## 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.

 Symbol Name Unit A $a_{\mathrm{0}}$ Coefficient a for partial transient temperature rise s² $a_{\mathrm{12}}$ Distance between phase 1 and 2 mm $a_{\mathrm{23}}$ Distance between phase 2 and 3 mm $a_{\mathrm{31}}$ Distance between phase 3 and 1 mm $A_{\mathrm{a}}$ Cross-sectional area of armour mm² $A_{\mathrm{a_{\mathrm{1}}}}$ Cross-sectional area of 1st armour mm² $A_{\mathrm{a_{\mathrm{2}}}}$ Cross-sectional area of 2nd armour mm² $A_{\mathrm{ab_{\mathrm{1}}}}$ Cross-sectional area of 1st armour bedding mm² $A_{\mathrm{ab_{\mathrm{2}}}}$ Cross-sectional area of 2nd armour bedding mm² $A_{\mathrm{c}}$ Cross-sectional area of conductor mm² $a_{\mathrm{c}}$ Skin and proximity effect coefficient a for GIL conductor $A_{\mathrm{comp}}$ Cross-sectional area of compartment m² $a_{\mathrm{constr}}$ Construction of armour $A_{\mathrm{d}}$ Cross-sectional area of duct wall mm² $A_{\mathrm{d_{\mathrm{fill}}}}$ Free cross-sectional area inside duct mm² $a_{\mathrm{encl}}$ Skin and proximity effect coefficient a for GIL enclosure $A_{\mathrm{encl}}$ Cross-sectional area of enclosure mm² $A_{\mathrm{f}}$ Cross-sectional area of filler mm² $A_{\mathrm{i}}$ Cross-sectional area of insulation mm² $A_{\mathrm{j}}$ Cross-sectional area of jacket mm² $A_{\mathrm{k}}$ Thermal property constant A (mm²/s)½ $a_{\mathrm{m}}$ Mean distance between the phases mm $A_{\mathrm{prot}}$ Cross-sectional area of protective cover mm² $a_{\mathrm{S1}}$ Length of 1st section p.u. $a_{\mathrm{S2}}$ Length of 2nd section p.u. $a_{\mathrm{S3}}$ Length of 3rd section p.u. $A_{\mathrm{sc}}$ Cross-sectional area of screen mm² $A_{\mathrm{scb}}$ Cross-sectional area of screen beddig mm² $A_{\mathrm{scs}}$ Cross-sectional area of screen serving mm² $A_{\mathrm{sh}}$ Cross-sectional area of sheath mm² $A_{\mathrm{t}}$ Cross-sectional area of the tunnel m² $a_{\mathrm{T}}$ Distance a of multi-layer backfill m $a_{\mathrm{VdW}}$ Van der Walls constant a bar.L²/mol² $\alpha_{\mathrm{ar}}$ Temperature coefficient of armour material 1/K $\alpha_{\mathrm{c}}$ Temperature coefficient of conductor material 1/K $\alpha_{\mathrm{encl}}$ Temperature coefficient of enclosure material 1/K $\alpha_{\mathrm{f}}$ Phase shifting ° $\alpha_{\mathrm{gas}}$ Thermal diffusivity for gas m²/s $\alpha_{\mathrm{M}}$ Factor αM $\alpha_{\mathrm{sc}}$ Temperature coefficient of screen material 1/K $\alpha_{\mathrm{sh}}$ Temperature coefficient of sheath material 1/K $\alpha_{\mathrm{t}}$ Conductor to surface attainment factor B $B$ Susceptance S/m $b_{\mathrm{0}}$ Coefficient b for partial transient temperature rise 1/s $B_{\mathrm{1_{\mathrm{1}}}}$ Loss coefficient B1 of 1st armour Ω/m $B_{\mathrm{1_{\mathrm{2}}}}$ Loss coefficient B1 of 2nd armour Ω/m $B_{\mathrm{2_{\mathrm{1}}}}$ Loss coefficient B2 of 1st armour Ω/m $B_{\mathrm{2_{\mathrm{2}}}}$ Loss coefficient B2 of 2nd armour Ω/m $b_{\mathrm{c}}$ Skin and proximity effect coefficient b for GIL conductor $B_{\mathrm{EMF}}$ Magnetic field strength µT $b_{\mathrm{encl}}$ Skin and proximity effect coefficient b for GIL enclosure $B_{\mathrm{k}}$ Thermal property constant B mm²/s $b_{\mathrm{T}}$ Distance b of multi-layer backfill m $b_{\mathrm{VdW}}$ Van der Walls constant b L/mol $b_{\mathrm{x}}$ Shorter side of backfill mm $b_{\mathrm{y}}$ Longer side of backfill mm $\beta_{\mathrm{1}}$ Substitution coefficient β1 for eddy-currents $\beta_{\mathrm{6}}$ Factor |1 - β(6)| $\beta_{\mathrm{a_{\mathrm{1}}}}$ Angle between armour and cable axis rad $\beta_{\mathrm{a_{\mathrm{2}}}}$ Angle between 2nd armour and cable axis rad $\beta_{\mathrm{air}}$ Volumetric thermal expansion coefficient of air 1/K $\beta_{\mathrm{ar}}$ Reciprocal of temperature coefficient of armour material K $\beta_{\mathrm{c}}$ Reciprocal of temperature coefficient of conductor material K $\beta_{\mathrm{encl}}$ Reciprocal of temperature coefficient of enclosure material K $\beta_{\mathrm{gas}}$ Volumetric thermal expansion coefficient for gas 1/K $\beta_{\mathrm{k}}$ Reciprocal of temperature coefficient of resistance K $\beta_{\mathrm{M}}$ Factor βM $\beta_{\mathrm{sc}}$ Reciprocal of temperature coefficient of screen material K $\beta_{\mathrm{sh}}$ Reciprocal of temperature coefficient of sheath material K $\beta_{\mathrm{T}}$ Equivalent thermal resistance of the soil per unit surface W/K.m² $\beta_{\mathrm{t}}$ Attainment factor cable surface to ambient $\beta_{\mathrm{X}}$ Crossing angle in radians rad $\beta_{\mathrm{xing}}$ Crossing angle in degrees ° C $C_{\mathrm{av}}$ Heat