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SymbolNameUnit
A $a_0$Coefficient a for partial transient temperature rise1/s
$a_{12}$Distance between phase 1 and 2mm
$a_{23}$Distance between phase 2 and 3mm
$a_{31}$Distance between phase 3 and 1mm
$A_{ab}$Cross-sectional area of armour beddingmm$^2$
$A_{ar}$Cross-sectional area of armourmm$^2$
$A_c$Cross-sectional area of conductormm$^2$
$a_c$Skin and proximity effect coefficient a for PAC/GIL conductor
$A_{comp}$Cross-sectional area of compartmentm$^2$
$A_d$Cross-sectional area of duct wallmm$^2$
$A_{d,fill}$Free cross-sectional area inside ductmm$^2$
$A_{di}$Surface of duct inner wallm$^2$
$A_{do}$Surface of duct outer wallm$^2$
$A_e$Surface of objectm$^2$
$A_{encl}$Cross-sectional area of enclosuremm$^2$
$a_{encl}$Skin and proximity effect coefficient a for PAC/GIL enclosure
$A_{er}$Surface of objectm$^2$
$A_f$Cross-sectional area of fillermm$^2$
$A_{fluid}$Cross-sectional area of fluidmm$^2$
$A_i$Cross-sectional area of insulationmm$^2$
$A_{it}$Cross-sectional area of insulation (IEC 60853)mm²
$A_j$Cross-sectional area of jacketmm$^2$
$A_k$Thermal property constant Amm/s$^{1/2}$
$a_m$Mean distance between the phasesmm
$A_{pipe}$Cross-sectional area of fluid-filled pipemm$^2$
$A_{prot}$Cross-sectional area of protective covermm$^2$
$a_{S1}$Length of 1st section (minor)p.u.
$a_{S2}$Length of 2nd section (medium)p.u.
$a_{S3}$Length of 3rd section (major)p.u.
$A_{sc}$Cross-sectional area of screenmm$^2$
$A_{scb}$Cross-sectional area of screen beddigmm$^2$
$A_{scs}$Cross-sectional area of screen servingmm$^2$
$A_{sh}$Cross-sectional area of sheathmm$^2$
$A_{shj}$Cross-sectional area of sheath jacketmm$^2$
$a_{shj}$Factor $a_{shj}$ for jacket around each core
$A_{skid}$Cross-sectional area of skid wiresmm$^2$
$A_{sp}$Cross-sectional area of steel pipemm$^2$
$A_t$Cross-sectional area of the tunnelm$^2$
$A_{tape}$Cross-sectional area of bedding/serving tapesmm$^2$
$a_{type}$Construction of armour
$\alpha_0$Constant depending on the burial depth
$\alpha_{ar}$Temperature coefficient of armour material1/K
$\alpha_{at}$Heat transfer coefficient to channel wallW/(K.m$^2$)
$\alpha_c$Temperature coefficient of conductor material1/K
$\alpha_{encl}$Temperature coefficient of enclosure material1/K
$\alpha_f$Phase shift°
$\alpha_{gas}$Thermal diffusivity for gasm$^2$/s
$\alpha_M$Factor $\alpha_M$
$\alpha_{sa}$Heat transfer coefficient for convectionW/(K.m$^2$)
$\alpha_{sc}$Temperature coefficient of screen material1/K
$\alpha_{sh}$Temperature coefficient of sheath material1/K
$\alpha_{skid}$Temperature coefficient of skid wire material1/K
$\alpha_{sp}$Temperature coefficient of steel pipe material1/K
$\alpha_{st}$Heat transfer coefficient for radiationW/(K.m$^2$)
$\alpha_{sys}$Inclination angle in degrees°
$\alpha_t$Conductor to surface attainment factor
B $B$SusceptanceS/m
$b_0$Coefficient b for partial transient temperature rise1/s
$B_1$Loss coefficient $B_1$ of armour$\Omega$/m
$B_2$Loss coefficient $B_2$ of armour$\Omega$/m
$b_c$Skin and proximity effect coefficient b for PAC/GIL conductor
$B_{EMF}$Magnetic field strength$\mu$T
$b_{encl}$Skin and proximity effect coefficient b for PAC/GIL enclosure
$B_k$Thermal property constant Bmm$^2$/s
$b_{Nu,r}$Factor b
$b_{shj}$Factor $b_{shj}$ for jacket around each core
$b_x$Shorter side of backfillmm
$b_y$Longer side of backfillmm
$\beta_0$Constant $\beta_0$ (Ovuworie)
$\beta_1$Substitution coefficient $\beta_1$ for eddy-currents
$\beta_6$Factor $|1-\beta(6)|$
$\beta_{ar}$Reciprocal of temperature coefficient of armour materialK
$\beta_b$Angle of exposed wetted surface of piperad
$\beta_c$Reciprocal of temperature coefficient of conductor materialK
$\beta_{encl}$Reciprocal of temperature coefficient of enclosure materialK
$\beta_{gas}$Volumetric thermal expansion coefficient for gas1/K
$\beta_k$Reciprocal of temperature coefficient of resistanceK
$\beta_M$Factor $\beta_M$
$\beta_{sc}$Reciprocal of temperature coefficient of screen materialK
$\beta_{sh}$Reciprocal of temperature coefficient of sheath materialK
$\beta_{skid}$Reciprocal of temperature coefficient of skid wire materialK
$\beta_{sp}$Reciprocal of temperature coefficient of steel pipe materialK
$\beta_t$Attainment factor cable surface to ambient
$\beta_X$Crossing angle [rad]rad
$\beta_{xing}$Crossing angle [°]°
$\mathrm{Bi}_g$Biot number of the ground
$\mathrm{Bi}_p$Biot number of the pipe
C $C_{av}$Heat capacity of the air flowW/K
$C_b$Capacitance of insulationF/m
$C_{bq}$Constants $C_1$ - $C_7$ of multi-layer backfill
$c_c$Distance between the axis of a conductor and the cable centermm
$C_{c1}$Thermal capacitance, 1st loopJ/m.K
$C_{c2}$Thermal capacitance, 2nd loopJ/m.K
$C_{c3}$Thermal capacitance, 3rd loopJ/m.K
$C_{c4}$Thermal capacitance, 4th loopJ/m.K
$c_{color}$Wiring color code
$C_{g1}$Factor C1 for partially buried pipes
$C_{g2}$Factor C2 for partially buried pipes
$C_{g3}$Factor C3 for partially buried pipes
$c_{gas}$Constant c for a gas under PAC/GIL conditions
$c_{ij}$Coefficient c for view factor
$C_{k1}$Non-adiabatic constant $C_1$mm/m
$C_{k2}$Non-adiabatic constant $C_2$K.m.mm$^2$/J
$C_{Nu,L}$Factor C
$c_{Nu,r}$Factor c
$C_{Nu,w}$Factor C
$c_{p,gas}$Specific heat capacity at constant pressureJ/kg.K
$c_{p,soil}$Specific heat capacity of soilJ/kg.K
$c_{p,w}$Specific heat capacity at constant pressureJ/kg.K
$c_{shj}$Factor $c_{shj}$ for jacket around each core
$c_{SI}$Surge velocity of propagationkm/s
$c_{type}$Construction of conductor
$c_{v,gas}$Specific heat capacity at constant volumeJ/kg.K
$C_{v,soil}$Volumetric heat capacity of soilJ/K.m$^3$
$c_{v,w}$Specific heat capacity at constant volumeJ/kg.K
$C_{vair}$Volumetric heat capacity of airJ/K.m$^3$
$CC$Charging capacitykvar/km
$CC_{pull}$Conduit clearancemm
$CF_{pull}$Conduit fill$\%$
