References Documents

Cableizer is based on international and american standards and uses additional methods from technical publications and books.

Cableizer is based mainly upon several standards from the International Electrotechnical Commission (IEC).

  • IEC 60038:2009 (Ed.7.0): Standard Voltages
  • IEC 60071-1:2006-01 (Ed.8.0) + Amd1:2010: Insulation co-ordination – Part 1: Definitions, principles and rules
  • IEC 60228:2004-11 (Ed.3.0): Conductors of insulated cables
  • IEC 60287: Electric Cables - Calculation of the current rating
    • Part 1-1:2014-11 (Ed.2.1): Current rating equations (100% load factor) and calculation of losses - General
    • Part 1-3:2002-05 (Ed.1.0): Current rating equations (100% load factor) and calculation of losses - Current sharing between parallel single-core cables and calculation of circulating current losses
    • Part 2-1:2015-04 (Ed.2.0): Thermal resistance - Calculation of thermal resistance
    • Part 2-2:1995-05 (Ed.1.0): Thermal resistance - A method for calculating reduction factors for groups of cables in free air, protected from solar radiation
    • Part 2-3:2017-04 (Ed.1.0): Thermal resistance - Cables installed in ventilated tunnels
    • Part 3-1:2017-06 (Ed.2.0): Sections on operating conditions - Reference operating conditions and selection of cable type
    • Part 3-3:2007-05 (Ed.1.0): Sections on operating conditions - Cables crossing external heat sources
  • IEC 60502: Power cables with extruded insulation and their accessories for rated voltages from 1 kv (Um = 1,2 kv) up to 30 kv (Um = 36 kv)
    • Part 1:2004 (Ed.2.0) + A1:2009: Cables for rated voltages of 1 kv (Um = 1,2 kv) and 3 kv (Um = 3,6 kv)
    • Part 2:2014 (Ed.3.0): Cables for rated voltages from 6 kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV)
  • IEC 60840:2011 (Ed.4.0): Power cables with extruded insulation and their accessories for rated voltages above 30 kV (Um = 36 kV) up to 150 kV (Um = 170 kV) – Test methods and requirements
  • IEC 60853: Electric Cables - Calculation of the cyclic and emergency current rating of cables
    • Part 1:1985 (Ed.1.0) + A1:1994 + A2:2008: Cyclic rating factor for cables up to and including 18/30 (36) kV
    • Part 2:1988 (Ed.1.0) + A1:2008 Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings for cables of all voltages
    • Part 3:2002 (Ed.1.0): Cyclic rating factor for cables of all voltages, with partial drying of the soil
  • IEC 60949:1988 (Ed.1.0) + A1:2008-09: Calculation of the thermally-permissible short-circuit currents, taking into account non-adiabatic heating effects
  • IEC 62067:2011 (Ed.2.0): Power cables with extruded insulation and their accessories for rated voltages above 150 kV (Um = 170 kV) up to 500 kV (Um = 550 kV) – Test methods and requirements
  • IEC 62440:2008 (Ed.1.0): Electric cables with a rated voltage not exceeding 450/750 V – Guide to use
  • IEC TR 62602:2009 (Draft Proposal): Conductors of insulated cables - Data for AWG and KCMIL sizes

Standard cables were designed according to recommendations in European Standards (EN) and Harmonized Documents (HD).

  • EN 50525 2011: Electric cables - Low voltage energy cables of rated voltages up to and including 450/750 V (U0/U)
  • DIN EN 50565-1 2015: Electric cables - Guide to use for cables with a rated voltage not exceeding 450/750 V - Part 1: General guidance
  • HD 21 S1 2006 (Withdrawn): Cables of rated voltages up to and including 450/750 V and having thermoplastic insulation
  • FprHD 603 S2 2016 & HD 603 S1 2010: Distribution cables of rated voltage 0,6/1 kV
  • HD 620 S2 2010: Distribution cables with extruded insulation for rated voltages from 3,6/6 (7,2) kV up to and including 20,8/36 (42) kV
  • HD 632 S3 2017 & SN HD 632 S2 2008: Power cables with extruded insulation and their accessories for rated voltages above 36 kV (Um = 42 kV) up to 150 kV (Um = 170 kV)

Cableizer used the standardized values for wire diameters and conductor resistances for AWG sizes from several American standards.

  • ANSI UL 1581-2011: Reference Standard for Electrical Wires, Cables, and Flexible Cords
  • ASTM B2-00: Standard Specification for Medium-Hard-Drawn Copper Wire
  • ASTM B8-04: Standard Specification for Concentric-Lay-Stranded Copper Conductors, Hard, Medium-Hard, or Soft
  • ASTM B226-04: Standard Specification for Cored, Annular, Concentric-Lay-Stranded Copper Conductors
  • ASTM B231-04: Standard Specification for Concentric-Lay-Stranded Aluminum 1350 Conductors
  • ASTM B258-02: Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors
  • ASTM B400-04: Standard Specification for Compact Round Concentric-Lay-Stranded Aluminum 1350 Conductors
  • ASTM F1883-2013: Standard Practice for Selection of Wire and Cable Size in AWG or Metric Units

The User Guides from CIGRE are a good source for better understanding of electrotechnical topics and sometimes provide additional methods not published in the IEC standards.

  • Guide 218_2003: Gas Insulated Transmission Lines (GIL)
  • Guide 283_2005: Special Bonding of High Voltage Power Cable Systems
  • Guide 338_2007: Statistics of AC underground cables in power networks
  • Guide 531_2013: Cable Systems Electrical Characteristics
  • Guide 559_2013: Impact of EMF on current ratings and cable systems
  • Guide 610_2015: Offshore generation cable connections
  • Guide 640_2015: A Guide for Rating Calculations of Insulated Cables
  • Guide 669_2016: Mechanical forces in large cross section cables systems
  • Guide 689_2017: Life cycle assessment of underground cables
  • Guide 714_2017: Long term performance of soil and backfill systems
  • Guide 720_2018: Fire issues for insulated cables in air

Following books we consulted and can recommend.

  • Ampacity of H.V. Multi-Insulation Cables at Different Cooling Methods: Mohammed Ramiz Almallah, Scholars' Press, 2016
  • Ampacity Optimization of Unequally Loaded Power Cables: by Wael Moutassem, VDM Verlag, 2008
  • Analysis of Nonlinear Heat Transfer in Electric Cables: Dvorsky Karl, Südwestdeutscher Verlag für Hochschulschriften AG and Company KG, 2013
  • Auswahl und Bemessung von Kabeln und Leitungen: Herbert Schmolke, Hüthig und Pflaum, 4. Auflage, 2010
  • Berechnung transienter Kabelerwärmungen unter Berücksichtigung möglicher Bodenaustrocknung: Uwe Beyer, 1985
  • Boden und Energiewende - Trassenbau, Erdverkabelung und Erdwärme: verschiedene Editoren, Springer Fachmedien Wiesbaden, 2015
  • Bonding of Underground Single-Core Cables and Sheath Losses: Ossama Gouda, Adel Farag, Lap Lambert Academic Publishing, 2013
  • Development of a Software Package for Calculating Current Rating of Medium Voltage Power Cables: D.G.A.K. Wijeratna, J.R. Lucas, University of Moratuwa, 2003
  • EHV AC Undergrounding Electrical Power - Performance and Planning: Roberto Benato, Antonio Paolucci, Springer-Verlag London, 2010
  • Electric Cables Handbook by BICC Cables: George F. Moore, Blackwell Science, 3. Edition 1997
  • Electrical Power Cable Engineering: William A. Thue, 1999
  • Electric Power Generation, Transmission, and Distribution: L.L. Grigsby, CRC Press, 3. Edition 2012
  • Elektrische Kraftwerke und Netze: D. Oeding, B.R. Oswald, Vieweg+Teubner Verlag, 8th Edition 2016
  • Electromagnetic Transients in Power Cables: Filipe Faria da Silva, Claus Leth Bak, Springer-Verlag London, 2013
  • Symmetrische Komponenten in Drehstromsystemen: August Hochrainer, Springer-Verlag, 1957
  • Extruded Cables For High-Voltage Direct-Current Transmission - Advances in Research and Development, G. Mazzanti, M. Marzinotto, John Wiley & Sons. 2013
  • Fundamentals of heat transfer: S.S. Kutateladze, Academic Press, 1. Edition 1963
  • Handbook of Electric Power Calculations: H. Wayne Beaty, Surya Santoso, McGraw-Hill Education, 4. edition 2015
  • High-Tension Underground Electric Cables: Henry Floy, Electrical Publishing Company, 1909
  • High Voltage Engineering: J.R. Lucas, University of Moratuwa
  • Kabel und Leitungen für Starkstrom - Grundlagen und Produkt-Know-How für das Projektieren von Kabelanlagen, L. Heinhold, R. Stubbe, Publicis Publishing, 5. Auflage 1999
  • Kabelanlagen für Hoch- und Höchstspannung: E.P. Peschke, R. v. Olshausen, Publicis MCF Verlag, 1998
  • Rating of Electric Power Cables: G.J. Anders, McGraw-Hill Professional, 1. Edition 1997
  • Rating of Electric Power Cables in Unfavorable Thermal Environment: G.J. Anders, Wiley-IEEE Press, 1. Edition 2005
  • Submarine Power Cables: T. Worzyk, Springer, 2009
  • The Mechanics of Soils and Foundations: John Atkinson, Taylor and Francis, 2007
  • Thermal Design of Underground Systems: B.M. Weedy, John Wiley & Sons, 1988
  • Underground Power Cables: S. Y. King, N. A. Halfter, Longman Group Ltd., 1. Edition 1982

