexible Systems: Theory and Practice ............. 40
5.1 Locking Bend Theory................................................................................................... 41
5.2 Flexible Loop Theory ................................................................................................... 48
5.3 The Transition Design Dilemma .................................................................................. 51
5.4 Transition Sections: Practice ....................................................................................... 52
Practice: Transition from a tunnel to an outdoor termination....................................... 52
Practice: Transition to tower mounted cable terminations........................................... 53
Practice: Transition from a buried installation to outdoor sealing end: rigid solution 54
Practice: Flexible loop transition from buried cable to outdoor or GIS termination ..... 55
Practice: Semi-flexible transition from a rigid cable system to a movable GIS term... 56
Practice: Transitions across bridge expansion joints................................................... 56

Page 3
6 Duct Installations: Theory and Practice .................................................................. 59
6.1 Behaviour of cables inside ducts ................................................................................. 59
6.2 Definitions: ................................................................................................................... 61
6.3 Thermo-mechanical Effects in a Duct System............................................................. 63
6.4 Design of the Duct System .......................................................................................... 67
6.5 Practices of Duct Installations...................................................................................... 68
6.6 Experiences in Japan with Duct Installations .............................................................. 74
7 Short Circuit Forces .................................................................................................. 77
8 Cleat Applications ..................................................................................................... 79
8.1 Guide-Cleating Applications ........................................................................................ 83
8.2 Clamp-Cleating Application ......................................................................................... 84
8.3 Anchoring-Cleat Application ........................................................................................ 85
8.4 Saddle-Cleating Application......................................................................................... 86
8.5 Recoil-Cleating Application.......................................................................................... 87
8.6 Short-circuit Strap Cleating Application ....................................................................... 88
9 Mechanical Cable Parameters: Measurements and Values .................................. 88
9.1 Description of Test Arrangements: .............................................................................. 89
9.1.1 Linear Expansion Coefficient (α) ................................................................................. 89
9.1.2 Effective Axial Stiffness (EAeff)..................................................................................... 90
9.1.3 Bending Stiffness (EI) .................................................................................................. 92
9.1.4 Side Wall Pressure ...................................................................................................... 95
9.2 Mechanical Parameters of Large Conductor XLPE Cables ........................................ 98
9.2.1 Linear Expansion Result............................................................................................ 100
9.2.2 Effective Axial Stiffness Results ................................................................................ 100
9.2.3 Effective Bending Stiffness Results........................................................................... 103
10 Conclusions ............................................................................................................. 104
11 Bibliography/References ........................................................................................ 105
Annex 1 Challenges with Determination of Cable Parameters [1]........................................... 106
Annex 2 Comparison of Different Sagging/Snaking Calculation Approaches ......................... 118
Annex 3 Minimum Initial Sag to Limit the Maximum Sheath Strain Change ........................... 121
Annex 4 Locking Waves........................................................................................................... 123
Annex 5 Transition Loop Methods ........................................................................................... 129
Annex 6 Flexible Loop Approach for a Circular Arc................................................................. 145
Annex 7 Comparison of Flexible Loop Methods ...................................................................... 151
Annex 8 Design of the Duct System [5] ................................................................................... 153
Annex 9 Summary of Japanese Measurement Results........................................................... 164
Annex 10Snaking of Cables in Empty Pipes – Analytical Calculation Method......................... 169
Annex 11Horizontal Cable Snaking with Water Cooling System in a Tunnel........................... 172

Page 4
Figure 1 Thermo-mechanical movement of cables off support arms at a tunnel bend...........................................................10
Figure 2 Thermo-mechanical disturbance of a cleat and joint in a manhole.........................................................................10
Figure 3 The benefit of wide cleat spacings in a flexibly sagged 400 kV 2500mm2
XLPE cable system ................................10
Figure 4 Thermo-mechanical forces for large stranded conductors vs. temperature…………………………………………… 14
Figure 5 Long term relaxation of cable due to repeated cyclic loading...............................................................................15
Figure 6 Thermo-mechanical forces for buried (slow heating) large stranded conductors vs temperature…………………….. 16
Figure 7 Thermo-mechanical forces for In-Air (rapid heating) large stranded conductors vs. temperature…………………….16
Figure 8 Buckling of a rigid cable span between cleats due to longitudinal force.................................................................19
Figure 9 500 kV XLPE cable in a straight rigid installation in a vertical shaft.....................................................................21
Figure 10 500 kV rigidly cleated bends at the upper end of a vertical shaft .........................................................................21
Figure 11 Typical trench cross-section for buried cable.....................................................................................................22
Figure 12 Cable locking bends installed adjacent to a joint bay..........................................................................................22
Figure 13 Joints and cable clamped to a concrete pad; 400 kV 1200 mm2
XLPE cable Denmark..........................................23
Figure 14 Horizontal cable waves adjacent to joint bay; 400 kV 1200 mm2
XLPE cable Denmark .......................................23
Figure 15 Vertically sagged flexible cable system ............................................................................................................25
Figure 16 Horizontally waved flexible cable system.........................................................................................................28
Figure 17 Vertical Snaking: Definition of Dimensions......................................................................................................30
Figure 18 Vertical Snaking: Lateral Deflection and Forces, W=cable weight/m ..................................................................30
Figure 19 Horizontal snaking: dimensions .......................................................................................................................32
Figure 20 Horizontal snaking: forces...............................................................................................................................33
Figure 21 400kV 2500mm2
XLPE cable in a vertically sagged system ...............................................................................36
XLPE cable in a vertically sagged system in trefoil formation ..................................................36
Figure 23 Cables hung on straps in a vertical sagged system in France...............................................................................37
XLPE cable and joints in a vertically sagged trefoil formation..................................................37
Figure 25 Diagram of 500kV 2500mm2
XLPE cable and joints in a vertically sagged system..............................................38
Figure 26 275 kV 2500mm2
XLPE horizontally snaked tunnel system in Japan ..................................................................39
Figure 27 66 kV XLPE cables in a horizontally waved bridge crossing in Singapore...........................................................39
Figure 28 Accumulation of bend angles in a rigidly constrained cable locking wave ...........................................................41
Figure 29 Reduction of axial force versus friction coefficient through bends of different angles...........................................43
Figure 30 Input force F1 v cumulative bend angle: Comparison of capstan theory and FEA .................................................44
Figure 31 Diagrammatic representation of a flexible cable loop and locking waves at a termination .....................................48
Figure 32 400 kV 2500 mm2
XLPE outdoor cable termination in Spain .............................................................................52
XLPE cable transitions: Left side: rigidly cleated. Right side flexible.......................................53
Figure 34 Transition of XLPE cable to tower mounted outdoor terminations in Spain .........................................................54
XLPE cable transition from buried cable to an outdoor termination..........................................54
Figure 36 Termination appraoch with large cumulative bend angles ..................................................................................55
Figure 37 Flexible loop with small 60o
cumulative bend angle, left: GIS, right: outdoor 275kV/2500mm2
...........................55
Figure 38 Flexible Loop of 220 kV 2500 mm2
XLPE CABLE IN New Zealand .................................................................56
Figure 39 Flexible transition support structure for a GIS termination .................................................................................56
Figure 40 Plan view of flexible cable offsets which absorb bridge expansion: 275 kV Australia...........................................57
Figure 41 Flexible transition support for a rigidly cleated cable passing over a bridge expansion joint ..................................58
Figure 42 Design principle for flexible transition support for a rigidly cleated cable passing over a bridge............................58
XLPE cable in a duct showing thermo-mechanical clearance...................................................61
Figure 44 Duct- manhole system containing cable thermo-mechanical patterns...................................................................62
Figure 45 Three 138 kV 750 mm2
cables in a pipe system.................................................................................................62
Figure 46 Thermo-mechanical cable patterns: rigid-bar and duct bend curvature patterns ....................................................64
Figure 47 Thermo-mechanical cable patterns: cylindrical sinusoid and helical patterns........................................................64
Figure 48 Thermo-mechanical cable patterns Measured in an Experimental set-up..............................................................65
Figure 49 FEA axial force vs. temperature rise for different duct clearances: 230 kV 1250 mm2
cable ..................................65