$CJ_{pull}$Conduit jamming ratio
$\mathrm{cos}\varphi$Power factor
$CR_{pull}$Conduit ratio
$cuw$Standard copper wiresmm
D $D_{ab}$Diameter over armour beddingmm
$D_{ar}$External diameter of armourmm
$d_{ar}$Mean diameter of armourmm
$d_b$Diameter of the backfillmm
$d_{b3}$Distance c of multi-layer backfillm
$d_{b4}$Distance d of multi-layer backfillm
$d_c$External diameter of conductormm
$D_c$Diameter of conductorm
$d_{ci}$Internal diameter of conductormm
$D_{comp}$Diameter of compartment (metric)m
$d_{comp}$Diameter of compartmentmm
$d_{ct}$External diameter of conductor for transient calculationsmm
$D_{di}$Inner diameter of ductm
$D_{do}$Outer diameter of ductm
$D_{dry}$Diameter of drying zonem
$D_e$External diameter of objectmm
$d_e$Equivalent diameter of screen/sheath and armourmm
$d_{encl}$Outer diameter of enclosuremm
$D_{encl}$Outer diameter of enclosure (metric)m
$D_{eq}$Equivalent diameter of a group of round objectsmm
$D_{ext}$Overall outer diameter of pipem
$D_f$External diameter of the fillermm
$d_f$Spacing from hottest object in groupm
$D_i$Diameter over insulationmm
$d_{im}$Imaginary layer of soilm
$D_{in}$Inner diameter of pipem
$D_{ins}$Diameter over insulation without insulation screenmm
$d_{ins}$Diameter of insulation around pipemm
$D_{it}$Diameter over insulation for transient calculationsmm
$d_j$Diameter below jacketmm
$D_j$Diameter over jacketmm
$D_o$Outer diameterm
$d_{pk1}$Distance to mirrored buried objectmm
$d_{pk2}$Distance between buried objectsmm
$d_{prot}$Diameter of protective covermm
$d_{psc}$Point source correctionm
$D_{ref}$Reference diameter for determination of OHTCm
$d_s$Equivalent diameter of screen and sheathmm
$D_{sc}$Diameter over screenmm
$d_{sc}$Mean diameter of screenmm
$D_{scb}$Diameter over screen beddingmm
$D_{scs}$Diameter over screen servingmm
$D_{sh}$Diameter over sheathmm
$d_{sh}$Mean diameter of sheathmm
$D_{shb}$Diameter below sheathmm
$D_{shj}$Diameter of sheath jacketmm
$D_{soil}$Outer diameter of soil layerm
$d_t$Channel coveringm
$d_w$Depth under waterm
$D_{wall}$Outer diameter of steel pipem
$d_x$Equivalent diameter of a conductormm
$D_x$Characteristic diametermm
$D_{x,w}$Characteristic diameter for weekly loadmm
$D_{x,y}$Characteristic diameter for yearly loadmm
$\Delta_1$Substitution coefficient $\Delta_1$ for eddy-currents
$\delta_1$Thickness of screening layermm
$\Delta_2$Substitution coefficient $\Delta_2$ for eddy-currents
$\delta_{ar}$Equivalent thickness of armourmm
$\delta_d$Distance between cable and ductm
$\delta_k$Thickness of screen, sheath or armourmm
$\delta_{soil}$Soil thermal diffusivitym$^2$/s
$\Delta d_{sh}$Depth of corrugationmm
$\Delta H_c$Heat of combustion coefficientMJ/kg
$\Delta t$Length of time steps
$\Delta \theta_{0t}$Air temperature in tunnel increaseK
$\Delta \theta_{0x}$Temperature rise by crossing heat sourcesK
$\Delta \theta_{0x,1}$Temperature rise of the conductor, first estimateK
$\Delta \theta_{0x,h}$Temperature rise of the conductor by source hK
$\Delta \theta_{a,t}$Corrected transient temperature rise of conductorK
$\Delta \theta_{air}$Temperature increase of airK
$\Delta \theta_c$Temperature rise of conductorK
$\delta \theta_c$Ohmic steady-state temperature riseK
$\Delta \theta_{c,t}$Transient temperature rise of conductor by ohmic lossesK
$\Delta \theta_{ce}$Temperature difference, conductor to surfaceK
$\Delta \theta_d$Temperature rise by dielectric lossesK
$\Delta \theta_{e,t}$Transient temperature rise of outer surfaceK
$\Delta \theta_{gas}$Temperature difference, conductor to enclosure°C
$\Delta \theta_{kp}$Temperature rise by buried object kK
$\Delta \theta_{max}$Maximum permissible conductor temperature riseK
$\Delta \theta_p$Temperature rise by other buried objectsK
$\Delta \theta_R$Conductor temperature rise above ambient temperatureK
$\Delta \theta_{R,\infty}$Maximum permissible conductor temperature rise°C
$\Delta \theta_s$Temperature difference surface to ambientK
$\delta \theta_{SPK}$Peak cyclic temperature riseK
$\Delta \theta_{sun}$Temperature rise by solar radiationK
$\Delta \theta_t$Transient temperature rise of conductorK
$\Delta \theta_{t,\infty}$Steady-state temperature rise of conductorK
$\Delta \theta_x$Critical soil temperature riseK
$\Delta \theta_{x0}$VDE soil temperature riseK
$\Delta W$Incremental heat generatedW
$\Delta z$Length of the intervalm
$Di_d$Inner diameter of ductmm
$di_{pipe}$Internal diameter of fluid-filled pipemm
$Di_{sp}$Inner diameter of steel pipemm
$Di_t$Tunnel inner diameterm
$Do_d$Outer diameter of ductmm
$do_{pipe}$External pipe diametermm
$Do_{sp}$Outer diameter of steel pipemm
$Do_t$Tunnel/trough outer diameterm
E $E_{bs}$Installation constant E
$e_{hor}$Horizontal clearancemm
$e_{limit}$Limit of thickness of soil layerm
$e_{soil}$Thickness of soil layerm
$E_{stress}$Electrical field strengthkV/mm
$e_{ver}$Vertical clearancemm
$e_{wall}$Clearance to wallmm
$EEC$Embodied energy and carbonMJ/kg
$\epsilon_0$Vacuum permittivityF/m
$\epsilon_c$Effective emissivity of conductor
$\epsilon_{di}$Emissivity of duct inner surface
$\epsilon_{do}$Emissivity of duct outer surface
$\epsilon_e$Emissivity of cable surface
$\epsilon_{encl}$Effective emissivity of enclosure
$\epsilon_{gas}$Dielectric constant of gas in compartment
$\epsilon_i$Relative permittivity of insulation
$\epsilon_k$Heat loss allowance factor
$\epsilon_{prot}$Effective emissivity of protective cover
$\epsilon_{rad}$Effective emissivity
$\eta 0_{gas}$Reference dynamic viscosity of gasPa.s
$\eta_{di}$Reflectivity of (opaque) duct inner surface
$\eta_{do}$Reflectivity of (opaque) duct outer surface
$\eta_e$Reflectivity of (opaque) cable surface
$\eta_{gas}$Dynamic viscosity of gasPa.s
$\eta_w$Dynamic viscosity of waterPa.s
F $f$System frequencyHz
$F_{\alpha}$Inclination derating factorp.u.