All parameters used in Cableizer are listed below. Click on the links for more information like values, used equations and references to other parameters.

List of parameters

The list of parameters is automatically generated from the Cableizer source code and is valid as of 2020-07-16.

Click on a parameter name in order to get more information about that specific parameter.

A $a_{0}$Coefficient a for partial transient temperature rise1/s
$a_{12}$Distance between phase 1 and 2mm
$a_{23}$Distance between phase 2 and 3mm
$a_{31}$Distance between phase 3 and 1mm
$A_{a}$Cross-sectional area of armourmm$^2$
$A_{a_{1}}$Cross-sectional area of 1st armourmm$^2$
$A_{a_{2}}$Cross-sectional area of 2nd armourmm$^2$
$A_{ab_{1}}$Cross-sectional area of 1st armour beddingmm$^2$
$A_{ab_{2}}$Cross-sectional area of 2nd armour beddingmm$^2$
$A_{c}$Cross-sectional area of conductormm$^2$
$a_{c}$Skin and proximity effect coefficient a for GIL conductor
$A_{comp}$Cross-sectional area of compartmentm$^2$
$A_{d}$Cross-sectional area of duct wallmm$^2$
$A_{d_{fill}}$Free cross-sectional area inside ductmm$^2$
$A_{encl}$Cross-sectional area of enclosuremm$^2$
$a_{encl}$Skin and proximity effect coefficient a for GIL enclosure
$A_{f}$Cross-sectional area of fillermm$^2$
$A_{fluid}$Cross-sectional area of fluidmm$^2$
$A_{ins}$Cross-sectional area of insulationmm$^2$
$A_{j}$Cross-sectional area of jacketmm$^2$
$A_{k}$Thermal property constant Amm/s$^{1/2}$
$a_{m}$Mean distance between the phasesmm
$A_{pipe}$Cross-sectional area of fluid-filled pipemm$^2$
$A_{prot}$Cross-sectional area of protective covermm$^2$
$a_{S1}$Length of 1st section (minor)p.u.
$a_{S2}$Length of 2nd section (medium)p.u.
$a_{S3}$Length of 3rd section (major)p.u.
$A_{sc}$Cross-sectional area of screenmm$^2$
$A_{scb}$Cross-sectional area of screen beddigmm$^2$
$A_{scs}$Cross-sectional area of screen servingmm$^2$
$A_{sh}$Cross-sectional area of sheathmm$^2$
$a_{T}$Distance a of multi-layer backfillm
$A_{t}$Cross-sectional area of the tunnelm$^2$
$a_{type}$Construction of armour
$a_{VdW}$Van der Walls constant abar.L$^2$/mol$^2$
$\alpha_{0}$Constant depending on the burial depth
$\alpha_{ar}$Temperature coefficient of armour material1/K
$\alpha_{at}$Heat transfer coefficient to channel wallW/K/m$^2$
$\alpha_{c}$Temperature coefficient of conductor material1/K
$\alpha_{encl}$Temperature coefficient of enclosure material1/K
$\alpha_{f}$Phase shift$^{\circ}$
$\alpha_{gas}$Thermal diffusivity for gasm$^2$/s
$\alpha_{M}$Factor $\alpha_M$
$\alpha_{sa}$Heat transfer coefficient for convectionW/K/m$^2$
$\alpha_{sc}$Temperature coefficient of screen material1/K
$\alpha_{sh}$Temperature coefficient of sheath material1/K
$\alpha_{st}$Heat transfer coefficient for radiationW/K/m$^2$
$\alpha_{surf}$Heat transfer coefficient earth surfaceW/K/m$^2$
$\alpha_{t}$Conductor to surface attainment factor
B $B$SusceptanceS/m
$b_{0}$Coefficient b for partial transient temperature rise1/s
$B_{1_{1}}$Loss coefficient $B_1$ of 1st armour$\Omega$/m
$B_{1_{2}}$Loss coefficient $B_1$ of 2nd armour$\Omega$/m
$B_{2_{1}}$Loss coefficient $B_2$ of 1st armour$\Omega$/m
$B_{2_{2}}$Loss coefficient $B_2$ of 2nd armour$\Omega$/m
$b_{c}$Skin and proximity effect coefficient b for GIL conductor
$B_{EMF}$Magnetic field strength$\mu$T
$b_{encl}$Skin and proximity effect coefficient b for GIL enclosure
$B_{k}$Thermal property constant Bmm$^2$/s
$b_{T}$Distance b of multi-layer backfillm
$b_{VdW}$Van der Walls constant bL/mol
$b_{x}$Shorter side of backfillmm
$b_{y}$Longer side of backfillmm
$\beta_{0}$Constant $\beta_0$ acc. Ovuworie
$\beta_{1}$Substitution coefficient $\beta_1$ for eddy-currents
$\beta_{6}$Factor $|1 - \beta(6)|$
$\beta_{a_{1}}$Angle between armour and cable axisrad
$\beta_{a_{2}}$Angle between 2nd armour and cable axisrad
$\beta_{air}$Volumetric thermal expansion coefficient of air1/K
$\beta_{ar}$Reciprocal of temperature coefficient of armour materialK
$\beta_{b}$Angle of exposed wetted surface of piperad
$\beta_{c}$Reciprocal of temperature coefficient of conductor materialK
$\beta_{encl}$Reciprocal of temperature coefficient of enclosure materialK
$\beta_{gas}$Volumetric thermal expansion coefficient for gas1/K
$\beta_{k}$Reciprocal of temperature coefficient of resistanceK
$\beta_{M}$Factor $\beta_M$
$\beta_{sc}$Reciprocal of temperature coefficient of screen materialK
$\beta_{sh}$Reciprocal of temperature coefficient of sheath materialK
$\beta_{t}$Attainment factor cable surface to ambient
$\beta_{T}$Equivalent thermal resistance of the soil per unit surfaceW/(K.m$^2$)
$\beta_{X}$Crossing angle in radiansrad
$\beta_{xing}$Crossing angle in degrees$^{\circ}$
$\mathrm{Bi}_{g}$Biot number of the ground
$\mathrm{Bi}_{p}$Biot number of the pipe
C $C_{av}$Heat capacity of the air flowW/K
$C_{b}$Capacitance of insulationF/m
$C_{b3}$Factor C3 for partially buried pipes
$C_{g1}$Factor C1 for partially buried pipes
$C_{g2}$Factor C2 for partially buried pipes
$c_{gas}$Constant c for a gas under GIL conditions
$c_{ij}$Coefficient c for view factor
$C_{k1}$Non-adiabatic constant $C_1$mm/m
$C_{k2}$Non-adiabatic constant $C_2$$^2$/J
$C_{\mathrm{Nu}_{L}}$Factor C
$C_{\mathrm{Nu}_{w}}$Factor C
$c_{p_{gas}}$Specific heat capacity at constant pressureJ/kg.K
$c_{p_{soil}}$Specific heat capacity of soilJ/kg.K
$c_{p_{w}}$Specific heat capacity at constant pressureJ/kg.K
$C_{q}$Constants $C_1$ to $C_7$ of multi-layer backfill
$c_{SI}$Surge velocity of propagationkm/s
$c_{T}$Distance c of multi-layer backfillm
$c_{type}$Construction of conductor
$c_{v_{gas}}$Specific heat capacity at constant volumeJ/kg.K
$c_{v_{w}}$Specific heat capacity at constant volumeJ/kg.K
$C_{vair}$Volumetric heat capacity of airJ/K.m$^3$
$CC$Charging capacitykvar/km
$CC_{p}$Conduit clearance%
$CF_{p}$Conduit fill%
$CR_{p}$Conduit ratio in duct%
$cuw$Standard copper wiresmm
D $D_{1}$Diameter below screenmm
$D_{2_{1}}$Diameter below 1st armourmm
$D_{2_{2}}$Diameter below 2nd armourmm
$d_{a}$Mean diameter of armourmm
$d_{a_{1}}$Mean diameter of 1st armourmm
$D_{a_{1}}$External diameter of 1st armourmm
$d_{a_{2}}$Mean diameter of 2nd armourmm
$D_{a_{2}}$External diameter of 2nd armourmm
$d_{b}$Diameter of the backfillmm
$d_{c}$External diameter of conductormm
$D_{c}$Diameter of conductorm
$d_{ci}$Internal diameter of conductormm
$D_{comp}$Diameter of compartment (metric)m
$d_{comp}$Diameter of compartmentmm
$d_{ct}$External diameter of conductor for transient calculationsmm
$D_{e}$External diameter of objectmm
$d_{e}$Diameter of sheath and armourmm
$d_{encl}$Outer diameter of enclosuremm
$D_{encl}$Outer diameter of enclosure (metric)m
$D_{eq}$Equivalent diameter of a group of cablesmm
$D_{ext}$Overall outer diameter of pipem
$D_{f}$External diameter of the fillermm
$d_{f}$Spacing from hottest object in groupm
$d_{f_{1}}$Thickness of 1st armourmm
$d_{f_{2}}$Thickness of 2nd armourmm
$d_{im}$Imaginary layer of soilm
$D_{in}$Inner diameter of pipem
$D_{ins}$Diameter over insulationmm
$d_{ins}$Diameter of insulation around pipemm
$D_{it}$Diameter below sheathmm
$d_{j}$Diameter below jacketm
$D_{o}$Outer diameterm
