Documentation

SymbolNameUnit
A$a_0$Coefficient a partial transient temperature rise1/s
$a_{12}$Distance phase 1 — phase 2mm
$a_{1t}$Distance phase 1 — earth continuity conductormm
$a_{23}$Distance phase 2 — phase 3mm
$a_{2t}$Distance phase 2 — earth continuity conductormm
$a_{31}$Distance phase 3 — phase 1mm
$a_{3t}$Distance phase 3 — earth continuity conductormm
$A_{ab}$Cross-sectional area armour beddingmm$^2$
$A_{ar}$Cross-sectional area armourmm$^2$
$A_c$Cross-sectional area conductormm$^2$
$a_c$Skin and proximity effect coefficient a PAC/GIL conductor
$A_{comp}$Cross-sectional area compartmentm$^2$
$A_d$Cross-sectional area duct wallmm$^2$
$A_{d,fill}$Free cross-sectional area inside ductmm$^2$
$A_{di}$Duct surface (inner)m$^2$
$A_{do}$Duct surface (outer)m$^2$
$A_e$Surface of objectm$^2$
$A_{encl}$Cross-sectional area enclosuremm$^2$
$a_{encl}$Skin and proximity effect coefficient a PAC/GIL enclosure
$A_{er}$Surface of objectm$^2$
$A_f$Cross-sectional area fillermm$^2$
$A_{hsf}$Cross-sectional area fluidmm$^2$
$A_{hsi}$Cross-sectional area pipe insulationmm$^2$
$A_{hsj}$Cross-sectional area protective jacketmm$^2$
$A_{hsp}$Cross-sectional area fluid-filled pipemm$^2$
$A_i$Cross-sectional area insulationmm$^2$
$a_i$Parameter a for radial derivative of dielectric losses
$A_{it}$Cross-sectional area insulation (IEC 60853)mm$^2$
$A_j$Cross-sectional area jacketmm$^2$
$A_k$Thermal property constant Amm/s$^{1/2}$
$a_m$Mean distance between the phasesmm
$A_{prot}$Cross-sectional area protective covermm$^2$
$a_{S1}$Length minor section 1p.u.
$a_{S2}$Length minor section 2p.u.
$a_{S3}$Length minor section 3p.u.
$A_{sc}$Cross-sectional area screenmm$^2$
$A_{scb}$Cross-sectional area screen beddingmm$^2$
$A_{scs}$Cross-sectional area screen servingmm$^2$
$A_{sh}$Cross-sectional area sheathmm$^2$
$A_{shj}$Cross-sectional area sheath jacketmm$^2$
$a_{shj}$Factor $a_{shj}$ for jacket around each core
$A_{skid}$Cross-sectional area skid wiresmm$^2$
$A_{sp}$Cross-sectional area steel pipemm$^2$
$A_t$Cross-sectional area (inner) tunnelm$^2$
$A_{tape}$Cross-sectional area tapesmm$^2$
$a_{type}$Construction of armour
$\alpha_0$Constant α burial depth
$\alpha_{ar}$Temperature coefficient armour material1/K
$\alpha_{at}$Heat transfer coefficient to channel wallW/(K.m$^2$)
$\alpha_c$Temperature coefficient conductor material1/K
$\alpha_{encl}$Temperature coefficient enclosure material1/K
$\alpha_f$Phase shift°
$\alpha_{gas}$Thermal diffusivity gasm$^2$/s
$\alpha_i$Temperature coefficient of conductivity insulation material1/K
$\alpha_p$Factor $\alpha_p$
$\alpha_{sa}$Heat transfer coefficient convectionW/(K.m$^2$)
$\alpha_{sc}$Temperature coefficient screen material1/K
$\alpha_{sh}$Temperature coefficient sheath material1/K
$\alpha_{skid}$Temperature coefficient skid wire material1/K
$\alpha_{sp}$Temperature coefficient steel pipe material1/K
$\alpha_{st}$Heat transfer coefficient radiationW/(K.m$^2$)
$\alpha_{sys}$Inclination angle°
$\alpha_t$Conductor to surface attainment factor
B$B$SusceptanceS/m
$b_0$Coefficient b partial transient temperature rise1/s
$B_1$Loss coefficient $B_1$ armour$\Omega$/m
$B_2$Loss coefficient $B_2$ armour$\Omega$/m
$b_c$Skin and proximity effect coefficient b PAC/GIL conductor
$B_{EMF}$Magnetic field strength$\mu$T
$b_{encl}$Skin and proximity effect coefficient b PAC/GIL enclosure
$B_k$Thermal property constant Bmm$^2$/s
$b_{shj}$Factor $b_{shj}$ for jacket around each core
$b_x$Shorter side backfillmm
$b_y$Longer side 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 armour materialK
$\beta_b$Angle of exposed wetted surface of piperad
$\beta_c$Reciprocal of temperature coefficient conductor materialK
$\beta_{encl}$Reciprocal of temperature coefficient enclosure materialK
$\beta_{gas}$Volumetric thermal expansion coefficient gas1/K
$\beta_k$Reciprocal of temperature coefficient metallic componentK
$\beta_p$Factor $\beta_p$
$\beta_{sc}$Reciprocal of temperature coefficient screen materialK
$\beta_{sh}$Reciprocal of temperature coefficient sheath materialK
$\beta_{skid}$Reciprocal of temperature coefficient skid wire materialK
$\beta_{sp}$Reciprocal of temperature coefficient steel pipe materialK
$\beta_t$Attainment factor cable surface—ambient
$\beta_X$Crossing angle [rad]rad
$\beta_{xing}$Crossing angle [°]°
$\mathrm{Bi}_g$Biot number ground
$\mathrm{Bi}_p$Biot number pipe
C$C_{ag}$Capacitance armour - groundF/m
$C_{av}$Heat capacity of the air flowW/K
$C_b$Capacitance insulationF/m
$C_{bq}$Constants $C_1$ - $C_7$ multi-layer backfill
$c_c$Distance axis of conductor—cable centermm
$C_{c1}$Thermal capacitance part 1J/(m.K)
$C_{c2}$Thermal capacitance part 2J/(m.K)
$C_{c3}$Thermal capacitance part 3J/(m.K)
$C_{c4}$Thermal capacitance part 4J/(m.K)