$F_{ar}$Factor $F_{ar}$ for armour losses
$f_{atm}$Relation atmospheric pressure to standard atmosphere
$f_{cb}$Factor for cross-bonded earthing
$F_e$Factor $F_e$ for eddy-current losses
$F_{eq}$Factor for envelope circle for a group of equal circles
$F_{form}$Form factor
$F_g$Gravitational forceN/m
$F_{ij}$View factor object-object
$F_k$Imperfect contact thermal factor
$F_{lay}$Effective length per unit lay length of armourmm
$F_m$Radiation coefficient mutual
$F_{mh}$Mutual heating coefficient
$f_{ppc}$Factor of permissible pullN/mm$^2$
$F_{ppc}$Permissible pull forceN
$F_{pt}$Function of pressure and temperature
$F_{pull}$Pulling forceN
$f_{rad}$Sidewall bearing pressure factorN/m
$F_{rad}$Sidewall bearing pressureN/m
$F_{red}$Reduction factor for the permissible current rating
$F_{T10,1}$Factor Table 10, single cablesp.u.
$F_{T10,3}$Factor Table 10, trefoil groupsp.u.
$F_{T11,s}$Factor Table 11, first partp.u.
$F_{T11,t}$Factor Table 11, second partp.u.
$F_{T12}$Factor Table 12p.u.
$F_{T13}$Factor Table 13p.u.
$f_{wc}$Weight correction factor
$F_x$Geometrical distance factor for multi-core cables
G $g$Standard acceleration of gravitym/s$^2$
$G$ConductanceS/m
$G_1$Geometric factor $G_1$
$G_2$Geometric factor $G_2$ for cables with separate sheaths
$g_a$Substitution coefficient g
$G_b$Geometric factor for backfill
$g_{bs}$Installation constant g
$G_{corr}$Geometric correction factor $G_{corr}$ for jacket around each core
$g_{dry}$Geometric constant of circle with dried-out soilp.u.
$G_{encl}$Factor G for the calculation of the Nusselt number
$G_{FEA}$Geometric reference factor $G_{FEA}$ based on FEM fitting
$G_{od}$Aspect ratio object/duct
$g_s$Substitution coefficient $g_s$ for eddy-currents
$G_{s00}$Factor $G_{s 0.0}$
$G_{s05}$Factor $G_{s 0.5}$
$G_{s10}$Factor $G_{s 1.0}$
$g_x$Geometric constant of circle with characteristic diameterp.u.
$\gamma_{bessel}$Bessel constantp.u.
$\gamma_c$Skin and proximity effect factor $\gamma$ for PAC/GIL conductor
$\gamma_{encl}$Skin and proximity effect factor $\gamma$ for PAC/GIL enclosure
$\gamma_{euler}$Euler's constantm/s$^2$
$\gamma_t$Attainment factor for groups of cables
$\gamma_X$Attenuation factor for crossing1/m
$GMD$Geometric mean distancemm
$GMR$Geometric mean radiusmm
$\mathrm{Gr}_c$Grashof number, conductor to gas
$\mathrm{Gr}_{da}$Grashof number, duct in air
$\mathrm{Gr}_{encl}$Grashof number, gas to enclosure
$\mathrm{Gr}_{gd}$Grashof number, gas to duct
$\mathrm{Gr}_L$Grashof number, ground to air
$\mathrm{Gr}_{od}$Grashof number, object to duct
$\mathrm{Gr}_{og}$Grashof number, object to gas
$\mathrm{Gr}_{prot}$Grashof number, surface to air
H $H$Distance center of pipe to groundm
$H_1$Component of inductance $H_1$ of armourH/m
$h_1$Factor $h_1$ for emergency load
$H_2$Component of inductance $H_2$ of armourH/m
$H_3$Component of inductance $H_3$ of armourH/m
$h_{amb}$Pseudo film coefficient of ambient fluid at ground levelW/(K.m$^2$)
$h_{atm}$Height above sea levelm
$h_b$Height of the backfillmm
$h_{bs}$Heat dissipation coefficient for black surfaces in free airW/m$^2$/K$^{5/4}$
$h_{buried}$Heat transfer coefficient wall to soilW/(K.m$^2$)
$H_c$Heat energy contentMJ/m
$h_{conv,c}$Convection heat transfer coefficient, conductor to gasW/(K.m$^2$)
$h_{conv,da}$Convection heat transfer coefficient, duct to airW/(K.m$^2$)
$h_{conv,encl}$Convection heat transfer coefficient, gas to enclosureW/m2.K
$h_{conv,gd}$Convection heat transfer coefficient, gas to ductW/(K.m$^2$)
$h_{conv,od}$Convection heat transfer coefficient, object to ductW/(K.m$^2$)
$h_{conv,og}$Convection heat transfer coefficient, object to gasW/(K.m$^2$)
$h_{conv,sa}$Convection heat transfer coefficient, surface to airW/(K.m$^2$)
$h_{era}$Convection heat transfer coefficient acc. ERAW/(K.m$^2$)
$h_{ext}$External heat transfer coefficientW/(K.m$^2$)
$h_{ground}$Heat transfer coefficient buried part of wall to soilW/(K.m$^2$)
$h_{in}$Heat transfer coefficient insideW/(K.m$^2$)
$h_{lg}$Ratio of heat dissipation coefficients
$h_{rad,ce}$Radiation heat transfer coefficient, conductor to enclosureW/(K.m$^2$)
$h_{rad,da}$Radiation heat transfer coefficient, duct to airW/(K.m$^2$)
$h_{rad,od}$Radiation heat transfer coefficient, object to ductW/(K.m$^2$)
$h_{rad,sa}$Radiation heat transfer coefficient, surface to airW/(K.m$^2$)
$H_s$Sheath conductanceH/m
$h_{soil}$Heat transfer coefficient wall-soilW/(K.m$^2$)
$H_{sun}$Intensity of solar radiationW/m$^2$
$h_t$Inner heightm
$h_{T4}$Ratio of thermal resistance to ambient
$H_{tc}$Parameter H for trough
$h_{tr}$Heat transfer coefficientW/(K.m$^2$)
$H_{ts}$Parameter H depending on air velocity
$H_x$Magnetic field x-componentmH
$H_y$Magnetic field y-componentmH
I $I_1$Steady-state current before transientA
$I_2$Emergency load currentA
$I_c$Conductor currentA
$I_C$Capacitive load currentA/km
$I_{c,max}$Highest current load of lineA
$I_{c,peak}$Permissible peak cyclic load currentA
$I_{Ce}$Capacitive earth short-circuit currentA/km
$I_{EMF}$Phase current for EMF calculationA
$I_k$Permissible short-circuit currentkA
$I_{k1}$Phase-to-ground short-circuit currentkA
$I_{k2}$Phase-to-phase short-circuit currentkA
$I_{k3}$Three-phase symmetric short-circuit currentkA
$I_{kAD}$Short-circuit current (adiabatic)kA
$I_{kSC}$Effective short-circuit currentkA
$I_{method}$Current calculation method
$I_R$Transient conductor currentA
$inst_{air}$Installation in air
$inst_{elec}$Installation of cables for electrical calculations
$inst_{riser}$Installation of cables in riser
$inst_{sea}$Installation of subsea cables
$inst_t$Installation in air inside a room
J $j_{max}$Phase angle range°
K $K$Screening factor
$K_0$Coefficient K for a gas under PAC/GIL conditions
$K_{02}$Factor $K_{0.2}$
$K_{06}$Factor $K_{0.6}$
$K_{10}$Factor $K_{1.0}$
$k_4$Thermal conductivity of soilW/(m.K)
$K_A$Coefficient K to calculate in air
$k_{air}$Thermal conductivity of airW/(m.K)
$k_{ar}$Thermal conductivity of armour materialW/(m.K)
$K_{BICC}$Constant relating to conductor formation
$k_{Boltzmann}$Boltzmann constantJ/K
$k_c$Thermal conductivity of conductor materialW/(K.m)
$K_{ce}$Radiation shape factor, conductor to enclosure
$K_{cv}$Convection factor
$K_{dyn}$Corrected dynamic friction coefficient
$k_{encl}$Thermal conductivity of enclosureW/(m.K)
$k_{fluid}$Thermal conductivity of fluidW/(m.K)
$k_{gas}$Thermal conductivity for gasW/(m.K)
$K_{GMR}$Geometric mean radius factor
$k_H$Heinhold characteristic diameter coefficient
$k_{ins}$Thermal conductivity of insulationW/(m.K)
$K_k$Specific short-circuit parameterA.s$^{1/2}$/mm$^2$
$k_l$Temperature rise factor in air
$k_{LF}$Load loss constant coefficientp.u.