capacity of the air flow W/K $C_{\mathrm{b}}$ Capacitance of insulation F/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 C1 mm/m $C_{\mathrm{k2}}$ Non-adiabatic constant C2 K.m.mm²/J $C_{\mathrm{Nu}}$ Factor C $c_{\mathrm{p_{\mathrm{gas}}}}$ Specific heat capacity at constant pressure J/kg.K $C_{\mathrm{q}}$ Constants C1 to C7 of multi-layer backfill $c_{\mathrm{SI}}$ Surge velocity of propagation km/s $c_{\mathrm{T}}$ Distance c of multi-layer backfill m $c_{\mathrm{v_{\mathrm{gas}}}}$ Specific heat capacity at constant volume J/kg.K $C_{\mathrm{vair}}$ Volumetric heat capacity of air J/K.m³ $CC$ Charging capacity kvar/km $CC_{\mathrm{p}}$ Conduit clearance % $CF_{\mathrm{p}}$ Conduit fill % $CR_{\mathrm{p}}$ Conduit ratio in duct % $cuw$ Standard copper wires mm D $D_{\mathrm{1}}$ Diameter below screen mm $D_{\mathrm{2_{\mathrm{1}}}}$ Diameter below 1st armour mm $D_{\mathrm{2_{\mathrm{2}}}}$ Diameter below 2nd armour mm $d_{\mathrm{a}}$ Mean diameter of armour mm $d_{\mathrm{a_{\mathrm{1}}}}$ Mean diameter of 1st armour mm $D_{\mathrm{a_{\mathrm{1}}}}$ External diameter of 1st armour mm $D_{\mathrm{a_{\mathrm{2}}}}$ External diameter of 2nd armour mm $d_{\mathrm{a_{\mathrm{2}}}}$ Mean diameter of 2nd armour mm $d_{\mathrm{b}}$ Diameter of the backfill mm $d_{\mathrm{c}}$ External diameter of conductor mm $D_{\mathrm{c}}$ Diameter of conductor m $d_{\mathrm{ci}}$ Internal diameter of conductor mm $D_{\mathrm{comp}}$ Diameter of compartment (metric) m $d_{\mathrm{comp}}$ Diameter of compartment mm $d_{\mathrm{ct}}$ External diameter of conductor for transient calculations mm $D_{\mathrm{e}}$ External diameter of object mm $d_{\mathrm{e}}$ Diameter of sheath and armour mm $D_{\mathrm{encl}}$ Outer diameter of enclosure (metric) m $d_{\mathrm{encl}}$ Outer diameter of enclosure mm $D_{\mathrm{eq}}$ Equivalent diameter of a group of cables mm $d_{\mathrm{f}}$ Spacing from hottest object in group m $D_{\mathrm{f}}$ External diameter of the filler mm $d_{\mathrm{f_{\mathrm{1}}}}$ Thickness of 1st armour mm $d_{\mathrm{f_{\mathrm{2}}}}$ Thickness of 2nd armour mm $D_{\mathrm{hs}}$ External diameter of heat source mm $D_{\mathrm{i}}$ Diameter over insulation mm $d_{\mathrm{im}}$ Imaginary layer of soil m $D_{\mathrm{it}}$ Diameter below sheath mm $D_{\mathrm{o}}$ Outer diameter m $D_{\mathrm{oc}}$ External diameter of sheath mm $d_{\mathrm{pk1}}$ Distance to mirrored buried object mm $d_{\mathrm{pk2}}$ Distance between buried objects mm $d_{\mathrm{prot}}$ Diameter of protective cover mm $d_{\mathrm{psc}}$ Point source correction m $D_{\mathrm{s}}$ Mean external diameter of the sheath mm $d_{\mathrm{s}}$ Mean diameter of sheath mm $D_{\mathrm{scm}}$ Mean diameter of screen mm $d_{\mathrm{soil}}$ Soil dry density kg/m³ $d_{\mathrm{T}}$ Distance d of multi-layer backfill m $d_{\mathrm{x}}$ Equivalent diameter of a conductor mm $D_{\mathrm{x}}$ Characteristic diameter mm $D_{\mathrm{x_{\mathrm{w}}}}$ Characteristic diameter for weekly load mm $D_{\mathrm{x_{\mathrm{y}}}}$ Characteristic diameter for yearly load mm $DC_{\mathrm{p}}$ Diameter factor in duct % $\delta _{\mathrm{1}}$ Thickness of screening layer mm $\Delta _{\mathrm{1}}$ Substitution coefficient Δ1 for eddy-currents $\Delta _{\mathrm{2}}$ Substitution coefficient Δ2 for eddy-currents $\delta _{\mathrm{ar}}$ Equivalent thickness of armour mm $\delta _{\mathrm{k}}$ Thickness of screen, sheath or armour mm $\delta _{\mathrm{soil}}$ Soil thermal diffusivity m²/s $\Delta d_{\mathrm{sh}}$ Depth of corrugation mm $\Delta H_{\mathrm{c}}$ Heat of combustion coefficient MJ/kg $\Delta t$ Length of time step s $\Delta \theta_{\mathrm{0t}}$ Air temperature in tunnel increase K $\Delta \theta_{\mathrm{0x}}$ Temperature rise of the conductor K $\Delta \theta_{\mathrm{0x_{\mathrm{1}}}}$ Temperature rise of the conductor, first estimate K $\Delta \theta_{\mathrm{0x_{\mathrm{h}}}}$ Temperature rise of the conductor by source h K $\Delta \theta_{\mathrm{a_{\mathrm{t}}}}$ Corrected transient temperature rise of conductor K $\delta \theta_{\mathrm{c}}$ Ohmic steady-state temperature rise K $\Delta \theta_{\mathrm{c}}$ Temperature rise of conductor K $\Delta \theta_{\mathrm{c_{\mathrm{t}}}}$ Transient temperature rise of conductor by ohmic losses K $\Delta \theta_{\mathrm{d}}$ Temperature rise by dielectric losses K $\Delta \theta_{\mathrm{d_{\mathrm{t}}}}$ Transient temperature rise by dielectric losses K $\Delta \theta_{\mathrm{e_{\mathrm{t}}}}$ Transient temperature rise of outer surface K $\Delta \theta_{\mathrm{gas}}$ Temperature difference