Page 5
Figure 50 FEA model of a cable in a duct system: one elemental beam length [5] ...............................................................67
Figure 51 Clamping cleat constraint system for a straight-through manhole layout..............................................................69
Figure 52 Clamp-cleat constraint system for a straight-through manhole layout ..................................................................70
Figure 53 Flexible offset manhole constraint system.........................................................................................................71
Figure 54 Trefoil duct entering duct, typical offset conditions, example for S-bend……………………………………………71
Figure 55 Duct with smooth inner walls. Left: smooth outer wall. Right: corrugated outer wall............................................72
Figure 56 Typical designs of a trefoil duct arrangement....................................................................................................73
Figure 57 Cable trefoil subducts installed in a larger duct .................................................................................................73
Figure 58 Shape of bend part..........................................................................................................................................77
Figure 59 Generic guide/clamping cleat With Rubber inlays .............................................................................................79
Figure 60 Axial movement vs. applied axial load measured on a guide/clamping cleat………………………………………... 82
Figure 61 Guide/clamping cleat......................................................................................................................................83
Figure 62 Generic clamping cleat 84
Figure 63 Anchoring cleat comprising six clamping cleats on a common plate ...................................................................85
Figure 64 Anchoring clamp cleat with an elongated body and ribbed liner) ........................................................................86
Figure 65 Saddle clamping cleat .....................................................................................................................................86
Figure 66 Recoiling cleat ...............................................................................................................................................87
Figure 67 Short circuit strap cleat………………………………………………………………………………………………. 88
Figure 68 Measurement of coefficient of thermal expansion α ..........................................................................................89
Figure 69 Measurement of coefficient of thermal expansion. Left: cable supports. Right: complete test rig. ..........................90
Figure 70 Measurement of conductor thrust and axial stiffness EA ....................................................................................90
Figure 71 Set-up for measurement of cable thrust during heat cycles .................................................................................91
Figure 72 Measurement of bending stiffness EI by the single point load method.................................................................93
Figure 73 Set-up for detection of Bending stiffness by the two point load method...............................................................94
Figure 74 Measurement of bending stiffness EI by moment method...................................................................................95
Figure 75 Smalltest rig for conductor movement under sidewall pressure...........................................................................97
Figure 76 Cable bending rig for conductor movement under sidewall pressure ...................................................................97
Figure 77 Reduction of measured conductor thrust with time [15] .....................................................................................99
Figure 78 Force v conductor temperature for a 220KV 2500mm2
XLPE, rapid heating......................................................102
Figure 79 Axial modulus E vs temperature for a 220kV 2500mm2
XLPE, rapid heating ....................................................102
Figure 80 120 kV XLPE cable......................................................................................................................................106
Figure 81 Coefficient of thermal expansion test rig.........................................................................................................107
Figure 82 Expansion test on 120 kV XLPE cable ...........................................................................................................108
Figure 83 Axial stiffness test rig ...................................................................................................................................109
Figure 84 Variation of axial stiffness modulus EA during the cable’s temperature-rise cycle .............................................110
Figure 85 Relaxation of axial stiffness modulus EA .......................................................................................................111
Figure 86 Bending stiffness EI test rig...........................................................................................................................112
Figure 87 Variation of bending modulus EI as a function of curvature for various conductor temperatures.........................113
Figure 88 Relaxation of bending stiffness modulus EI ....................................................................................................114
Figure 89 Diagram of vertically sagged system ..............................................................................................................118
Figure 90 Diagram of horizontally waved system...........................................................................................................119
Figure 91 FEA model of a rigidly constrained locking wave of four half waves: 220 kV 2500mm2
XLPE ..........................124
Figure 92 Effect on locking wave holding force of increasing sheath radial clearance........................................................125
Figure 93 Effect on locking wave holding force of increasing cable bending radius...........................................................125
Figure 94 Effect on locking wave holding force of increasing number of half waves .........................................................126
Figure 95 Effect on locking wave holding force of increasing coefficient of friction..........................................................126
Figure 96 Effect on locking wave holding force of increasing wave offset amplitude ........................................................127
Figure 97 Input force F1 v cumulative bend angle: Comparison of FEA and capstan theory ...............................................128
Figure 98 Transition between rigid and flexible sections.................................................................................................130
Figure 99 The equilibrium graph for the Extension/Force characteristic of the rigid Wave and flexible Loop ......................133

Page 6
Figure 100 Addition of Straight Cable Characteristic to the equilibrium diagram in Figure 99............................................136
Figure 101 Extension ∆Lo vs End Force Fo Characteristic: Locking Wave for a 400 kV 2500 mm2 cable ..........................138
Figure 102 Locking Wave Length X vs End Force Fo: for a 400 kV 2500 mm2 cable .......................................................139
Figure 103 Cumulative Bend Angle Ө vs End Force Fo: Locking Wave for a 400 kV 2500 mm2
cable................................139
Figure 104 Extension of ∆L0 vs End Force F0 Characteristic Rigidly Constrained 400 kV Cable 140
Figure 105 End Effect Length X vs End Force Fo: Locking Wave in a 400 kV 2500 mm2
cable.........................................140
Figure 106 Example for transtion between flexible loop and locking wave section............................................................141
Figure 107 Determination of equilibrium condition between locking wave and flexible loop .............................................143
Figure 108 Definitions at locking wave section ..............................................................................................................143
Figure 109 Geometrical conditions for a cable bend between two cleats...........................................................................145
Figure 110 Bend angle function f(φ) for calculation of force H........................................................................................147
Figure 111 Comparisons of analytical and FEM calculation for flexible loops ..................................................................148
Figure 112 Geometrical arrangement of bending with 3m straight cable interaction ..........................................................149
Figure 113 Comparison of the force calculated by three methods for large bend angles .....................................................152
Figure 114 Comparison of the force calculated by three methods for small bend angles.....................................................152
Figure 115 Idealised symmetrical locations for manholes in a duct span 155
Figure 116 Non-anchor straight joint components ..........................................................................................................157
Figure 117 Clamp cleating and offset bend constraint system in a manhole ......................................................................157
Figure 118 Non-linear force distribution along a train of clamping cleats .........................................................................158
Figure 119 Diagram of recoil clamping cleat: top at rest. Bottom: cleat extended..............................................................159
Figure 120 Recoiling cleat and off-set bend manhole constraint system (from an FEA model) ...........................................160
Figure 121 Prefabricated composite anchor joint: components.........................................................................................161
Figure 122 Clamping cleat and offset bend constraint system with an anchor joint............................................................161
Figure 123 Manhole offset bends generating internal friction restraint on XLPE core........................................................162
Figure 124 Plan view of an in-line manhole layout .........................................................................................................163
Figure 125 Clamping cleat and quadrant bend constraint system at a cable termination .....................................................163
Figure 126 Total cable energy vs. Thermal rise ..............................................................................................................170
Figure 127 Test schematic............................................................................................................................................171
Figure 128 Picture from inside duct with sinusoidial cable Snaking .................................................................................171
Figure 129 Picture of Horizontal 257kV / 2500mm2
Snaked Cable in Trough with Water Cooling Pipe..............................172
Figure 130 Water Cooling System of 275kV 2500mm2
Cable in Japan Installed in FRP Trough ........................................172

Page 7
EXECUTIVE SUMMARY
This TB is the final issue of the report published by WG B1.34.
After completion of the task by the Working Group, this document has been circulated within SC B1 and has
received tens of comments from the SC Members which have been for most of them rejected by the WG Convener.
The rejected comments were mostly coming from one National Committee while there was a member nominated
by this National Committee in the Working Group B1.34.
During the progress of the Working Group, in compliance with CIGRE Rules, this member expressed the opinion of
his Country as confirmed by the experts of the National Committee.
As there was no possible consensus within the Working Group, this final document cannot be considered as official
CIGRE recommendations for updating TB 194, published by WG 21.17 in 2001.
During their 2016 plenary Annual Meeting (August 23rd
2016), the members of SCB1, upon proposal of the
Strategic Advisory Group, unanimously decided to launch a new Working Group, titled WG B1.61 ( Installation of
HV Cable Systems) to update the TB 194, taking into account the work of following Working Groups/Task Force:
• WG B1.35: Guide for Cable Rating Calculations
• WG B1.41: Long Term performance of soil and backfill of cable systems
• WG B1.48: Trenchless Technologies
• TF B1.53: Installation Related Cable Damages
This TB published by WG B1.34 will be considered as input data for the updating of TB 194 which remains the
only reference document of SC B1 regarding Installation of Extruded and SCFF HV Cable systems.
Anyhow, the reader might take this TB as summary of methods given by various experts and guidance to analyze
and understand thermo-mechanical forces effects with large conductor cross section XLPE cable systems:
The use of cables with extruded insulation and large conductor cross-sections has become usual in recent years.
With larger conductor cross-sections the thermo-mechanical force in cable systems is increased and so thermo-
mechanical design requires special attention.
Cables with extruded insulation have differences in their thermo-mechanical characteristics to the former
generation of fluid filled paper insulated cables upon which established thermo-mechanical design practices were
based, e.g. TB 194 Chapter 4.
In general the equations in TB 194, Chapter 4 were found to be valid and, for completeness, are included in this
technical brochure together with their derivations. Additional engineering tools are suggested and explained for
more installation conditions than those described in TB 194.
This technical brochure is intended as a guide to thermo-mechanical design of cable systems with 1000 mm2
and
greater conductor cross-sections and extruded insulation with the objective of increasing reliability and reducing the
risk of poor planning and installation.
1 Scope and Definitions
This brochure focuses on high voltage, AC and DC land cable systems with extruded insulation. It is necessary to
consider thermo-mechanical aspects in the design of extruded insulation cable systems of all conductor sizes, but
special consideration is necessary with larger conductor cross sections as the forces are higher.
• This brochure considers thermo-mechanical design for:
- Conductors of 1000 mm
2
and higher cross-sections.
- Copper and aluminium conductors.
- Conductors of all construction types, e.g. circular stranded, circular segmental, circular solid and
Milliken stranded.