$c_{color}$Wiring color code
$C_{cs}$Capacitance conductor - shieldF/m
$C_E$Capacitance to earthF/m
$C_{g1}$Factor C1 pipe
$C_{g2}$Factor C2 pipe
$C_{g3}$Factor C3 pipe
$c_{gas}$Constant c gas (PAC/GIL)
$c_{ij}$Coefficient c view factor
$C_{k1}$Non-adiabatic constant $C_1$mm/m
$C_{k2}$Non-adiabatic constant $C_2$K.m.mm$^2$/J
$C_{Mie}$Factor $C$ (Mie1905)
$C_{Nu,L}$Factor C
$c_{Nu,r}$Factor c
$C_{Nu,w}$Factor C
$c_{p,gas}$Specific heat capacity gas, constant pressureJ/(kg.K)
$c_{p,soil}$Volumetric heat capacity soil materialJ/(kg.K)
$c_{p,w}$Specific heat capacity water, constant pressureJ/(kg.K)
$C_{sa}$Capacitance shield - armourF/m
$C_{sg}$Capacitance shield - groundF/m
$c_{shj}$Factor $c_{shj}$ for jacket around each core
$c_{type}$Construction conductor
$c_{v,gas}$Specific heat capacity gas, constant volumeJ/(kg.K)
$C_{v,soil}$Heat capacity of a unit volume of soilJ/(K.m$^3$)
$c_{v,w}$Specific heat capacity water, constant volumeJ/(kg.K)
$C_{vair}$Volumetric heat capacity airJ/(K.m$^3$)
$CC_{pull}$Conduit clearancemm
$CF_{pull}$Conduit fill$\%$
$CJ_{pull}$Conduit jamming ratio
$\mathrm{cos}\varphi$Power factor
$CR_{pull}$Conduit ratio
$cuw_{sc}$Standard copper wire size
D$d$Geometric mean shield diameterm
$D_{ab}$Diameter over armour beddingmm
$D_{ar}$Diameter over armourmm
$d_{ar}$Mean diameter armourmm
$d_b$Diameter backfillmm
$d_{b3}$Distance c multi-layer backfillm
$d_{b4}$Distance d multi-layer backfillm
$d_c$External diameter conductormm
$D_c$Diameter conductor (outer)m
$d_{ci}$Internal diameter conductormm
$D_{ci}$Diameter conductor (inner)m
$D_{comp}$Diameter compartmentm
$D_{core}$Diameter over core cablemm
$D_{cs}$Diameter over conductor shieldmm
$d_{ct}$External diameter conductor, transientmm
$d_{cw}$Diameter of wires conductor (average)mm
$D_{di}$Inner diameter ductm
$D_{do}$Outer diameter ductm
$D_{dry}$Characteristic diameter drying zonem
$D_e$External diameter objectmm
$d_e$Equivalent diameter of screen/sheath and armourmm
$D_E$Equivalent depth of earth return pathm
$d_{ecc}$Diameter earth continuity conductormm
$D_{encl}$Diameter enclosure (outer)m
$D_{eq}$Equivalent diameter of a group of round objectsmm
$D_{ext}$Diameter externalm
$D_f$Diameter over fillermm
$d_f$Spacing from hottest object in groupm
$D_{hsi}$Diameter over pipe insulationmm
$D_{hsj}$Diameter over protective jacketmm
$D_i$Diameter over insulation incl. insulation screenmm
$d_{im}$Non-isothermal earth surface imaginary layer of soilm
$D_{in}$Diameter pipe (inner)m
$D_{ins}$Diameter over insulationmm
$D_{is}$Diameter over insulation screenmm
$D_{it}$Diameter over insulation, transientmm
$D_j$Diameter over jacketmm
$D_{lay,3c}$Diameter of mechanical neutral linemm
$D_o$Outer diameterm
$d_{pk1}$Distance to mirrored objectmm
$d_{pk2}$Distance to buried objectsmm
$D_{prot}$Diameter protective coverm
$d_{psc}$Point source correctionm
$D_{ref}$Diameter OHTC referencem
$d_s$Equivalent diameter of screen and sheathmm
$D_{sc}$Diameter over screenmm
$d_{sc}$Mean diameter screenmm
$D_{scb}$Diameter over screen beddingmm
$D_{scs}$Diameter over screen servingmm
$D_{sh}$Diameter over sheathmm
$d_{sh}$Mean diameter sheathmm
$D_{shb}$Diameter below sheathmm
$D_{shj}$Diameter over sheath jacketmm
$D_{soil}$Diameter soil layerm
$d_{sw}$Diameter skywiremm
$d_t$Channel coveringm
$d_w$Depth under waterm
$D_{wall}$Diameter pipe wallm
$d_x$Equivalent diameter conductormm
$D_x$Characteristic diameter daily loadmm
$D_{x,w}$Characteristic diameter weekly loadmm
$D_{x,y}$Characteristic diameter yearly loadmm
$\Delta_1$Substitution coefficient $\Delta_1$ for eddy-currents
$\delta_1$Thickness screening layermm
$\Delta_2$Substitution coefficient $\Delta_2$ for eddy-currents
$\delta_{ar}$Equivalent thickness of armourmm
$\delta_d$Distance cable—ductm
$\delta_i$Electrical thickness of insulation materialm
$\delta_k$Thickness metallic componentmm
$\delta_{soil}$Thermal diffusivity soilm$^2$/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 increaseK
$\Delta \theta_{0x}$Temperature rise by crossing heat sourcesK
$\Delta \theta_{0x,h}$Temperature rise of the conductor by source hK
$\Delta \theta_{air}$Temperature increase airK
$\Delta \theta_c$Temperature rise conductorK
$\delta \theta_c$Ohmic steady-state temperature riseK
$\Delta \theta_{c,t}$Transient temperature rise conductorK
$\Delta \theta_{c,t,corr}$Corrected transient temperature rise conductorK
$\Delta \theta_{c,t,\infty}$Steady-state temperature rise conductorK
$\Delta \theta_{c,t,o}$Transient temperature rise conductor by ohmic lossesK
$\Delta \theta_{ce}$Temperature difference conductor—surfaceK
$\Delta \theta_d$Temperature rise dielectric lossesK
$\Delta \theta_{d,t}$Transient temperature rise by dielectric lossesK