$K_{od}$Diameter ratio object/duct
$k_p$Proximity effect coefficient
$K_{par}$Constant $K_{par}$ (Ovuworie)
$k_{pipe}$Thermal conductivity of fluid-filled pipeW/(m.K)
$k_{prot}$Thermal conductivity of protective coverW/(m.K)
$K_r$Radiation shape factor
$k_{r2}$Temperature rise ratio $\delta\theta_{SPK}/\delta\theta_c$p.u.
$k_s$Skin effect coefficient
$k_{sa}$Convection factor (Heinhold)
$k_{sa,1}$Factor 1 for convection heat transfer coefficient
$k_{sa,2}$Factor 2 for convection heat transfer coefficient
$k_{sc}$Thermal conductivity of screen materialW/(m.K)
$k_{sh}$Thermal conductivity of sheath materialW/(m.K)
$k_{skid}$Thermal conductivity of skid wires
$k_t$Temperature rise ratiop.u.
$K_t$Effective emissivity of surface
$K_{vermeer}$Vermeer constant for convection heat transfer
$k_w$Thermal conductivity of waterW/(m.K)
$K_x$Factor for fictitious diameter by Neher
$k_X$Number of heat sources crossing
L $L_0$Reference length of the tunnelm
$L_1$Inductance of phase 1H/m
$L_2$Inductance of phase 2H/m
$L_3$Inductance of phase 3H/m
$L_b$Vertical center of backfillmm
$L_{b4}$Trench depth of multi-layer backfillm
$L_c$Depth of laying of sourcesmm
$L_{char}$Characteristic length earth surface
$L_{cm}$Depth of layingm
$L_{crit}$Critical system lengthkm
$L_d$Length of ductm
$L_{deep}$Equivalent depth for deep burialm
$L_{dry}$Depth of characteristic diameter of drying zonem
$L_{dw}$Length of duct in waterm
$L_{earth}$Equivalent depth of earth return pathmm
$L_h$Depth of laying of crossing elementmm
$L_{leg}$Length of a sectionm
$L_r$Depth of laying of the rated objectmm
$L_{sys}$System lengthkm
$L_T$Length of the tunnelm
$\\lambda_0$Substitution coefficient $\lambda_0$ for eddy-currents
$\\lambda_1$Loss factor of shield (screen and sheath)
$\\lambda_{11}$Loss factor of shield by circulating currents
$\\lambda_{12}$Loss factor of shield by eddy currents
$\\lambda_2$Loss factor of armour
$\\lambda_{21}$Loss factor of armour by circulating currents
$\\lambda_{22}$Loss factor of armour by eddy currents
$\\lambda_3$Loss factor of steel pipes for pipe-type cables
$\\lambda_4$Loss factor of magnetic steel ducts
$\\lambda_d$Factor for dielectric losses
$\\lambda_{gas}$Ratio $c_p/c_v$
$\\lambda_t$Relaxation parameter
$LF$Load factorp.u.
$LF_w$Weekly load factorp.u.
$LF_y$Yearly load factorp.u.
$LME$London Metal ExchangeUSD/mt
M $M$Cyclic rating factorp.u.
$m_0$Substitution coefficient $m_0$ for eddy-currentsHz.m/$\Omega$
$M_0$Coefficient M for partial transient temperature rises
$M_1$Corrected cyclic rating factorK
$M_{ab}$Material of armour bedding
$m_{ab}$Mass of armour beddingkg/km
$M_{ar}$Material of armour
$m_{ar}$Mass of armourkg/km
$M_c$Material of conductor
$m_c$Mass of conductorkg/km
$M_{cable}$List of materials in a cable
$M_{comp}$Material of insulating gas
$M_d$Material of duct pipe
$M_e$Substitution coefficient $M_e$ to calculate factor $F_e$
$m_{EMF}$Number of time steps
$M_{encl}$Material of enclosure
$M_f$Material of filler
$m_f$Mass of fillerkg/km
$M_{fluid}$Fluid material
$M_{gas}$Gas and gas-mixtures
$m_{hollow}$Mass of hollow cablekg/km
$M_i$Material of insulation
$m_i$Mass of insulationkg/km
$M_{IEEE}$Materials acc. IEEE 442
$M_{ins}$Material of insulation around pipe
$M_j$Material of jacket
$m_j$Mass of jacketkg/km
$M_k$Thermal contact factors$^{1/2}$
$m_{metal}$Mass of the metallic partskg/km
$M_{mol}$Molar massg/mol
$m_{mol}$Molecular massmol
$m_{Nu,L}$Factor m
$m_{Nu,w}$Factor m
$M_{pipe}$Material of fluid-filled pipe
$M_{prot}$Material of protective cover
$M_{riser}$Material of riser
$M_s$Factor $M_s$
$M_{sc}$Material of screen
$m_{sc}$Mass of metallic screenkg/km
$M_{seabed}$Material of seabed
$M_{sh}$Material of sheath
$m_{sh}$Mass of metallic sheathkg/km
$M_{shj}$Material of sheath jacket
$m_{shj}$Mass of jacket over each corekg/km
$M_{skid}$Material of skid wires
$m_{skid}$Mass of skid wireskg/km
$M_{soil}$Type of soils
$M_{sp}$Material of containment for pipe-type cables
$m_{sp}$Mass of steel pipekg/km
$M_{spf}$Steel pipe filling medium
$m_{tape}$Mass of tapeskg/km
$m_{tot}$Mass of cablekg/km
$\mu$Loss factorp.u.
$\mu_0$Vacuum permeabilityH/m
$\mu_{dyn}$Dynamic friction coefficient
$\mu_e$Longitudinal relative permeability
$\mu_s$Relative permeability
$\mu_t$Traverse relative permeability of steel wires
$\mu_w$Loss factor for weekly load variationp.u.
$\mu_y$Loss factor for yearly load variationp.u.