conductor-enclosure °C $\Delta \theta_{\mathrm{kp}}$ Temperature rise by buried object k K $\Delta \theta_{\mathrm{max}}$ Maximum permissible conductor temperature rise K $\Delta \theta_{\mathrm{p}}$ Temperature rise by other buried objects K $\Delta \theta_{\mathrm{R}}$ Conductor temperature rise above ambient temperature K $\Delta \theta_{\mathrm{R_{\mathrm{\infty}}}}$ 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 ambient K $\delta \theta_{\mathrm{SPK}}$ Peak cyclic temperature rise K $\Delta \theta_{\mathrm{sun}}$ Temperature rise by solar radiation K $\Delta \theta_{\mathrm{t}}$ Transient temperature rise of conductor K $\Delta \theta_{\mathrm{t_{\mathrm{\infty}}}}$ Steady-state temperature rise of conductor K $\Delta \theta_{\mathrm{tr}}$ Temperature increase of air in trough K $\Delta \theta_{\mathrm{x}}$ Critical soil temperature rise K $\Delta W$ Incremental heat generated W $\Delta W_{\mathrm{0}}$ Incremental heat 0 generated W $\Delta z$ Length of the interval m $DF_{\mathrm{X}}$ Derating factor for the permissible current $Di_{\mathrm{d}}$ Inside diameter of duct mm $Di_{\mathrm{t}}$ Diameter of the tunnel (inner) m $Do_{\mathrm{d}}$ Outside diameter of duct mm $Do_{\mathrm{t}}$ Diameter of the tunnel or trough (outer) m E $E_{\mathrm{bs}}$ Installation constant E $e_{\mathrm{hor}}$ Horizontal clearance mm $E_{\mathrm{stress}}$ Electrical field strength kV/mm $e_{\mathrm{ver}}$ Vertical clearance mm $e_{\mathrm{wall}}$ Clearance to wall mm $EEC$ Embodied energy and carbon MJ/kg $\epsilon_{\mathrm{0}}$ Vacuum permittivity F/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 gas Pa.s $\eta_{\mathrm{gas}}$ Dynamic viscosity of gas Pa.s F $f$ System frequency Hz $F_{\mathrm{a_{\mathrm{1}}}}$ Effective length per unit lay length of 1st armour mm $F_{\mathrm{a_{\mathrm{2}}}}$ Effective length per unit lay length of 2nd armour mm $F_{\mathrm{cable}}$ Maximum effective pulling force N/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 section daN $F_{\mathrm{k}}$ Imperfect contact thermal factor $F_{\mathrm{m}}$ Radiation coefficient mutual $F_{\mathrm{out}}$ Pulling force at end of a section daN $F_{\mathrm{ppc}}$ Permissible pull force on cable daN $f_{\mathrm{ppc}}$ Factor of permissible pull N/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 gravity m/s² $G$ Conductance S/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 angle rad $\gamma_{\mathrm{c}}$ 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 crossing 1/m $GMD$ Geometric mean distance mm $GMR$ Geometric mean radius mm $\mathrm{Gr}_{\mathrm{c}}$ 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>1 H/m $h_{\mathrm{1}}$ Factor h1 for emergency load $H_{\mathrm{1_{\mathrm{2}}}}$ Component of inductance Hsub>1 of 2nd armour H/m $h_{\mathrm{2}}$ Factor h2 for emergency load $H_{\mathrm{2}}$ Component of inductance Hsub>2 H/m $H_{\mathrm{2_{\mathrm{2}}}}$ Component of inductance Hsub>2 of 2nd armour H/m $H_{\mathrm{3}}$ Component of inductance Hsub>3 H/m $H_{\mathrm{3_{\mathrm{2}}}}$ Component of inductance Hsub>3 of 2nd armour H/m $h_{\mathrm{b}}$ Height of the backfill mm $h_{\mathrm{bs}}$ Heat dissipation coefficient for black surfaces in free air W/m²/K5/4 $H_{\mathrm{c}}$ Heat energy content MJ/m $h_{\mathrm{c}}$ Convective heat transfer coefficient conductor-gas W/K.m² $h_{\mathrm{encl}}$ Convective heat transfer coefficient gas to enclosure W/m2.K $h_{\mathrm{lg}}$ Ratio of heat dissipation coefficients $h_{\mathrm{prot}}$ Convective heat transfer coefficient surface-air W/K.m² $h_{\mathrm{rad_{\mathrm{ce}}}}$ Radiation heat transfer coefficient conductor-enclosure W/K.m² $h_{\mathrm{rad_{\mathrm{sa}}}}$ Radiation heat transfer coefficient surface-air W/K.m² $h_{\mathrm{roll}}$ Height of roller above bottom m $H_{\mathrm{s}}$ Sheath conductance H/m $H_{\mathrm{sun}}$ Intensity of solar radiation W/m² $h_{\mathrm{t}}$ Inner height m $H_{\mathrm{T}}$ Trench depth to bedding layer in multi-layer backfill m $h_{\mathrm{T4}}$ Ratio of thermal resistance to ambient $H_{\mathrm{tc}}$ Parameter H for trough $h_{\mathrm{tr}}$ Heat transfer coefficient W/K.m² $H_{\mathrm{ts}}$ Parameter H depending on air velocity $H_{\mathrm{x}}$ Magnetic field x-component mH $H_{\mathrm{y}}$ Magnetic field y-component mH I $I_{\mathrm{1}}$ Steady-state current before transient A $I_{\mathrm{2}}$ Emergency load current A $I_{\mathrm{C}}$ Capacitive load current A/km $I_{\mathrm{c}}$ Permissible current rating A $I_{\mathrm{c_{\mathrm{max}}}}$ Highest current load of line A $I_{\mathrm{c_{\mathrm{peak}}}}$ Permissible peak cyclic