Page 8
- AC and DC cable systems.
- Land cable applications and those parts of subsea installations that are above water e.g. on land and
on platforms and rigs. (The subsea parts of installations are not considered.)
• General aspects considered in this brochure:
- The magnitudes of the thermo-mechanical forces and/or movements that are experienced by the cable,
the accessories, the cleats and the support structures during service operation.
- Cable design aspects (different types of metallic sheath, variations of friction between core and sheath)
- Installation components e.g. design and application of cable cleats
- General arrangements for rigid installations, flexible installations, duct-manhole systems, expansion
bends, vertical shafts, transition between rigid and flexible, interaction with accessories and clamping
arrangements for “rigid” and “flexible” systems.
- Installation designs available to reduce the magnitudes of the cable forces and/or movements to
acceptable limits for the required service life of the cable system.
- Measurement of cable parameters (coefficient of thermal expansion, effective axial stiffness during a
constrained cable thrust test and effective bending stiffness during a bending test etc.)
• Excluded from the scope are the forces and movements that occur during the installation of the cable and
accessories as well as the designs of the cable, accessory and support structures necessary to withstand
the thermo-mechanical effects.
• For the purpose of this brochure:
- A cable system is defined as the cable, the accessories (joints and terminations) and the installation
design.
- A large conductor is defined as having an area of greater than, or equal to, 1000 mm2
of either copper
or aluminium and of any accepted construction, e.g. stranded circular, segmental circular, solid circular
and stranded segmental circular (Milliken).
2 Introduction
This Technical Brochure is a guide to inform the reader of:
1. The presence of forces that are generated within cable systems having extruded insulation and conductors
of large cross sectional area.
2. The thermo-mechanical forces and movements generated by the thermal expansion and contraction of the
cable.
3. The component parts of the installation designs available to reduce the magnitudes of the cable forces
and/or movements to acceptable limits for the required service life of the cable system. These being:
a. Rigidly constrained cables (buried and close cleated systems).
b. Flexibly constrained cables (snaked and waved cables).
c. Transition sections between rigidly and flexibly constrained cables in the same installation.
d. Duct installations (i.e. semi-flexibly constrained cable within a pipe).
e. Cable cleats.
4. Examples of existing cable installation practices.
5. The formulae and the range of cable mechanical parameters that are available to calculate the magnitudes
of the forces and movements.
6. The test methods that may be used to measure the cable’s thermo-mechanical parameters.
The reader is advised that the design of cable thermo-mechanical installations is a complex subject that is
particular to each cable application. Formulae and mechanical parameters are suggested in this technical brochure
to help the cable installation designer. The cable installation designer is responsible for the choice of the formulae
and parameters suggested in this technical brochure, and for the development of different design approaches,

Page 9
formulae and parameters. The technical brochure also indicates the importance of the execution of experimental
measurements on either representative sample of cable or on real cable installations to confirm the suitability of the
overall design of the installation system.
This brochure reviews, and extends Chapter 4 of TB194, 2001 with respect to extruded insulation cables with large
conductors of 1000mm2
and greater cross-section. The review is performed in the context of:
1. XLPE cable system applications have evolved since 2001 and now have higher system voltages, larger
conductor sizes and new types of metallic sheath.
2. Ten to twenty years of satisfactory service experience has been accumulated with applications of large
conductor XLPE cable systems.
2.1 Findings of the Working Group
The Working Group found that in general:
1. For extruded cables with conductor sizes of 1000 mm
2
and greater, an increased use has been made of:
a. Transition sections between rigid and flexible sections
b. Increased span lengths in vertically waved systems
c. Duct systems in which the duct is air-filled
2. For extruded cables with conductor sizes of 1000 mm
2
and greater the thermo-mechanical equations in
TB 194, Chapter 4 were valid and so, for completeness, are included in this technical brochure together
with their derivations and their applicability are given.
3. For extruded cables with conductor sizes of less than 1000 mm2
either the guidance given in this brochure,
or in TB 194 Chapter 4 may be followed.
4. The following topics should be described in greater detail in this technical brochure as they were
inadequately covered in TB 194, Chapter 4:
a. Transitions between rigid and flexible systems
b. Duct systems, in which the duct is air filled
c. Cable cleats
d. Methods of measuring cable mechanical parameters and examples of published magnitudes of the
parameters.
5. Thermo-mechanical design practices were being followed and in consequence service experience with
large conductor cables with extruded insulation has been good.
A few negative aspects were noted; for example:
1. Cable support structures that had inadequate design and/or strength to restrain cable and accessory
movements, as shown in Figure 1 and Figure 2.
2. A lack of understanding of the design principles, which was manifested in the use of qualitative rather than
quantitative design solutions.
Positive aspects were noted; for example;
• XLPE cables have been demonstrated to be mechanically robust.
• Economic benefits have arisen from the ability of XLPE cables in flexibly sagged and waved systems to be
cleated at significantly wider spacings, thus resulting in fewer cleats and support arms, Figure 3.
• Designs of cable transition sections have been installed in the same application that permit both flexibly
and rigidly constrained XLPE cable sections to be used to advantage.
• The knowledge base has been widened by:
o The development of thermo-mechanical formulae, FEA modelling and the techniques to measure
parameters
o The availability of measured parameters for large conductor XLPE cables.

Page 10
FIGURE 1 THERMO-MECHANICAL MOVEMENT OF CABLES OFF SUPPORT ARMS AT A TUNNEL BEND
FIGURE 2 THERMO-MECHANICAL DISTURBANCE OF A CLEAT AND JOINT IN A MANHOLE
FIGURE 3 THE BENEFIT OF WIDE CLEAT SPACINGS IN A FLEXIBLY SAGGED 400 KV 2500MM2
XLPE CABLE SYSTEM

Page 11
2.2 Categories and Principles of Types of Thermo-mechanical
Installations
This brochure follows the established practice of categorising thermo-mechanical installations by their primary
method of mechanical constraint, devoting one chapter to each:
• Rigid installations: Chapter 3
• Flexible installations: Chapter 4
• Transitions between rigid and flexible systems: Chapter 5
• Duct installations (i.e. at semi-flexible systems): Chapter 6
For each type of thermo-mechanical installation:
• No practical system is completely rigid (i.e. a small transverse movement exists at certain locations)
• No practical system is completely flexible (i.e. a small residual longitudinal force exists)
• Equilibrium always exists in the axial conductor thermo-mechanical forces on either side of any position
along its length.
The principles and formulae for the equilibrium of conductor thermo-mechanical force are given in the 1967 seminal
thermo-mechanical theoretical and experimental work on 82 m sample lengths of 275 kV, 2000 mm2
, lead
sheathed, SCFF, paper insulated cables (3). The Working Group found the theoretical principles to be equally
applicable to extruded insulation cable, but, in view of the significant difference in cable construction, the
parameters are recommended to be particular to the construction of the large conductor extruded cables. For
example:
• In a rigidly waved cable (locking waves) the frictional constraint on the insulated core was provided by the
frictional constraint between the paper insulated core and metallic sheath and by the increased sidewall
pressure due to the capstan effect. In an extruded cable the same mechanism is considered to apply.
In a straight cable the frictional constraining force on the conductor was demonstrated to have been
provided by the combination of friction between the paper tapes and the lapping pressure; this resulted in
the phenomenon of telescopic movement of the tapes. In an extruded cable the core is solid and grips the
conductor and so the frictional constraining force is formed by the coefficient of friction between the
extruded core and the metallic sheath via the various water blocking and cushioning tape layers and the
weight of the cable core.
Force Equilibrium in a Rigid System, Chapter 3
The distributed axial thermal conductor strain, α.∆θ, and the cumulative elongation ∆L = L α.∆ θ are locked-in and
so generate the maximum axial force Fth, as given in Chapter 3, Equations 1, 2 and 3. In a practical system a very
small lateral deflection, for example a small ‘wave’ between cleats, will permit a small proportion of the local,
locked-in, axial strain to be absorbed by the increased length of the ‘wave’. According to Equation 3, the axial force
will then fall locally. Equilibrium, however, must be restored and so a small longitudinal movement of the cable core
from the adjacent cable occurs until the forces are again equal and of high magnitude, (albeit slightly reduced). The
amount of movement is limited by the magnitude of the internal friction force between the extruded cable core and
the metallic sheath.
Force Equilibrium in a Flexible System, Chapter 4
The locked-in distributed axial thermal strain and cumulative elongation are absorbed by the lateral deflection of
trains of waves distributed along the cable for this purpose. However, in a practical flexible system it is not possible
for all of the thermal strain to be absorbed as the waves possess bending stiffness and so create a small axial
reaction force that opposes the thermo-mechanical force. A point of equilibrium is attained at which the two forces
balance and are of low magnitude. If a small imbalance exists in the geometry between two adjacent waves, then

