References Documents

Cableizer is based on international and american standards and makes references to 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 & 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 et.al., 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&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 September 21, 2019.

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

SymbolNameUnit
A $a_{\mathrm{0}}$Coefficient a for partial transient temperature rise
$a_{\mathrm{12}}$Distance between phase 1 and 2mm
$a_{\mathrm{23}}$Distance between phase 2 and 3mm
$a_{\mathrm{31}}$Distance between phase 3 and 1mm
$A_{\mathrm{a}}$Cross-sectional area of armourmm²
$A_{\mathrm{a_{\mathrm{1}}}}$Cross-sectional area of 1st armourmm²
$A_{\mathrm{a_{\mathrm{2}}}}$Cross-sectional area of 2nd armourmm²
$A_{\mathrm{ab_{\mathrm{1}}}}$Cross-sectional area of 1st armour beddingmm²
$A_{\mathrm{ab_{\mathrm{2}}}}$Cross-sectional area of 2nd armour beddingmm²
$A_{\mathrm{c}}$Cross-sectional area of conductormm²
$a_{\mathrm{c}}$Skin and proximity effect coefficient a for GIL conductor
$A_{\mathrm{comp}}$Cross-sectional area of compartment
$a_{\mathrm{constr}}$Construction of armour
$A_{\mathrm{d}}$Cross-sectional area of duct wallmm²
$A_{\mathrm{d_{\mathrm{fill}}}}$Free cross-sectional area inside ductmm²
$a_{\mathrm{encl}}$Skin and proximity effect coefficient a for GIL enclosure
$A_{\mathrm{encl}}$Cross-sectional area of enclosuremm²
$A_{\mathrm{f}}$Cross-sectional area of fillermm²
$A_{\mathrm{i}}$Cross-sectional area of insulationmm²
$A_{\mathrm{j}}$Cross-sectional area of jacketmm²
$A_{\mathrm{k}}$Thermal property constant A(mm²/s)½
$a_{\mathrm{m}}$Mean distance between the phasesmm
$A_{\mathrm{prot}}$Cross-sectional area of protective covermm²
$a_{\mathrm{S1}}$Length of 1st sectionp.u.
$a_{\mathrm{S2}}$Length of 2nd sectionp.u.
$a_{\mathrm{S3}}$Length of 3rd sectionp.u.
$A_{\mathrm{sc}}$Cross-sectional area of screenmm²
$A_{\mathrm{scb}}$Cross-sectional area of screen beddigmm²
$A_{\mathrm{scs}}$Cross-sectional area of screen servingmm²
$A_{\mathrm{sh}}$Cross-sectional area of sheathmm²
$A_{\mathrm{t}}$Cross-sectional area of the tunnel
$a_{\mathrm{T}}$Distance a of multi-layer backfillm
$a_{\mathrm{VdW}}$Van der Walls constant abar.L²/mol²
$\alpha_{\mathrm{ar}}$Temperature coefficient of armour material1/K
$\alpha_{\mathrm{c}}$Temperature coefficient of conductor material1/K
$\alpha_{\mathrm{encl}}$Temperature coefficient of enclosure material1/K
$\alpha_{\mathrm{f}}$Phase shifting°
$\alpha_{\mathrm{gas}}$Thermal diffusivity for gasm²/s
$\alpha_{\mathrm{M}}$Factor αM
$\alpha_{\mathrm{sc}}$Temperature coefficient of screen material1/K
$\alpha_{\mathrm{sh}}$Temperature coefficient of sheath material1/K
$\alpha_{\mathrm{t}}$Conductor to surface attainment factor
B $B$SusceptanceS/m
$b_{\mathrm{0}}$Coefficient b for partial transient temperature rise1/s
$B_{\mathrm{1_{\mathrm{1}}}}$Loss coefficient B1 of 1st armourΩ/m
$B_{\mathrm{1_{\mathrm{2}}}}$Loss coefficient B1 of 2nd armourΩ/m
$B_{\mathrm{2_{\mathrm{1}}}}$Loss coefficient B2 of 1st armourΩ/m
$B_{\mathrm{2_{\mathrm{2}}}}$Loss coefficient B2 of 2nd armourΩ/m
$b_{\mathrm{c}}$Skin and proximity effect coefficient b for GIL conductor
$B_{\mathrm{EMF}}$Magnetic field strengthµT
$b_{\mathrm{encl}}$Skin and proximity effect coefficient b for GIL enclosure
$B_{\mathrm{k}}$Thermal property constant Bmm²/s
$b_{\mathrm{T}}$Distance b of multi-layer backfillm
$b_{\mathrm{VdW}}$Van der Walls constant bL/mol
$b_{\mathrm{x}}$Shorter side of backfillmm
$b_{\mathrm{y}}$Longer side of backfillmm
$\beta_{\mathrm{1}}$Substitution coefficient β1 for eddy-currents
$\beta_{\mathrm{6}}$Factor |1 - β(6)|
$\beta_{\mathrm{a_{\mathrm{1}}}}$Angle between armour and cable axisrad
$\beta_{\mathrm{a_{\mathrm{2}}}}$Angle between 2nd armour and cable axisrad
$\beta_{\mathrm{air}}$Volumetric thermal expansion coefficient of air1/K
$\beta_{\mathrm{ar}}$Reciprocal of temperature coefficient of armour materialK
$\beta_{\mathrm{c}}$Reciprocal of temperature coefficient of conductor materialK
$\beta_{\mathrm{encl}}$Reciprocal of temperature coefficient of enclosure materialK
$\beta_{\mathrm{gas}}$Volumetric thermal expansion coefficient for gas1/K
$\beta_{\mathrm{k}}$Reciprocal of temperature coefficient of resistanceK
$\beta_{\mathrm{M}}$Factor βM
$\beta_{\mathrm{sc}}$Reciprocal of temperature coefficient of screen materialK
$\beta_{\mathrm{sh}}$Reciprocal of temperature coefficient of sheath materialK
$\beta_{\mathrm{T}}$Equivalent thermal resistance of the soil per unit surfaceW/K.m²
$\beta_{\mathrm{t}}$Attainment factor cable surface to ambient
$\beta_{\mathrm{X}}$Crossing angle in radiansrad
$\beta_{\mathrm{xing}}$Crossing angle in degrees°
C $C_{\mathrm{av}}$Heat capacity of the air flowW/K
$C_{\mathrm{b}}$Capacitance of insulationF/m
$c_{\mathrm{constr}}$Construction of conductor
$c_{\mathrm{gas}}$Constant c for a gas under GIL conditions
$c_{\mathrm{ij}}$Coefficient c for view factor
$C_{\mathrm{k1}}$Non-adiabatic constant C1mm/m
$C_{\mathrm{k2}}$Non-adiabatic constant C2K.m.mm²/J
$C_{\mathrm{Nu}}$Factor C
$c_{\mathrm{p_{\mathrm{gas}}}}$Specific heat capacity at constant pressureJ/kg.K
$C_{\mathrm{q}}$Constants C1 to C7 of multi-layer backfill
$c_{\mathrm{SI}}$Surge velocity of propagationkm/s
$c_{\mathrm{T}}$Distance c of multi-layer backfillm
$c_{\mathrm{v_{\mathrm{gas}}}}$Specific heat capacity at constant volumeJ/kg.K
$C_{\mathrm{vair}}$Volumetric heat capacity of airJ/K.m³
$CC$Charging capacitykvar/km
$CC_{\mathrm{p}}$Conduit clearance%
$CF_{\mathrm{p}}$Conduit fill%
$CR_{\mathrm{p}}$Conduit ratio in duct%
$cuw$Standard copper wiresmm
D $D_{\mathrm{1}}$Diameter below screenmm