$D_{oc}$External diameter of sheathmm
$d_{pk1}$Distance to mirrored buried objectmm
$d_{pk2}$Distance between buried objectsmm
$d_{prot}$Diameter of protective covermm
$d_{psc}$Point source correctionm
$D_{ref}$Reference diameter for determination of OHTCm
$D_{s}$Mean external diameter of the sheathmm
$d_{s}$Mean diameter of screen/sheathmm
$d_{sc}$Mean diameter of screenmm
$d_{sh}$Mean diameter of sheathmm
$d_{soil}$Soil dry densitykg/m$^3$
$D_{soil}$Outer diameter of soil layerm
$d_{T}$Distance d of multi-layer backfillm
$d_{t}$Channel coveringm
$d_{w}$Depth under waterm
$D_{wall}$Outer diameter of steel pipem
$d_{x}$Equivalent diameter of a conductormm
$D_{x}$Characteristic diametermm
$D_{x_{w}}$Characteristic diameter for weekly loadmm
$D_{x_{y}}$Characteristic diameter for yearly loadmm
$DC_{p}$Diameter factor in duct%
$\Delta _{1}$Substitution coefficient $\Delta_1$ for eddy-currents
$\delta _{1}$Thickness of screening layermm
$\Delta _{2}$Substitution coefficient $\Delta_2$ for eddy-currents
$\delta _{ar}$Equivalent thickness of armourmm
$\delta _{k}$Thickness of screen, sheath or armourmm
$\delta _{soil}$Soil thermal diffusivitym$^2$/s
$\delta _{t}$Channel covering correctionm
$\Delta d_{sh}$Depth of corrugationmm
$\Delta H_{c}$Heat of combustion coefficientMJ/kg
$\Delta t$Length of time steps
$\Delta \theta_{0t}$Air temperature in tunnel increaseK
$\Delta \theta_{0x}$Temperature rise of the conductorK
$\Delta \theta_{0x_{1}}$Temperature rise of the conductor, first estimateK
$\Delta \theta_{0x_{h}}$Temperature rise of the conductor by source hK
$\Delta \theta_{a_{t}}$Corrected transient temperature rise of conductorK
$\Delta \theta_{air}$Temperature increase of airK
$\Delta \theta_{c}$Temperature rise of conductorK
$\delta \theta_{c}$Ohmic steady-state temperature riseK
$\Delta \theta_{c_{t}}$Transient temperature rise of conductor by ohmic lossesK
$\Delta \theta_{ce}$Temperature difference conductor to surfaceK
$\Delta \theta_{d}$Temperature rise by dielectric lossesK
$\Delta \theta_{e_{t}}$Transient temperature rise of outer surfaceK
$\Delta \theta_{gas}$Temperature difference conductor-enclosure$^{\circ}$C
$\Delta \theta_{kp}$Temperature rise by buried object kK
$\Delta \theta_{max}$Maximum permissible conductor temperature riseK
$\Delta \theta_{p}$Temperature rise by other buried objectsK
$\Delta \theta_{R}$Conductor temperature rise above ambient temperatureK
$\Delta \theta_{R_{\infty}}$Maximum permissible conductor temperature rise$^{\circ}$C
$\Delta \theta_{s}$Temperature difference surface to ambientK
$\delta \theta_{SPK}$Peak cyclic temperature riseK
$\Delta \theta_{sun}$Temperature rise by solar radiationK
$\Delta \theta_{t}$Transient temperature rise of conductorK
$\Delta \theta_{t_{\infty}}$Steady-state temperature rise of conductorK
$\Delta \theta_{tube}$Temperature difference surface to tubeK
$\Delta \theta_{x}$Critical soil temperature riseK
$\Delta W$Incremental heat generatedW
$\Delta W_{0}$Incremental heat 0 generatedW
$\Delta z$Length of the intervalm
$DF$Derating factor for the permissible current
$Di_{d}$Inner diameter of ductmm
$di_{pipe}$Internal diameter of fluid-filled pipemm
$Di_{t}$Tunnel inner diameterm
$Do_{d}$Outer diameter of ductmm
$do_{pipe}$External pipe diametermm
$Do_{t}$Tunnel/trough outer diameterm
E $E_{bs}$Installation constant E
$e_{hor}$Horizontal clearancemm
$e_{limit}$Limit of thickness of soil layerm
$e_{soil}$Thickness of soil layerm
$E_{stress}$Electrical field strengthkV/mm
$e_{ver}$Vertical clearancemm
$e_{wall}$Clearance to wallmm
$EEC$Embodied energy and carbonMJ/kg
$\epsilon_{0}$Vacuum permittivityF/m
$\epsilon_{c}$Effective emissivity of conductor
$\epsilon_{cable}$Emissivity of cable surface
$\epsilon_{di}$Emissivity of tube inner surface
$\epsilon_{do}$Emissivity of tube outer surface
$\epsilon_{encl}$Effective emissivity of enclosure
$\epsilon_{gas}$Dielectric constant of gas in compartment
$\epsilon_{i}$Relative permittivity of insulation
$\epsilon_{k}$Heat loss allowance factor
$\epsilon_{prot}$Effective emissivity of protective cover
$\epsilon_{rad}$Effective emissivity
$\eta0_{gas}$Reference dynamic viscosity of gasPa.s
$\eta_{gas}$Dynamic viscosity of gasPa.s
$\eta_{w}$Dynamic viscosity of waterPa.s
F $f$System frequencyHz
$F_{a_{1}}$Effective length per unit lay length of 1st armourmm
$F_{a_{2}}$Effective length per unit lay length of 2nd armourmm
$f_{atm}$Relation atmospheric pressure to standard atmosphere
$F_{cable}$Maximum effective pulling forceN/m
$f_{cb}$Factor for cross-bonded earthing
$F_{e}$Factor $F_e$ for eddy-current losses
$F_{eq}$Mutual heating coefficient
$F_{form}$Form factor
$F_{ij}$View factor object-object
$F_{in}$Pulling force at beginning of a sectiondaN
$F_{k}$Imperfect contact thermal factor
$F_{m}$Radiation coefficient mutual
$F_{out}$Pulling force at end of a sectiondaN
$f_{ppc}$Factor of permissible pullN/mm$^2$
$F_{ppc}$Permissible pull force on cabledaN
$F_{pt}$Function of pressure and temperature
$f_{SHF}$Sheath factor
$F_{x}$Geometrical distance factor for multi-core cables
G $g$Standard acceleration of gravitym/s$^2$
$G_{1}$Geometric factor $G_1$
$G_{2}$Geometric factor $G_2$ for cables with separate sheaths
$G_{b}$Geometric factor for backfill
$g_{bs}$Installation constant g
$G_{encl}$Factor G to calculate Nusselt number
$g_{s}$Substitution coefficient $g_s$ for eddy-currents
$G_{s00}$Factor $G_{s 0.0}$
$G_{s05}$Factor $G_{s 0.5}$
$G_{s10}$Factor $G_{s 1.0}$
$\gamma_{a}$Armour anglerad
$\gamma_{bessel}$Bessel constantp.u.
$\gamma_{c}$Skin and proximity effect factor $\gamma$ for GIL conductor
$\gamma_{encl}$Skin and proximity effect factor $\gamma$ for GIL enclosure
$\gamma_{euler}$Euler's constantm/s$^2$
$\gamma_{t}$Attainment factor for groups of cables
$\gamma_{X}$Attenuation factor for crossing1/m
$GMD$Geometric mean distancemm
$GMR$Geometric mean radiusmm
$\mathrm{Gr}_{c}$Grashof number conductor-gas
$\mathrm{Gr}_{encl}$Grashof number gas-enclosure
$\mathrm{Gr}_{L}$Grashof number ground-air
$\mathrm{Gr}_{prot}$Grashof number surface-air
H $H$Distance center of pipe to groundm
$h_{1}$Factor $h_1$ for emergency load
$H_{1_{1}}$Component of inductance $H_1$H/m
$H_{1_{2}}$Component of inductance $H_1$ of 2nd armourH/m
$H_{2_{1}}$Component of inductance $H_2$H/m
$H_{2_{2}}$Component of inductance $H_2$ of 2nd armourH/m
$H_{3_{1}}$Component of inductance $H_3$H/m
$H_{3_{2}}$Component of inductance $H_3$ of 2nd armourH/m
$h_{amb}$Pseudo film coefficient of ambient fluid at ground levelW/(K.m$^2$)
$h_{atm}$Height above sea levelm
$h_{b}$Height of the backfillmm
$h_{bs}$Heat dissipation coefficient for black surfaces in free airW/m$^2$/K$^{5/4}$
$h_{buried}$Heat transfer coefficient wall to soilW/(K.m$^2$)
$H_{c}$Heat energy contentMJ/m
$h_{c}$Convective heat transfer coefficient conductor-gasW/(K.m$^2$)
$h_{conv_{sa}}$Convective heat transfer coefficient surface-airW/(K.m$^2$)
$h_{encl}$Convective heat transfer coefficient gas to enclosureW/m2.K
$h_{ext}$External heat transfer coefficientW/(K.m$^2$)
$h_{ground}$Heat transfer coefficient buried part of wall to soilW/(K.m$^2$)