Page 12
one also exists in the resultant axial reaction forces. To restore equilibrium a small movement of the extruded core
within the sheath will occur.
Force Equilibrium in a Transition Section, Chapter 5
In the design of a transition section between a rigid and a flexible section use is made on a larger scale of the
phenomena described above. The design objective is to obtain equilibrium between the elongation of the extruded
core from the end of the rigid cable and the absorption of axial movement by one or more flexible loops (Annex 5).
Typical applications are to i) reduce the magnitude of axial force acting on a cable termination and/or ii) prevent the
magnitude of cumulative thermal elongation from the rigid cable moving uncontrolled into the flexible loop. The core
elongation and the magnitude of force from the rigid cable is reduced by increase the frictional constraining forces
between core and sheath by forming locking waves, according to the capstan principle. The axial absorption of the
flexible loop is increased and its reaction force reduced by increasing the bend angle and bend radius. The design
is considered to be satisfactory when the resultant axial force has achieved the low level set and the resultant core
movement within the sheath is considered to be small enough to be acceptable without incurring risk of damage.
Force Equilibrium in a Duct System, Chapter 6.
In the design of a duct system if the duct diameter is minimised, consistent with the clearance required for
installation, then the lateral deflection of the cable is small and the cable generates a high magnitude of axial thrust
at the manholes. Alternatively, the internal diameter of the duct can be increased to give room for lateral deflection
of the cable and so form thermo-mechanical patterns. The thermo-mechanical patterns are capable of beneficently
absorbing a significant proportion of the locked-in axial thermal strain. The axial force acting on the joints and cable
in the manhole is reduced to a design level that can be withstood by the selected type of constraint system. The
patterns within the duct are likely to comprise lengths of straight cable, sinusoidal formed cable and helically
formed cable. The lengths of the patterns change according to the temperature rise and the particular geometry of
the duct span. Throughout the duct length equilibrium is maintained between the high axial forces in the straight
cable, the low forces in the cable patterns and the frictional forces between the cable and duct walls.
2.3 Input Factors and Effects on Large Conductor Cable Systems
The relevant input factors and effects on large conductor cable systems can be summarised as follows:
1. Temperature, cyclic load, overload
2. Physical properties of the cable – i.e. stiffness, effective modulus etc.
3. Short circuit forces
4. Gravity (weight, e.g. vertical installations)
5. Friction (duct installation)
6. Vibration
7. “Walking” of cable
Items 1 to 5 are considered in detail in the design methods described in this technical brochure. Items 6 and 7 are
relevant to cables installed in air filled ducts and to cables that have a loose metallic sheath. The latter is unusual in
the design of a large conductor cable with extruded insulation. (Reference 5, in Chapters 9 therein, considers the
‘walking’ phenomenon in a duct installation due to traffic induced vibration and Reference 5, Chapter 10 therein,
considers the ‘walking’ phenomenon in a duct installation due to perturbation from short circuit current.)

Page 13
3 Rigid Installations: Theory and Practice
In a rigid installation cables and accessories are fixed in such a way that thermal expansion and contraction do not
lead to significant movements.
A rigid installation is obtained when cables and joints are directly embedded in well compacted ground. The burial
depth needs to be sufficient so that the cable cannot push up the backfill. The conditions of the soil are to be taken
into consideration.
When cables are installed in air, usually a flexible installation is preferred for longer installations. If, for example due
to confined space, a rigid installation is more suitable, the cables should be cleated at short intervals. Joints are to
be rigidly fixed accordingly.
3.1 Forces
During operation the cable will be heated due to the thermal losses produced in the conductor. The temperature
rise will cause longitudinal expansion of the conductor. As the rigid installation prevents significant elongation of the
cable, compressive stress is developed inside the cable. Similarly tensile stress occurs during cooling of the cable.
The mechanical stresses lead to forces acting on the cables, joints, terminations, cleats and support structure.
3.1.1 Calculation
The expansion of the cable depends on the particular construction and temperature distribution inside the cable.
Usually the cable conductor is considered to be the dominant factor. This is because its temperature variation and
elastic modulus are high. This dominance may be different in the case of a small conductor cable with smooth and
thick aluminium sheath. The Working Group has found generally that measured values of axial stiffness, EAeff,
have been published for large conductor XLPE cables complete with their metallic sheaths and oversheaths,
Chapter 9 and Annex 1. The TB 194 [6] method of allowing for different types of metallic sheath is given later in this
Section.
When the expansion is prevented a force in the longitudinal direction is produced which is proportional to the
conductor size and calculated as follows, (1)(2):
l
l
AEF ceffth
∆
⋅=
EQUATION 1
ϑα ∆⋅=
∆
th
l
l
EQUATION 2
ϑα ∆⋅⋅= thceffth AEF
EQUATION 3

Page 14
where
Fth : thermo-mechanical force (kN)
Ac : cross-sectional area of the conductor (mm2
)
Eeff : effective axial modulus of elasticity of the conductor for a particular cable (kN/mm
2
)
EeffAc : effective axial stiffness of the particular conductor for a particular cable (kN)
αth : coefficient of thermal expansion of the conductor (K
-1
)
∆ϑ : temperature difference (K)
l : conductor length (mm)
∆l : change in conductor length (mm)
The effective axial modulus of the conductor, Eeff , depends not only on the material but also on its construction. It
shows different values under compression and under tension and in both cases it is non-linear with temperature
change (see Chapter 3.1.2).
3.1.2 Forces Measured on Cables
In the 1960’s measurements of force were made on SCFF (self-contained, fluid filled cables) with stranded
conductors (3). Values were provided for different conductor cross-sections and temperatures. Tests performed
under service conditions showed that a SCFF 2000 mm² segmental copper conductor cable in a buried condition
can produce a maximum thrust of approximately 60kN when no longitudinal movement is permitted and the rate of
heating is slow. In a more rapidly heated, in-air condition, the same cable can produced a maximum thrust of up to
105kN (3). The working Group has found that with extruded cables, although similar mechanisms apply, the
magnitudes of force given in Chapter 9 and Annex 1 are not identical to those reported for SCFF cables.
A typical curve illustrating the non-linear relation between conductor force and temperature during initial heating is
shown in Figure 4.
FIGURE 4 THERMO-MECHANICAL FORCES FOR LARGE STRANDED CONDUCTORS VS. TEMPERATURE

Page 15
At the initial start of temperature rise the force exerted by the cable with stranded conductor follows an almost
linear behaviour (line B in Figure 4).
If temperature rise is rapid (i.e. <10hrs to Tmax) then the force will continue to rise at this rate. This force is
significantly smaller than with a rigid bar having the same cross section (line A). The difference depends on the
particular conductor design (stranding effect, compactness, length of lay, etc.). In an in-air application the heating
time is determined by the thermal capacitance of the cable and thermal resistance of the cable and the heat
transfer to the air. In this application high current ratings are possible and so the rate of heating to the rated
temperature is likely to be short (for example 8-10hours, which is thermal time typical temperature time constant of
the cable itself).
In a buried application the surrounding ground increases the thermal resistance and capacitance. In this application
current ratings are lower and hence the rate of heating to the operating temperature is much lower (for example
100-250hours). In determining the thermo-mechanical force it is important that the rate of heating is representative
of that in the particular service application as the magnitude of the thrust developed in an in-air application (line B)
is likely to be higher than in a buried application (line C). Here, the thermal time constant depends on the
environment together with the cable thermal time constant, which is in total much longer than the cable’s thermal
time constant.
At the slower rate of heating typical for a buried cable, the force in the cable is likely to follow the curve in line C
with a peak force possibly occurring before reaching maximum temperature (3). This is because the rate of heating
is so slow that the relaxation effect occurs. The difference between line B and line C is therefore attributed to the
relaxation of the conductor metal (i.e. the creep and reduction in length under compressive load over time).
As the relaxation results in a shortening of cable length, the cable will develop tensile forces on cooling to ambient
temperature as shown in line D in Figure 5. With repeated load cycles, the cable temperature varies cyclically about
a mean operating temperature which is likely to result in forces almost equal to zero at the mean cyclic temperature
(TC mean). Examples of the reduction of force during load cycling are given in Section 9.2 and Annex 1. When
selecting an ‘effective’ EAeff value for thermo-mechanical design, the conductor relaxation behaviour should be
taken into account.
FIGURE 5 LONG TERM RELAXATION OF CABLE DUE TO REPEATED CYCLIC LOADING
B/C : Conductor heated to max
temperature on first
energisation (slow or rapid
heating)
D : Return to ambient temperature
after first load cycle
E : Simplistic Model of cable at
equilibrium during repeated
cyclic loading

Page 16
Figure 6 and Figure 7 below shows the determination of EAeff from the Force v Temperature graphs from a typical
buried cable (slow heating) and a typical cable in air (rapid heating).
The value of EAeff is obtained from the slope ∆
in either Figure 6 or Figure 7:
∆
= EA .α, thus EA . = ∆
.
FIGURE 6 THERMO-MECHANICAL FORCES FOR BURIED (SLOW HEATING) LARGE STRANDED CONDUCTORS VS TEMPERATURE
FIGURE 7 THERMO-MECHANICAL FORCES FOR IN-AIR (RAPID HEATING) LARGE STRANDED CONDUCTORS VS. TEMPERATURE
X : Stranded Conductor
heated rapidly(rate
similar to in-service
heating rate for cable in
air)
Y : Simplified model
EAeff to peak force