load current A $I_{\mathrm{Ce}}$ Capacitive earth short-circuit current A/km $I_{\mathrm{EMF}}$ Phase current for EMF calculation A $I_{\mathrm{k}}$ Permissible short-circuit current kA $I_{\mathrm{kAD}}$ Short-circuit current (adiabatic) kA $I_{\mathrm{kSC}}$ Effective short-circuit current kA $I_{\mathrm{method}}$ Current calculation method $I_{\mathrm{R}}$ Transient conductor current, step value A $inst_{\mathrm{air}}$ 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 layer W/K.m $K_{\mathrm{10}}$ Factor K1.0 $k_{\mathrm{2}}$ Thermal conductivity of mid backfill layer W/K.m $k_{\mathrm{3}}$ Thermal conductivity of bedding layer W/K.m $k_{\mathrm{4}}$ Thermal conductivity of soil W/K.m $K_{\mathrm{A}}$ Coefficient K to calculate in air $k_{\mathrm{air}}$ Thermal conductivity of air W/m.K $K_{\mathrm{BICC}}$ Constant relating to conductor formation $k_{\mathrm{Boltzmann}}$ Boltzmann constant J/K $k_{\mathrm{c}}$ Thermal conductivity of conductor material K.m/W $K_{\mathrm{c}}$ Constant Kc for convection heat transfer $K_{\mathrm{cv}}$ Convection factor $K_{\mathrm{E}}$ Surface heat conductance W/m² $k_{\mathrm{encl}}$ Thermal conductivity of enclosure W/m.K $k_{\mathrm{gas}}$ Thermal conductivity for gas W/m.K $K_{\mathrm{GMR}}$ Geometric mean radius factor $k_{\mathrm{H}}$ Heinhold characteristic diameter coefficient $K_{\mathrm{k}}$ Specific short-circuit parameter A.s½/mm² $k_{\mathrm{l}}$ Temperature rise factor in air $k_{\mathrm{LF}}$ Load loss constant coefficient p.u. $k_{\mathrm{p}}$ Proximity effect coefficient $k_{\mathrm{prot}}$ Thermal conductivity of protective cover W/m.K $K_{\mathrm{r}}$ Radiation shape factor $k_{\mathrm{r2}}$ Temperature rise ratio δθSPK/δθc p.u. $k_{\mathrm{s}}$ Skin effect coefficient $K_{\mathrm{t}}$ Effective emissivity of surface $k_{\mathrm{t}}$ Temperature rise ratio p.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 tunnel m $L_{\mathrm{1}}$ Inductance of phase 1 H/m $L_{\mathrm{2}}$ Inductance of phase 2 H/m $L_{\mathrm{3}}$ Inductance of phase 3 H/m $L_{\mathrm{b}}$ Vertical center of backfill mm $L_{\mathrm{c}}$ Depth of laying of sources mm $L_{\mathrm{char}}$ Characteristic length $L_{\mathrm{cm}}$ Depth of laying (metric) m $L_{\mathrm{cni}}$ Imaginary laying depth with non-isothermal earth surface m $L_{\mathrm{crit}}$ Critical system length km $L_{\mathrm{deep}}$ Equivalent depth for deep burial m $L_{\mathrm{h}}$ Depth of laying of crossing element mm $L_{\mathrm{m}}$ Mean inductance of the phases H/m $L_{\mathrm{p}}$ Length of a section m $L_{\mathrm{r}}$ Depth of laying of the rated object mm $L_{\mathrm{sys}}$ System length km $L_{\mathrm{T}}$ Length of the tunnel m $\lambda_{\mathrm{0}}$ 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 factor p.u. $LF_{\mathrm{w}}$ Weekly load factor p.u. $LF_{\mathrm{y}}$ Yearly load factor p.u. $LME$ London Metal Exchange USD/mt M $M$ Cyclic rating factor p.u. $m$ Mass of object kg/m $M_{\mathrm{0}}$ Coefficient M for partial transient temperature rise s $m_{\mathrm{0}}$ Substitution coefficient m0 for eddy-currents Hz.m/Ω $M_{\mathrm{1}}$ Corrected cyclic rating factor K $M_{\mathrm{ab}}$ 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 factor s½ $M_{\mathrm{m}}$ Mean mutual inductance of sheath H/m $m_{\mathrm{mol}}$ Molecular mass mol $M_{\mathrm{mol}}$ Molar mass g/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 factor p.u. $\mu_{\mathrm{0}}$ Vacuum permeability H/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 variation p.u. $\mu_{\mathrm{y}}$ Loss factor for yearly load variation p.u. N $N_{\mathrm{0}}$ Coefficient N for partial transient temperature rise s² $n_{\mathrm{a_{\mathrm{1}}}}$ Number of wires of 1st armour $n_{\mathrm{a_{\mathrm{2}}}}$ Number of wires of 2nd armour $N_{\mathrm{Avogrado}}$ Avogadro constant 1/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 air m²/s $\mathrm{Nu}_{\mathrm{c}}$ Nusselt number conductor-gas $\mathrm{Nu}_{\mathrm{encl}}$ Nusselt number gas-enclosure $\nu_{\mathrm{gas}}$ Kinematic viscosity for gas m²/s $\mathrm{Nu}_{\mathrm{L}}$ Nusselt number $\mathrm{Nu}_{\mathrm{prot}}$ Nusselt number surface-air $\nu_{\mathrm{soil}}$ Soil moisture content % O $\omega$ Angular frequency rad/s P $p_{\mathrm{a_{\mathrm{1}}}}$ Length of lay of 1st armour mm $p_{\mathrm{a_{\mathrm{2}}}}$ Length of lay of 2nd armour mm $p_{\mathrm{ab1}}$ 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 compartment bar $p_{\mathrm{gas}}$ Gas pressure Pa $p_{\mathrm{i}}$ Factor apportioning the insulation $p_{\mathrm{j}}$ Factor apportioning the jacket $P_{\mathrm{L}}$ Active power at load receptor kW $p_{\mathrm{soil}}$ Depth of image source $p_{\mathrm{tr}}$ Effective perimeter of trough m $p_{\mathrm{VdW}}$ Van der Walls equation Pa $\phi_{\mathrm{b}}$ Parameter φ for trough $\phi_{\mathrm{p}}$ Angle of a bend rad $\pi$ 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 circuit J/m.K $Q_{\mathrm{a_{\mathrm{1}}}}$ Thermal capacitance of 1st armour J/m.K $Q_{\mathrm{a_{\mathrm{2}}}}$ Thermal capacitance of 2nd armour J/m.K $Q_{\mathrm{ab_{\mathrm{1}}}}$ Thermal capacitance of 1st armour bedding J/m.K $Q_{\mathrm{ab_{\mathrm{2}}}}$ Thermal capacitance of 2nd armour bedding J/m.K $Q_{\mathrm{B}}$ Element B of two-part thermal circuit J/m.K $Q_{\mathrm{B_{\mathrm{ab1}}}}$ Element B of two-part thermal circuit, 1st armour bedding J/m.K $Q_{\mathrm{B_{\mathrm{ab2}}}}$ Element B of two-part thermal circuit, 2nd armour bedding J/m.K $Q_{\mathrm{B_{\mathrm{d}}}}$ Element B of two-part thermal circuit, duct J/m.K $Q_{\mathrm{B_{\mathrm{f}}}}$ Element B of two-part thermal circuit, filler J/m.K $Q_{\mathrm{B_{\mathrm{i}}}}$ Element B of two-part thermal circuit, insulation J/m.K $Q_{\mathrm{B_{\mathrm{j}}}}$ Element B of two-part thermal circuit, jacket J/m.K $Q_{\mathrm{B_{\mathrm{s}}}}$ Element B of two-part thermal circuit, screen/sheath J/m.K $Q_{\mathrm{c}}$ Thermal capacitance of conductor J/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 wall J/m.K $Q_{\mathrm{d_{\mathrm{fill}}}}$ Thermal capacitance of duct filling J/m.K $Q_{\mathrm{f}}$ Thermal capacitance of filler J/m.K $q_{\mathrm{f}}$ Ratio of losses affecting the filler $Q_{\mathrm{i}}$ Thermal capacitance of insulation J/m.K $Q_{\mathrm{i1}}$ Thermal capacitance of insulation, 1st portion J/m.K $Q_{\mathrm{i2}}$ Thermal capacitance of insulation, 2nd portion J/m.K $Q_{\mathrm{j}}$ Thermal capacitance of jacket J/m.K $Q_{\mathrm{p}}$ Quantity of lubricant l/m $Q_{\mathrm{sc}}$ Thermal capacitance of screen J/m.K $Q_{\mathrm{scb}}$ Thermal capacitance of screen bedding J/m.K $Q_{\mathrm{scs}}$ Thermal capacitance of screen serving J/m.K $Q_{\mathrm{sh}}$ Thermal capacitance of sheath J/m.K $Q_{\mathrm{t}}$ Total thermal capacitance, transient J/m.K $q_{\mathrm{x}}$ Factor for characteristic diameter R $R_{\mathrm{0}}$ Zero sequence resistance Ω/m $R_{\mathrm{1}}$ Resistance of conductor before emergency rating Ω/m $R_{\mathrm{A}}$ Electrical resistance of armour Ω/m $R_{\mathrm{A_{\mathrm{1}}}}$ Electrical resistance of 1st armour layer Ω/m $R_{\mathrm{A_{\mathrm{2}}}}$ Electrical resistance of 2nd armour layer Ω/m $r_{\mathrm{b}}$ Equivalent radius of backfill mm $R_{\mathrm{c}}$ Resistance of conductor Ω/m $r_{\mathrm{c}}$ Radius of conductor mm $R_{\mathrm{CG}}$ Thermal resistance of multi-layer backfill K.m/W $R_{\mathrm{co}}$ DC resistance of conductor at 20°C Ω/m $R_{\mathrm{e}}$ Electrical resistance of sheath and armour Ω/m $R_{\mathrm{e_{\mathrm{1}}}}$ Electrical resistance of sheath and 1st armour Ω/m $R_{\mathrm{e_{\mathrm{2}}}}$ Electrical resistance of sheath and 2nd armour Ω/m $R_{\mathrm{encl}}$ Electrical resistance of enclosure Ω/m $R_{\mathrm{encl20}}$ DC resistance of enclosure at 20°C Ω/m $r_{\mathrm{F}}$ Radius below the insulation mm $R_{\mathrm{gas}}$ Specific gas constant $R_{\mathrm{gas0}}$ Universal molar gas constant $r_{\mathrm{I}}$ Radius of the insulation mm $r_{\mathrm{ij}}$ Coefficient r for view factor $R_{\mathrm{max}}$ Resistance of conductor at emergency rating Ω/m $r_{\mathrm{mbi}}$ Minimal bending radius for installation m $r_{\mathrm{mbif}}$ Factor of minimal installation bending radius $r_{\mathrm{mbp}}$ Minimal bending radius during cable pulling m $r_{\mathrm{mbpf}}$ Factor of minimal pulling bending radius $R_{\mathrm{p}}$ Radius of a bend m $R_{\mathrm{q1}}$ Thermal resistance 1 of multi-layer backfill method K.m/W $R_{\mathrm{q11}}$ Thermal resistance 11 of multi-layer backfill method K.m/W $R_{\mathrm{q12}}$ Thermal resistance 12 of multi-layer backfill method K.m/W $R_{\mathrm{q13}}$ Thermal resistance 13 of multi-layer backfill method K.m/W $R_{\mathrm{q2}}$ Thermal resistance 2 of multi-layer backfill method K.m/W $R_{\mathrm{q21}}$ Thermal resistance 21 of multi-layer backfill method K.m/W $R_{\mathrm{q22}}$ Thermal resistance 22 of multi-layer backfill method K.m/W $R_{\mathrm{q23}}$ Thermal resistance 23 of multi-layer backfill method K.m/W $R_{\mathrm{q24}}$ Thermal resistance 24 of multi-layer backfill method K.m/W $R_{\mathrm{q3}}$ Thermal resistance 3 of multi-layer backfill method K.m/W $R_{\mathrm{q31}}$ Thermal resistance 