N $N_0$Coefficient N for partial transient temperature rises$^2$
$n_{a,1}$Number of wires of 1st armour
$n_{a,2}$Number of wires of 2nd armour
$n_{ar}$Number of wires of armour
$N_{Avogrado}$Avogadro constant1/mol
$N_b$Number of loaded objects in backfill
$n_c$Number of conductors in object
$N_c$Number of sources in system
$n_{cc}$Number of conductors combined
$n_{cg}$Number of conductors in PAC/GIL
$n_{cw}$Number of wires in conductor
$n_{cycle}$Number of load cycles
$N_e$Substitution coefficient $N_e$ to calculate factor $F_e$
$n_{Nu,r}$Factor n
$N_{sea}$Number of subsea cables
$N_{sum}$Total number of objects in an air-filled space
$n_{sw}$Number of screen wires
$N_{sys}$Number of parallel systems in the same confinement
$N_X$Number of intervals
$\nu$Summation step 1 - $N_X$
$\nu_{air}$Kinematic viscosity for airm$^2$/s
$\mathrm{Nu}_c$Nusselt number, conductor to gas
$\mathrm{Nu}_{da}$Nusselt number, duct to air
$\mathrm{Nu}_{encl}$Nusselt number, gas to enclosure
$\nu_{gas}$Kinematic viscosity for gasm$^2$/s
$\mathrm{Nu}_{gd}$Nusselt number, gas to duct
$\mathrm{Nu}_L$Nusselt number, ground to air
$\mathrm{Nu}_{od}$Nusselt number, object to duct
$\mathrm{Nu}_{og}$Nusselt number, object to gas
$\mathrm{Nu}_{prot}$Nusselt number, surface to air
$\nu_{sc}$Elongation of screen$\%$
$\nu_{soil}$Soil moisture content$\%$
$\mathrm{Nu}_w$Nusselt number, surface to water
$\nu_w$Kinematic viscosity for waterm$^2$/s
O $\omega$Angular frequencyrad/s
P $p_{a,1}$Length of lay of 1st armourmm
$p_{a,2}$Length of lay of 2nd armourmm
$p_{ab}$Factor apportioning the armour bedding
$p_{ar}$Length of lay of armourmm
$p_{atm}$Atmospheric air pressurehPa
$p_{cb}$Minor ratio of section lengths
$p_{comp}$Gas pressure in compartmentbar
$p_{gas}$Gas pressurePa
$p_i$Factor apportioning the insulation
$p_j$Factor apportioning the jacket
$P_L$Active power at load receptorkW
$p_{Nu,r}$Factor p
$p_{shj}$Factor apportioning the sheath jacket
$p_{soil}$Depth of image source
$p_{tr}$Effective perimeter of troughm
$p_w$Water pressurebar
$P_X$Substitution coefficient P to calculate loss factor by circulating currents
$\Phi_{air}$Relative humidity of air$\%$
$\phi_{ar}$Angle between armour and cable axisrad
$\phi_{arc}$Angle of a bendrad
$\phi_{el}$Angle to the plane of a sectionrad
$\phi_{tr}$Parameter $\phi$ for trough
$\pi$Archimedes' constant $\pi$
$\mathrm{Pr}_{air}$Prandtl number for air
$\mathrm{Pr}_{gas}$Prandtl number for gas
$\mathrm{Pr}_w$Prandtl number for liquids
Q $q_1$Ratio of losses affecting screen bedding/serving
$q_2$Ratio of losses affecting armour bedding
$q_3$Ratio of losses affecting jacket
$q_4$Ratio of losses affecting environment
$Q_A$Element A of two-part thermal circuitJ/m.K
$Q_{ab}$Thermal capacitance of armour beddingJ/m.K
$Q_{ar}$Thermal capacitance of armourJ/m.K
$q_{ar}$Ratio of losses armour
$Q_B$Element B of two-part thermal circuitJ/m.K
$Q_{B,ab}$Element B of two-part thermal circuit of armour beddingJ/m.K
$Q_{B,d}$Element B of two-part thermal circuit, ductJ/m.K
$Q_{B,f}$Element B of two-part thermal circuit, fillerJ/m.K
$Q_{B,i}$Element B of two-part thermal circuit, insulationJ/m.K
$Q_{B,j}$Element B of two-part thermal circuit, jacketJ/m.K
$Q_{B,s}$Element B of two-part thermal circuit, screen/sheathJ/m.K
$Q_c$Thermal capacitance of conductorJ/m.K
$q_{cb}$Major ratio of section lengths
$Q_{ct}$Thermal capacitance of conductor (IEC 60853)J/m.K
$Q_d$Thermal capacitance of duct wallJ/m.K
$Q_{d,fill}$Thermal capacitance of duct fillingJ/m.K
$Q_f$Thermal capacitance of fillerJ/m.K
$q_f$Ratio of losses affecting the filler
$Q_i$Thermal capacitance of insulationJ/m.K
$Q_{it}$Thermal capacitance of insulation (IEC 60853)J/m.K
$Q_{it1}$Thermal capacitance of insulation, 1st portion (IEC 60853)J/m.K
$Q_{it2}$Thermal capacitance of insulation, 2nd portion (IEC 60853)J/m.K
$Q_j$Thermal capacitance of jacketJ/m.K
$Q_s$Thermal capacitance of screen+sheathJ/m.K
$q_s$Ratio of losses screen/sheath
$Q_{sc}$Thermal capacitance of screenJ/m.K
$Q_{scb}$Thermal capacitance of screen beddingJ/m.K
$Q_{scs}$Thermal capacitance of screen servingJ/m.K
$Q_{sh}$Thermal capacitance of sheathJ/m.K
$Q_{shj}$Thermal capacitance of sheath jacketJ/m.K
$Q_{sp}$Thermal capacitance of steel pipeJ/m.K
$Q_{tot}$Total thermal capacitance, transientJ/m.K
$Q_X$Substitution coefficient Q to calculate loss factor by circulating currents
$q_x$Factor for characteristic diameter
R $R_0$Zero sequence resistance$\Omega$/m
$r_1$Radius of the circle circumscribing the three shaped conductorsmm
$R_1$Resistance of conductor before emergency rating$\Omega$/m
$R_{ar}$Electrical resistance of armour$\Omega$/m
$r_{arc}$Radius of a bendm
$r_b$Equivalent radius of backfillmm
$r_c$Radius of conductormm
$R_c$Electrical resistance of conductor$\Omega$/m
$R_{c1}$Thermal resistance, 1st loopK.m/W
$R_{c2}$Thermal resistance, 2nd loopK.m/W
$R_{c20}$DC resistance of conductor at 20°C$\Omega$/m
$R_{c3}$Thermal resistance, 3rd loopK.m/W
$R_{c4}$Thermal resistance, 4th loopK.m/W
$R_{cDC}$Electrical DC resistance of conductor$\Omega$/m
$R_{CG}$Thermal resistance of multi-layer backfillK.m/W
$R_{co}$DC resistance of conductor at 20°C$\Omega$/km
$R_e$Electrical resistance of shield and armour$\Omega$/m
$R_{earth}$Equivalent resistance of earth return pathp.u.