Page 17
The maximum force should be taken when designing a cable system. Determination of EAeff for a cable system
design would ideally be derived from experiment and using a rate of heating representative of the in-service
application (e.g. 8-10hrs for in-air and 100-250hrs for buried), and using the same, or a similar construction cable.
This would provide curve P as shown in Figure 6 and X in Figure 7. For the particular application it is assumed that,
during the first heating cycle, the cable will reach its maximum design temperature (for example 90°C). In this case
the thermo-mechanical design is based on the maximum possible compressive force that can be generated in the
conductor. Using the experimental results then simplified models of EAeff can be determined (lines R and Y in
Figure 6 and Figure 7. For information, typical measured values of Eeff and EAeff for large conductor cables heated
using either a slow rate or rapid rate of temperature rise are given in Chapter 9 and Annex 1 of this brochure.
Whilst it is recommended that experimental testing on the cable is carried out to determine a value for Eeff it is
acknowledged that this is not always feasible. An approximation of Eeff can be taken from experimental values
measured on a similar cable with a different cross-sectional area and multiplied by the particular conductor area to
determine thrust. For example, the practice in Japan is to derive the value of EAeff from a simplified linear model of
experimental results i.e. to construct the line R in Figure 6 and Y in Figure 7. As part of an industry initiative
Japanese manufacturers measured the values of EAeff for different constructions of large conductor XLPE cable
and then agreed a common value for thermo-mechanical design. These values are given in Chapter 9 for
information.
When it is known with some certainty that the cable system will not reach its maximum design temperature after
first energisation, but has time to relax in service at a low level of loading that is gradually increased with time then
a reduced maximum thrust can be used. In this case, the maximum load will be reduced to between that shown in
curves B/C and E in Figure 5.
Relaxation coefficients are given in CIGRE TB194 and are based upon the assumption that it is unusual for a newly
installed cable to carry full load immediately and that load growth is usually gradual and cyclic. Suggested
relaxation coefficients based on self-contained fluid filled paper insulated cables are given in TB194 to allow for the
lower maximum values of thrust developed in this approach. This design approach would not be suitable for
application to, for example, a generator feeder cable that is expected to operate immediately upon energisation at a
high sustained load, or to circuits in which the magnitude of the load pattern is uncertain.
The total thrust generated by the cable is the combination of the thrust generated by the single components of the
cable, therefore the thrust F should be calculated for each layer. In many practical cases the thrust F is calculated
only for the conductor and the metallic sheath since the contribution of the other layers of the cable is generally
negligible. The impact of the metallic sheath depends on detail installation conditions and friction between metallic
sheath and cable core.
To use this relaxation approach, an EAeff value (Line Y, Figure 7) is derived experimentally from rapidly
heating( <10hrs) the large conductor extruded cable. This gives the linear reference value of the axial modulus Eeff
(the Equivalent Young’s Modulus referred to in TB194) for the particular stranded conductor with no creep
relaxation present. The thrust with relaxation present can then be estimated using Equation 4 below –
ϑα ∆⋅⋅= thceffth AEKF .
EQUATION 4
WHERE
EeffAc: axial stiffness at the 1st load cycle
∆ϑ: increase in temperature
αth: coefficient of thermal expansion of the material taken from measured values
K: relaxation coefficient
TB194 provides some indications on the possible values of K. However, a different value of K may be selected and
chosen for large conductor extruded cables during the design phase to take into consideration various aspects
such as the load pattern of the circuit, specific design requirements and the actual thermo-mechanical behaviour of

Page 18
the cable based on the cable manufacturer’s service and test experiences. For example in the case in which a
cable circuit is designed to rapidly reach the maximum cable design temperature in the 1st load cycle then the
value of K should be close or equal to 1. CIGRE TB194 gives the following suggested values of relaxation
coefficients:
To be applied to the conductor thrust:
• K1 is given to be ‘of the order of 0.75 for conductor load temperature variation, depending on cable
constructions’
• K2 is given to be ‘of the order of 0.45 for conductor ambient temperature variations where applicable,
depending on cable constructions’.
To be applied to the sheath thrust:
• K3 is given to be ‘of the order of 0.30 for lead sheaths, and of the order of 0.65 for aluminium sheaths for
load temperature variation, depending on cable constructions’.
• K4 is given for sheath ambient temperature variations to be ‘of the order of 0.10 for lead sheaths, and of
the order of 0.45 for aluminium sheaths.
It should be noted that the relaxation coefficients given in CIGRE TB194 were derived from measurements on
SCFF cables and should only be considered in the absence of a measured value for large conductor extruded
cables, or well established experience.
It is of note that with a relaxed cable, a tensile force of significant magnitude is produced in the conductor upon
cooling back to the installation temperature.
Examples in the determination of Eeff and cable forces Fth are given below:
Example 1
Experimental tests were carried out on a 2500mm2
stranded copper conductors, cylindrical aluminium sheath cable.
The sample was heated from 20°C to 90°C over a period over 8 hours representing the cable in an in-air
application. A maximum force of 80kN was measured. In separate tests, the coefficient of expansion for the cable
was determined to be 18.3·10-6
K-1
. The effective axial modulus for the cable is calculated to be –
ϑα ∆⋅⋅= th
c
eff
A
F
E
Therefore Eeff =25kN/mm2
for this particular cable construction in an in-air application and maximum force F=80kN
as measured experimentally.
Example 2
A cable of a similar construction to that in Example 1 and also laid in-air but with a cross-sectional area of
2000mm
2
instead of 2500mm
2
. Using the experimental data for Example 1 Eeff is taken to be 25kN/mm
2
. The
equivalent value of EAeff can therefore be calculated as 50MN. The equivalent maximum thrust for a conductor
temperature rise from 20°C to 90°C is 64kN.
Example 3
The same cable in Example 1 is to be laid in the ground and is known for certain that, although it will be heated by
loading, it will not have to operate at its maximum design temperature for the first 6 months of load cycles. In this
case it is possible to assume that the cable will have time to relax in service. The Eeff can be taken from the
experimental results as 25kN/mm2
. The ambient temperature variation is taken to be negligible as the cable is
buried. A relaxation coefficient for the conductor thrust of 0.75 is considered appropriate in the absence of other
experimentally derived values therefore –

Page 19
kN
K
Kmm
mm
kN
FEAKF theff 60
1
103.187025002575.0 62
2
=⋅⋅⋅⋅⋅=→∆⋅⋅⋅= −
ϑα
Therefore the calculated relaxed maximum thrust F is taken as 60kN.
3.1.3 Cable Fixing
Cables in air require appropriate fixing to form a rigid system. This means that cable cleats are to be arranged at
comparatively short intervals to hold the cable similar to buried conditions.
Short-circuit forces and permissible deflections caused by such forces are decisive in determining the cleating
distance of single-core cables. This is especially valid for smaller cables which are usually less rigid.
When short-circuit loads are low, it is advisable to consider preventing potential buckling of the cable length
between cleats due to thermo-mechanical stress. The buckling length is identical to the length between cleats,
Figure 8. Euler’s buckling theory is used to calculate the force needed to initiate buckling Equation 5:
2
2
4
k
eff
l
EI
F
⋅
≥
π
EQUATION 5
where
F : longitudinal force
E Ieff : bending stiffness of cable
lk : “buckling length”
l1 : length of cable between cleats
FIGURE 8 BUCKLING OF A RIGID CABLE SPAN BETWEEN CLEATS DUE TO LONGITUDINAL FORCE
F
l1=lk

Page 20
The product EIeff is named effective ‘bending stiffness’ or ‘flexural rigidity and is composed of the different layers of
the cable each of which provide significant resistance to bending. The bending stiffness can be calculated for the
different components and the individual values are added to obtain a value for the complete cable. It is important to
note that the bending stiffness of the cable will vary depending on the curvature and temperature of the cable.
While it is easy to calculate values for components of solid and simple structure, it is difficult to calculate correct
values for stranded or corrugated layers. Approximations are provided in (7) for example. More accurate values for
the cable’s bending stiffness can be obtained by measurements.
For a straight, rigid HV/EHV large diameter cable with metallic sheath and high density polythene oversheath, the
cable bending stiffness will be dominated by the sheaths effective bending stiffness.
The maximum cleat spacing is obtained from equation:
F
EI
s
l effπ2
1 ≤
EQUATION 6
Where F is obtained from Equation 3 and s is a factor of safety with a typical value of 2.
EIeff is the effective bending stiffness of the cable. It should be noted that the value of Eeff for the stranded conductor
in bending is not the same as that derived for the axial modulus in item 3.1.2. The value of Eeff for the sheath and
oversheath in bending can be taken as the Young’s modulus for the materials at the cable rated operating
temperature. In the case of sheath that has been corrugated to increase its bending flexibility, lower values of Eeff
would be expected. (e.g. 25-40% of a rigid smooth sheath). Examples of bending stiffness values obtained by
experiment are shown in chapter 9.2 and Annex 1.
3.2 Practical Examples for Rigid Applications
A: Rigid installations in shafts and tunnels (air installations)
A rigid installation in a straight vertical shaft is shown in Figure 9. Here, the cleats spacing is approximately 1.5 m.
Cleat designs and applications are described in Chapter 8. The distance between the cleats is determined from:
1. The Euler buckling theorem, Equation 6, and depends on the bending stiffness EIeff of the cable.
2. The short circuit forces per metre length and depends upon the magnitude of the peak current and the
spacing between the cables.
3. The vertical support of the cable and depends upon the weight of the cable to be supported vertically.
In this application the cleats have:
1. A guide requirement to hold the cable spans in straight axial alignment.
2. A lateral requirement to withstand the short circuit force.
3. An axial requirement to hold the weight of the cable. In consequence there will be a small downwards axial
deflection of the cleat liner.