$D_{\mathrm{2_{\mathrm{1}}}}$Diameter below 1st armourmm
$D_{\mathrm{2_{\mathrm{2}}}}$Diameter below 2nd armourmm
$d_{\mathrm{a}}$Mean diameter of armourmm
$d_{\mathrm{a_{\mathrm{1}}}}$Mean diameter of 1st armourmm
$D_{\mathrm{a_{\mathrm{1}}}}$External diameter of 1st armourmm
$D_{\mathrm{a_{\mathrm{2}}}}$External diameter of 2nd armourmm
$d_{\mathrm{a_{\mathrm{2}}}}$Mean diameter of 2nd armourmm
$d_{\mathrm{b}}$Diameter of the backfillmm
$d_{\mathrm{c}}$External diameter of conductormm
$D_{\mathrm{c}}$Diameter of conductorm
$d_{\mathrm{ci}}$Internal diameter of conductormm
$D_{\mathrm{comp}}$Diameter of compartment (metric)m
$d_{\mathrm{comp}}$Diameter of compartmentmm
$d_{\mathrm{ct}}$External diameter of conductor for transient calculationsmm
$D_{\mathrm{e}}$External diameter of objectmm
$d_{\mathrm{e}}$Diameter of sheath and armourmm
$D_{\mathrm{encl}}$Outer diameter of enclosure (metric)m
$d_{\mathrm{encl}}$Outer diameter of enclosuremm
$D_{\mathrm{eq}}$Equivalent diameter of a group of cablesmm
$d_{\mathrm{f}}$Spacing from hottest object in groupm
$D_{\mathrm{f}}$External diameter of the fillermm
$d_{\mathrm{f_{\mathrm{1}}}}$Thickness of 1st armourmm
$d_{\mathrm{f_{\mathrm{2}}}}$Thickness of 2nd armourmm
$D_{\mathrm{hs}}$External diameter of heat sourcemm
$D_{\mathrm{i}}$Diameter over insulationmm
$d_{\mathrm{im}}$Imaginary layer of soilm
$D_{\mathrm{it}}$Diameter below sheathmm
$D_{\mathrm{o}}$Outer diameterm
$D_{\mathrm{oc}}$External diameter of sheathmm
$d_{\mathrm{pk1}}$Distance to mirrored buried objectmm
$d_{\mathrm{pk2}}$Distance between buried objectsmm
$d_{\mathrm{prot}}$Diameter of protective covermm
$d_{\mathrm{psc}}$Point source correctionm
$D_{\mathrm{s}}$Mean external diameter of the sheathmm
$d_{\mathrm{s}}$Mean diameter of sheathmm
$D_{\mathrm{scm}}$Mean diameter of screenmm
$d_{\mathrm{soil}}$Soil dry densitykg/m³
$d_{\mathrm{T}}$Distance d of multi-layer backfillm
$d_{\mathrm{x}}$Equivalent diameter of a conductormm
$D_{\mathrm{x}}$Characteristic diametermm
$D_{\mathrm{x_{\mathrm{w}}}}$Characteristic diameter for weekly loadmm
$D_{\mathrm{x_{\mathrm{y}}}}$Characteristic diameter for yearly loadmm
$DC_{\mathrm{p}}$Diameter factor in duct%
$\delta _{\mathrm{1}}$Thickness of screening layermm
$\Delta _{\mathrm{1}}$Substitution coefficient Δ1 for eddy-currents
$\Delta _{\mathrm{2}}$Substitution coefficient Δ2 for eddy-currents
$\delta _{\mathrm{ar}}$Equivalent thickness of armourmm
$\delta _{\mathrm{k}}$Thickness of screen, sheath or armourmm
$\delta _{\mathrm{soil}}$Soil thermal diffusivitym²/s
$\Delta d_{\mathrm{sh}}$Depth of corrugationmm
$\Delta H_{\mathrm{c}}$Heat of combustion coefficientMJ/kg
$\Delta t$Length of time steps
$\Delta \theta_{\mathrm{0t}}$Air temperature in tunnel increaseK
$\Delta \theta_{\mathrm{0x}}$Temperature rise of the conductorK
$\Delta \theta_{\mathrm{0x_{\mathrm{1}}}}$Temperature rise of the conductor, first estimateK
$\Delta \theta_{\mathrm{0x_{\mathrm{h}}}}$Temperature rise of the conductor by source hK
$\Delta \theta_{\mathrm{a_{\mathrm{t}}}}$Corrected transient temperature rise of conductorK
$\delta \theta_{\mathrm{c}}$Ohmic steady-state temperature riseK
$\Delta \theta_{\mathrm{c}}$Temperature rise of conductorK
$\Delta \theta_{\mathrm{c_{\mathrm{t}}}}$Transient temperature rise of conductor by ohmic lossesK
$\Delta \theta_{\mathrm{d}}$Temperature rise by dielectric lossesK
$\Delta \theta_{\mathrm{d_{\mathrm{t}}}}$Transient temperature rise by dielectric lossesK
$\Delta \theta_{\mathrm{e_{\mathrm{t}}}}$Transient temperature rise of outer surfaceK
$\Delta \theta_{\mathrm{gas}}$Temperature difference conductor-enclosure°C
$\Delta \theta_{\mathrm{kp}}$Temperature rise by buried object kK
$\Delta \theta_{\mathrm{max}}$Maximum permissible conductor temperature riseK
$\Delta \theta_{\mathrm{p}}$Temperature rise by other buried objectsK
$\Delta \theta_{\mathrm{R}}$Conductor temperature rise above ambient temperatureK
$\Delta \theta_{\mathrm{R_{\mathrm{\infty}}}}$Temperature rise in max. permissible°C
$\Delta \theta_{\mathrm{R_{\mathrm{t}}}}$Temperature rise neglecting resistance change°C
$\Delta \theta_{\mathrm{s}}$Temperature difference surface to ambientK
$\delta \theta_{\mathrm{SPK}}$Peak cyclic temperature riseK
$\Delta \theta_{\mathrm{sun}}$Temperature rise by solar radiationK
$\Delta \theta_{\mathrm{t}}$Transient temperature rise of conductorK
$\Delta \theta_{\mathrm{t_{\mathrm{\infty}}}}$Steady-state temperature rise of conductorK
$\Delta \theta_{\mathrm{tr}}$Temperature increase of air in troughK
$\Delta \theta_{\mathrm{x}}$Critical soil temperature riseK
$\Delta W$Incremental heat generatedW
$\Delta W_{\mathrm{0}}$Incremental heat 0 generatedW
$\Delta z$Length of the intervalm
$DF_{\mathrm{X}}$Derating factor for the permissible current
$Di_{\mathrm{d}}$Inside diameter of ductmm
$Di_{\mathrm{t}}$Diameter of the tunnel (inner)m
$Do_{\mathrm{d}}$Outside diameter of ductmm
$Do_{\mathrm{t}}$Diameter of the tunnel or trough (outer)m
E $E_{\mathrm{bs}}$Installation constant E
$e_{\mathrm{hor}}$Horizontal clearancemm
$E_{\mathrm{stress}}$Electrical field strengthkV/mm
$e_{\mathrm{ver}}$Vertical clearancemm
$e_{\mathrm{wall}}$Clearance to wallmm
$EEC$Embodied energy and carbonMJ/kg
$\epsilon_{\mathrm{0}}$Vacuum permittivityF/m
$\epsilon_{\mathrm{c}}$Effective emissivity of conductor
$\epsilon_{\mathrm{encl}}$Effective emissivity of enclosure
$\epsilon_{\mathrm{gas}}$Dielectric constant of gas in compartment
$\epsilon_{\mathrm{i}}$Relative permittivity of insulation
$\epsilon_{\mathrm{k}}$Heat loss allowance factor
$\epsilon_{\mathrm{rad}}$Effective emissivity
$\eta0_{\mathrm{gas}}$Reference dynamic viscosity of gasPa.s