The internal heat transfer coefficient (or inside film coefficient) is also a convection coefficient, calculated from the Nusselt number of the internal fluid. It is the heat transfer by convection at the inner surface of the pipe wall in contact with the pipeline product (gas, oil, water, and possibly solids.

In cables, there is no fluid flow at the inner surface of the insulation. In GIL, the convection of the gas inside the chamber is considered separately. In both cases, the value of $h_{in}$ is set to quasi-infinity in order to eliminate the its influence.

$h_{lg}$Ratio of heat dissipation coefficients
$h_{rad_{ce}}$Radiation heat transfer coefficient conductor-enclosureW/(K.m$^2$)
$h_{rad_{sa}}$Radiation heat transfer coefficient surface-airW/(K.m$^2$)
$h_{roll}$Height of roller above bottomm
$H_{s}$Sheath conductanceH/m
$h_{soil}$Heat transfer coefficient wall-soilW/(K.m$^2$)
$H_{sun}$Intensity of solar radiationW/m$^2$
$H_{T}$Trench depth to bedding layer in multi-layer backfillm
$h_{t}$Inner heightm
$h_{T4}$Ratio of thermal resistance to ambient
$H_{tc}$Parameter H for trough
$h_{tr}$Heat transfer coefficientW/(K.m$^2$)
$H_{ts}$Parameter H depending on air velocity
$H_{x}$Magnetic field x-componentmH
$H_{y}$Magnetic field y-componentmH
I $I_{1}$Steady-state current before transientA
$I_{2}$Emergency load currentA
$I_{c}$Conductor currentA
$I_{C}$Capacitive load currentA/km
$I_{c_{max}}$Highest current load of lineA
$I_{c_{peak}}$Permissible peak cyclic load currentA
$I_{Ce}$Capacitive earth short-circuit currentA/km
$I_{EMF}$Phase current for EMF calculationA
$I_{k}$Permissible short-circuit currentkA
$I_{kAD}$Short-circuit current (adiabatic)kA
$I_{kSC}$Effective short-circuit currentkA
$I_{method}$Current calculation method
$I_{R}$Transient conductor currentA
$inst_{air}$Installation in air
$inst_{sea}$Installation of subsea cables
$inst_{t}$Installation in air inside a room
J $j_{max}$Phase angle range$^{\circ}$
$JR_{p}$Jam ratio in duct%
K $K$Screening factor
$K_{0}$Coefficient K for a gas under GIL conditions
$K_{02}$Factor $K_{0.2}$
$K_{06}$Factor $K_{0.6}$
$k_{1}$Thermal conductivity of surface layerW/(m.K)
$K_{10}$Factor $K_{1.0}$
$k_{2}$Thermal conductivity of mid backfill layerW/(m.K)
$k_{3}$Thermal conductivity of bedding layerW/(m.K)
$k_{4}$Thermal conductivity of soilW/(m.K)
$K_{A}$Coefficient K to calculate in air
$k_{air}$Thermal conductivity of airW/(m.K)
$K_{BICC}$Constant relating to conductor formation
$k_{Boltzmann}$Boltzmann constantJ/K
$k_{c}$Thermal conductivity of conductor materialK.m/W
$K_{ce}$Radiation shape factor conductor-enclosure
$K_{cv}$Convection factor
$K_{E}$Surface heat conductanceW/m$^2$
$k_{encl}$Thermal conductivity of enclosureW/(m.K)
$k_{fluid}$Thermal conductivity of fluidW/(m.K)
$k_{gas}$Thermal conductivity for gasW/(m.K)
$K_{GMR}$Geometric mean radius factor
$k_{H}$Heinhold characteristic diameter coefficient
$k_{ins}$Thermal conductivity of insulationW/(m.K)
$K_{int}$Radiation shape factor cable-tube
$K_{k}$Specific short-circuit parameterA.s$^{1/2}$/mm$^2$
$k_{l}$Temperature rise factor in air
$k_{LF}$Load loss constant coefficientp.u.
$k_{p}$Proximity effect coefficient
$K_{par}$Constant acc. Ovuworie
$k_{pipe}$Thermal conductivity of fluid-filled pipeW/(m.K)
$k_{prot}$Thermal conductivity of protective coverW/(m.K)
$K_{r}$Radiation shape factor to ambient
$k_{r2}$Temperature rise ratio $\delta\theta_{SPK}/\delta\theta_c$p.u.
$k_{s}$Skin effect coefficient
$k_{sa}$Convection factor acc. Heinhold
$k_{sa_{1}}$Factor 1 for convectional heat transfer coefficient
$k_{sa_{2}}$Factor 2 for convectional heat transfer coefficient
$k_{t}$Temperature rise ratiop.u.
$K_{t}$Effective emissivity of surface
$K_{vermeer}$Vermeer constant for convection heat transfer
$k_{w}$Thermal conductivity of waterW/(m.K)
$K_{x}$Factor for fictitious diameter by Neher
$k_{X}$Number of heat sources crossing
L $L_{0}$Reference length of the tunnelm
$L_{1}$Inductance of phase 1H/m
$L_{2}$Inductance of phase 2H/m
$L_{3}$Inductance of phase 3H/m
$L_{b}$Vertical center of backfillmm
$L_{c}$Depth of laying of sourcesmm
$L_{char}$Characteristic length earth surface
$L_{cm}$Depth of layingm
$L_{crit}$Critical system lengthkm
$L_{deep}$Equivalent depth for deep burialm
$L_{earth}$Equivalent depth of earth return pathp.u.
$L_{h}$Depth of laying of crossing elementmm
$L_{p}$Length of a sectionm
$L_{r}$Depth of laying of the rated objectmm
$L_{sys}$System lengthkm
$L_{T}$Length of the tunnelm
$\lambda_{0}$Substitution coefficient $\lambda_0$ for eddy-currents
$\lambda_{1}$Loss factor of screen and sheath
$\lambda_{1c}$Loss factor by circulating currents
$\lambda_{1cb}$Loss factor for solid bonding
$\lambda_{1e}$Loss factor by eddy currents
$\lambda_{1es}$Loss factor for single point bonding
$\lambda_{2}$Loss factor of armour
$\lambda_{3}$Loss factor of steel pipes
$\lambda_{d}$Factor for dielectric losses
$\lambda_{gas}$Ratio $c_p$/$c_v$
$\lambda_{t}$Relaxation parameter
$LF$Load factorp.u.
$LF_{w}$Weekly load factorp.u.
$LF_{y}$Yearly load factorp.u.
$LME$London Metal ExchangeUSD/mt
M $m$Mass of objectkg/m
$M$Cyclic rating factorp.u.
$m_{0}$Substitution coefficient $m_0$ for eddy-currentsHz.m/$\Omega$
$M_{0}$Coefficient M for partial transient temperature rises
$M_{1}$Corrected cyclic rating factorK
$M_{ab}$Material of armour bedding
$M_{c}$Material of conductor
$M_{cable}$List of materials in a cable
$M_{comp}$Insulating gas material
$M_{d}$Material of duct pipe
$M_{e}$Substitution coefficient $M_e$ to calculate factor $F_e$
$m_{EMF}$Number of time steps
$M_{encl}$Material of enclosure
$M_{f}$Material of filler
$M_{fluid}$Fluid material
$M_{gas}$Gas and gas-mixtures