$\Delta \theta_{duct}$Temperature rise duct (magnetic)K
$\Delta \theta_{e,t}$Transient temperature rise outer surfaceK
$\Delta \theta_{gas}$Temperature difference conductor—enclosure°C
$\Delta \theta_i$Temperature difference insulationK
$\Delta \theta_{i,max}$Limitation of temperature rise insulation materialK
$\Delta \theta_{kp}$Temperature rise by object kK
$\Delta \theta_{kp,t}$Transient temperature rise outer surface by object kK
$\Delta \theta_{max}$Maximum permissible conductor temperature riseK
$\Delta \theta_p$Temperature rise by other buried objectsK
$\Delta \theta_{p,t}$Transient temperature rise outer surface 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—ambientK
$\delta \theta_{SPK}$Peak cyclic temperature riseK
$\Delta \theta_{sun}$Temperature difference conductor—enclosureK
$\Delta \theta_{uh}$Temperature rise by crossing heat sources zK
$\Delta \theta_x$Critical soil temperature riseK
$\Delta \theta_{x0}$Critical soil temperature rise (VDE)K
$\Delta W$Incremental heat generatedW
$\Delta w_d$Increment of volumetric density of dielectric losses in HVDC cablesW/m$^3$
$\Delta z$Length of the intervalm
$Di_d$Inner diameter ductmm
$Di_{hsp}$Inner diameter fluid-filled pipemm
$Di_p$Inner diameter enclosing pipem
$Di_{sp}$Inner diameter steel pipemm
$Di_t$Diameter (inner) tunnelm
$Do_d$Outer diameter ductmm
$Do_{hsp}$Outer diameter fluid-filled pipemm
$Do_p$Outer diameter enclosing pipem
$Do_{sp}$Outer diameter steel pipemm
$Do_t$Diameter (outer) tunnelm
E$E_a$Induced shield voltage phase aV/m
$E_b$Induced shield voltage phase bV/m
$E_{bs}$Installation constant E
$E_c$Induced shield voltage phase cV/m
$e_{hor}$Horizontal clearancemm
$E_i$Electrical field strengthkV/mm
$e_{limit}$Limit of thickness of soil layerm
$E_p$Induced shield voltage conductor pV/m
$e_{soil}$Thickness soil layerm
$e_{ver}$Vertical clearancemm
$e_{wall}$Clearance to wallmm
$EC$Embodied carbonkgCO$_2$/kg
$EE$Embodied energyMJ/kg
$\epsilon_0$Vacuum permittivityF/m
$\epsilon_{ab}$Relative permittivity armour bedding
$\epsilon_c$Effective emissivity conductor
$\epsilon_{di}$Emissivity duct surface (inner)
$\epsilon_{do}$Emissivity duct surface (outer)
$\epsilon_e$Emissivity cable
$\epsilon_{encl}$Effective emissivity enclosure
$\epsilon_f$Relative permittivity filler
$\epsilon_{gas}$Dielectric constant of gas in compartment
$\epsilon_{hsj}$Effective emissivity protective jacket
$\epsilon_i$Relative permittivity insulation material
$\epsilon_j$Relative permittivity jacket
$\epsilon_k$Heat loss allowance factor
$\epsilon_{prot}$Effective emissivity protective cover
$\epsilon_{rad}$Effective emissivity
$\epsilon_{shj}$Relative permittivity sheath jacket material
$\eta 0_{gas}$Reference dynamic viscosity gasPa.s
$\eta_{di}$Reflectivity duct surface (outer)
$\eta_{do}$Reflectivity duct surface (outer)
$\eta_e$Reflectivity cable
$\eta_{gas}$Dynamic viscosity gasPa.s
$\eta_w$Dynamic viscosity waterPa.s
F$f$System frequencyHz
$F_{\alpha}$Inclination derating factorp.u.
$F_{ar}$Factor $F$ armour losses
$f_{ar}$Factor between AC and DC resistance armour$\Omega$/m
$f_{atm}$Relation atmospheric pressure to standard atmosphere
$f_{cb}$Factor for cross-bonded earthing
$F_{cor,sh}$Effective length per unit pitch length corrugated sheath
$F_e$Factor $F_e$ 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
$F_{lay,3c}$Effective length per unit lay length twisted conductors
$F_{lay,ar}$Effective length per unit lay length armour
$F_{lay,c}$Effective length per unit lay length conductor strands
$F_{lay,sc}$Effective length per unit lay length screen wires
$F_m$Mutual radiation coefficient
$F_{mh}$Mutual heating coefficient
$f_{ppc}$Factor permissible pull forceN/mm$^2$
$F_{ppc}$Permissible pull forceN
$F_{pt}$Function of pressure and temperature
$F_{pull}$Pulling forceN
$f_{rad}$Factor sidewall bearing pressureN/m
$F_{rad}$Sidewall bearing pressureN/m
$F_{red}$Derating factor
$F_{T10,1}$Table 10.1, VDE 0276-1000p.u.
$F_{T10,3}$Table 10.3, VDE 0276-1000p.u.
$F_{T11,s}$Table 11.1, VDE 0276-1000p.u.
$F_{T11,t}$Table 11.2, VDE 0276-1000p.u.
$F_{T12}$Table 12, VDE 0276-1000p.u.
$F_{T13}$Table 13, VDE 0276-1000p.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 $G_2$ cables with separate sheaths
$g_a$Substitution coefficient g
$G_b$Geometric factor backfill
$g_{bs}$Installation constant g
$G_{corr}$Geometric factor $G_{corr}$ for jacket around each core
$g_{dry}$Geometric constant of circle drying zonep.u.
$G_{encl}$Factor G for the calculation of the Nusselt number
$G_{FEA}$Geometric 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 $G_{s 1.0}$
$g_u$Geometric constant of circle buried
$g_x$Geometric constant of circle characteristic diameterp.u.
$\gamma_{bessel}$Bessel constantp.u.