$\eta_{\mathrm{gas}}$Dynamic viscosity of gasPa.s
F $f$System frequencyHz
$F_{\mathrm{a_{\mathrm{1}}}}$Effective length per unit lay length of 1st armourmm
$F_{\mathrm{a_{\mathrm{2}}}}$Effective length per unit lay length of 2nd armourmm
$F_{\mathrm{cable}}$Maximum effective pulling forceN/m
$f_{\mathrm{cb}}$Factor for cross-bonded earthing
$F_{\mathrm{e}}$Factor Fe for eddy-current losses
$F_{\mathrm{eq}}$Mutual heating coefficient
$F_{\mathrm{form}}$Form factor
$F_{\mathrm{ij}}$View factor object-object
$F_{\mathrm{in}}$Pulling force at beginning of a sectiondaN
$F_{\mathrm{k}}$Imperfect contact thermal factor
$F_{\mathrm{m}}$Radiation coefficient mutual
$F_{\mathrm{out}}$Pulling force at end of a sectiondaN
$F_{\mathrm{ppc}}$Permissible pull force on cabledaN
$f_{\mathrm{ppc}}$Factor of permissible pullN/mm²
$F_{\mathrm{pt}}$Function of pressure and temperature
$f_{\mathrm{SHF}}$Sheath factor
$F_{\mathrm{x}}$Geometrical distance factor for multi-core cables
G $g$Standard acceleration of gravitym/s²
$G$ConductanceS/m
$G_{\mathrm{1}}$Geometric factor G1
$G_{\mathrm{2}}$Geometric factor G2 for cables with separate sheaths
$G_{\mathrm{b}}$Geometric factor for backfill
$g_{\mathrm{bs}}$Installation constant g
$G_{\mathrm{encl}}$Factor G to calculate Nusselt number
$g_{\mathrm{s}}$Substitution coefficient gs for eddy-currents
$G_{\mathrm{s00}}$Factor Gs 0.0
$G_{\mathrm{s05}}$Factor Gs 0.5
$G_{\mathrm{s10}}$Factor Gs 1.0
$\gamma_{\mathrm{a}}$Armour anglerad
$\gamma_{\mathrm{c}}$Skin and proximity effect factor γ for GIL conductor
$\gamma_{\mathrm{encl}}$Skin and proximity effect factor γ for GIL enclosure
$\gamma_{\mathrm{t}}$Attainment factor for groups of cables
$\gamma_{\mathrm{X}}$Attenuation factor for crossing1/m
$GMD$Geometric mean distancemm
$GMR$Geometric mean radiusmm
$\mathrm{Gr}_{\mathrm{c}}$Grashof number conductor-gas
$\mathrm{Gr}_{\mathrm{encl}}$Grashof number gas-enclosure
$\mathrm{Gr}_{\mathrm{L}}$Grashof number
$\mathrm{Gr}_{\mathrm{prot}}$Grashof number surface-air
H $H_{\mathrm{1}}$Component of inductance Hsub>1H/m
$h_{\mathrm{1}}$Factor h1 for emergency load
$H_{\mathrm{1_{\mathrm{2}}}}$Component of inductance Hsub>1 of 2nd armourH/m
$h_{\mathrm{2}}$Factor h2 for emergency load
$H_{\mathrm{2}}$Component of inductance Hsub>2H/m
$H_{\mathrm{2_{\mathrm{2}}}}$Component of inductance Hsub>2 of 2nd armourH/m
$H_{\mathrm{3}}$Component of inductance Hsub>3H/m
$H_{\mathrm{3_{\mathrm{2}}}}$Component of inductance Hsub>3 of 2nd armourH/m
$h_{\mathrm{b}}$Height of the backfillmm
$h_{\mathrm{bs}}$Heat dissipation coefficient for black surfaces in free airW/m²/K5/4
$H_{\mathrm{c}}$Heat energy contentMJ/m
$h_{\mathrm{c}}$Convective heat transfer coefficient conductor-gasW/K.m²
$h_{\mathrm{encl}}$Convective heat transfer coefficient gas to enclosureW/m2.K
$h_{\mathrm{lg}}$Ratio of heat dissipation coefficients
$h_{\mathrm{prot}}$Convective heat transfer coefficient surface-airW/K.m²
$h_{\mathrm{rad_{\mathrm{ce}}}}$Radiation heat transfer coefficient conductor-enclosureW/K.m²
$h_{\mathrm{rad_{\mathrm{sa}}}}$Radiation heat transfer coefficient surface-airW/K.m²
$h_{\mathrm{roll}}$Height of roller above bottomm
$H_{\mathrm{s}}$Sheath conductanceH/m
$H_{\mathrm{sun}}$Intensity of solar radiationW/m²
$h_{\mathrm{t}}$Inner heightm
$H_{\mathrm{T}}$Trench depth to bedding layer in multi-layer backfillm
$h_{\mathrm{T4}}$Ratio of thermal resistance to ambient
$H_{\mathrm{tc}}$Parameter H for trough
$h_{\mathrm{tr}}$Heat transfer coefficientW/K.m²
$H_{\mathrm{ts}}$Parameter H depending on air velocity
$H_{\mathrm{x}}$Magnetic field x-componentmH
$H_{\mathrm{y}}$Magnetic field y-componentmH
I $I_{\mathrm{1}}$Steady-state current before transientA
$I_{\mathrm{2}}$Emergency load currentA
$I_{\mathrm{C}}$Capacitive load currentA/km
$I_{\mathrm{c}}$Permissible current ratingA
$I_{\mathrm{c_{\mathrm{max}}}}$Highest current load of lineA
$I_{\mathrm{c_{\mathrm{peak}}}}$Permissible peak cyclic load currentA
$I_{\mathrm{Ce}}$Capacitive earth short-circuit currentA/km
$I_{\mathrm{EMF}}$Phase current for EMF calculationA
$I_{\mathrm{k}}$Permissible short-circuit currentkA
$I_{\mathrm{kAD}}$Short-circuit current (adiabatic)kA
$I_{\mathrm{kSC}}$Effective short-circuit currentkA
$I_{\mathrm{method}}$Current calculation method
$I_{\mathrm{R}}$Transient conductor current, step valueA
$inst_{\mathrm{air}}$Installation in air
$inst_{\mathrm{sea}}$Installation of subsea cables
$inst_{\mathrm{t}}$Installation in air
J $j_{\mathrm{max}}$Phase angle range°
$JR_{\mathrm{p}}$Jam ratio in duct%
K $K$Screening factor
$K_{\mathrm{0}}$Coefficient K for a gas under GIL conditions
$K_{\mathrm{02}}$Factor K0.2
$K_{\mathrm{06}}$Factor K0.6
$k_{\mathrm{1}}$Thermal conductivity of surface layerW/K.m
$K_{\mathrm{10}}$Factor K1.0
$k_{\mathrm{2}}$Thermal conductivity of mid backfill layerW/K.m
$k_{\mathrm{3}}$Thermal conductivity of bedding layerW/K.m
$k_{\mathrm{4}}$Thermal conductivity of soilW/K.m
$K_{\mathrm{A}}$Coefficient K to calculate in air
$k_{\mathrm{air}}$Thermal conductivity of airW/m.K
$K_{\mathrm{BICC}}$Constant relating to conductor formation
$k_{\mathrm{Boltzmann}}$Boltzmann constantJ/K
$k_{\mathrm{c}}$Thermal conductivity of conductor materialK.m/W
$K_{\mathrm{c}}$Constant Kc for convection heat transfer
$K_{\mathrm{cv}}$Convection factor
$K_{\mathrm{E}}$Surface heat conductanceW/m²
$k_{\mathrm{encl}}$Thermal conductivity of enclosureW/m.K
$k_{\mathrm{gas}}$Thermal conductivity for gasW/m.K
$K_{\mathrm{GMR}}$Geometric mean radius factor
$k_{\mathrm{H}}$Heinhold characteristic diameter coefficient
$K_{\mathrm{k}}$Specific short-circuit parameterA.s½/mm²
$k_{\mathrm{l}}$Temperature rise factor in air
$k_{\mathrm{LF}}$Load loss constant coefficientp.u.