$R_{encl}$Electrical AC resistance of enclosure$\Omega$/m
$R_{encl20}$Electrical DC resistance of enclosure at 20°C$\Omega$/m
$R_{enclDC}$Electrical DC resistance of enclosure$\Omega$/m
$r_F$Radius below the insulationmm
$R_{gas}$Specific gas constantJ/kg.K
$R_{gas0}$Universal molar gas constant
$r_I$Radius of the insulationmm
$r_{ij}$Coefficient r for view factor
$R_{max}$Resistance of conductor at emergency rating$\Omega$/m
$r_{mbi}$Minimal bending radius for installationm
$r_{mbif}$Factor of minimal installation bending radius
$r_{mbp}$Minimal bending radius during cable pullingm
$r_{mbpf}$Factor of minimal pulling bending radius
$r_o$Radius of objectm
$R_{q11}$Thermal resistance 11 of multi-layer backfillK.m/W
$R_{q12}$Thermal resistance 12 of multi-layer backfillK.m/W
$R_{q13}$Thermal resistance 13 of multi-layer backfillK.m/W
$R_{q21}$Thermal resistance 21 of multi-layer backfillK.m/W
$R_{q22}$Thermal resistance 22 of multi-layer backfillK.m/W
$R_{q31}$Thermal resistance 31 of multi-layer backfillK.m/W
$R_{q32}$Thermal resistance 32 of multi-layer backfillK.m/W
$R_s$Electrical resistance of shield$\Omega$/m
$R_{sc}$Electrical resistance of screen$\Omega$/m
$R_{sh}$Electrical resistance of sheath$\Omega$/m
$R_{so}$Resistance of screen and sheath at 20°C$\Omega$/m
$R_{sp}$Electrical resistance of steel pipe$\Omega$/m
$r_x$Radius to point x in insulationmm
$\mathrm{Ra}_c$Rayleigh number, conductor to gas
$\mathrm{Ra}_{encl}$Rayleigh number, gas to enclosure
$\mathrm{Ra}_{gas}$Rayleigh number gas/duct
$\mathrm{Ra}_L$Rayleigh number, ground to air
$\mathrm{Ra}_{prot}$Rayleigh number, surface to air
$\mathrm{Re}_{air}$Reynolds number for air
$\mathrm{Re}_w$Reynolds number for water
$RF$Reduction factor
$\rho_4$Thermal resistivity of soilK.m/W
$\rho_{4d}$Thermal resistivity of dry soilK.m/W
$\rho_{ab}$Thermal resistivity of armour beddingK.m/W
$\rho_{ab,1}$Thermal resistivity of 1st armour beddingK.m/W
$\rho_{ab,2}$Thermal resistivity of 2nd armour beddingK.m/W
$\rho_{ar}$Specific electrical resistivity of armour material$\Omega$.m
$\rho_b$Thermal resistivity backfillK.m/W
$\rho_{b1}$Thermal resistivity of surface layerK.m/W
$\rho_{b2}$Thermal resistivity of middle layerK.m/W
$\rho_c$Electrical resistivity of conductor material$\Omega$.m
$\rho_{corr}$Thermal resistivity of corrugation fillingK.m/W
$\rho_{cr}$Thermal resistivity of conductor materialK.m/W
$\rho_d$Thermal resistivity of duct materialK.m/W
$\rho_{d,fill}$Thermal resistivity of bentonite fillingK.m/W
$\rho_{earth}$Specific electrical resistivity of soil$\Omega$.m
$\rho_{encl}$Specific electrical resistivity of enclosure material$\Omega$.m
$\rho_f$Thermal resistivity of fillerK.m/W
$\rho_{gas}$Gas densitykg/m$^3$
$\rho_i$Thermal resistivity of insulationK.m/W
$\rho_j$Thermal resistivity of jacket materialK.m/W
$\rho_{k2}$Thermal resistivity of the layer located aboveK.m/W
$\rho_{k20}$Electrical resistivity of metallic component$\Omega$.m
$\rho_{k3}$Thermal resistivity of the layer located belowK.m/W
$\rho_{ki}$Thermal resistivity of adjacent materialK.m/W
$\rho_{sc}$Specific electrical resistivity of screen material$\Omega$.m
$\rho_{scb}$Thermal resistivity of screen beddingK.m/W
$\rho_{scs}$Thermal resistivity of screen servingK.m/W
$\rho_{sh}$Specific electrical resistivity of sheath material$\Omega$.m
$\rho_{shj}$Thermal resistivity of sheath jacket materialK.m/W
$\rho_{skid}$Specific electrical resistivity of skid wire material$\Omega$.m
$\rho_{sp}$Specific electrical resistivity of steep pipe material$\Omega$.m
$\rho_t$Thermal resistivity of wallK.m/W
S $s_{air}$Axial spacing between objectsm
$s_{b1}$Thickness of surface layerm
$s_{b2}$Thickness of middle layerm
$s_{b3}$Thickness from object to top of bedding layerm
$s_{b4}$Thickness from object to bottom of bedding layerm
$s_c$Separation of conductors in a systemmm
$s_{cm}$Separation of conductors in a systemm
$S_G$Apparent power at injecting pointkVA
$S_{gas}$Sutherland's constantK
$s_{ij}$Spacing between object i and j
$S_k$Cross-sectional area of current carrying componentmm$^2$
$s_{S1}$Spacing between phases in 1st sectionp.u.
$s_{S2}$Spacing between phases in 2nd sectionp.u.
$s_{S3}$Spacing between phases in 3rd sectionp.u.
$SI$Surge Impedance$\Omega$
$\sigma$Stefan Boltzmann constantW/m$^2$K$^4$
$\sigma_{ab}$Volumetric heat capacity of armour beddingJ/K.m$^3$
$\sigma_{ab,1}$Volumetric heat capacity of 1st armour beddingJ/K.m$^3$
$\sigma_{ab,2}$Volumetric heat capacity of 2nd armour beddingJ/K.m$^3$
$\sigma_{ar}$Volumetric heat capacity of armour materialJ/K.m$^3$
$\sigma_c$Volumetric heat capacity of conductor materialJ/K.m$^3$
$\sigma_d$Volumetric heat capacity of duct materialJ/K.m$^3$
$\sigma_{d,fill}$Volumetric heat capacity of duct fillingJ/K.m$^3$
$\sigma_{encl}$Volumetric heat capacity of enclosure materialJ/K.m$^3$
$\sigma_f$Volumetric heat capacity of fillerJ/K.m$^3$
$\sigma_{fluid}$Volumetric heat capacity of fluidJ/K.m$^3$
$\sigma_i$Volumetric heat capacity of insulation materialJ/K.m$^3$
$\sigma_{ins}$Volumetric heat capacity of insulationJ/K.m$^3$
$\sigma_j$Volumetric heat capacity of jacket materialJ/K.m$^3$
$\sigma_{k2}$Specific isobaric volumetric heat capacity of layer located belowJ/K.m$^3$
$\sigma_{k3}$Volumetric heat capacity of layer located aboveJ/K.m$^3$
$\sigma_{kc}$Volumetric heat capacity of metallic componentJ/K.m$^3$
$\sigma_{ki}$Volumetric heat capacity of adjacent materialJ/K.m$^3$
$\sigma_{pipe}$Volumetric heat capacity of fluid-filled pipeJ/K.m$^3$
$\sigma_{prot}$Specific isobaric volumetric heat capacity of protective coverJ/K.m$^3$
$\sigma_{sc}$Volumetric heat capacity of screen materialJ/K.m$^3$
$\sigma_{scb}$Volumetric heat capacity of screen beddingJ/K.m$^3$
$\sigma_{scs}$Volumetric heat capacity of screen servingJ/K.m$^3$
$\sigma_{sh}$Volumetric heat capacity of sheath materialJ/K.m$^3$
$\sigma_{shj}$Volumetric heat capacity of sheath jacket materialJ/K.m$^3$
$\sigma_{skid}$Volumetric heat capacity of skid wiresJ/K.m$^3$
$\sigma_{sp}$Volumetric heat capacity of steel pipe materialJ/K.m$^3$