$M_{i}$Material of insulation
$M_{IEEE}$Materials acc. IEEE 442
$M_{ins}$Material of insulation around pipe
$M_{j}$Material of jacket
$M_{k}$Thermal contact factors$^{1/2}$
$M_{mol}$Molar massg/mol
$m_{mol}$Molecular massmol
$m_{\mathrm{Nu}_{L}}$Factor m
$m_{\mathrm{Nu}_{w}}$Factor m
$M_{pipe}$Material of fluid-filled pipe
$M_{prot}$Material of protective cover
$M_{s}$Factor $M_s$
$M_{sc}$Material of screen
$M_{seabed}$Material of seabed
$M_{sh}$Material of sheath
$M_{soil}$Type of soils
$\mu$Loss factorp.u.
$\mu_{0}$Vacuum permeabilityH/m
$\mu_{e}$Longitudinal relative permeability
$\mu_{p}$Friction coefficient
$\mu_{s}$Relative permeability
$\mu_{t}$Traverse relative permeability of steel wires
$\mu_{w}$Loss factor for weekly load variationp.u.
$\mu_{y}$Loss factor for yearly load variationp.u.
N $N_{0}$Coefficient N for partial transient temperature rises$^2$
$n_{a_{1}}$Number of wires of 1st armour
$n_{a_{2}}$Number of wires of 2nd armour
$N_{Avogrado}$Avogadro constant1/mol
$N_{b}$Number of loaded objects in backfill
$n_{c}$Number of conductors in object
$N_{c}$Number of sources in system
$n_{cc}$Number of conductors combined
$n_{cg}$Number of conductors in GIL
$n_{cw}$Number of wires in conductor
$n_{cycle}$Number of load cycles
$N_{e}$Substitution coefficient $N_e$ to calculate factor $F_e$
$n_{ppc}$Number of conductors/cables being pulled
$N_{sea}$Number of subsea cables
$N_{sum}$Total number of objects in an air-filled space
$n_{sw}$Number of screen wires
$N_{X}$Number of intervals
$\nu$Summation step 1 to $N_X$
$\nu_{air}$Kinematic viscosity for airm$^2$/s
$\mathrm{Nu}_{c}$Nusselt number conductor-gas
$\mathrm{Nu}_{encl}$Nusselt number gas-enclosure
$\nu_{gas}$Kinematic viscosity for gasm$^2$/s
$\mathrm{Nu}_{L}$Nusselt number ground-air
$\mathrm{Nu}_{prot}$Nusselt number surface-air
$\nu_{soil}$Soil moisture content%
$\mathrm{Nu}_{w}$Nusselt number surface-water
$\nu_{w}$Kinematic viscosity for waterm$^2$/s
O $\omega$Angular frequencyrad/s
P $p_{a_{1}}$Length of lay of 1st armourmm
$p_{a_{2}}$Length of lay of 2nd armourmm
$p_{ab1}$Factor apportioning the 1st armour bedding
$p_{ab2}$Factor apportioning the 2nd armour bedding
$p_{atm}$Atmospheric air pressurehPa
$p_{cb}$Minor ratio of section lengths
$P_{cc}$Substitution coefficient P to calculate loss factor by circulating currents
$p_{comp}$Gas pressure in compartmentbar
$p_{gas}$Gas pressurePa
$p_{i}$Factor apportioning the insulation
$p_{j}$Factor apportioning the jacket
$P_{L}$Active power at load receptorkW
$p_{soil}$Depth of image source
$p_{tr}$Effective perimeter of troughm
$p_{VdW}$Van der Walls equationPa
$p_{w}$Water pressurebar
$\phi_{b}$Parameter $\phi$ for trough
$\phi_{p}$Angle of a bendrad
$\pi$Archimedes' constant $\pi$
$\mathrm{Pr}_{air}$Prandtl number for air
$\mathrm{Pr}_{gas}$Prandtl number for gas
$\mathrm{Pr}_{w}$Prandtl number for liquids
Q $q_{1}$Ratio of losses affecting screen bedding/serving
$q_{2_{1}}$Ratio of losses affecting 1st armour bedding
$q_{2_{2}}$Ratio of losses affecting 2nd armour bedding
$q_{3}$Ratio of losses affecting jacket
$q_{4}$Ratio of losses affecting environment
$Q_{A}$Element A of two-part thermal circuitJ/m.K
$Q_{a_{1}}$Thermal capacitance of 1st armourJ/m.K
$Q_{a_{2}}$Thermal capacitance of 2nd armourJ/m.K
$Q_{ab_{1}}$Thermal capacitance of 1st armour beddingJ/m.K
$Q_{ab_{2}}$Thermal capacitance of 2nd armour beddingJ/m.K
$Q_{B}$Element B of two-part thermal circuitJ/m.K
$Q_{B_{ab1}}$Element B of two-part thermal circuit, 1st armour beddingJ/m.K
$Q_{B_{ab2}}$Element B of two-part thermal circuit, 2nd armour beddingJ/m.K
$Q_{B_{d}}$Element B of two-part thermal circuit, ductJ/m.K
$Q_{B_{f}}$Element B of two-part thermal circuit, fillerJ/m.K
$Q_{B_{i}}$Element B of two-part thermal circuit, insulationJ/m.K
$Q_{B_{j}}$Element B of two-part thermal circuit, jacketJ/m.K
$Q_{B_{s}}$Element B of two-part thermal circuit, screen/sheathJ/m.K
$Q_{c}$Thermal capacitance of conductorJ/m.K
$q_{cb}$Major ratio of section lengths
$Q_{cc}$Substitution coefficient Q to calculate loss factor by circulating currents
$Q_{d}$Thermal capacitance of duct wallJ/m.K
$Q_{d_{fill}}$Thermal capacitance of duct fillingJ/m.K
$Q_{f}$Thermal capacitance of fillerJ/m.K
$q_{f}$Ratio of losses affecting the filler
$Q_{i}$Thermal capacitance of insulationJ/m.K
$Q_{i1}$Thermal capacitance of insulation, 1st portionJ/m.K
$Q_{i2}$Thermal capacitance of insulation, 2nd portionJ/m.K
$Q_{j}$Thermal capacitance of jacketJ/m.K
$Q_{p}$Quantity of lubricantl/m
$Q_{sc}$Thermal capacitance of screenJ/m.K
$Q_{scb}$Thermal capacitance of screen beddingJ/m.K
$Q_{scs}$Thermal capacitance of screen servingJ/m.K
$Q_{sh}$Thermal capacitance of sheathJ/m.K
$Q_{t}$Total thermal capacitance, transientJ/m.K
$q_{x}$Factor for characteristic diameter
R $R_{0}$Zero sequence resistance$\Omega$/m
$R_{1}$Resistance of conductor before emergency rating$\Omega$/m
$R_{A}$Electrical resistance of armour$\Omega$/m
$R_{A_{1}}$Electrical resistance of 1st armour layer$\Omega$/m
$R_{A_{2}}$Electrical resistance of 2nd armour layer$\Omega$/m
$r_{b}$Equivalent radius of backfillmm
$r_{c}$Radius of conductormm
$R_{c}$Resistance of conductor$\Omega$/m
$R_{CG}$Thermal resistance of multi-layer backfill methodK.m/W
$R_{co}$DC resistance of conductor at 20$^{\circ}$C$\Omega$/m
$R_{e}$Electrical resistance of sheath and armour$\Omega$/m
$R_{e_{1}}$Electrical resistance of sheath and 1st armour$\Omega$/m
$R_{e_{2}}$Electrical resistance of sheath and 2nd armour$\Omega$/m
$R_{earth}$Equivalent resistance of earth return pathp.u.
$R_{encl}$Electrical resistance of enclosure$\Omega$/m
$R_{encl20}$DC resistance of enclosure at 20$^{\circ}$C$\Omega$/m