31 of multi-layer backfill method K.m/W $R_{\mathrm{q32}}$ Thermal resistance 32 of multi-layer backfill method K.m/W $R_{\mathrm{q33}}$ Thermal resistance 33 of multi-layer backfill method K.m/W $R_{\mathrm{q34}}$ Thermal resistance 34 of multi-layer backfill method K.m/W $R_{\mathrm{R}}$ Resistance of conductor in steady-state Ω/m $R_{\mathrm{s}}$ Electrical resistance of screen||sheath Ω/m $R_{\mathrm{sc}}$ Electrical resistance of screen Ω/m $R_{\mathrm{sh}}$ Electrical resistance of sheath Ω/m $R_{\mathrm{so}}$ Resistance of screen and sheath at 20°C Ω/m $r_{\mathrm{\theta}}$ Factor r for emergency load current $r_{\mathrm{x}}$ Radius to point x in insulation mm $\mathrm{Ra}_{\mathrm{c}}$ 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 soil K.m/W $\rho_{\mathrm{4d}}$ Thermal resistivity of dry soil K.m/W $\rho_{\mathrm{ab}}$ Thermal resistivity of armour bedding K.m/W $\rho_{\mathrm{ab_{\mathrm{2}}}}$ Thermal resistivity of bedding between armour layers K.m/W $\rho_{\mathrm{ar}}$ Specific electrical resistivity of armour material Ω.m $\rho_{\mathrm{b}}$ Thermal resistivity backfill K.m/W $\rho_{\mathrm{b1}}$ Thermal resistivity of surface layer K.m/W $\rho_{\mathrm{b2}}$ Thermal resistivity of mid backfill layer K.m/W $\rho_{\mathrm{c}}$ Electrical resistivity of conductor material Ω.m $\rho_{\mathrm{corr}}$ Thermal resistivity of corrugation filling K.m/W $\rho_{\mathrm{cr}}$ Thermal resistivity of conductor material K.m/W $\rho_{\mathrm{d}}$ Thermal resistivity of duct material K.m/W $\rho_{\mathrm{d_{\mathrm{fill}}}}$ Thermal resistivity of bentonite filling K.m/W $\rho_{\mathrm{encl}}$ Specific electrical resistivity of enclosure material Ω.m $\rho_{\mathrm{f}}$ Thermal resistivity of filler K.m/W $\rho_{\mathrm{gas}}$ Gas density kg/m³ $\rho_{\mathrm{i}}$ Thermal resistivity of insulation K.m/W $\rho_{\mathrm{j}}$ Thermal resistivity of jacket material K.m/W $\rho_{\mathrm{k2}}$ Thermal resistivity of the layer located above K.m/W $\rho_{\mathrm{k20}}$ Electrical resistivity of metallic component Ω.m $\rho_{\mathrm{k3}}$ Thermal resistivity of the layer located below K.m/W $\rho_{\mathrm{ki}}$ Thermal resistivity of adjacent material K.m/W $\rho_{\mathrm{m}}$ Thermal resistivity of the screen K.m/W $\rho_{\mathrm{sc}}$ Specific electrical resistivity of screen material Ω.m $\rho_{\mathrm{sh}}$ Specific electrical resistivity of sheath material Ω.m $\rho_{\mathrm{soil}}$ Specific electrical resistivity of soil Ω $\rho_{\mathrm{t}}$ Thermal resistivity of tunnel wall K.m/W S $s_{\mathrm{1}}$ Thickness of surface layer m; $s_{\mathrm{2}}$ Thickness of mid backfill layer m² $s_{\mathrm{3}}$ Thickness from object to upper boundary of bedding layer m² $s_{\mathrm{4}}$ Thickness from object to lower boundary of bedding layer m² $s_{\mathrm{air}}$ Axial spacing between objects m $s_{\mathrm{c}}$ Separation of conductors in a system mm $s_{\mathrm{c2}}$ Separation of cables mm $S_{\mathrm{G}}$ Apparent power at injecting point kW $S_{\mathrm{gas}}$ Sutherland's constant K $s_{\mathrm{ij}}$ Spacing between object i and j $S_{\mathrm{k}}$ Cross-sectional area of current carrying component mm² $s_{\mathrm{roll}}$ Roller distance m $s_{\mathrm{S1}}$ Variation of spacing in 1st section p.u. $s_{\mathrm{S2}}$ Variation of spacing in 2nd section p.u. $s_{\mathrm{S3}}$ Variation of spacing in 3rd section p.u. $s_{\mathrm{T}}$ Distance to lateral edge of multi-layer backfill m $s_{\mathrm{x}}$ Separation of conductors in a cable mm $SI$ Surge Impedance Ω $\sigma$ Stefan Boltzmann constant W/m²K4 $\sigma_{\mathrm{ab}}$ Specific heat capacity of armour bedding J/K.m³ $\sigma_{\mathrm{ar}}$ Specific heat capacity of armour material J/K.m³ $\sigma_{\mathrm{c}}$ Specific heat capacity of conductor material J/K.m³ $\sigma_{\mathrm{d}}$ Specific heat capacity of duct material J/K.m³ $\sigma_{\mathrm{d_{\mathrm{fill}}}}$ Specific heat capacity of duct filling J/K.m³ $\sigma_{\mathrm{encl}}$ Specific heat capacity of enclosure material J/K.m³ $\sigma_{\mathrm{f}}$ Specific heat capacity of filler J/K.m³ $\sigma_{\mathrm{i}}$ Specific heat capacity of insulation material J/K.m³ $\sigma_{\mathrm{j}}$ Specific heat capacity of jacket material J/K.m³ $\sigma_{\mathrm{k2}}$ Specific heat capacity of layer located below J/K.m³ $\sigma_{\mathrm{k3}}$ Specific heat capacity of layer located above J/K.m³ $\sigma_{\mathrm{kc}}$ Specific heat capacity of metallic component J/K.m³ $\sigma_{\mathrm{ki}}$ Specific heat capacity of adjacent material J/K.m³ $\sigma_{\mathrm{sc}}$ Specific heat capacity of screen material