$k_{\mathrm{p}}$Proximity effect coefficient
$k_{\mathrm{prot}}$Thermal conductivity of protective coverW/m.K
$K_{\mathrm{r}}$Radiation shape factor
$k_{\mathrm{r2}}$Temperature rise ratio δθSPK/δθcp.u.
$k_{\mathrm{s}}$Skin effect coefficient
$K_{\mathrm{t}}$Effective emissivity of surface
$k_{\mathrm{t}}$Temperature rise ratiop.u.
$k_{\mathrm{X}}$Number of heat sources crossing
$K_{\mathrm{x}}$Factor for fictitious diameter by Neher
L $L_{\mathrm{0}}$Reference length of the tunnelm
$L_{\mathrm{1}}$Inductance of phase 1H/m
$L_{\mathrm{2}}$Inductance of phase 2H/m
$L_{\mathrm{3}}$Inductance of phase 3H/m
$L_{\mathrm{b}}$Vertical center of backfillmm
$L_{\mathrm{c}}$Depth of laying of sourcesmm
$L_{\mathrm{char}}$Characteristic length
$L_{\mathrm{cm}}$Depth of laying (metric)m
$L_{\mathrm{cni}}$Imaginary laying depth with non-isothermal earth surfacem
$L_{\mathrm{crit}}$Critical system lengthkm
$L_{\mathrm{deep}}$Equivalent depth for deep burialm
$L_{\mathrm{h}}$Depth of laying of crossing elementmm
$L_{\mathrm{m}}$Mean inductance of the phasesH/m
$L_{\mathrm{p}}$Length of a sectionm
$L_{\mathrm{r}}$Depth of laying of the rated objectmm
$L_{\mathrm{sys}}$System lengthkm
$L_{\mathrm{T}}$Length of the tunnelm
$\lambda_{\mathrm{0}}$Substitution coefficient λ0 for eddy-currents
$\lambda_{\mathrm{1}}$Loss factor of screen and sheath
$\lambda_{\mathrm{1c}}$Loss factor by circulating currents
$\lambda_{\mathrm{1cb}}$Loss factor for solid bonding
$\lambda_{\mathrm{1e}}$Loss factor by eddy currents
$\lambda_{\mathrm{1es}}$Loss factor for single point bonding
$\lambda_{\mathrm{2}}$Loss factor of armour
$\lambda_{\mathrm{3}}$Loss factor of steel pipes
$\lambda_{\mathrm{d}}$Factor for dielectric losses
$\lambda_{\mathrm{gas}}$Ratio cp/cv
$\lambda_{\mathrm{t}}$Relaxation parameter
$LF$Load factorp.u.
$LF_{\mathrm{w}}$Weekly load factorp.u.
$LF_{\mathrm{y}}$Yearly load factorp.u.
$LME$London Metal ExchangeUSD/mt
M $M$Cyclic rating factorp.u.
$m$Mass of objectkg/m
$M_{\mathrm{0}}$Coefficient M for partial transient temperature rises
$m_{\mathrm{0}}$Substitution coefficient m0 for eddy-currentsHz.m/Ω
$M_{\mathrm{1}}$Corrected cyclic rating factorK
$M_{\mathrm{ab}}$Material of armour bedding
$M_{\mathrm{c}}$Material of conductor
$M_{\mathrm{cable}}$List of materials in a cable
$M_{\mathrm{comp}}$Insulating gas material
$M_{\mathrm{d}}$Material of duct pipe
$M_{\mathrm{e}}$Substitution coefficient Me to calculate factor $F_e$
$m_{\mathrm{EMF}}$Number of time steps
$M_{\mathrm{encl}}$Material of enclosure
$M_{\mathrm{f}}$Material of filler
$M_{\mathrm{gas}}$Gas and gas-mixtures
$M_{\mathrm{i}}$Material of insulation
$M_{\mathrm{IEEE}}$Materials acc. IEEE 442
$M_{\mathrm{j}}$Material of jacket
$M_{\mathrm{k}}$Thermal contact factors½
$M_{\mathrm{m}}$Mean mutual inductance of sheathH/m
$m_{\mathrm{mol}}$Molecular massmol
$M_{\mathrm{mol}}$Molar massg/mol
$m_{\mathrm{Nu}}$Factor m
$M_{\mathrm{prot}}$Material of protective cover
$M_{\mathrm{s}}$Factor Ms
$M_{\mathrm{sc}}$Material of screen
$M_{\mathrm{sh}}$Material of sheath
$M_{\mathrm{soil}}$Type of soils
$\mu$Loss factorp.u.
$\mu_{\mathrm{0}}$Vacuum permeabilityH/m
$\mu_{\mathrm{e}}$Longitudinal relative permeability
$\mu_{\mathrm{p}}$Friction coefficient
$\mu_{\mathrm{s}}$Relative permeability
$\mu_{\mathrm{t}}$Traverse relative permeability of steel wires
$\mu_{\mathrm{w}}$Loss factor for weekly load variationp.u.
$\mu_{\mathrm{y}}$Loss factor for yearly load variationp.u.