$\gamma_C$Propagation constant
$\gamma_c$Skin and proximity effect factor $\gamma$ PAC/GIL conductor
$\gamma_{encl}$Skin and proximity effect factor $\gamma$ PAC/GIL enclosure
$\gamma_{euler}$Euler's constantm/s$^2$
$\gamma_i$Electrical field coefficient insulation materialmm/kV
$\gamma_{prop}$Cable propagation constant
$\gamma_t$Attainment factor cables
$\gamma_X$Attenuation factor for crossing1/m
$GMD$Geometric mean distance between phases of the same systemm
$GMD_t$Geometric mean distance between earth continuity conductor and the cables of the same systemm
$GMR_{ar}$Geometric mean radius armourm
$GMR_c$Geometric mean radius conductorm
$GMR_{cc}$Geometric mean radius conductor bundlemm
$GMR_{sc}$Geometric mean radius screenm
$GMR_{sp}$Geometric mean radius steel pipem
$\mathrm{Gr}_c$Grashof number conductor→gas
$\mathrm{Gr}_{encl}$Grashof number gas→enclosure
$\mathrm{Gr}_{ext}$Grashof number riser—air
$\mathrm{Gr}_{gd}$Grashof number gas—duct
$\mathrm{Gr}_L$Grashof number, ground—air
$\mathrm{Gr}_{og}$Grashof number cable—gas
$\mathrm{Gr}_{prot}$Grashof number surface→air
H$H$Distance pipe center—groundm
$H_1$Inductance $H_1$ armourH/m
$H_2$Inductance $H_2$ armourH/m
$H_3$Inductance $H_3$ 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 backfillmm
$h_{bs}$Heat dissipation coefficient for black surfaces in free airW/m$^2$/K$^{5/4}$
$h_{buried}$Heat transfer coefficient pipe fully buriedW/(K.m$^2$)
$H_c$Heat energy contentMJ/m
$h_{conv,c}$Heat transfer coefficient convection conductor—gasW/(K.m$^2$)
$h_{conv,encl}$Heat transfer coefficient convection gas—enclosureW/m2.K
$h_{conv,ext}$Heat transfer coefficient convection riser—airW/(K.m$^2$)
$h_{conv,gd}$Heat transfer coefficient convection gas—ductW/(K.m$^2$)
$h_{conv,int}$Heat transfer coefficient convection cable—riserW/(K.m$^2$)
$h_{conv,og}$Heat transfer coefficient convection cable—gasW/(K.m$^2$)
$h_{conv,sa}$Heat transfer coefficient convection surface—airW/(K.m$^2$)
$h_{em}$Factor $h$ emergency overload
$h_{era}$Heat transfer coefficient convection ERAW/(K.m$^2$)
$h_{ext}$Heat transfer coefficient externalW/(K.m$^2$)
$h_{ground}$Heat transfer coefficient part of pipe in contact with groundW/(K.m$^2$)
$h_{in}$Heat transfer coefficient internalW/(K.m$^2$)
$h_{lg}$Ratio of heat dissipation coefficients
$h_{rad,ce}$Heat transfer coefficient radiation conductor—enclosureW/(K.m$^2$)
$h_{rad,ext}$Heat transfer coefficient radiation riser—airW/(K.m$^2$)
$h_{rad,int}$Heat transfer coefficient radiation cable—riserW/(K.m$^2$)
$h_{rad,sa}$Heat transfer coefficient radiation surface—airW/(K.m$^2$)
$H_s$Conductance sheathH/m
$h_{soil}$Heat transfer coefficient wall—soilW/(K.m$^2$)
$H_{sun}$Intensity of solar radiationW/m$^2$
$h_t$Height (inner)m
$h_{T4}$Ratio of thermal resistance to ambient
$H_{tc}$Parameter Hc trough cover
$h_{tr}$Heat transfer coefficientW/(K.m$^2$)
$H_{ts}$Parameter Hs depending on air velocity
$H_x$Magnetic field xmH
$H_y$Magnetic field ymH
I$I_{ar}$Induced circulating current armourA
$I_c$Conductor currentA
$I_C$Capacitive load currentA/m
$I_{c,LF}$Conductor root mean square currentA
$I_{c,max}$Highest current load of lineA
$I_{c,peak}$Permissible peak cyclic load currentA
$I_{c,sum}$Total current for all parallel systemsA
$I_{Ce}$Capacitive earth short-circuit currentA/m
$I_{em}$Emergency overload currentA
$I_{EMF}$Phase current for EMF calculationA
$I_k$Complex conductor currentA
$I_{k0}$Phase-to-ground fault currentA
$I_{k1}$Phase-to-neutral fault currentA
$I_{k2}$Phase-to-phase fault currentA
$I_{k3}$Three-phase symmetrical fault currentA
$I_{k,per}$Short-circuit current, permissiblekA
$I_{ka}$Complex conductor current aA
$I_{kAD}$Short-circuit current, adiabatickA
$I_{kb}$Complex conductor current aA
$I_{kc}$Complex conductor current cA
$I_{kSC}$Short-circuit current, effectivekA
$I_{kx}$Split fault currentA
$I_{method}$Current calculation method
$I_R$Transient conductor currentA
$I_s$Induced circulating current shieldA
$I_{sp}$Induced circulating current pipeA
$I_{ss}$Steady-state current before transientA
$inst_{air}$Installation in air
$inst_{buried}$Installation buried
$inst_{elec}$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$K_0$Coefficient K gas (PAC/GIL)
$K_{02}$Factor $K_{0.2}$
$K_{06}$Factor $K_{0.6}$
$K_1$Screening factor
$K_{10}$Factor $K_{1.0}$
$k_4$Thermal conductivity soilW/(m.K)
$K_A$Coefficient K in air
$k_{air}$Thermal conductivity airW/(m.K)
$k_{ar}$Thermal conductivity armour materialW/(m.K)
$K_{BICC}$Constant relating to conductor formation
$k_{Boltz}$Boltzmann constantJ/K
$k_c$Thermal conductivity conductor materialW/(m.K)
$K_{ce}$Radiation shape factor conductor—enclosure
$K_{cv}$Convection factor
$K_{dyn}$Corrected dynamic friction coefficient
$k_{encl}$Thermal conductivity enclosureW/(m.K)
$K_G$Factor $K_G$
$k_{gas}$Thermal conductivity gasW/(m.K)
$K_{GMR}$Factor geometric mean radius
$k_H$Heinhold characteristic diameter coefficient
$k_{hsf}$Thermal conductivity fluidW/(m.K)
$k_{hsi}$Thermal conductivity pipe insulation materialW/(m.K)
$k_{hsj}$Thermal conductivity protective jacket materialW/(m.K)
$k_{hsp}$Thermal conductivity fluid-filled pipe materialW/(m.K)
$K_k$Specific short-circuit parameterA.s$^{1/2}$/mm$^2$
$k_l$Temperature rise factor in air
$k_{LF}$Load loss coefficientp.u.