$r_{F}$Radius below the insulationmm
$R_{gas}$Specific gas constant
$R_{gas0}$Universal molar gas constant
$r_{I}$Radius of the insulationmm
$r_{ij}$Coefficient r for view factor
$R_{max}$Resistance of conductor at emergency rating$\Omega$/m
$r_{mbi}$Minimal bending radius for installationm
$r_{mbif}$Factor of minimal installation bending radius
$r_{mbp}$Minimal bending radius during cable pullingm
$r_{mbpf}$Factor of minimal pulling bending radius
$r_{o}$Radius of objectm
$R_{p}$Radius of a bendm
$R_{q1}$Thermal resistance 1 of multi-layer backfill methodK.m/W
$R_{q11}$Thermal resistance 11 of multi-layer backfill methodK.m/W
$R_{q12}$Thermal resistance 12 of multi-layer backfill methodK.m/W
$R_{q13}$Thermal resistance 13 of multi-layer backfill methodK.m/W
$R_{q2}$Thermal resistance 2 of multi-layer backfill methodK.m/W
$R_{q21}$Thermal resistance 21 of multi-layer backfill methodK.m/W
$R_{q22}$Thermal resistance 22 of multi-layer backfill methodK.m/W
$R_{q23}$Thermal resistance 23 of multi-layer backfill methodK.m/W
$R_{q24}$Thermal resistance 24 of multi-layer backfill methodK.m/W
$R_{q3}$Thermal resistance 3 of multi-layer backfill methodK.m/W
$R_{q31}$Thermal resistance 31 of multi-layer backfill methodK.m/W
$R_{q32}$Thermal resistance 32 of multi-layer backfill methodK.m/W
$R_{q33}$Thermal resistance 33 of multi-layer backfill methodK.m/W
$R_{q34}$Thermal resistance 34 of multi-layer backfill methodK.m/W
$R_{s}$Electrical resistance of screen$||$sheath$\Omega$/m
$R_{sc}$Electrical resistance of screen$\Omega$/m
$R_{sh}$Electrical resistance of sheath$\Omega$/m
$R_{so}$Resistance of screen and sheath at 20$^{\circ}$C$\Omega$/m
$r_{x}$Radius to point x in insulationmm
$\mathrm{Ra}_{c}$Rayleigh number conductor-gas
$\mathrm{Ra}_{encl}$Rayleigh number gas-enclosure
$\mathrm{Ra}_{L}$Rayleigh number ground-air
$\mathrm{Ra}_{prot}$Rayleigh number surface-air
$\mathrm{Re}_{air}$Reynolds number for air
$\mathrm{Re}_{w}$Reynolds number for water
$RF$Reduction factor
$\rho_{4}$Thermal resistivity of soilK.m/W
$\rho_{4d}$Thermal resistivity of dry soilK.m/W
$\rho_{ab}$Thermal resistivity of armour beddingK.m/W
$\rho_{ab_{2}}$Thermal resistivity of bedding between armour layersK.m/W
$\rho_{ar}$Specific electrical resistivity of armour material$\Omega$.m
$\rho_{b}$Thermal resistivity backfillK.m/W
$\rho_{b1}$Thermal resistivity of surface layerK.m/W
$\rho_{b2}$Thermal resistivity of mid backfill layerK.m/W
$\rho_{c}$Electrical resistivity of conductor material$\Omega$.m
$\rho_{cable}$Reflectivity of cable surface
$\rho_{corr}$Thermal resistivity of corrugation fillingK.m/W
$\rho_{cr}$Thermal resistivity of conductor materialK.m/W
$\rho_{d}$Thermal resistivity of duct materialK.m/W
$\rho_{d_{fill}}$Thermal resistivity of bentonite fillingK.m/W
$\rho_{di}$Reflectivity of tube inner surface
$\rho_{do}$Reflectivity of tube outer surface
$\rho_{earth}$Specific electrical resistivity of soil$\Omega$.m
$\rho_{encl}$Specific electrical resistivity of enclosure material$\Omega.m$
$\rho_{f}$Thermal resistivity of fillerK.m/W
$\rho_{gas}$Gas densitykg/m$^3$
$\rho_{i}$Thermal resistivity of insulationK.m/W
$\rho_{j}$Thermal resistivity of jacket materialK.m/W
$\rho_{k2}$Thermal resistivity of the layer located aboveK.m/W
$\rho_{k20}$Electrical resistivity of metallic component$\Omega$.m
$\rho_{k3}$Thermal resistivity of the layer located belowK.m/W
$\rho_{ki}$Thermal resistivity of adjacent materialK.m/W
$\rho_{m}$Thermal resistivity of the screenK.m/W
$\rho_{sc}$Specific electrical resistivity of screen material$\Omega$.m
$\rho_{sh}$Specific electrical resistivity of sheath material$\Omega$.m
$\rho_{t}$Thermal resistivity of wallK.m/W
$\rho_{w}$Density of waterkg/m$^3$
S $s_{1}$Thickness of surface layerm
$s_{2}$Thickness of mid backfill layerm$^2$
$s_{3}$Thickness from object to upper boundary of bedding layerm$^2$
$s_{4}$Thickness from object to lower boundary of bedding layerm$^2$
$s_{air}$Axial spacing between objectsm
$s_{c}$Separation of conductors in a systemmm
$S_{G}$Apparent power at injecting pointkVA
$S_{gas}$Sutherland's constantK
$s_{ij}$Spacing between object i and j
$S_{k}$Cross-sectional area of current carrying componentmm$^2$
$s_{roll}$Roller distancem
$s_{S1}$Spacing between phases in 1st sectionp.u.
$s_{S2}$Spacing between phases in 2nd sectionp.u.
$s_{S3}$Spacing between phases in 3rd sectionp.u.
$s_{T}$Distance to lateral edge of multi-layer backfillm
$SI$Surge Impedance$\Omega$
$\sigma$Stefan Boltzmann constantW/m$^2$K$^4$
$\sigma_{ab}$Specific heat capacity of armour beddingJ/K.m$^3$
$\sigma_{ar}$Specific heat capacity of armour materialJ/K.m$^3$
$\sigma_{c}$Specific heat capacity of conductor materialJ/K.m$^3$
$\sigma_{d}$Specific heat capacity of duct materialJ/K.m$^3$
$\sigma_{d_{fill}}$Specific heat capacity of duct fillingJ/K.m$^3$
$\sigma_{encl}$Specific heat capacity of enclosure materialJ/K.m$^3$
$\sigma_{f}$Specific heat capacity of fillerJ/K.m$^3$
$\sigma_{fluid}$Specific heat capacity of fluidJ/K.m$^3$
$\sigma_{i}$Specific heat capacity of insulation materialJ/K.m$^3$
$\sigma_{ins}$Specific heat capacity of insulationJ/K.m$^3$
$\sigma_{j}$Specific heat capacity of jacket materialJ/K.m$^3$
$\sigma_{k2}$Specific heat capacity of layer located belowJ/K.m$^3$
$\sigma_{k3}$Specific heat capacity of layer located aboveJ/K.m$^3$
$\sigma_{kc}$Specific heat capacity of metallic componentJ/K.m$^3$
$\sigma_{ki}$Specific heat capacity of adjacent materialJ/K.m$^3$
$\sigma_{pipe}$Specific heat capacity of fluid-filled pipeJ/K.m$^3$
$\sigma_{prot}$Specific heat capacity of protective coverJ/K.m$^3$
$\sigma_{sc}$Specific heat capacity of screen materialJ/K.m$^3$
$\sigma_{scb}$Specific heat capacity of screen beddingJ/K.m$^3$