$\sigma_{sun}$Absorption coefficient of solar radiation
T $T0_{gas}$Gas reference temperatureK
$T_1$Thermal resistance between one conductor and sheathK.m/W
$t_1$Thickness of insulation to sheathmm
$t_{1t}$Thickness of insulation to sheath, transientmm
$T_2$Thermal resistance of armour beddingK.m/W
$t_2$Thickness of bedding under armourmm
$t_{2i}$Thickness of insulation between conductorsmm
$T_3$Thermal resistance of jacketK.m/W
$t_3$Thickness of serving over armourmm
$T_{4d}$Transient thermal resistance for daily loadK.m/W
$T_{4db}$Correction of thermal resistance for backfillK.m/W
$T_{4i}$Thermal resistance of medium in the ductK.m/W
$T_{4ii}$Thermal resistance of the duct wallK.m/W
$T_{4iii}$Thermal resistance to ambientK.m/W
$T_{4mu}$Thermal resistance to ambientK.m/W
$T_{4ss}$Steady-state thermal resistanceK.m/W
$T_{4t}$Equivalent thermal resistance for tunnelK.m/W
$T_{4w}$Transient thermal resistance for weekly loadK.m/W
$T_{4y}$Transient thermal resistance for yearly loadK.m/W
$T_A$Element A of equivalent thermal circuitK.m/W
$T_a$Star thermal resistance of airK.m/W
$T_{a0}$Apparent thermal resistance aK.m/W
$t_{a,1}$Thickness of 1st armourmm
$t_{a,2}$Thickness of 2nd armourmm
$t_{ab}$Thickness of armour beddingmm
$T_{ab}$Thermal resistance of armour beddingK.m/W
$t_{ab,1}$Thickness of 1st armour beddingmm
$t_{ab,2}$Thickness of 2nd armour beddingmm
$T_{air}$Absolute air temperatureK
$t_{ar}$Thickness of armourmm
$T_{at}$Thermal resistance by convection, air to tunnelK.m/W
$T_{axial}$Axial thermal resistance due to the movement of air through the tunnelK.m/W
$T_B$Element B of equivalent thermal circuitK.m/W
$T_{b0}$Apparent thermal resistance bK.m/W
$T_{bulk}$Bulk temperatureK
$t_c$Thickness of hollow conductormm
$T_C$Element C of equivalent thermal circuitK.m/W
$t_{comp}$Thickness of compartmentmm
$T_{conv,ce}$Thermal resistance by convection, conductor to enclosureK.m/W
$T_{conv,od}$Thermal resistance by convection, object to ductK.m/W
$T_{conv,sa}$Thermal resistance by convection, surface to airK.m/W
$t_{corr}$Thickness of corrugation fillingmm
$t_{cs}$Thickness of conductor shieldmm
$t_{ct}$Thickness of conductor tapemm
$T_d$Internal thermal resistance for dielectric lossesK.m/W
$t_d$Thickness of ductmm
$T_e$External thermal resistance of tunnelK.m/W
$t_{EMF}$Time step to calculate current sources
$t_{encl}$Thickness of enclosuremm
$T_{eq}$Equivalent thermal resistanceK.m/W
$t_f$Thickness of filler/belt insulationmm
$T_{gas}$Absolute gas temperatureK
$T_i$Thermal resistance of insulationK.m/W
$t_i$Thickness of insulationmm
$t_{icore}$Thickness of core insulationmm
$t_{ins}$Thickness of insulationmm
$T_{ins}$Thermal resistance of insulationK.m/W
$T_{int}$Internal thermal resistance for current lossesK.m/W
$t_{is}$Thickness of insulation screenmm
$T_{is}$Thermal resistance of insulation screenK.m/W
$t_j$Thickness of jacketmm
$T_j$Thermal resistance of jacketK.m/W
$t_{jj}$Thickness of additional layer over jacketmm
$t_k$Duration of short-circuits
$T_L$Thermal longitudinal resistanceK.m/W
$T_{mh}$Mutual thermal resistance between rated and crossing objectK.m/W
$T_{mh,v}$Mutual thermal resistance per sliceK.m/W
$T_o$Thermal resistance of the oil in the pipeK.m/W
$t_{prot}$Thickness of protective covermm
$T_{prot}$Thermal resistance of protective coverK.m/W
$T_r$Total thermal resistanceK.m/W
$T_{rad,ce}$Radiation thermal resistance, conductor to enclosureK.m/W
$T_{rad,od}$Radiation thermal resistance, object to ductK.m/W
$T_{rad,sa}$Radiation thermal resistance, surface to airK.m/W
$T_{rad,sun}$Solar radiation thermal resistanceK.m/W
$T_{riser}$Thermal resistance of riser/J-tubes in air/waterK.m/W
$T_s$Star thermal resistance of objectK.m/W
$T_{sa}$Thermal resistance by convection, surface to airK.m/W
$t_{sc}$Thickness of the screenmm
$t_{scb}$Thickness of screen beddingmm
$T_{scb}$Thermal resistance of screen beddingK.m/W
$t_{scs}$Thickness of screen servingmm
$T_{scs}$Thermal resistance of screen beddingK.m/W
$t_{sh}$Thickness of the sheathmm
$t_{sha}$Total thickness between separate sheath and armourmm
$t_{shj}$Thickness of sheath jacketmm
$T_{shj}$Thermal resistance of sheath jacketK.m/W
$t_{skid}$Thickness of skid wiresmm
$t_{sp}$Thickness of steel pipemm
$T_{st}$Radiation thermal resistance, surface to tunnelK.m/W
$T_{surf}$Absolute surface temperatureK
$t_t$Wall thicknessm
$T_t$Star thermal resistance of tunnelK.m/W
$T_{tot}$Total thermal resistance, transientK.m/W
$T_{tr}$Thermal resistance of troughK.m/W
$T_{tw}$Thermal resistance of tunnel wallK.m/W
$T_{wall}$Thermal resistance of pipe wallK.m/W
$\mathrm{tan} \delta_i$Loss factor of insulation
$\tau$Transient load periods
$\tau_{ar}$Armour anglerad
$\tau_L$Transient load period for deep burials
$\theta_{2K}$Temperature rise for 2K criterion°C
$\theta_a$Ambient temperature°C
$\theta_{abs}$Absolute temperatureK
$\theta_{air}$Ambient air temperature°C
$\theta_{ar}$Temperature of armour°C
$\theta_{at}$Air temperature with load°C
$\theta_{at,0}$Air temperature with no load°C
$\theta_{at,i}$Air temperature of previous iteration cycle°C
$\theta_{at,L}$Air temperature in tunnel at outlet°C
$\theta_{at,z}$Air temperature in tunnel at z°C
$\theta_c$Temperature of conductor°C
$\theta_{c,z}$Conductor temperature at z°C
$\theta_{cmax}$Max. conductor temperature°C
$\theta_{cmaxeo}$Max. emergency overload conductor temperature°C
$\theta_{cmaxsc}$Max. short-circuit conductor temperature°C
$\theta_{de}$Temperature of duct outer wall°C
$\theta_{di}$Temperature of duct inner wall°C
$\theta_{dm}$Mean temperature of the medium in the duct°C
$\theta_e$External temperature of the object°C
$\theta_{encl}$Temperature of enclosure°C
$\theta_f$Temperature of filler for multi-core cables type SS with sheath°C
$\theta_{film}$Film temperature°C
$\theta_{gas}$Gas temperature°C
$\theta_{hs}$Temperature of heat source°C
$\theta_{kf}$Final temperature°C
$\theta_{ki}$Initial temperature°C
$\theta_{kmax}$Maximal temperature of non-insulation material°C
$\theta_{max}$Temperature of conductor at end of emergency loading°C