N $N_{\mathrm{0}}$Coefficient N for partial transient temperature rise
$n_{\mathrm{a_{\mathrm{1}}}}$Number of wires of 1st armour
$n_{\mathrm{a_{\mathrm{2}}}}$Number of wires of 2nd armour
$N_{\mathrm{Avogrado}}$Avogadro constant1/mol
$N_{\mathrm{b}}$Number of loaded objects in backfill
$N_{\mathrm{c}}$Number of sources in system
$n_{\mathrm{c}}$Number of conductors in object
$n_{\mathrm{cc}}$Number of conductors combined
$n_{\mathrm{cg}}$Number of conductors in GIL
$n_{\mathrm{cw}}$Number of wires in conductor
$N_{\mathrm{e}}$Substitution coefficient Ne to calculate factor $F_e$
$n_{\mathrm{ppc}}$Number of conductors/cables being pulled
$N_{\mathrm{sea}}$Number of subsea cables
$N_{\mathrm{sum}}$Total number of objects in an air-filled space
$n_{\mathrm{sw}}$Number of screen wires
$N_{\mathrm{X}}$Number of intervals
$\nu$Summation step 1 to $N_X$
$\nu_{\mathrm{air}}$Kinematic viscosity for airm²/s
$\mathrm{Nu}_{\mathrm{c}}$Nusselt number conductor-gas
$\mathrm{Nu}_{\mathrm{encl}}$Nusselt number gas-enclosure
$\nu_{\mathrm{gas}}$Kinematic viscosity for gasm²/s
$\mathrm{Nu}_{\mathrm{L}}$Nusselt number
$\mathrm{Nu}_{\mathrm{prot}}$Nusselt number surface-air
$\nu_{\mathrm{soil}}$Soil moisture content%
O $\omega$Angular frequencyrad/s
P $p_{\mathrm{a_{\mathrm{1}}}}$Length of lay of 1st armourmm
$p_{\mathrm{a_{\mathrm{2}}}}$Length of lay of 2nd armourmm
$p_{\mathrm{ab1}}$Factor apportioning the 1st armour bedding
$p_{\mathrm{ab2}}$Factor apportioning the 2nd armour bedding
$p_{\mathrm{cb}}$Minor ratio of section lengths
$P_{\mathrm{cc}}$Substitution coefficient P to calculate loss factor by circulating currents
$p_{\mathrm{comp}}$Gas pressure in compartmentbar
$p_{\mathrm{gas}}$Gas pressurePa
$p_{\mathrm{i}}$Factor apportioning the insulation
$p_{\mathrm{j}}$Factor apportioning the jacket
$P_{\mathrm{L}}$Active power at load receptorkW
$p_{\mathrm{soil}}$Depth of image source
$p_{\mathrm{tr}}$Effective perimeter of troughm
$p_{\mathrm{VdW}}$Van der Walls equationPa
$\phi_{\mathrm{b}}$Parameter φ for trough
$\phi_{\mathrm{p}}$Angle of a bendrad
$\pi$Archimedes' constant π
$\mathrm{Pr}_{\mathrm{air}}$Prandtl number for air
$\mathrm{Pr}_{\mathrm{gas}}$Prandtl number for gas
Q $q_{\mathrm{1}}$Ratio of losses affecting screen bedding/serving
$q_{\mathrm{2_{\mathrm{1}}}}$Ratio of losses affecting 1st armour bedding
$q_{\mathrm{2_{\mathrm{2}}}}$Ratio of losses affecting 2nd armour bedding
$q_{\mathrm{3}}$Ratio of losses affecting jacket
$q_{\mathrm{4}}$Ratio of losses affecting environment
$Q_{\mathrm{A}}$Element A of two-part thermal circuitJ/m.K
$Q_{\mathrm{a_{\mathrm{1}}}}$Thermal capacitance of 1st armourJ/m.K
$Q_{\mathrm{a_{\mathrm{2}}}}$Thermal capacitance of 2nd armourJ/m.K
$Q_{\mathrm{ab_{\mathrm{1}}}}$Thermal capacitance of 1st armour beddingJ/m.K
$Q_{\mathrm{ab_{\mathrm{2}}}}$Thermal capacitance of 2nd armour beddingJ/m.K
$Q_{\mathrm{B}}$Element B of two-part thermal circuitJ/m.K
$Q_{\mathrm{B_{\mathrm{ab1}}}}$Element B of two-part thermal circuit, 1st armour beddingJ/m.K
$Q_{\mathrm{B_{\mathrm{ab2}}}}$Element B of two-part thermal circuit, 2nd armour beddingJ/m.K
$Q_{\mathrm{B_{\mathrm{d}}}}$Element B of two-part thermal circuit, ductJ/m.K
$Q_{\mathrm{B_{\mathrm{f}}}}$Element B of two-part thermal circuit, fillerJ/m.K
$Q_{\mathrm{B_{\mathrm{i}}}}$Element B of two-part thermal circuit, insulationJ/m.K
$Q_{\mathrm{B_{\mathrm{j}}}}$Element B of two-part thermal circuit, jacketJ/m.K
$Q_{\mathrm{B_{\mathrm{s}}}}$Element B of two-part thermal circuit, screen/sheathJ/m.K
$Q_{\mathrm{c}}$Thermal capacitance of conductorJ/m.K
$q_{\mathrm{cb}}$Major ratio of section lengths
$Q_{\mathrm{cc}}$Substitution coefficient Q to calculate loss factor by circulating currents
$Q_{\mathrm{d}}$Thermal capacitance of duct wallJ/m.K
$Q_{\mathrm{d_{\mathrm{fill}}}}$Thermal capacitance of duct fillingJ/m.K
$Q_{\mathrm{f}}$Thermal capacitance of fillerJ/m.K
$q_{\mathrm{f}}$Ratio of losses affecting the filler
$Q_{\mathrm{i}}$Thermal capacitance of insulationJ/m.K
$Q_{\mathrm{i1}}$Thermal capacitance of insulation, 1st portionJ/m.K
$Q_{\mathrm{i2}}$Thermal capacitance of insulation, 2nd portionJ/m.K
$Q_{\mathrm{j}}$Thermal capacitance of jacketJ/m.K
$Q_{\mathrm{p}}$Quantity of lubricantl/m
$Q_{\mathrm{sc}}$Thermal capacitance of screenJ/m.K
$Q_{\mathrm{scb}}$Thermal capacitance of screen beddingJ/m.K
$Q_{\mathrm{scs}}$Thermal capacitance of screen servingJ/m.K
$Q_{\mathrm{sh}}$Thermal capacitance of sheathJ/m.K
$Q_{\mathrm{t}}$Total thermal capacitance, transientJ/m.K
$q_{\mathrm{x}}$Factor for characteristic diameter
R $R_{\mathrm{0}}$Zero sequence resistanceΩ/m
$R_{\mathrm{1}}$Resistance of conductor before emergency ratingΩ/m
$R_{\mathrm{A}}$Electrical resistance of armourΩ/m
$R_{\mathrm{A_{\mathrm{1}}}}$Electrical resistance of 1st armour layerΩ/m
$R_{\mathrm{A_{\mathrm{2}}}}$Electrical resistance of 2nd armour layerΩ/m
$r_{\mathrm{b}}$Equivalent radius of backfillmm
$R_{\mathrm{c}}$Resistance of conductorΩ/m
$r_{\mathrm{c}}$Radius of conductormm
$R_{\mathrm{CG}}$Thermal resistance of multi-layer backfillK.m/W
$R_{\mathrm{co}}$DC resistance of conductor at 20°CΩ/m
$R_{\mathrm{e}}$Electrical resistance of sheath and armourΩ/m
$R_{\mathrm{e_{\mathrm{1}}}}$Electrical resistance of sheath and 1st armourΩ/m
$R_{\mathrm{e_{\mathrm{2}}}}$Electrical resistance of sheath and 2nd armourΩ/m
$R_{\mathrm{encl}}$Electrical resistance of enclosureΩ/m
$R_{\mathrm{encl20}}$DC resistance of enclosure at 20°CΩ/m
$r_{\mathrm{F}}$Radius below the insulationmm
$R_{\mathrm{gas}}$Specific gas constant
$R_{\mathrm{gas0}}$Universal molar gas constant
$r_{\mathrm{I}}$Radius of the insulationmm
$r_{\mathrm{ij}}$Coefficient r for view factor
$R_{\mathrm{max}}$Resistance of conductor at emergency ratingΩ/m