Page 21
Figure 9 shows rigidly cleated straight runs of cable in a vertical shaft. The cleat support structure is designed to
withstand the combined forces from all the cables. In this case there are more than three cables.
FIGURE 9 500 KV XLPE CABLE IN A STRAIGHT RIGID INSTALLATION IN A VERTICAL SHAFT
Figure 10 shows the rigidly cleated transition at the upper end of a vertical shaft and the reduced cleat spacing.
The span between each cleat is curved and this reduces the Euler critical buckling length. The Euler length is
reduced by an empirical multiplication factor, e.g. 0.6. The curved cable spans will exhibit a slight lateral flex
between the cleats under axial thermo-mechanical load, it is important to check that the bending radius and the
cyclic strain in the metallic sheath (radial water barrier) are within the cable manufacturer’s limits.
FIGURE 10 500 KV RIGIDLY CLEATED BENDS AT THE UPPER END OF A VERTICAL SHAFT
B: Buried installations
Figure 11 shows a typical arrangement for a buried cable installation. A buried cable installation can be considered
rigid if the laying depth is sufficient to hold the cable lateral (i.e. vertical and horizontal) thermo-mechanical forces
by the weight, type, and compaction of the backfill materials above. Large conductor, high voltage cables are
usually backfilled with stabilised backfill materials that maintain the required value of thermal resistivity when dried
out. Such materials may be, for example, cement bound sand (CBS), cement bearing fluidised thermal backfill
(FTB) or stabilised high compaction sand. These materials generally have a higher density and a higher degree of
structural load bearing rigidity than that of the surrounding indigenous soil. The minimum depth of burial is normally
set by other considerations than thermo-mechanical forces, such as local regulations for depths under roads,
walkways and farmland. The minimum known depth is 900 mm, but may extend to greater than 1200 mm. No

Page 22
cases of thermo-mechanical disturbance have been reported at these depths with thermally stabilised backfill
materials in typical, non-waterlogged, load-bearing ground.
FIGURE 11 TYPICAL TRENCH CROSS-SECTION FOR BURIED CABLE
Joints in a rigid buried system may require to be protected from disturbance by longitudinal thermo-mechanical
forces. Figure 12 shows a project in which the supplier chose to reduce the axial force acting on the joints by
installing the cables with vertical snaking (‘blocking bends’) before and after each joint. Refer to Chapter 5.1 for
more information on transition sections.
FIGURE 12 CABLE LOCKING BENDS INSTALLED ADJACENT TO A JOINT BAY
Isolated cases of thermo-mechanical disturbance have occurred with rigidly constrained cables installed in:
1. Filled surface concrete troughs in which the vertical component of thermo-mechanical axial thrust has
lifted the weight of the backfill and concrete lid. It is good practice to ensure that the weight of the backfill
and lids and in some cases the trough himself is sufficient to hold the cable up-thrust. If the weight is
insufficient then the lids should be mechanically clamped to the trough by straps or other suitable means
or the cable clamped to the floor of the trough. The up-thrust force per metre length may be calculated
from Equation 7. It is of note that, if the cable starts to lift the trough at a particular point, the radius of the
bend is reduced, the force is increased and the lifting is accelerated. Even in a horizontal route some
undulations will be present in the cable and so it is advisable to design for the presence of a ‘fictitious’
bending radius to suit the bending characteristics of the particular cable and trough route.
R
F
FL =
EQUATION 7
Laying
depth

Page 23
Where
FL : cable thermo-mechanical lateral (radial) force per unit length
F : cable thermo-mechanical axial force from Equation 3
R : local radius in the slope elevation of the cable, as installed
2. Horizontal lateral disturbance can occur to adjacent underground structures such as the basement of walls
in a substation. The magnitude of the horizontal thrust per metre length may be calculated by inserting the
radius R of the horizontal, plan-view bend in the Equation 7. A suitable thrust block or other civil
engineering structure can then be designed to withstand this thrust.
3. Poor load bearing ground (water logged, sand, peat etc) in which the cable thermal expansion in
combination with ground subsidence has moved joints out of alignment incurring risk of disturbance to the
outer joint box electrical insulation and to the conductor primary insulation. It is good practice to:
a. Support the joint and adjacent cable such that the interface between cable and joint is protected and
disturbance prevented by, for example:
i. Cleating the joint and adjacent cable to a frame on a concrete floor, Figure 13
ii. Supporting the joint and adjacent cables with a suitable and stable concrete floor.
b. Provide an offset cable bend adjacent to the joint bay that is capable of absorbing some of the cable’s
thermal expansion, thereby reducing the magnitude of the axial thrust acting on the joint, Figure 14
FIGURE 13 JOINTS AND CABLE CLAMPED TO A CONCRETE PAD; 400 KV 1200 MM2
XLPE CABLE DENMARK
Figure 14 Horizontal cable waves adjacent to joint bay; 400 kV 1200 mm
2
XLPE cable Denmark

Page 24
4 Flexible Installations: Theory and Practice
Two approaches are described to design flexible installations:
- Western approach
- Japanese approach
Both approaches employ similar principles and are described in detailed.
4.1 Flexible Systems (Western Approach)
Flexible cable systems are those that allow the cable to expand thermally in length by deflecting laterally and to
return to the original formation on cooling. In order to control the movement of the cable within pre-determined
limits it is usually installed in an approximate sinusoidal formation. Cleats are positioned at appropriate intervals so
that expansion takes place by an increase in the amplitude in each loop of the sine wave. As the flexible system
allows cable expansion to take place it is not characterised by the high values of thrust that occur in the rigidly
restrained system.
The cable possesses bending stiffness and so the thermo-mechanical axial force is not reduced to zero, but to a
small residual magnitude.
To ensure that cable expansion does not move from one flexible wave to another it is important to achieve uniform
wave geometry by:
1. Locating the cable wave fixing points, which are usually cleats, at a constant spacing along the route.
2. Setting constant wave amplitude (the offset) in each cable wave.
If the wave geometry is uniform:
1. The cable is placed in a low compressive force.
2. The forces on the cleat will be of equal and opposite magnitude.
3. There will be no longitudinal cable movement between wave spans.
The limited force difference generated by geometrical imbalance between adjacent waves may be restrained by the
holding force of a cleat, if deemed necessary for the design of the cable system.
If there is a significant geometrical imbalance between wave geometry, for example at a point of significant
transition in the route geometry:
1. The axial cable forces acting on the cleat and its support fixings may be of different magnitude.
2. The cable fixing should be designed to withstand the difference in force. This may require a cleat of slightly
higher axial holding strength (a clamping cleat), a cleat of high holding strength (an anchoring cleat), or a
locking wave (blocking wave) to reduce longitudinal expansion.

Page 25
Case A: Cables cleated with movement in a vertical plane
Figure 15 shows a flexible system of the vertically sagged type. The cable is held in widely spaced cleats with an
initial sag fo, which increases with temperature rise. The sag is selected to ensure satisfactory expansion and
contraction movement. In a vertically sagged system, Figure 15, the deflection fo is measured from the top of the
cable and is the total lateral sag of the system. The length l between the cleats is the wavelength of the sag.
FIGURE 15 VERTICALLY SAGGED FLEXIBLE CABLE SYSTEM
The spacing of the cleats l is not critical and, within the limits given below, can be chosen to suit the fixings
available. The weight of the cable is supported by the cleat. If the cleat spacing is too large, the side pressure on
the cable at the cleat will become excessive and there will be a tendency to concentrate bending at the edge of the
cleat. On the assumption that the cleat length is approximately equal to the cable diameter De and has suitably
rounded edges the following practical rule is suggested:
W
D
l e
65
2
≤
EQUATION 8
where:
l : cleat spacing (m)
W : specific cable weight (kg/m)
De : cable outside diameter (mm)
Having determined the cleat spacing l it is necessary to fix the value of fo, the initial sag between cleats. Experience
with large conductor XLPE insulated cables has shown that the deflection fo can be reduced below the criterion
given in CIGRE TB 194, 2001, page 79 [6].
Table 4 in Item 4.3 shows examples of the sag fo for large XLPE cables to be in the range of 1.3-2 De. This
supersedes the previous recommendation in TB 194 that the sag fo be set to be greater than 5 times the natural
deflection δ to avoid concentration of stress on the metal sheath adjacent to the cleat. It is noted that the TB 194
design practices for sagged systems evolved with the fluid filled paper insulated cable, the original deigns of which
were provided with heavy, pressure retaining, reinforced lead sheaths. Modern large conductor XLPE cables that

Page 26
are installed in-air in tunnels have lighter weight metallic aluminium water barriers for example i) foil laminates with
stranded copper shield conductors, ii) welded thin wall cylindrical plain or corrugated sheaths or iii) extruded thicker
wall corrugated sheaths.
It should be checked that concentrated cable deflection due to its own weight is absent at the edge of the cleat.
Saddle cleats may be of assistance.
The value of fo should be checked to ensure that the change of strain in the sheath due to thermal cycling does not
exceed the maximum imposed by the fatigue properties of the metallic sheath.
As described in Annex 3 the calculation of the sheath strain assumes that the longitudinal expansion of the
complete cable follows the expansion of the conductor. The total sheath strain is then the sum of the absolute
values of the strain due to the movement of the cable together with the strain due to the differential expansion of
the conductor and the sheath. On this basis it can be shown that the maximum sheath strain change ∆εmax will not
be exceeded provided:
sscc
scc
TT
DT
f
∆−∆−∆
∆
≥
ααε
α
max
0
2
EQUATION 9
where:
fo : minimum initial sag (m)
αc : coefficient of thermal expansion of the conductor (1/K)
∆Tc : daily cyclic temperature rise of the conductor (K)
αs : coefficient of the thermal expansion of the sheath (1/K)
∆Ts : daily temperature rise of the sheath (K)
Ds : outside diameter of the metal sheath
(or average outside diameter for a corrugated sheath) (m)
∆εmax : maximum allowable sheath strain change due to daily load cycles.
Taking into account many years of excellent service experience with extruded cables, slightly less conservative
values can be considered for ∆ε such as 0.35% for aluminium and 0.12% for lead alloy.
The flexibly sagged system described above is suitable for straight or gently curved cable routes. When it becomes
necessary to install the cable around a bend of small radius in the route, the cable loop should be supported on a
horizontal plane within the bend with suitable means of minimising friction when the cable slides laterally to
accommodate thermal expansion.