$\sigma_{scs}$Specific heat capacity of screen servingJ/K.m$^3$
$\sigma_{sh}$Specific heat capacity of sheath materialJ/K.m$^3$
$\sigma_{sun}$Absorption coefficient of solar radiation
$\sigma_{y}$Yield strength of metals for armourMPa
$SP_{p}$Sidewall pressureN/m
T $t$Thickness of insulation between conductorsmm
$T0_{gas}$Gas reference temperatureK
$T_{1}$Thermal resistance between one conductor and sheathK.m/W
$t_{1}$Thickness of insulation to sheathmm
$T_{1t}$Thermal resistance between one conductor and sheath, transientK.m/W
$t_{1t}$Thickness of insulation to sheath, transientmm
$T_{2}$Thermal resistance between sheath and armourK.m/W
$t_{2}$Thickness of bedding under armourmm
$T_{2_{1}}$Thermal resistance between sheath and 1st armour layerK.m/W
$T_{2_{2}}$Thermal resistance of material between armour layersK.m/W
$T_{2_{f}}$Thermal resistance between sheath and armour beddingK.m/W
$T_{3}$Thermal resistance of jacketK.m/W
$t_{3}$Thickness of serving over armourmm
$T_{4d}$Transient thermal resistance for daily loadK.m/W
$T_{4db}$Correction of thermal resistance for backfillK.m/W
$T_{4i}$Thermal resistance of medium in the ductK.m/W
$T_{4ii}$Thermal resistance of the duct wallK.m/W
$T_{4iii}$Thermal resistance to ambientK.m/W
$T_{4\mu}$Thermal resistance to ambientK.m/W
$T_{4ss}$Steady-state thermal resistanceK.m/W
$T_{4t}$Equivalent thermal resistance for tunnelK.m/W
$T_{4w}$Transient thermal resistance for weekly loadK.m/W
$T_{4y}$Transient thermal resistance for yearly loadK.m/W
$T_{A}$Element A of equivalent thermal circuitK.m/W
$T_{a}$Star thermal resistance of airK.m/W
$T_{a0}$Apparent thermal resistance aK.m/W
$t_{ab_{1}}$Thickness of 1st armour beddingmm
$t_{ab_{2}}$Thickness of armour separationmm
$T_{air}$Absolute air temperatureK
$T_{at}$Thermal resistance by convection air-tunnelK.m/W
$T_{B}$Element B of equivalent thermal circuitK.m/W
$T_{b0}$Apparent thermal resistance bK.m/W
$t_{c}$Thickness of hollow conductormm
$T_{C}$Element C of equivalent thermal circuitK.m/W
$t_{comp}$Thickness of compartmentmm
$T_{conv_{ce}}$Thermal resistance by convection conductor-enclosureK.m/W
$T_{conv_{sa}}$Thermal resistance by convection surface-airK.m/W
$t_{corr}$Thickness of corrugation fillingmm
$t_{cs}$Thickness of conductor shieldmm
$t_{ct}$Thickness of s.c. tape wrapped around conductormm
$T_{d}$Internal thermal resistance for dielectric lossesK.m/W
$T_{e}$External thermal resistance of tunnelK.m/W
$t_{EMF}$Time step to calculate current sources
$t_{encl}$Thickness of enclosuremm
$T_{eq}$Equivalent thermal resistanceK.m/W
$t_{f}$Thickness of filler/belt insulationmm
$T_{f}$Axial thermal resistance due to the movement of air through the tunnelK.m/W
$T_{gas}$Absolute gas temperatureK
$T_{i}$Internal thermal resistance for current lossesK.m/W
$t_{icore}$Thickness of core insulationmm
$T_{\infty}$Infinite bulk temperature (the ambient air temperature)K
$T_{ins}$Thermal resistance of insulationK.m/W
$t_{ins}$Thickness of insulationmm
$t_{is}$Thickness of insulation screenmm
$t_{j}$Thickness of jacketmm
$t_{jj}$Thickness of additional layer over jacketmm
$t_{k}$Duration of short-circuits
$T_{L}$Thermal longitudinal resistanceK.m/W
$T_{mh}$Mutual thermal resistance between rated and crossing objectK.m/W
$T_{mh_{v}}$Mutual thermal resistance per sliceK.m/W
$T_{o}$Thermal resistance of the oil in the pipeK.m/W
$t_{prot}$Thickness of protective covermm
$T_{prot}$Thermal resistance of protective coverK.m/W
$T_{r}$Total thermal resistanceK.m/W
$T_{rad_{ce}}$Radiation thermal resistance conductor-enclosureK.m/W
$T_{rad_{ext}}$Radiation thermal resistance tube-airK.m/W
$T_{rad_{int}}$Radiation thermal resistance surface-tubeK.m/W
$T_{rad_{sa}}$Radiation thermal resistance surface-airK.m/W
$T_{rad_{sun}}$Solar radiation thermal resistanceK.m/W
$T_{s}$Star thermal resistance of objectK.m/W
$T_{sa}$Thermal resistance by convection surface-airK.m/W
$t_{sc}$Thickness of the screenmm
$t_{scb}$Thickness of screen beddingmm
$t_{scs}$Thickness of screen servingmm
$t_{sh}$Thickness of the sheathmm
$T_{st}$Radiation thermal resistance surface-tunnelK.m/W
$T_{surf}$Absolute surface temperatureK
$t_{t}$Tunnel wall thicknessm
$T_{t}$Star thermal resistance of tunnelK.m/W
$T_{tot}$Total thermal resistance, transientK.m/W
$T_{tr}$Thermal resistance of troughK
$T_{tw}$Thermal resistance of tunnel wallK.m/W
$T_{wall}$Thermal resistance of pipe wallK.m/W
$\mathrm{tan}\delta _{i}$Loss factor of insulation
$\tau$Transient load periods
$\tau_{L}$Transient load period deep burials
$\theta_{2K}$Temperature rise for 2K criterion$^{\circ}$C
$\theta_{a}$Ambient temperature$^{\circ}$C
$\theta_{abs}$Absolute temperatureK
$\theta_{air}$Ambient air temperature$^{\circ}$C
$\theta_{ar}$Temperature of armour$^{\circ}$C
$\theta_{ar_{1}}$Temperature of 1st armour layer$^{\circ}$C
$\theta_{ar_{2}}$Temperature of 2nd armour layer$^{\circ}$C
$\theta_{at}$Air temperature with load$^{\circ}$C
$\theta_{at_{0}}$Air temperature with no load$^{\circ}$C
$\theta_{at_{i}}$Air temperature of previous iteration cycle$^{\circ}$C
$\theta_{at_{L}}$Air temperature in tunnel at outlet$^{\circ}$C
$\theta_{at_{z}}$Air temperature in tunnel at z$^{\circ}$C
$\theta_{c}$Temperature of conductor$^{\circ}$C
$\theta_{c_{z}}$Conductor temperature at z$^{\circ}$C
$\theta_{cmax}$Max. conductor temperature$^{\circ}$C
$\theta_{cmaxeo}$Max. emergency overload conductor temperature$^{\circ}$C
$\theta_{cmaxsc}$Max. short-circuit conductor temperature$^{\circ}$C
$\theta_{de}$Temperature of duct outer wall$^{\circ}$C
$\theta_{di}$Temperature of duct inner wall$^{\circ}$C
$\theta_{dm}$Mean temperature of the medium in the duct$^{\circ}$C