$r_{\mathrm{mbi}}$Minimal bending radius for installationm
$r_{\mathrm{mbif}}$Factor of minimal installation bending radius
$r_{\mathrm{mbp}}$Minimal bending radius during cable pullingm
$r_{\mathrm{mbpf}}$Factor of minimal pulling bending radius
$R_{\mathrm{p}}$Radius of a bendm
$R_{\mathrm{q1}}$Thermal resistance 1 of multi-layer backfill methodK.m/W
$R_{\mathrm{q11}}$Thermal resistance 11 of multi-layer backfill methodK.m/W
$R_{\mathrm{q12}}$Thermal resistance 12 of multi-layer backfill methodK.m/W
$R_{\mathrm{q13}}$Thermal resistance 13 of multi-layer backfill methodK.m/W
$R_{\mathrm{q2}}$Thermal resistance 2 of multi-layer backfill methodK.m/W
$R_{\mathrm{q21}}$Thermal resistance 21 of multi-layer backfill methodK.m/W
$R_{\mathrm{q22}}$Thermal resistance 22 of multi-layer backfill methodK.m/W
$R_{\mathrm{q23}}$Thermal resistance 23 of multi-layer backfill methodK.m/W
$R_{\mathrm{q24}}$Thermal resistance 24 of multi-layer backfill methodK.m/W
$R_{\mathrm{q3}}$Thermal resistance 3 of multi-layer backfill methodK.m/W
$R_{\mathrm{q31}}$Thermal resistance 31 of multi-layer backfill methodK.m/W
$R_{\mathrm{q32}}$Thermal resistance 32 of multi-layer backfill methodK.m/W
$R_{\mathrm{q33}}$Thermal resistance 33 of multi-layer backfill methodK.m/W
$R_{\mathrm{q34}}$Thermal resistance 34 of multi-layer backfill methodK.m/W
$R_{\mathrm{R}}$Resistance of conductor in steady-stateΩ/m
$R_{\mathrm{s}}$Electrical resistance of screen||sheathΩ/m
$R_{\mathrm{sc}}$Electrical resistance of screenΩ/m
$R_{\mathrm{sh}}$Electrical resistance of sheathΩ/m
$R_{\mathrm{so}}$Resistance of screen and sheath at 20°CΩ/m
$r_{\mathrm{\theta}}$Factor r for emergency load current
$r_{\mathrm{x}}$Radius to point x in insulationmm
$\mathrm{Ra}_{\mathrm{c}}$Rayleigh number conductor-gas
$\mathrm{Ra}_{\mathrm{encl}}$Rayleigh number gas-enclosure
$\mathrm{Ra}_{\mathrm{L}}$Rayleigh number
$\mathrm{Ra}_{\mathrm{prot}}$Rayleigh number surface-air
$\mathrm{Re}_{\mathrm{air}}$Reynolds number for air
$RF$Reduction factor
$\rho_{\mathrm{4}}$Thermal resistivity of soilK.m/W
$\rho_{\mathrm{4d}}$Thermal resistivity of dry soilK.m/W
$\rho_{\mathrm{ab}}$Thermal resistivity of armour beddingK.m/W
$\rho_{\mathrm{ab_{\mathrm{2}}}}$Thermal resistivity of bedding between armour layersK.m/W
$\rho_{\mathrm{ar}}$Specific electrical resistivity of armour materialΩ.m
$\rho_{\mathrm{b}}$Thermal resistivity backfillK.m/W
$\rho_{\mathrm{b1}}$Thermal resistivity of surface layerK.m/W
$\rho_{\mathrm{b2}}$Thermal resistivity of mid backfill layerK.m/W
$\rho_{\mathrm{c}}$Electrical resistivity of conductor materialΩ.m
$\rho_{\mathrm{corr}}$Thermal resistivity of corrugation fillingK.m/W
$\rho_{\mathrm{cr}}$Thermal resistivity of conductor materialK.m/W
$\rho_{\mathrm{d}}$Thermal resistivity of duct materialK.m/W
$\rho_{\mathrm{d_{\mathrm{fill}}}}$Thermal resistivity of bentonite fillingK.m/W
$\rho_{\mathrm{encl}}$Specific electrical resistivity of enclosure materialΩ.m
$\rho_{\mathrm{f}}$Thermal resistivity of fillerK.m/W
$\rho_{\mathrm{gas}}$Gas densitykg/m³
$\rho_{\mathrm{i}}$Thermal resistivity of insulationK.m/W
$\rho_{\mathrm{j}}$Thermal resistivity of jacket materialK.m/W
$\rho_{\mathrm{k2}}$Thermal resistivity of the layer located aboveK.m/W
$\rho_{\mathrm{k20}}$Electrical resistivity of metallic componentΩ.m
$\rho_{\mathrm{k3}}$Thermal resistivity of the layer located belowK.m/W
$\rho_{\mathrm{ki}}$Thermal resistivity of adjacent materialK.m/W
$\rho_{\mathrm{m}}$Thermal resistivity of the screenK.m/W
$\rho_{\mathrm{sc}}$Specific electrical resistivity of screen materialΩ.m
$\rho_{\mathrm{sh}}$Specific electrical resistivity of sheath materialΩ.m
$\rho_{\mathrm{soil}}$Specific electrical resistivity of soilΩ
$\rho_{\mathrm{t}}$Thermal resistivity of tunnel wallK.m/W
S $s_{\mathrm{1}}$Thickness of surface layerm;
$s_{\mathrm{2}}$Thickness of mid backfill layer
$s_{\mathrm{3}}$Thickness from object to upper boundary of bedding layer
$s_{\mathrm{4}}$Thickness from object to lower boundary of bedding layer
$s_{\mathrm{air}}$Axial spacing between objectsm
$s_{\mathrm{c}}$Separation of conductors in a systemmm
$s_{\mathrm{c2}}$Separation of cablesmm
$S_{\mathrm{G}}$Apparent power at injecting pointkW
$S_{\mathrm{gas}}$Sutherland's constantK
$s_{\mathrm{ij}}$Spacing between object i and j
$S_{\mathrm{k}}$Cross-sectional area of current carrying componentmm²
$s_{\mathrm{roll}}$Roller distancem
$s_{\mathrm{S1}}$Variation of spacing in 1st sectionp.u.
$s_{\mathrm{S2}}$Variation of spacing in 2nd sectionp.u.
$s_{\mathrm{S3}}$Variation of spacing in 3rd sectionp.u.
$s_{\mathrm{T}}$Distance to lateral edge of multi-layer backfillm
$s_{\mathrm{x}}$Separation of conductors in a cablemm
$SI$Surge ImpedanceΩ
$\sigma$Stefan Boltzmann constantW/m²K4
$\sigma_{\mathrm{ab}}$Specific heat capacity of armour beddingJ/K.m³
$\sigma_{\mathrm{ar}}$Specific heat capacity of armour materialJ/K.m³
$\sigma_{\mathrm{c}}$Specific heat capacity of conductor materialJ/K.m³
$\sigma_{\mathrm{d}}$Specific heat capacity of duct materialJ/K.m³
$\sigma_{\mathrm{d_{\mathrm{fill}}}}$Specific heat capacity of duct fillingJ/K.m³
$\sigma_{\mathrm{encl}}$Specific heat capacity of enclosure materialJ/K.m³
$\sigma_{\mathrm{f}}$Specific heat capacity of fillerJ/K.m³
$\sigma_{\mathrm{i}}$Specific heat capacity of insulation materialJ/K.m³
$\sigma_{\mathrm{j}}$Specific heat capacity of jacket materialJ/K.m³
$\sigma_{\mathrm{k2}}$Specific heat capacity of layer located belowJ/K.m³
$\sigma_{\mathrm{k3}}$Specific heat capacity of layer located aboveJ/K.m³
$\sigma_{\mathrm{kc}}$Specific heat capacity of metallic componentJ/K.m³
$\sigma_{\mathrm{ki}}$Specific heat capacity of adjacent materialJ/K.m³
$\sigma_{\mathrm{sc}}$Specific heat capacity of screen materialJ/K.m³