Page 27
Sag calculation
The additional sag caused by the temperature increase is calculated using the CIGRE TB194 formula. In the
following section, this formula is derived by first considering the axial expansion of the cable:
The initial sinusoidal arc length larc of the cable between the clamps can be calculated Equation 10 (Heinhold, [4])
using the following simplification of the arc length of a sine wave, which is sufficiently accurate for fo/l ratios < 0.1:














+⋅=
2
0
2
1
l
f
llarc
π
EQUATION 10
where:
larc : arc length of the cable between cleats (m)
l : distance between clamps (m)
fo : initial sag of the cable between cleats (m)
The increased arc length at higher conductor temperatures is given by:
[ ]T
l
f
llarc ∆+⋅














+⋅= α
π
1
2
1
2
0
EQUATION 11
where:
α : effective coefficient of expansion of the cable (K
-1
)
∆T : difference between conductor and installation temperatures (K)
Measurements on installed vertically sagged system show that the effective thermal expansion depends on the
design details of the conductor and sheath. It was shown that the theoretical equations and parameters given in
this brochure are on the safe side i.e. the measured sag fi was less than calculated.
The sag fi changes with conductor temperature variation, both increasing and decreasing. The geometry of the
sagged waveform and its clearances to the tunnel must allow all possible movements including those during high
short circuit conductor temperatures and low ambient temperatures when off-load.
The sag can be calculated from the different arc lengths by Equation 12, which is derived from Equation 10. (see
also Annex 2). The formula is identical to that in CIGRE TB 194:
1
2
−=
l
ll
f i
i
π
EQUATION 12

Page 28
where
fi : sag at increased temperature (m)
li : arc length from Equation 11 at increased temperature (m)
Special attention should be taken in cases where in-service temperatures are lower than the cable installation
temperature. This leads to a “negative sag”, i.e. a sag fi < f0 , which must be compensated by selecting a larger
initial installation sag f0.
Case B: Flexible system with cable movement in a horizontal plane
In this type of installation the cables are arranged in a sinusoidal waved formation in a horizontal plane with cleats
fixed at the points of flexure of these sinusoids, as shown in Figure 17. In a horizontally waved system the
deflection fo is measured from the centre axis to the centre of the cable at the wave peak. It should be noted that
here fo is half of the total deflection in a vertically sagged system, Figure 15. Here, the length l between the cleats
is half of the wavelength of the vertically sagged system.
Swivelling cleats may be used, capable of rotating on a vertical axis as the cable moves, but it is preferred to use
fixed cleats with a length approximately equal to the cable diameter and having a rubber lining of about 3 to 5 mm
thickness.
FIGURE 16 HORIZONTALLY WAVED FLEXIBLE CABLE SYSTEM
It is essential that the cable should be supported so that it moves only in the horizontal plane on a low friction
support, whilst allowing adequate air movement around the cable to avoid de-rating. The cleats should be installed
at an angle appropriate to the shape of the sine wave. The movement of the cable due to thermal cycles will be
largely influenced by the friction between the outside surface of the cable and the support between cleats.
As a practical rule the cleat spacing should be approximately:
eDl 50=
EQUATION 13
where:
l : cleat spacing (mm)
De : outside diameter of the cable (mm)
The initial deflection of the cable fo should be determined using the same rules as given in Case A for cable moving
in a vertical plane.

Page 29
Calculation of cable thrust:
As already mentioned, the cable thermal expansion in both vertical and horizontal flexible configurations gives rise
to a small axial thrust F when the cable is heated.
Simple formulae can be used to calculate these parameters, which assume that the initial configuration is a
sinusoid. With reference to flexible systems with movement in the vertical plane (from Annex 2) the deflection f is
given by the formula,
2
2
2
0
4
π
α lT
ff cc ∆
+=
EQUATION 14
Where the symbols are the same to the one used before.
Equation 14 is identical to the Japanese approach given in Item 4.2.
The axial thrust F generated in one wavelength of a vertical sag, where l is the distance between two cleats is
given by the formula below (for derivation see Annex 2)
f
ff
l
EI
F
eff 0
2
2
4 −
⋅=
π
EQUATION 15
With reference to flexible systems with movement in the horizontal plane, where l is the distance between two
fastening clamps (a half wavelength) the thrust can be calculated:
f
ff
l
EI
F
eff 0
2
2
−
⋅=
π
EQUATION 16
It is easily verified that the axial thrust in a flexible system, Equation 15, is much lower than in a rigid system,
Equation 3. However, it is important to check that the cleats and other fixings have sufficient holding strength to
withstand any force imbalance that may be present due to geometric variations in normal spans and in particular
imbalance at a transition region.

Page 30
4.2 Flexible Installations (Japanese Approach)
The vertical and horizontal snaked and designs are described under Case A and Case B below:
Case A: Japanese Approach: Cables cleated with movement in a vertical plane
Vertically sagged system
The basic dimensions are shown in Figure 18.
B: Initial snake width: 1⋅De or more
2L: Wave length: snake pitch
FIGURE 17 VERTICAL SNAKING: DEFINITION OF DIMENSIONS
The lateral thermal displacement n is shown in Figure 18 and given in Equation 17:
BlLBn −∆+= 8.022
EQUATION 17
FIGURE 18 VERTICAL SNAKING: LATERAL DEFLECTION AND FORCES, W=CABLE WEIGHT/M

Page 31
Vertical Snaking: Formulas for axial and vertical forces
Figure 19 shows i) the cable axial force Fa due to the cable expansion and ii) the vertical reaction force on the cleat
due to the cable weight.
From the same viewpoint as horizontal snaking installations, the formulas for axial force Fa in Table 1 are used for
cables with or without metal sheaths:
TABLE 1 VERTICAL SNAKING: AXIAL FORCE FA
Here, the maximum cable radial surface pressure at the cleat due to the cable weight (4.W.RӨ) is limited to
≤ 3.33 kg/cm² (3.33 bar).
At the end section of vertically snaked installation the necessary number (N) of terminal fastening cleats is
generally determined as follows:
N = Fa/F + 1 (or Fa/F · Sf)
EQUATION 18
Where:
F : Restraining force of terminal fastening cleats
Sf : Safety factor (typically 1.5)
Middle section of vertically snaked installation:
The cable is supported by direct cable rests (saddle) at crests of the vertical snaking. In some installations,
restraining cleats are used at every several pitches.

Page 32
Case B: Japanese Approach: Cables cleated with snaking movement in a horizontal plane
Horizontally waved system
The basic dimensions are shown in Figure 20:
FIGURE 19 HORIZONTAL SNAKING: DIMENSIONS
The following design rules are applied
Initial snaking width B: 1⋅De or more (equals initial sag for horizontal installations)
Wave length (2 L): 6-9 m
Occupied width (W):
W = D + B + n + σ
EQUATION 19
Where
D : Cable occupied width (= outside diameter of the cable De, 2De when trefoil installation)
B : Initial snake width
n : Total lateral snake displacement due to thermal expansion (n/2 at each wave crest)
σ : Tolerance
The total lateral displacement n due to thermal expansion (n/2 at each peak) is shown in Figure 21 and given in
Equation 20:
BlLBn −∆+= 8.022
EQUATION 20
Where:
∆l : Cable expansion = α ⋅ ∆T ⋅L
α : Coefficient of linear cable expansion of cable
∆T : Temperature rise
(this formula is identical to the Western approach)

Page 33
FIGURE 20 HORIZONTAL SNAKING: FORCES
Horizontal Snaking: Formulas for axial and vertical forces
Figure 21 shows i) the cable axial force Fa due to the cable expansion and ii) the horizontal friction force on the
cable lateral slide supports due to the cable weight.
From the same viewpoint as vertical snaking installations, the formulas for axial force Fa in Table 2 are used for
cables with or without metal sheaths:
TABLE 2 VERTICAL HORIZONTAL SNAKING: AXIAL FORCE FA
Table 2 legend:
Low temperature: no load (ambient temperature),
High temperature: on load (operation temperature)
Without metal sheath: thin laminated sheath (50µm foil)
+ ve: tensile force
- ve: compressive force
Where:
EI : Cable bending stiffness
w : Unit cable weight
µ : Coefficient of friction between cable and lateral slide supports

Page 34
Horizontal snaking installation: End section
The necessary number (N) of fastening cleats is generally determined as follows:
N = Fa/F + 1 (or Fa/F ⋅ Sf)
EQUATION 21
where:
Fa : Cable axial force
F : Restraining force of cable terminal clamping cleats
Sf : Safety factor (typically 1.5)
Horizontal snaking installation: Middle section
The snake formation is fastened at every inflection points to keep the shape. At certain intervals of pitch length
clamping cleats are installed with guiding cleats in between as shown in the diagram.
Vertical Installation Design
Vertical installations that are used in shafts and up towers can generally be classified as listed in Table 3:
TABLE 3 VERTICAL CABLE INSTALLATIONS IN SHAFTS