$K_{od}$Diameter ratio object/duct
$k_p$Proximity effect coefficient
$K_{par}$Constant $K_{par}$ (Ovuworie)
$k_{prot}$Thermal conductivity 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 heat transfer coefficient convection
$k_{sa,2}$Factor 2 heat transfer coefficient convection
$k_{sc}$Thermal conductivity screen materialW/(m.K)
$k_{sh}$Thermal conductivity sheath materialW/(m.K)
$k_{skid}$Thermal conductivity skid wires
$k_{sp}$Thermal conductivity steel pipe materialW/(m.K)
$k_t$Temperature rise ratiop.u.
$K_t$Effective emissivity object surface
$K_{vermeer}$Vermeer constant for convection heat transfer
$k_w$Thermal conductivity waterW/(m.K)
$K_x$Factor for fictitious diameter by Neher
$k_X$Number of heat sources crossing
$\kappa_i$Electrical conductivity insulation materialS/m
$\kappa_j$Electrical conductivity jacket materialS/m
L$L$Inductance matrixH/m
$L_0$Reference length of the tunnelm
$L_a$Self inductance conductorH/m
$L_b$Vertical center backfillmm
$L_{b4}$Depth trench multi-layer backfillm
$L_c$Depth of laying of sourcesmm
$L_{char}$Characteristic length earth surface
$L_{cm}$Depth of layingm
$L_{cor,sh}$Length corrugated sheathmm
$L_{crit}$Critical lengthkm
$L_d$Length ductm
$L_{deep}$Deep burial thermal inertia equivalent depthm
$L_{dry}$Depth characteristic diameter drying zonem
$L_{dw}$Length of duct in waterm
$L_h$Depth of laying of crossing elementmm
$L_i$Inductance conductor iH/m
$L_{lay,3c}$Length of lay twisted conductorsmm
$L_{lay,ar}$Length of lay armourmm
$L_{lay,c}$Length of lay conductor strandsmm
$L_{lay,sc}$Length of lay screen wiresmm
$L_{leg}$Section lengthm
$L_{link}$Span lengthm
$L_m$Inductance (mean)H/m
$L_{pitch}$Length corrugated sheath (pitch)mm
$L_r$Depth of laying of the rated objectmm
$L_{sys}$System lengthm
$L_T$Length tunnelm
$\lambda_0$Substitution coefficient $\lambda_0$ for eddy-currents
$\lambda_1$Loss factor shield (screen/sheath)
$\lambda_{11}$Loss factor shield, circulating currents
$\lambda_{12}$Loss factor shield, eddy currents
$\lambda_2$Loss factor armour
$\lambda_{21}$Loss factor armour, circulating currents
$\lambda_{22}$Loss factor shield, eddy currents
$\lambda_3$Loss factor steel pipe pipe-type cable
$\lambda_4$Loss factor magnetic duct
$\lambda_d$Factor dielectric losses
$\lambda_{gas}$Ratio $c_p/c_v$
$\lambda_i$Parameter $\lambda$ for linear density of dielectric losses
$\lambda_t$Relaxation parameter
$LF$Load factor, dailyp.u.
$LF_w$Load factor, weeklyp.u.
$LF_y$Load factor, yearlyp.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 partial transient temperature rises
$M_1$Corrected cyclic rating factorK
$M_{ab}$Armour bedding material
$m_{ab}$Mass armour beddingkg/m
$M_{ar}$Armour material
$m_{ar}$Mass armourkg/m
$M_c$Conductor material
$m_c$Mass conductorkg/m
$M_{cable}$Cable material
$M_{comp}$Insulating gas material
$M_d$Duct material
$M_e$Substitution coefficient $M_e$ to calculate factor $F_e$
$m_E$Parameter m earth return
$m_{EMF}$Number of time steps
$M_{encl}$Enclosure material
$M_f$Filler material
$m_f$Mass fillerkg/m
$M_{gas}$Gas and gas-mixtures
$m_{hollow}$Mass hollow cablekg/m
$M_{hsf}$Fluid material
$M_{hsi}$Pipe insulation material
$M_{hsj}$Protective jacket material
$M_{hsp}$Fluid-filled pipe material
$M_i$Insulation material
$m_i$Mass insulationkg/m
$M_{IEEE}$Soil material IEEE 442
$M_j$Jacket material
$m_j$Mass jacketkg/m
$M_k$Thermal contact factors$^{1/2}$
$m_{metal}$Mass metallic partskg/m
$M_{mol}$Molar massg/mol
$m_{mol}$Molecular massmol
$m_{Nu,L}$Factor m
$m_{Nu,w}$Factor m
$M_p$Pipe material
$M_{prot}$Protective cover material
$M_{riser}$Riser material
$M_{sc}$Screen material
$m_{sc}$Mass metallic screenkg/m
$M_{seabed}$Seabed material
$M_{sh}$Sheath material
$m_{sh}$Mass metallic sheathkg/m
$M_{shj}$Sheath jacket material
$m_{shj}$Mass jacket over each corekg/m
$M_{skid}$Skid wire material
$m_{skid}$Mass skid wireskg/m
$M_{soil}$Soil material
$M_{sp}$Steel pipe material
$m_{sp}$Mass steel pipekg/m
$M_{spf}$Steel pipe filling medium
$m_{tape}$Mass tapeskg/m
$m_{tot}$Mass cablekg/m
$m_{z,ar}$Parameter m armour
$m_{z,c}$Parameter m conductor
$m_{z,e}$Parameter m earth
$m_{z,s}$Parameter m shield
$m_{z,sc}$Parameter m screen
$m_{z,sh}$Parameter m sheath
$\mu$Loss factor daily load variationp.u.
$\mu_0$Vacuum permeabilityH/m
$\mu_{dyn}$Dynamic friction coefficient
$\mu_e$Longitudinal relative permeability steel wires
$\mu_E$Magnetic permeability of earthH/m
$\mu_s$Relative permeability steel wires
$\mu_t$Transverse relative permeability steel wires
$\mu_w$Loss factor weekly load variationp.u.