$\sigma_{\mathrm{scb}}$Specific heat capacity of screen beddingJ/K.m³
$\sigma_{\mathrm{scs}}$Specific heat capacity of screen servingJ/K.m³
$\sigma_{\mathrm{sh}}$Specific heat capacity of sheath materialJ/K.m³
$\sigma_{\mathrm{sun}}$Absorption coefficient of solar radiation
$\sigma_{\mathrm{y}}$Yield strength of metals for armourMPa
$SP_{\mathrm{p}}$Sidewall pressureN/m
T $t$Thickness of insulation between conductorsmm
$T0_{\mathrm{gas}}$Gas reference temperatureK
$T_{\mathrm{1}}$Thermal resistance between one conductor and sheathK.m/W
$t_{\mathrm{1}}$Thickness of insulation to sheathmm
$t_{\mathrm{1t}}$Thickness of insulation to sheath, transientmm
$T_{\mathrm{1t}}$Thermal resistance between one conductor and sheath, transientK.m/W
$t_{\mathrm{2}}$Thickness of bedding under armourmm
$T_{\mathrm{2}}$Thermal resistance between sheath and armourK.m/W
$T_{\mathrm{2_{\mathrm{1}}}}$Thermal resistance between sheath and 1st armour layerK.m/W
$T_{\mathrm{2_{\mathrm{2}}}}$Thermal resistance of material between armour layersK.m/W
$T_{\mathrm{2_{\mathrm{f}}}}$Thermal resistance between sheath and armour beddingK.m/W
$T_{\mathrm{3}}$Thermal resistance of jacketK.m/W
$t_{\mathrm{3}}$Thickness of serving over armourmm
$T_{\mathrm{4d}}$Transient thermal resistance for daily loadK.m/W
$T_{\mathrm{4db}}$Correction of thermal resistance for backfillK.m/W
$T_{\mathrm{4i}}$Thermal resistance of medium in the ductK.m/W
$T_{\mathrm{4ii}}$Thermal resistance of the duct wallK.m/W
$T_{\mathrm{4iii}}$Thermal resistance to ambientK.m/W
$T_{\mathrm{4\mu}}$Thermal resistance to ambientK.m/W
$T_{\mathrm{4ss}}$Steady-state thermal resistanceK.m/W
$T_{\mathrm{4t}}$Equivalent thermal resistance for tunnelK.m/W
$T_{\mathrm{4w}}$Transient thermal resistance for weekly loadK.m/W
$T_{\mathrm{4y}}$Transient thermal resistance for yearly loadK.m/W
$T_{\mathrm{a}}$Star thermal resistance of airK.m/W
$T_{\mathrm{A}}$Element A of equivalent thermal circuitK.m/W
$T_{\mathrm{a0}}$Apparent thermal resistance a1/s
$t_{\mathrm{ab_{\mathrm{1}}}}$Thickness of 1st armour beddingmm
$t_{\mathrm{ab_{\mathrm{2}}}}$Thickness of 2nd bedding betweenmm
$T_{\mathrm{at}}$Thermal resistance by convection air-tunnelK.m/W
$T_{\mathrm{B}}$Element B of equivalent thermal circuitK.m/W
$T_{\mathrm{b0}}$Apparent thermal resistance b
$t_{\mathrm{c}}$Thickness of hollow conductormm
$T_{\mathrm{C}}$Element C of equivalent thermal circuitK.m/W
$t_{\mathrm{comp}}$Thickness of compartmentmm
$T_{\mathrm{conv_{\mathrm{ce}}}}$Thermal resistance by convection conductor-enclosureW/m
$T_{\mathrm{conv_{\mathrm{sa}}}}$Thermal resistance by convection surface-airW/m
$t_{\mathrm{corr}}$Thickness of corrugation fillingmm
$t_{\mathrm{cs}}$Thickness of conductor shieldmm
$t_{\mathrm{ct}}$Thickness of s.c. tape wrapped around conductormm
$T_{\mathrm{d}}$Internal thermal resistance for dielectric lossesK.m/W
$T_{\mathrm{e}}$External thermal resistance of tunnelK.m/W
$t_{\mathrm{EMF}}$Time step to calculate current sources
$t_{\mathrm{encl}}$Thickness of enclosuremm
$T_{\mathrm{eq}}$Equivalent thermal resistanceK.m/W
$T_{\mathrm{f}}$Axial thermal resistance due to the movement of air through the tunnelK.m/W
$t_{\mathrm{f}}$Thickness of filler/belt insulationmm
$T_{\mathrm{gas}}$Absolute gas temperatureK
$T_{\mathrm{i}}$Internal thermal resistance for current lossesK.m/W
$t_{\mathrm{i}}$Thickness of core insulationmm
$T_{\mathrm{\infty}}$Infinite bulk temperature (the ambient air temperature)K
$t_{\mathrm{ins}}$Thickness of insulationmm
$t_{\mathrm{is}}$Thickness of insulation screenmm
$t_{\mathrm{j}}$Thickness of jacketmm
$t_{\mathrm{jj}}$Thickness of additional layer over jacketmm
$t_{\mathrm{k}}$Duration of short-circuits
$T_{\mathrm{L}}$Thermal longitudinal resistanceK.m/W
$T_{\mathrm{mh}}$Mutual thermal resistance between rated and crossing objectK.m/W
$T_{\mathrm{mh_{\mathrm{v}}}}$Mutual thermal resistance per sliceK.m/W
$T_{\mathrm{o}}$Thermal resistance of the oil in the pipeK.m/W
$T_{\mathrm{prot}}$Thermal resistance of protective coverK.m/W
$t_{\mathrm{prot}}$Thickness of protective covermm
$T_{\mathrm{r}}$Total thermal resistanceK.m/W
$T_{\mathrm{rad_{\mathrm{ce}}}}$Radiation thermal resistance conductor-enclosureW/m
$T_{\mathrm{rad_{\mathrm{sa}}}}$Radiation thermal resistance surface-airW/m
$T_{\mathrm{s}}$Star thermal resistance of objectK.m/W
$T_{\mathrm{sa}}$Thermal resistance by convection surface-airK.m/W
$t_{\mathrm{sc}}$Thickness of the screenmm
$t_{\mathrm{scb}}$Thickness of screen beddingmm
$t_{\mathrm{scs}}$Thickness of screen servingmm
$t_{\mathrm{sh}}$Thickness of the sheathmm
$T_{\mathrm{st}}$Radiation thermal resistance surface-tunnelK.m/W
$T_{\mathrm{surf}}$Absolute surface temperatureK
$t_{\mathrm{t}}$Tunnel wall thicknessm
$T_{\mathrm{t}}$Star thermal resistance of tunnelK.m/W
$T_{\mathrm{tot}}$Total thermal resistance, transientK.m/W
$T_{\mathrm{tr}}$Thermal resistance of troughK
$T_{\mathrm{tw}}$Thermal resistance of tunnel wallK.m/W
$\mathrm{tan}\delta _{\mathrm{i}}$Loss factor of insulation
$\tau$Transient load periods
$\theta_{\mathrm{2K}}$Temperature rise for 2K criterion°C
$\theta_{\mathrm{a}}$Ambient temperature°C
$\theta_{\mathrm{abs}}$Absolute temperatureK
$\theta_{\mathrm{air}}$Ambient air temperature°C
$\theta_{\mathrm{ar}}$Temperature of armour°C
$\theta_{\mathrm{ar_{\mathrm{1}}}}$Temperature of 1st armour layer°C
$\theta_{\mathrm{ar_{\mathrm{2}}}}$Temperature of 2nd armour layer°C
$\theta_{\mathrm{at}}$Air temperature°C
$\theta_{\mathrm{at_{\mathrm{0}}}}$Air temperature in tunnel at inlet°C
$\theta_{\mathrm{at_{\mathrm{L}}}}$Air temperature in tunnel at outlet°C
$\theta_{\mathrm{at_{\mathrm{z}}}}$Air temperature in tunnel at z°C
$\theta_{\mathrm{c}}$Temperature of conductor°C