Page 35
4.3 Practices of Flexible Installations in Tunnels
In the case of cable in flexible sagged (festooned) and horizontally waved systems) the cable thrust is significant
lower (one order of magnitude) than generated in a rigid system.
Vertically Sagged Systems
Examples of the dimensions of flexible, vertically sagged systems of large conductor XLPE insulated cables that
were installed by European manufactures in tunnels are given in Table 4.
TABLE 4 OVERVIEW OF TYPICAL FLEXIBLE INSTALLATIONS IN TUNNELS FROM EUROPEAN AND ASIAN MANUFACTURERS
Voltage/
Conductor Cross
Section Area
400kV/
1600mm²
400kV/
1600mm²
400kV/
2500mm²
400kV/
2500mm²
345kV/
2500mm²
trefoil
400kV/
2500mm2
275kV /
2500mm2
Type of Sheath
Laminated
foil/copper
wire Screen
Corrugated
aluminium
Laminated
foil/copper
wire screen
Smooth
aluminium-
welded
Laminated
foil/copper
wire Screen
Smooth
aluminium
welded
Corrugated
stainless steel/
copper wire
screen
Cable diameter
De/mm
136 150 143 132 141 143 159
Cable weight
W/kg/m
26 27 40 37 40 37 43
Initial sag
fo,/mm
175 225 225 200 225 250 250
Saddle distance
l/m
7.8 7.8 8.4 8.7 5.3 8.4 4.5
Sag/diameter
fo/De
1.3 1.5 1.5 1.5 1.3 1.75 1.6
Measurements on qualification loops demonstrate that the sag is generally in line with the theoretical calculations,
but on the safe side.
Measurements on two installed 400kV 1600mm2
extruded cables in vertically sagged systems show that the
effective thermal expansion is influenced by the design details of the conductor and sheath.
Figure 21, left, shows a 400kV 2500mm2
vertically sagged system with saddle cleats spaced at 8.4 m. The saddle
has a specially shaped geometry to prevent concentrated and excessive cyclic strain being applied to the cable
sheath. The individual phase cables are clamped together mid-span by short circuit straps to prevent the cables
flying apart under high short circuit forces. For some applications full size short circuit tests have been performed to
demonstrate the mechanical strength of the particular combination of cable, saddle cleats, short-circuit straps and
support metalwork.
Figure 21, right, shows the same vertically sagged system at a position where a small radius change occurs in the
tunnel route direction. Four closely spaced cleats and associated support metalwork hold the cable in a laterally
curved alignment with no sag. The two end cleats are saddle cleats that support the cable in the long spans. The

Page 36
two central cleats are guide/clamping cleats that hold the cable in rigid alignment around the bend. The additional
thermal expansion from the short rigid length of cable is absorbed by and added to the expansion of the two
adjacent flexible spans.
FIGURE 21 400KV 2500MM2
XLPE CABLE IN A VERTICALLY SAGGED SYSTEM
Figure 22 shows three groups of 220 kV 1600mm
2
XLPE cable in close trefoil formation installed in a vertically
sagged system. The use of the trefoil formation has permitted three groups of nine 1600 mm2
cables to be installed
in comparison to one group of three 2500 mm2
cables as shown in Figure 21. The advantage of vertical spacing
compared to trefoil spacing is that the heat dissipation to the surrounding air is improved.
The trefoil saddle cleats support and protect the long cable span during load cycling and also clamp the cables
together to withstand the short circuit repulsive forces. Short circuit straps to hold the cables together mid-span
have also been used. To the right of the photograph the top two trefoil cable groups can be seen to have been
transposed.
XLPE CABLE IN A VERTICALLY SAGGED SYSTEM IN TREFOIL FORMATION
Figure 23 shows up to sixteen trefoil cable groups in a tunnel in France. Most if not all of the circuits are in vertically
sagged trefoil formation vertically. The cable spans are not fixed by cleats but are suspended by straps. Non
suspension short circuit straps are fitted mid-span. These cables are of comparatively small conductor size. A

Page 37
tunnel containing this concentration of circuits would require to be cooled by air ventilation and perhaps with the
assistance of water chilling to ensure that the cable operating temperatures and the thermo-mechanical forces and
movements are within the design limits.
FIGURE 23 CABLES HUNG ON STRAPS IN A VERTICAL SAGGED SYSTEM IN FRANCE
Figure 24, left, shows two groups of 345 kV cable in trefoil formation and a joint position. As shown in Table 4 this
installation has a shorter span between the support cleats. The cables in each trefoil group are bound together by
close spaced short circuit straps.
Figure 24, right, shows the joints in the top group of cables. Each cable is seen to rise up to its jointing position and
then descend back to rejoin the group of cables. The three cables in the bottom group pass below. It is usual to
keep the length of rigidly cleated cable straight cable to a minimum to both reduce the magnitude of the thermo-
mechanical axial force on the joints, cleats and support metalwork and to reduce the amount of additional thermal
expansion that the adjacent flexible vertical spans are required to absorb.
XLPE CABLE AND JOINTS IN A VERTICALLY SAGGED TREFOIL FORMATION
The diagram in Figure 25 shows a ‘joint bay’ in a 500 kV 2500 mm
2
XLPE trefoil cable system that is vertically
sagged. The cables in the adjacent sagged spans are bound together mid span with four short-circuit straps in

Page 38
addition to the cleats. Each of the cables rises in turn to its joint and then descends to rejoin the group. It is seen
that the cables are transposed, that is they do not return to their original position in the trefoil group. This facilitates
the use of special bonding of the metallic sheaths and the balancing of the impedances of each phase.
FIGURE 25 DIAGRAM OF 500KV 2500MM2
XLPE CABLE AND JOINTS IN A VERTICALLY SAGGED SYSTEM
A consideration in the planning of a joint bay in a flexible system is to reduce the differential axial thrust that may
act on each joint to an acceptable level. The joints in Figure 25 are seen to have an equal length of sagged cable
on either side, thus the thermo-mechanical axial forces can be expected to be balanced and sum to near zero.
Horizontally Waved Systems
Figure 26 shows a horizontally waved 275 kV 2500mm2
XLPE cable system in trefoil formation horizontally system
in Japan. The cable to the right of the photograph is rigidly close-cleated in trefoil clamping cleats for a short
distance around a bend. It then passes into a horizontally waved span where it is supported on three low friction
slides. There are two short circuit straps binding the cables together in the flexible span. The first waved span is
designed to absorb the additional thermal expansion from the short rigid cleated section. Trough lids are later fitted
to cover the cables.

Page 39
FIGURE 26 275 KV 2500MM2
XLPE HORIZONTALLY SNAKED TUNNEL SYSTEM IN JAPAN
Figure 27 shows a horizontally waved cable system in trefoil formation prior to the fitting of sunshields.
FIGURE 27 66 KV XLPE CABLES IN A HORIZONTALLY WAVED BRIDGE CROSSING IN SINGAPORE

Page 40
5 Transitions between Rigid and Flexible Systems: Theory and
Practice
Transition sections between rigid and flexible runs of cable occur most commonly adjacent to cable terminations.
Transition sections also occur adjacent to joints in some designs of duct-manhole systems, between buried cable
and bridge crossings at bridge expansion joints. Transition sections give useful design solutions and are a normal
part of the cable system.
The method of transition from the underground buried cable or tunnel cable has a significant effect on the
magnitude of the axial thrust and retraction forces that the cable termination is required to withstand in service. In
concept it is simpler to design a system with no need for transition sections i.e. either an:
1. All-rigid system throughout the cable route, at the end of which the full cable thermo-mechanical thrust is
applied to the cable termination. The advantage is that this system occupies the least space in a
substation. The downside is that the cable termination and support structure must be designed to
withstand the force.
or an:
2. All-flexible system in which the cable thrust and retraction forces acting on the cable termination are
minimised. The advantage is that the cable termination and offgoing equipment such as GIS busbar does
not have to be designed to withstand the full magnitude of thrust. The disadvantages are:
a. Sufficient space is required to accommodate i) the flexible length of cable where it passes from the
horizontal cable approach, through the quadrant bend, to the vertical termination and ii) its lateral
deflection, this generally being small. With large conductor areas and large cable diameter EHV
cables the bending radius is large and so in some congested sub-stations this method may be
impracticable due to lack of space.
b. The flexible cables are not completely free as they must be constrained to withstand violent
disturbance by the short circuit expulsive force.
c. The termination of the cable’s metallic sheath at the base of the cable termination must be
protected against disturbance by thermo-mechanical and short-circuit bending moment.
The following methods are available for cable installations close to terminations:
1. Rigid cleating
2. Flexible bends or waves.
3. Rigid cleating on a flexible support that allows a limited degree of movement of the termination (for
example, connection to a particular GIS termination that is designed to have some lateral movement).
In cable routes with slopes or vertical parts, it may be required to avoid slipping of the cable expansion length and
to avoid its accumulation at the lower position. In horizontal in-air installations it may be desirable to fully decouple
flexible and rigid sections.
To achieve this aim, locking (blocking) bends and waves may be installed. These can be several bends or a rigidly
fixed snaking section.

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