$\mu_y$Loss factor yearly load variationp.u.
N$N_0$Coefficient N partial transient temperature rises$^2$
$n_{a,1}$Number of wires armour 1
$n_{a,2}$Number of wires armour 2
$n_{ar}$Number of wires armour
$N_{Avogrado}$Avogadro constant1/mol
$N_b$Number of loaded objects in backfill
$n_c$Number of conductors cable
$N_c$Number of sources in system
$n_{cc}$Number of conductors combined
$n_{cg}$Number of conductors PAC/GIL
$n_{cw}$Number of wires conductor
$n_{cycle}$Number of load cycles
$N_e$Substitution coefficient $N_e$ to calculate factor $F_e$
$N_{hor}$Number of cable groups beside each other
$n_{Nu,r}$Factor n
$N_{ph}$Number of phases in system
$n_{ph}$Number of phases in a cable
$N_{sea}$Number of subsea cables
$n_{seg}$Number of segments in Milliken conductor
$N_{sum}$Total number of objects in an air-filled space
$n_{sw}$Number of wires screen
$N_{sys}$Number of parallel systems in the same confinement
$N_{ver}$Number of cable groups above each other
$N_X$Number of intervals
$\nu$Summation step 1 - $N_X$
$\nu_{air}$Kinematic viscosity airm$^2$/s
$\mathrm{Nu}_c$Nusselt number conductor—gas
$\mathrm{Nu}_{encl}$Nusselt number gas—enclosure
$\mathrm{Nu}_{ext}$Nusselt number riser—air
$\nu_{gas}$Kinematic viscosity gasm$^2$/s
$\mathrm{Nu}_{gd}$Nusselt number gas—duct
$\mathrm{Nu}_{int}$Nusselt number cable—riser
$\mathrm{Nu}_L$Nusselt number, ground—air
$\mathrm{Nu}_{og}$Nusselt number cable—gas
$\mathrm{Nu}_{prot}$Nusselt number surface—air
$\nu_{sc}$Elongation screen$\%$
$\nu_{soil}$Soil moisture content$\%$
$\mathrm{Nu}_w$Nusselt number surface—water
$\nu_w$Kinematic viscosity waterm$^2$/s
O$\omega$Angular frequencyrad/s
P$p_{a,1}$Length of lay armour 1mm
$p_{a,2}$Length of lay armour 2mm
$p_{ab}$Apportioning factor armour bedding
$p_{atm}$Atmospheric air pressurehPa
$P_C$Charging capacityvar/m
$p_{cb}$Minor ratio of section lengths
$p_{comp}$Gas pressure in compartmentbar
$P_G$Active power generator-sidekW
$p_{gas}$Pressure gasPa
$p_i$Apportioning factor insulation
$p_j$Apportioning factor jacket
$P_L$Active power load-sidekW
$p_{Mie}$Factor $p$ (Mie1905)
$p_{Nu,r}$Factor p
$p_{shj}$Apportioning factor sheath jacket
$p_{soil}$Depth of image source
$p_{tr}$Effective perimeter troughm
$p_w$Pressure waterbar
$P_X$Substitution coefficient P to calculate loss factor by circulating currents
$\phi$Angle of power factorrad
$\Phi_{air}$Relative humidity air$\%$
$\phi_{ar}$Angle between armour and cable axisrad
$\phi_{arc}$Bend anglerad
$\phi_{el}$Angle to the plane of a sectionrad
$\phi_{tr}$Parameter $\phi$ trough
$\pi$Archimedes' constant $\pi$
$\mathrm{Pr}_{air}$Prandtl number air
$\mathrm{Pr}_{gas}$Prandtl number gas
$\mathrm{Pr}_w$Prandtl number water
Q$q_1$Ratio of losses screen bedding,screen serving
$q_2$Ratio of losses armour bedding
$q_3$Ratio of losses affecting jacket
$q_4$Ratio of losses environment
$Q_A$Thermal capacitance A transient thermal circuitJ/(m.K)
$Q_{ab}$Thermal capacitance armour beddingJ/(m.K)
$Q_{ar}$Thermal capacitance armourJ/(m.K)
$q_{ar}$Ratio of losses armour
$Q_B$Thermal capacitance B transient thermal circuitJ/(m.K)
$Q_{B,ab}$Thermal capacitance B transient thermal circuit, armour beddingJ/(m.K)
$Q_{B,d}$Thermal capacitance B transient thermal circuit, ductJ/(m.K)
$Q_{B,f}$Thermal capacitance B transient thermal circuit, fillerJ/(m.K)
$Q_{B,i}$Thermal capacitance B transient thermal circuit, insulationJ/(m.K)
$Q_{B,j}$Thermal capacitance B transient thermal circuit, jacketJ/(m.K)
$Q_{B,s}$Thermal capacitance B transient thermal circuit, screen/sheathJ/(m.K)
$Q_c$Thermal capacitance conductorJ/(m.K)
$q_{cb}$Major ratio of section lengths
$Q_{ct}$Thermal capacitance conductor tape (IEC 60853)J/(m.K)
$Q_d$Thermal capacitance duct wallJ/(m.K)
$Q_{d,fill}$Thermal capacitance duct fillingJ/(m.K)
$Q_f$Thermal capacitance fillerJ/(m.K)
$q_f$Ratio of losses filler
$Q_G$Reactive power generator-sidekvar
$Q_i$Thermal capacitance insulationJ/(m.K)
$Q_{it}$Thermal capacitance insulation (IEC 60853)J/(m.K)
$Q_{it1}$Thermal capacitance insulation, 1st portion (IEC 60853)J/(m.K)
$Q_{it2}$Thermal capacitance insulation, 2nd portion (IEC 60853)J/(m.K)
$Q_j$Thermal capacitance jacketJ/(m.K)
$Q_L$Reactive power load-sidekvar
$q_{Mie}$Factor $q$ (Mie1905)
$Q_s$Thermal capacitance sheath+sheathJ/(m.K)
$q_s$Ratio of losses screen/sheath
$Q_{sc}$Thermal capacitance screenJ/(m.K)
$Q_{scb}$Thermal capacitance screen beddingJ/(m.K)
$Q_{scs}$Thermal capacitance screen servingJ/(m.K)
$Q_{sh}$Thermal capacitance sheathJ/(m.K)
$Q_{shj}$Thermal capacitance sheath jacketJ/(m.K)