$\theta_{\mathrm{c_{\mathrm{t}}}}$Temperature of conductor after transient°C
$\theta_{\mathrm{c_{\mathrm{z}}}}$Conductor temperature at z°C
$\theta_{\mathrm{cmax}}$Max. conductor temperature°C
$\theta_{\mathrm{cmaxeo}}$Max. emergency overload conductor temperature°C
$\theta_{\mathrm{cmaxsc}}$Max. short-circuit conductor temperature°C
$\theta_{\mathrm{de}}$Temperature of duct outer wall°C
$\theta_{\mathrm{di}}$Temperature of duct inner wall°C
$\theta_{\mathrm{dm}}$Mean temperature of the medium in the duct°C
$\theta_{\mathrm{e}}$External temperature of the object°C
$\theta_{\mathrm{encl}}$Temperature of enclosure°C
$\theta_{\mathrm{f}}$Temperature of filler for multi-core cables type SS with sheath°C
$\theta_{\mathrm{gas}}$Gas temperature°C
$\theta_{\mathrm{hs}}$Temperature of heat source°C
$\theta_{\mathrm{kf}}$Final temperature°C
$\theta_{\mathrm{ki}}$Initial temperature°C
$\theta_{\mathrm{kmax}}$Maximal temperature of non-insulation material°C
$\theta_{\mathrm{max}}$Temperature of conductor at end of emergency loading°C
$\theta_{\mathrm{o_{\mathrm{L}}}}$Temperature of the surface of object at outlet°C
$\theta_{\mathrm{o_{\mathrm{z}}}}$Temperature of the surface of object at z°C
$\theta_{\mathrm{p}}$Angle to the plane of a sectionrad
$\theta_{\mathrm{R}}$Rated current transient to steady-state ratio
$\theta_{\mathrm{s}}$Temperature of screen/sheath°C
$\theta_{\mathrm{sc}}$Temperature of screen°C
$\theta_{\mathrm{sh}}$Temperature of sheath°C
$\theta_{\mathrm{surf}}$Surface temperature°C
$\theta_{\mathrm{t}}$Temperature of inner tunnel wall°C
$\theta_{\mathrm{t_{\mathrm{L}}}}$Temperature of tunnel wall at outlet°C
$\theta_{\mathrm{t_{\mathrm{z}}}}$Temperature of tunnel wall at z°C
$\theta_{\mathrm{to}}$Temperature of outer tunnel wall°C
$\theta_{\mathrm{to_{\mathrm{z}}}}$Temperature of outer tunnel wall at z°C
$\theta_{\mathrm{x}}$Critical soil temperature°C
$TQ$Cable thermal time constants
U $u$Substitution coefficient u
$U_{\mathrm{0}}$Value of U0 for determination of test voltageskV
$U_{\mathrm{d}}$Constant U for cables in ductsK.m/W
$U_{\mathrm{e}}$Line-to-ground voltagekV
$U_{\mathrm{m}}$Highest voltage for equipmentkV
$U_{\mathrm{n}}$Rated line-to-line voltagekV
$U_{\mathrm{o}}$Operating voltagekV
V $v_{\mathrm{4}}$Ratio of the thermal resistivities of dry and moist soils
$V_{\mathrm{air}}$Air velocitym/s
$V_{\mathrm{comp}}$Gas volume
$V_{\mathrm{d}}$Constant V for cables in ductsK.m/W
$V_{\mathrm{drop}}$Voltage dropV/A/km
$V_{\mathrm{gas}}$Volume percentage of second gas%
$V_{\mathrm{m}}$Molar volumem³/mol
W $W_{\mathrm{A}}$Armour lossesW/m
$W_{\mathrm{a_{\mathrm{L}}}}$Heat removed by air at outletW/m
$W_{\mathrm{a_{\mathrm{z}}}}$Heat removed by air at zW/m
$w_{\mathrm{b}}$Width of the backfillmm
$W_{\mathrm{c}}$Conductor lossesW/m
$W_{\mathrm{conv_{\mathrm{ce}}}}$Convection heat transfer conductor-enclosureW/m
$W_{\mathrm{conv_{\mathrm{sa}}}}$Convection heat transfer surface-airW/m
$W_{\mathrm{d}}$Dielectric lossesW/m
$W_{\mathrm{encl}}$Enclosure lossesW/m
$w_{\mathrm{f_{\mathrm{1}}}}$Width of flat wires of 1st armourmm
$w_{\mathrm{f_{\mathrm{2}}}}$Width of flat wires of 2nd armourmm
$W_{\mathrm{h}}$Heat generated by external objectW/m
$W_{\mathrm{hs}}$Heat dissipation of heat sourceW/m
$W_{\mathrm{I}}$Ohmic losses per phaseW/m
$W_{\mathrm{p}}$Losses in ferromagnetic steel pipeW/m
$w_{\mathrm{p}}$Weight correction factor
$W_{\mathrm{rad_{\mathrm{ce}}}}$Radiation heat transfer conductor-enclosureW/m
$W_{\mathrm{rad_{\mathrm{sa}}}}$Radiation heat transfer surface-airW/m
$W_{\mathrm{s}}$Screen and sheath lossesW/m
$W_{\mathrm{sA}}$Total loss in sheath and armourW/m
$W_{\mathrm{sA_{\mathrm{1}}}}$Total loss in sheath and 1st armourW/m
$W_{\mathrm{sA_{\mathrm{2}}}}$Total loss in sheath and 2nd armourW/m
$w_{\mathrm{sc}}$Width of flat screen wiremm
$W_{\mathrm{sum}}$Sum of total losses of all systemsW/m
$W_{\mathrm{sys}}$Total losses of the systemW/m
$W_{\mathrm{T}}$Trench width in multi-layer backfillm
$W_{\mathrm{t}}$Total losses per phaseW/m
$w_{\mathrm{t}}$Inner widthm
$W_{\mathrm{tot}}$Total losses per objectW/m
X $X_{\mathrm{0}}$Zero sequence reactanceΩ/m
$x_{\mathrm{b}}$Horizontal center of backfillmm
$X_{\mathrm{c}}$Reactance of conductorΩ/m
$X_{\mathrm{G}}$Factor XG
$X_{\mathrm{G2}}$Factor XG2
$X_{\mathrm{K}}$Factor XK
$X_{\mathrm{m}}$Mutual reactanceΩ/m
$x_{\mathrm{p}}$Factor for proximity effect of conductors
$x_{\mathrm{pos}}$Horizontal x-position in multi-layer backfillmm
$x_{\mathrm{s}}$Factor for skin effect on conductor
$X_{\mathrm{s}}$Reactance of screen/sheathΩ/m
$X_{\mathrm{S1}}$Reactance section 1Ω/m
$X_{\mathrm{S2}}$Reactance section 2Ω/m
$X_{\mathrm{S3}}$Reactance section 3Ω/m
$\xi_{\mathrm{cb}}$Parameter ξ for calculation of loss factor
Y $Y$AdmittanceS/m
$y_{\mathrm{2K}}$Depth for 2K criterionmm
$y_{\mathrm{c}}$Skin and proximity effect factor for GIL conductor
$Y_{\mathrm{d}}$Constant Y for cables in ductsK.m/W
$y_{\mathrm{encl}}$Skin and proximity effect factor for GIL enclosure
$Y_{\mathrm{G}}$Factor YG
$Y_{\mathrm{i}}$Ordinates of the loss-load cyclep.u.
$Y_{\mathrm{K}}$Factor YK
$y_{\mathrm{p}}$Proximity effect factor of conductors
$y_{\mathrm{s}}$Skin effect factor of conductor
Z $Z_{\mathrm{0}}$Zero sequence impedanceΩ/m
$Z_{\mathrm{bs}}$Installation constant Z
$z_{\mathrm{c}}$Factor z to calculate skin effect coefficients for conductor
$z_{\mathrm{encl}}$Factor z to calculate skin effect coefficients for enclosure
$z_{\mathrm{h}}$Location of the heat sourcem
$Z_{\mathrm{K}}$Factor ZK
$z_{\mathrm{max}}$Logitudinal thermal limit distancem
$Z_{\mathrm{neg}}$Negative sequence impedanceΩ/m
$Z_{\mathrm{pos}}$Positive sequence impedanceΩ/m
$z_{\mathrm{r}}$Location of the hottest pointm
$\zeta_{\mathrm{M}}$Density of materialg/cm³