$\theta_{e}$External temperature of the object$^{\circ}$C
$\theta_{encl}$Temperature of enclosure$^{\circ}$C
$\theta_{f}$Temperature of filler for multi-core cables type SS with sheath$^{\circ}$C
$\theta_{gas}$Gas temperature$^{\circ}$C
$\theta_{hs}$Temperature of heat source$^{\circ}$C
$\theta_{kf}$Final temperature$^{\circ}$C
$\theta_{ki}$Initial temperature$^{\circ}$C
$\theta_{kmax}$Maximal temperature of non-insulation material$^{\circ}$C
$\theta_{max}$Temperature of conductor at end of emergency loading$^{\circ}$C
$\theta_{o}$Outer temperature$^{\circ}$C
$\theta_{o_{L}}$Temperature of the surface of object at outlet$^{\circ}$C
$\theta_{o_{z}}$Temperature of the surface of object at z$^{\circ}$C
$\theta_{p}$Angle to the plane of a sectionrad
$\theta_{R}$Rated current transient to steady-state ratio
$\theta_{s}$Temperature of screen/sheath$^{\circ}$C
$\theta_{sc}$Temperature of screen$^{\circ}$C
$\theta_{sh}$Temperature of sheath$^{\circ}$C
$\theta_{surf}$Surface temperature$^{\circ}$C
$\theta_{t}$Temperature of inner tunnel wall$^{\circ}$C
$\theta_{t_{L}}$Temperature of tunnel wall at outlet$^{\circ}$C
$\theta_{t_{z}}$Temperature of tunnel wall at z$^{\circ}$C
$\theta_{tm}$Mean temperature between surface and air in tunnel or trough$^{\circ}$C
$\theta_{to}$Temperature of outer tunnel wall$^{\circ}$C
$\theta_{to_{z}}$Temperature of outer tunnel wall at z$^{\circ}$C
$\theta_{tube}$Temperature of tube$^{\circ}$C
$\theta_{w}$Water temperature$^{\circ}$C
$\theta_{x}$Critical soil temperature$^{\circ}$C
$TQ$Cable thermal time constants
U $u$Substitution coefficient u
$U_{0}$Base voltage for testskV
$u_{b}$Substitution coefficient u
$U_{buried}$OHTC of fully buried pipeW/(K.m$^2$)
$U_{d}$Constant U for cables in ductsK.m/W
$U_{e}$Line-to-ground voltagekV
$U_{exposed}$OHTC of part of pipe in contact with waterW/(K.m$^2$)
$U_{ground}$OHTC of part of pipe in contact with groundW/(K.m$^2$)
$U_{inwall}$OHTC of inside film and pipe wallW/(K.m$^2$)
$U_{m}$Highest voltage for equipmentkV
$U_{n}$Rated line-to-line voltagekV
$U_{o}$Operating voltagekV
$U_{OHTC}$Overall heat transfer coefficientW/(K.m$^2$)
$U_{partially}$OHTC of partially buried pipeW/(K.m$^2$)
$U_{ti}$Circumference of inner rectangular tunnel wallm
$U_{wall}$OHTC of pipe wallW/(K.m$^2$)
V $v_{4}$Ratio thermal resistivity dry/moist soil
$V_{air}$Air velocitym/s
$V_{comp}$Gas volumem$^3$
$V_{d}$Constant V for cables in ductsK.m/W
$V_{drop}$Voltage dropV/A/km
$V_{fluid}$Velocity of fluidcm/s
$V_{gas}$Volume percentage of second gas%
$V_{m}$Molar volumem$^3$/mol
$V_{w}$Velocity of watercm/s
W $W_{A}$Armour lossesW/m
$W_{a_{L}}$Heat removed by air at outletW/m
$W_{a_{z}}$Heat removed by air at zW/m
$W_{air}$Losses between cable and j-tubeW/m
$w_{b}$Width of the backfillmm
$W_{c}$Conductor lossesW/m
$W_{conv_{ce}}$Convection heat transfer conductor-enclosureW/m
$W_{conv_{sa}}$Convection heat transfer surface-airW/m
$W_{d}$Dielectric lossesW/m
$W_{encl}$Enclosure lossesW/m
$w_{f_{1}}$Width of flat wires of 1st armourmm
$w_{f_{2}}$Width of flat wires of 2nd armourmm
$W_{h}$Heat generated by external objectW/m
$W_{hs}$Heat dissipation of heat sourceW/m
$W_{I}$Ohmic losses per phaseW/m
$W_{p}$Losses in pipeW/m
$w_{p}$Weight correction factor
$W_{rad_{ce}}$Radiation heat transfer conductor-enclosureW/m
$W_{rad_{ext}}$Radiation heat transfer tube-airW/m
$W_{rad_{int}}$Radiation heat transfer surface-tubeW/m
$W_{rad_{sa}}$Radiation heat transfer surface-airW/m
$W_{s}$Screen and sheath lossesW/m
$W_{sA}$Total loss in sheath and armourW/m
$W_{sA_{1}}$Total loss in sheath and 1st armourW/m
$W_{sA_{2}}$Total loss in sheath and 2nd armourW/m
$w_{sc}$Width of flat screen wiremm
$W_{sum}$Sum of total losses of all systemsW/m
$W_{sun}$Solar radiation heat transfer to surfaceW/m
$W_{sys}$Total losses of the systemW/m
$W_{t}$Total losses per phaseW/m
$W_{T}$Trench width in multi-layer backfillm
$w_{t}$Inner widthm
$W_{tot}$Total losses per objectW/m
$W_{tube}$Losses outside of j-tubeW/m
X $X_{0}$Zero sequence reactance$\Omega$/m
$x_{b}$Horizontal center of backfillmm
$X_{c}$Self reactance of conductor$\Omega$/m
$X_{G}$Factor $X_G$
$X_{G2}$Factor $X_{G2}$
$X_{K}$Factor $X_K$
$X_{m}$Mutual reactance between cables$\Omega$/m
$x_{p}$Factor for proximity effect of conductors
$x_{pos}$Horizontal x-position in multi-layer backfillmm
$x_{s}$Factor for skin effect on conductor
$X_{s}$Self reactance of screen/sheath$\Omega$/m
$X_{S1}$Reactance section 1$\Omega$/m
$X_{S2}$Reactance section 2$\Omega$/m
$X_{S3}$Reactance section 3$\Omega$/m
$\xi_{cb}$Parameter $\xi$ for calculation of loss factor
Y $Y$AdmittanceS/m
$y_{2K}$Depth for 2K criterionmm
$y_{c}$Skin and proximity effect factor for GIL conductor
$Y_{d}$Constant Y for cables in ductsK.m/W
$y_{encl}$Skin and proximity effect factor for GIL enclosure
$Y_{G}$Factor $Y_G$
$Y_{i}$Ordinates of the loss-load cyclep.u.
$Y_{K}$Factor $Y_K$
$y_{p}$Proximity effect factor of conductors
$y_{s}$Skin effect factor of conductor
Z $Z_{0}$Zero sequence impedance$\Omega$/m
$Z_{bs}$Installation constant Z
$Z_{c}$Self impedance of phase conductor$\Omega$/m
$z_{c}$Factor z to calculate skin effect coefficients for conductor
$z_{encl}$Factor z to calculate skin effect coefficients for enclosure
$z_{h}$Location of the heat sourcem
$Z_{K}$Factor $Z_K$
$Z_{m}$Mutual impedance between conductor and metal screen$\Omega$/m
$z_{max}$Logitudinal thermal limit distancem
$Z_{neg}$Negative sequence impedance$\Omega$/m
$Z_{pos}$Positive sequence impedance$\Omega$/m
$z_{r}$Location of the hottest pointm
$Z_{s}$Self impedance of metal screen$\Omega$/m
$Z_{x}$Equivalent mutual impedance between cables$\Omega$/m
$\zeta_{M}$Density of materialg/cm$^3$