J/K.m³ $\sigma_{\mathrm{scb}}$ Specific heat capacity of screen bedding J/K.m³ $\sigma_{\mathrm{scs}}$ Specific heat capacity of screen serving J/K.m³ $\sigma_{\mathrm{sh}}$ Specific heat capacity of sheath material J/K.m³ $\sigma_{\mathrm{sun}}$ Absorption coefficient of solar radiation $\sigma_{\mathrm{y}}$ Yield strength of metals for armour MPa $SP_{\mathrm{p}}$ Sidewall pressure N/m T $t$ Thickness of insulation between conductors mm $T0_{\mathrm{gas}}$ Gas reference temperature K $T_{\mathrm{1}}$ Thermal resistance between one conductor and sheath K.m/W $t_{\mathrm{1}}$ Thickness of insulation to sheath mm $t_{\mathrm{1t}}$ Thickness of insulation to sheath, transient mm $T_{\mathrm{1t}}$ Thermal resistance between one conductor and sheath, transient K.m/W $t_{\mathrm{2}}$ Thickness of bedding under armour mm $T_{\mathrm{2}}$ Thermal resistance between sheath and armour K.m/W $T_{\mathrm{2_{\mathrm{1}}}}$ Thermal resistance between sheath and 1st armour layer K.m/W $T_{\mathrm{2_{\mathrm{2}}}}$ Thermal resistance of material between armour layers K.m/W $T_{\mathrm{2_{\mathrm{f}}}}$ Thermal resistance between sheath and armour bedding K.m/W $T_{\mathrm{3}}$ Thermal resistance of jacket K.m/W $t_{\mathrm{3}}$ Thickness of serving over armour mm $T_{\mathrm{4d}}$ Transient thermal resistance for daily load K.m/W $T_{\mathrm{4db}}$ Correction of thermal resistance for backfill K.m/W $T_{\mathrm{4i}}$ Thermal resistance of medium in the duct K.m/W $T_{\mathrm{4ii}}$ Thermal resistance of the duct wall K.m/W $T_{\mathrm{4iii}}$ Thermal resistance to ambient K.m/W $T_{\mathrm{4\mu}}$ Thermal resistance to ambient K.m/W $T_{\mathrm{4ss}}$ Steady-state thermal resistance K.m/W $T_{\mathrm{4t}}$ Equivalent thermal resistance for tunnel K.m/W $T_{\mathrm{4w}}$ Transient thermal resistance for weekly load K.m/W $T_{\mathrm{4y}}$ Transient thermal resistance for yearly load K.m/W $T_{\mathrm{a}}$ Star thermal resistance of air K.m/W $T_{\mathrm{A}}$ Element A of equivalent thermal circuit K.m/W $T_{\mathrm{a0}}$ Apparent thermal resistance a 1/s $t_{\mathrm{ab_{\mathrm{1}}}}$ Thickness of 1st armour bedding mm $t_{\mathrm{ab_{\mathrm{2}}}}$ Thickness of 2nd bedding between mm $T_{\mathrm{at}}$ Thermal resistance by convection air-tunnel K.m/W $T_{\mathrm{B}}$ Element B of equivalent thermal circuit K.m/W $T_{\mathrm{b0}}$ Apparent thermal resistance b s² $t_{\mathrm{c}}$ Thickness of hollow conductor mm $T_{\mathrm{C}}$ Element C of equivalent thermal circuit K.m/W $t_{\mathrm{comp}}$ Thickness of compartment mm $T_{\mathrm{conv_{\mathrm{ce}}}}$ Thermal resistance by convection conductor-enclosure W/m $T_{\mathrm{conv_{\mathrm{sa}}}}$ Thermal resistance by convection surface-air W/m $t_{\mathrm{corr}}$ Thickness of corrugation filling mm $t_{\mathrm{cs}}$ Thickness of conductor shield mm $t_{\mathrm{ct}}$ Thickness of s.c. tape wrapped around conductor mm $T_{\mathrm{d}}$ Internal thermal resistance for dielectric losses K.m/W $T_{\mathrm{e}}$ External thermal resistance of tunnel K.m/W $t_{\mathrm{EMF}}$ Time step to calculate current source s $t_{\mathrm{encl}}$ Thickness of enclosure mm $T_{\mathrm{eq}}$ Equivalent thermal resistance K.m/W $T_{\mathrm{f}}$ Axial thermal resistance due to the movement of air through the tunnel K.m/W $t_{\mathrm{f}}$ Thickness of filler/belt insulation mm $T_{\mathrm{gas}}$ Absolute gas temperature K $T_{\mathrm{i}}$ Internal thermal resistance for current losses K.m/W $t_{\mathrm{i}}$ Thickness of core insulation mm $T_{\mathrm{\infty}}$ Infinite bulk temperature (the ambient air temperature) K $t_{\mathrm{ins}}$ Thickness of insulation mm $t_{\mathrm{is}}$ Thickness of insulation screen mm $t_{\mathrm{j}}$ Thickness of jacket mm $t_{\mathrm{jj}}$ Thickness of additional layer over jacket mm $t_{\mathrm{k}}$ Duration of short-circuit s $T_{\mathrm{L}}$ Thermal longitudinal resistance K.m/W $T_{\mathrm{mh}}$ Mutual thermal resistance between rated and crossing object K.m/W $T_{\mathrm{mh_{\mathrm{v}}}}$ Mutual thermal resistance per slice K.m/W $T_{\mathrm{o}}$ Thermal resistance of the oil in the pipe K.m/W $T_{\mathrm{prot}}$ Thermal resistance of protective cover K.m/W $t_{\mathrm{prot}}$ Thickness of protective cover mm $T_{\mathrm{r}}$ Total thermal resistance K.m/W $T_{\mathrm{rad_{\mathrm{ce}}}}$ Radiation thermal resistance conductor-enclosure W/m $T_{\mathrm{rad_{\mathrm{sa}}}}$ Radiation thermal resistance surface-air W/m $T_{\mathrm{s}}$ Star thermal resistance of object K.m/W $T_{\mathrm{sa}}$ Thermal resistance by convection surface-air K.m/W $t_{\mathrm{sc}}$ Thickness of the screen mm $t_{\mathrm{scb}}$ Thickness of screen bedding mm $t_{\mathrm{scs}}$ Thickness of screen serving mm $t_{\mathrm{sh}}$ Thickness of the sheath mm $T_{\mathrm{st}}$ Radiation thermal resistance surface-tunnel K.m/W $T_{\mathrm{surf}}$ Absolute surface temperature K $t_{\mathrm{t}}$ Tunnel wall thickness m $T_{\mathrm{t}}$ Star thermal resistance of tunnel K.m/W $T_{\mathrm{tot}}$ Total thermal resistance, transient K.m/W $T_{\mathrm{tr}}$ Thermal resistance of trough K $T_{\mathrm{tw}}$ Thermal resistance of tunnel wall K.m/W $\mathrm{tan}\delta _{\mathrm{i}}$ Loss factor of insulation $\tau$ Transient load period s $\theta_{\mathrm{2K}}$ Temperature rise for 2K criterion °C $\theta_{\mathrm{a}}$ Ambient temperature °C $\theta_{\mathrm{abs}}$ Absolute temperature K $\theta_{\mathrm{air}}$ 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 section rad $\theta_{\mathrm{R}}$ 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 constant s U $u$ Substitution coefficient u $U_{\mathrm{0}}$ Value of U0 for determination of test voltages kV $U_{\mathrm{d}}$ Constant U for cables in ducts K.m/W $U_{\mathrm{e}}$ Line-to-ground voltage kV $U_{\mathrm{m}}$ Highest voltage for equipment kV $U_{\mathrm{n}}$ Rated line-to-line voltage kV $U_{\mathrm{o}}$ Operating voltage kV V $v_{\mathrm{4}}$ Ratio of the thermal resistivities of dry and moist soils $V_{\mathrm{air}}$ Air velocity m/s $V_{\mathrm{comp}}$ Gas volume m³ $V_{\mathrm{d}}$ Constant V for cables in ducts K.m/W $V_{\mathrm{drop}}$ Voltage drop V/A/km $V_{\mathrm{gas}}$ Volume percentage of second gas % $V_{\mathrm{m}}$ Molar volume m³/mol W $W_{\mathrm{A}}$ Armour losses W/m $W_{\mathrm{a_{\mathrm{L}}}}$ Heat removed by air at outlet W/m $W_{\mathrm{a_{\mathrm{z}}}}$ Heat removed by air at z W/m $w_{\mathrm{b}}$ Width of the backfill mm $W_{\mathrm{c}}$ Conductor losses W/m $W_{\mathrm{conv_{\mathrm{ce}}}}$ Convection heat transfer conductor-enclosure W/m $W_{\mathrm{conv_{\mathrm{sa}}}}$ Convection heat transfer surface-air W/m $W_{\mathrm{d}}$ Dielectric losses W/m $W_{\mathrm{encl}}$ Enclosure losses W/m $w_{\mathrm{f_{\mathrm{1}}}}$ Width of flat wires of 1st armour mm $w_{\mathrm{f_{\mathrm{2}}}}$ Width of flat wires of 2nd armour mm $W_{\mathrm{h}}$ Heat generated by external object W/m $W_{\mathrm{hs}}$ Heat dissipation of heat source W/m $W_{\mathrm{I}}$ Ohmic losses per phase W/m $W_{\mathrm{p}}$ Losses in ferromagnetic steel pipe W/m $w_{\mathrm{p}}$ Weight correction factor $W_{\mathrm{rad_{\mathrm{ce}}}}$ Radiation heat transfer conductor-enclosure W/m $W_{\mathrm{rad_{\mathrm{sa}}}}$ Radiation heat transfer surface-air W/m $W_{\mathrm{s}}$ Screen and sheath losses W/m $W_{\mathrm{sA}}$ Total loss in sheath and armour W/m $W_{\mathrm{sA_{\mathrm{1}}}}$ Total loss in sheath and 1st armour W/m $W_{\mathrm{sA_{\mathrm{2}}}}$ Total loss in sheath and 2nd armour W/m $w_{\mathrm{sc}}$ Width of flat screen wire mm $W_{\mathrm{sum}}$ Sum of total losses of all systems W/m $W_{\mathrm{sys}}$ Total losses of the system W/m $W_{\mathrm{T}}$ Trench width in multi-layer backfill m $W_{\mathrm{t}}$ Total losses per phase W/m $w_{\mathrm{t}}$ Inner width m $W_{\mathrm{tot}}$ Total losses per object W/m X $X_{\mathrm{0}}$ Zero sequence reactance Ω/m $x_{\mathrm{b}}$ Horizontal center of backfill mm $X_{\mathrm{c}}$ Reactance of conductor Ω/m $X_{\mathrm{G}}$ Factor XG $X_{\mathrm{G2}}$ Factor XG2 $X_{\mathrm{K}}$ Factor XK $X_{\mathrm{m}}$ Mutual reactance Ω/m $x_{\mathrm{p}}$ Factor for proximity effect of conductors $x_{\mathrm{pos}}$ Horizontal x-position in multi-layer backfill mm $x_{\mathrm{s}}$ Factor for skin effect on conductor $X_{\mathrm{s}}$ Reactance of screen/sheath Ω/m $X_{\mathrm{S1}}$ Reactance section 1 Ω/m $X_{\mathrm{S2}}$ Reactance section 2 Ω/m $X_{\mathrm{S3}}$ Reactance section 3 Ω/m $\xi_{\mathrm{cb}}$ Parameter ξ for calculation of loss factor Y $Y$ Admittance S/m $y_{\mathrm{2K}}$ Depth for 2K criterion mm $y_{\mathrm{c}}$ Skin and proximity effect factor for GIL conductor $Y_{\mathrm{d}}$ Constant Y for cables in ducts K.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 cycle p.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 impedance Ω/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 source m $Z_{\mathrm{K}}$ Factor ZK $z_{\mathrm{max}}$ Logitudinal thermal limit distance m $Z_{\mathrm{neg}}$ Negative sequence impedance Ω/m $Z_{\mathrm{pos}}$ Positive sequence impedance Ω/m $z_{\mathrm{r}}$ Location of the hottest point m $\zeta_{\mathrm{M}}$ Density of material g/cm³