$Q_{sp}$Thermal capacitance steel pipeJ/(m.K)
$Q_{sr}$Reactive power shunt reactorkvar
$Q_{tot}$Thermal capacitance, transientJ/(m.K)
$Q_X$Substitution coefficient Q to calculate loss factor by circulating currents
$q_x$Factor characteristic diameter
R$r_1$Construction circle circumscribing the shaped conductorsmm
$R_1$Positive sequence resistance$\Omega$/m
$R_{ar}$Electrical resistance armour$\Omega$/m
$r_{arc}$Bend radiusm
$r_b$Equivalent radius backfillmm
$r_c$Radius conductormm
$R_c$Electrical resistance conductor$\Omega$/m
$R_{c1}$Thermal resistance part 1K.m/W
$R_{c2}$Thermal resistance part 2K.m/W
$R_{c20}$Electrical resistance DC conductor 20°C$\Omega$/m
$R_{c3}$Thermal resistance part 3K.m/W
$R_{c4}$Thermal resistance part 4K.m/W
$R_{cDC}$Electrical resistance DC conductor$\Omega$/m
$R_{CG}$Thermal resistance multi-layer backfillK.m/W
$R_{co}$Standard DC resistance of conductor$\Omega$/km
$r_{core}$Radius over core cablemm
$R_{ct}$Resistance earth continuity conductor$\Omega$/m
$R_e$Electrical resistance shield/armour$\Omega$/m
$R_E$Equivalent resistance of earth return path$\Omega$/m
$R_{encl}$Electrical resistance enclosure$\Omega$/m
$R_{encl20}$Electrical resistance DC enclosure 20°C$\Omega$/m
$R_{enclDC}$Electrical resistance DC enclosure$\Omega$/m
$R_f$Tower footing impedance$\Omega$
$r_g$Geometric mean radius of the ground conductorm
$R_{gas}$Specific gas constantJ/(kg.K)
$R_{gas0}$Universal molar gas constant
$R_h$Resistance link$\Omega$/m
$r_{ij}$Coefficient r view factor
$r_{isc}$Radius above the inner semi-conducting layermm
$R_l$Ground resistance load$\Omega$
$R_{max}$Resistance of conductor at emergency rating$\Omega$/m
$r_{mbi}$Minimal bending radius, installationm
$r_{mbif}$Factor minimal bending radius, installation
$r_{mbp}$Minimal bending radius, pullingm
$r_{mbpf}$Factor minimal bending radius, pulling
$r_o$Radius of objectm
$r_{osc}$Radius over capacitive insulation layersmm
$R_{q11}$Thermal resistance 11 multi-layer backfillK.m/W
$R_{q12}$Thermal resistance 12 multi-layer backfillK.m/W
$R_{q13}$Thermal resistance 13 multi-layer backfillK.m/W
$R_{q21}$Thermal resistance 21 multi-layer backfillK.m/W
$R_{q22}$Thermal resistance 22 multi-layer backfillK.m/W
$R_{q31}$Thermal resistance 31 multi-layer backfillK.m/W
$R_{q32}$Thermal resistance 32 multi-layer backfillK.m/W
$R_r$Ground resistance receiving end$\Omega$
$R_s$Electrical resistance shield$\Omega$/m
$r_s$Mean radius shieldm
$R_{sc}$Electrical resistance screen$\Omega$/m
$R_{sh}$Electrical resistance sheath$\Omega$/m
$R_{skid}$Electrical resistance skid wires$\Omega$/m
$R_{so}$Electrical resistance screen/sheath 20°C$\Omega$/m
$r_{sp}$Mean radius steel pipemm
$R_{sp}$Electrical resistance steel pipe$\Omega$/m
$R_{ss}$Resistance of conductor before emergency rating$\Omega$/m
$R_{sw}$Resistance skywire$\Omega$/m
$r_x$Radius to point x in insulationmm
$r_{z1}$Radius conductorm
$r_{z2}$Radius shield (inner)m
$r_{z2,sc}$Radius screen (inner)m
$r_{z2,sh}$Radius sheath (inner)m
$r_{z3}$Radius shield (outer)m
$r_{z3,sc}$Radius screen (outer)m
$r_{z3,sh}$Radius sheath (outer)m
$r_{z4}$Radius armour (inner)m
$r_{z5}$Radius armour (outer)m
$r_{z6}$Radius outersheathm
$\mathrm{Ra}_c$Rayleigh number conductor→gas
$\mathrm{Ra}_{encl}$Rayleigh number gas→enclosure
$\mathrm{Ra}_{ext}$Rayleigh number riser—air
$\mathrm{Ra}_{int}$Rayleigh number gas→riser
$\mathrm{Ra}_L$Rayleigh number ground—air
$\mathrm{Ra}_{prot}$Rayleigh number surface→air
$\mathrm{Re}_{air}$Reynolds number air
$\mathrm{Re}_w$Reynolds number water
$RF$Reduction factor
$\rho_4$Thermal resistivity soilK.m/W
$\rho_{4d}$Thermal resistivity dry soilK.m/W
$\rho_{ab}$Thermal resistivity armour beddingK.m/W
$\rho_{ab,1}$Thermal resistivity armour bedding 1K.m/W
$\rho_{ab,2}$Thermal resistivity armour bedding 2K.m/W
$\rho_{ar}$Specific electrical resistivity armour material$\Omega$.m
$\rho_b$Thermal resistivity backfillK.m/W
$\rho_{b1}$Thermal resistivity surface layerK.m/W
$\rho_{b2}$Thermal resistivity middle layerK.m/W
$\rho_c$Electrical resistivity conductor material$\Omega$.m
$\rho_{cr}$Thermal resistivity conductor materialK.m/W
$\rho_{cs}$Thermal resistivity conductor shieldK.m/W
$\rho_{ct}$Thermal resistivity conductor tapeK.m/W
$\rho_d$Thermal resistivity duct materialK.m/W
$\rho_{d,fill}$Thermal resistivity duct fillingK.m/W
$\rho_E$Specific electrical resistivity of soil$\Omega$.m
$\rho_{encl}$Specific electrical resistivity enclosure material$\Omega$.m
$\rho_f$Thermal resistivity fillerK.m/W