$\theta_o$Outer surface temperature°C
$\theta_{o,L}$Temperature of the surface of object at outlet°C
$\theta_{o,z}$Temperature of the surface of object at z°C
$\theta_{omax}$Max. outer surface temperature°C
$\theta_R$Rated current transient to steady-state ratio
$\theta_s$Temperature of screen/sheath°C
$\theta_{sc}$Temperature of screen°C
$\theta_{sh}$Temperature of sheath°C
$\theta_{sp}$Temperature of steel pipe°C
$\theta_{spf}$Mean temperature of the medium in the steel pipe°C
$\theta_{surf}$Surface temperature°C
$\theta_t$Temperature of inner tunnel wall°C
$\theta_{t,L}$Temperature of tunnel wall at outlet°C
$\theta_{t,z}$Temperature of tunnel wall at z°C
$\theta_{tm}$Mean temperature between surface and air in tunnel or trough°C
$\theta_{to}$Temperature of outer tunnel wall°C
$\theta_{to,z}$Temperature of outer tunnel wall at z°C
$\theta_w$Water temperature°C
$\theta_x$Critical soil temperature°C
$TQ$Cable thermal time constants
U $u$Substitution coefficient u
$U_0$Base voltage for testskV
$u_b$Substitution coefficient u
$U_{buried}$OHTC of fully buried pipeW/(K.m$^2$)
$U_d$Constant U for cables in ductsK.m/W
$U_e$Line-to-ground voltagekV
$U_{exposed}$OHTC of part of pipe in contact with waterW/(K.m$^2$)
$U_{ground}$OHTC of part of pipe in contact with groundW/(K.m$^2$)
$U_{inwall}$OHTC of inside film and pipe wallW/(K.m$^2$)
$U_m$Highest voltage for equipmentkV
$U_n$Rated line-to-line voltagekV
$U_o$Operating voltagekV
$U_{OHTC}$Overall heat transfer coefficientW/(K.m$^2$)
$U_{partially}$OHTC of partially buried pipeW/(K.m$^2$)
$U_{spf}$Constant U for pipe-type cablesK.m/W
$U_{ti}$Circumference of inner rectangular tunnel wallm
$U_{wall}$OHTC of pipe wallW/(K.m$^2$)
V $v_4$Ratio thermal resistivity dry/moist soil
$V_{air}$Air velocitym/s
$V_{comp}$Gas volumem$^3$
$V_d$Constant V for cables in ductsK.m/W
$V_{drop}$Voltage dropV/A/km
$V_{fluid}$Velocity of fluidcm/s
$V_{gas}$Volume percentage of second gas$\%$
$V_{spf}$Constant V for pipe-type cablesK.m/W
$V_w$Velocity of watercm/s
W $w_{a,1}$Width of flat wires of 1st armourmm
$w_{a,2}$Width of flat wires of 2nd armourmm
$W_{a,L}$Heat removed by air at outletW/m
$W_{a,z}$Heat removed by air at zW/m
$W_{ar}$Armour lossesW/m
$w_{ar}$Width of armourmm
$w_b$Width of the backfillmm
$w_{b4}$Distance to lateral edge of multi-layer backfillm
$W_c$Conductor lossesW/m
$W_{conv,ce}$Convection heat transfer, conductor to enclosureW/m
$W_{conv,da}$Convection heat transfer, duct to airW/m
$W_{conv,gd}$Convection heat transfer, gas to ductW/m
$W_{conv,od}$Convection heat transfer, object to ductW/m
$W_{conv,og}$Convection heat transfer, object to gasW/m
$W_{conv,sa}$Convection heat transfer, surface to airW/m
$W_d$Dielectric lossesW/m
$W_{de}$Losses outside of riser/J-tubeW/m
$W_{di}$Losses between cable and riser/J-tubeW/m
$W_{duct}$Losses in ductW/m
$W_{encl}$Enclosure lossesW/m
$W_h$Heat generated by external objectW/m
$W_{hs}$Heat dissipation of heat sourceW/m
$W_I$Ohmic losses per phaseW/m
$W_{rad,ce}$Radiation heat transfer, conductor to enclosureW/m
$W_{rad,da}$Radiation heat transfer, duct to airW/m
$W_{rad,od}$Radiation heat transfer, object to ductW/m
$W_{rad,sa}$Radiation heat transfer, surface to airW/m
$W_s$Screen and sheath lossesW/m
$W_{sar}$Total loss in shield and magnetic armourW/m
$w_{sc}$Width of flat screen wiremm
$W_{sp}$Losses in steel pipeW/m
$W_{sum}$Sum of total losses of all systemsW/m
$W_{sun}$Solar radiation heat transfer to surfaceW/m
$W_{sys}$Total losses of the systemW/m
$W_t$Total losses per phaseW/m
$w_t$Inner widthm
$W_{tot}$Total losses per objectW/m
X $X_0$Zero sequence reactance$\Omega$/m
$x_b$Horizontal center of backfillmm
$X_c$Self reactance of conductor$\Omega$/m
$X_G$Factor $X_G$
$X_{G2}$Factor $X_{G2}$
$X_K$Factor $X_K$
$X_m$Mutual reactance between conductors$\Omega$/m
$x_p$Factor for proximity effect of conductors
$x_{pos}$Horizontal x-position of multi-layer backfillm
$x_s$Factor for skin effect on conductor
$X_s$Self reactance of screen/sheath$\Omega$/m
$X_{S1}$Reactance section 1$\Omega$/m
$X_{S2}$Reactance section 2$\Omega$/m
$X_{S3}$Reactance section 3$\Omega$/m
$\xi_X$Parameter $\xi$ for calculation of loss factor
Y $Y$AdmittanceS/m
$y_{2K}$Depth for 2K criterionmm
$y_c$Skin and proximity effect factor for PAC/GIL conductor
$Y_d$Constant Y for cables in ductsK.m/W
$y_{encl}$Skin and proximity effect factor for PAC/GIL enclosure
$Y_G$Factor $Y_G$
$Y_i$Ordinates of the loss-load cyclep.u.
$Y_K$Factor $Y_K$
$y_p$Proximity effect factor of conductors
$y_s$Skin effect factor of conductor
$Y_{spf}$Constant Y for pipe-type cablesK.m/W
Z $Z_0$Zero sequence impedance$\Omega$/m
$Z_{bs}$Installation constant Z
$Z_c$Self impedance of phase conductor$\Omega$/m
$z_c$Factor z to calculate skin effect coefficients for conductor
$z_{encl}$Factor z to calculate skin effect coefficients for enclosure
$z_h$Location of the heat sourcem
$Z_K$Factor $Z_K$
$Z_m$Mutual impedance between conductor and metal screen$\Omega$/m
$z_{max}$Logitudinal thermal limit distancem
$Z_{neg}$Negative sequence impedance$\Omega$/m
$Z_{pos}$Positive sequence impedance$\Omega$/m
$z_r$Location of the hottest pointm
$Z_s$Self impedance of metal screen$\Omega$/m
$Z_x$Equivalent mutual impedance between cables$\Omega$/m
$\zeta_{ab}$Density of armour bedding materialg/cm$^3$
$\zeta_{ar}$Density of armour materialg/cm$^3$
$\zeta_c$Density of conductor materialg/cm$^3$
$\zeta_f$Density of filler materialg/cm$^3$
$\zeta_i$Density of insulation materialg/cm$^3$
$\zeta_j$Density of jacket materialg/cm$^3$
$\zeta_M$Density of materialg/cm$^3$
$\zeta_{od}$Radiation shape factor for touching cables
$\zeta_{sc}$Density of metallic screen materialg/cm$^3$
$\zeta_{sh}$Density of metallic sheath materialg/cm$^3$
$\zeta_{shj}$Density of jacket material over each coreg/cm$^3$
$\zeta_{skid}$Density of metallic skid wire materialg/cm$^3$
$\zeta_{soil}$Density of soilkg/m$^3$
$\zeta_{sp}$Density of steel pipeg/cm$^3$
$\zeta_{tape}$Density of tapesg/cm$^3$
$\zeta_w$Density of waterkg/m$^3$