$\rho_{gas}$Density gaskg/m$^3$
$\rho_i$Thermal resistivity insulation materialK.m/W
$\rho_{is}$Thermal resistivity insulation screenK.m/W
$\rho_j$Thermal resistivity jacket materialK.m/W
$\rho_{k2}$Thermal resistivity layer belowK.m/W
$\rho_{k20}$Electrical resistivity metallic component$\Omega$.m
$\rho_{k3}$Thermal resistivity layer aboveK.m/W
$\rho_{ki}$Thermal resistivity adjacent non-metallic materialK.m/W
$\rho_p$Thermal resistivity pipe materialK.m/W
$\rho_s$Specific electrical resistivity shield (screen/sheath)$\Omega$.m
$\rho_{sc}$Specific electrical resistivity screen material$\Omega$.m
$\rho_{scb}$Thermal resistivity screen beddingK.m/W
$\rho_{scs}$Thermal resistivity screen servingK.m/W
$\rho_{sh}$Specific electrical resistivity sheath material$\Omega$.m
$\rho_{shj}$Thermal resistivity sheath jacket materialK.m/W
$\rho_{skid}$Specific electrical resistivity skid wire material$\Omega$.m
$\rho_{sp}$Specific electrical resistivity steel pipe material$\Omega$.m
$\rho_{spf}$Thermal resistivity steel pipe filling mediumJ/(K.m$^3$)
$\rho_t$Thermal resistivity wallK.m/W
S$S$Mean distance between the phasesm
$S_{ab}$Distance phases a — bm
$S_{ac}$Distance phases a — cm
$s_{air}$Axial spacing between objectsm
$S_{ap}$Distance phases a — p (ground)m
$s_{b1}$Thickness surface layerm
$s_{b2}$Thickness middle layerm
$s_{b3}$Thickness from object to top of bedding layerm
$s_{b4}$Thickness from object to bottom of bedding layerm
$S_{bc}$Distance phases b — cm
$S_{bp}$Distance phases b — p (ground)m
$s_c$Separation of conductors in a systemmm
$S_{cp}$Distance phases c — p (ground)m
$S_G$Apparent power generator-sidekVA
$S_{gas}$Sutherland's constantK
$s_{ij}$Spacing object—object
$S_k$Cross-sectional area metallic componentmm$^2$
$S_m$Separation of conductors in a systemm
$s_{Nu,r}$Factor s
$S_p$Distance between phases a/b/c + conductor pm
$s_{S1}$Spacing between phases minor section 1p.u.
$s_{S2}$Spacing between phases minor section 2p.u.
$s_{S3}$Spacing between phases minor section 3p.u.
$S_{sp}$Mean distance between the phases, pipe-type cables$\Omega$/m
$\sigma$Stefan Boltzmann constantW/m$^2$K$^4$
$\sigma_{ab}$Volumetric heat capacity armour beddingJ/(K.m$^3$)
$\sigma_{ab,1}$Volumetric heat capacity armour bedding 1J/(K.m$^3$)
$\sigma_{ab,2}$Volumetric heat capacity armour bedding 2J/(K.m$^3$)
$\sigma_{ar}$Volumetric heat capacity armour materialJ/(K.m$^3$)
$\sigma_c$Volumetric heat capacity conductor materialJ/(K.m$^3$)
$\sigma_d$Volumetric heat capacity duct materialJ/(K.m$^3$)
$\sigma_{d,fill}$Volumetric heat capacity duct fillingJ/(K.m$^3$)
$\sigma_{encl}$Volumetric heat capacity enclosure materialJ/(K.m$^3$)
$\sigma_f$Volumetric heat capacity fillerJ/(K.m$^3$)
$\sigma_i$Volumetric heat capacity insulation materialJ/(K.m$^3$)
$\sigma_j$Volumetric heat capacity jacket materialJ/(K.m$^3$)
$\sigma_{k2}$Volumetric heat capacity layer belowJ/(K.m$^3$)
$\sigma_{k3}$Volumetric heat capacity layer aboveJ/(K.m$^3$)
$\sigma_{kc}$Volumetric heat capacity metallic componentJ/(K.m$^3$)
$\sigma_{ki}$Volumetric heat capacity adjacent non-metallic materialJ/(K.m$^3$)
$\sigma_{prot}$Volumetric heat capacity protective coverJ/(K.m$^3$)
$\sigma_{sc}$Volumetric heat capacity screen materialJ/(K.m$^3$)
$\sigma_{scb}$Volumetric heat capacity screen beddingJ/(K.m$^3$)
$\sigma_{scs}$Volumetric heat capacity screen servingJ/(K.m$^3$)
$\sigma_{sh}$Volumetric heat capacity sheath materialJ/(K.m$^3$)
$\sigma_{shj}$Volumetric heat capacity sheath jacket materialJ/(K.m$^3$)
$\sigma_{skid}$Volumetric heat capacity skid wiresJ/(K.m$^3$)
$\sigma_{sp}$Volumetric heat capacity steel pipe materialJ/(K.m$^3$)
$\sigma_{spf}$Volumetric heat capacity steel pipe filling mediumJ/(K.m$^3$)
$\sigma_{sun}$Absorption coefficient solar radiation
$SIL$Surge impedance loadingMW
T$T0_{gas}$Gas reference temperatureK
$T_1$Thermal resistance conductor—sheathK.m/W
$t_1$Thickness conductor—sheathmm
$t_{1t}$Thickness conductor—sheath, transientmm
$T_2$Thermal resistance armour beddingK.m/W
$t_2$Thickness sheath—armourmm
$t_{2i}$Thickness of insulation between conductorsmm
$T_3$Thermal resistance jacketK.m/W
$t_3$Thickness armour—surfacemm
$T_{4d}$Thermal resistance daily load cycleK.m/W
$T_{4db}$Thermal resistance backfill correctionK.m/W
$T_{4fem}$Thermal resistance finite element methodK.m/W
$T_{4i}$Thermal resistance medium in the ductK.m/W
$T_{4ii}$Thermal resistance duct wallK.m/W
$T_{4iii}$Thermal resistance ambientK.m/W
$T_{4\mu}$Thermal resistance ambientK.m/W
$T_{4pi}$Thermal resistance of medium in the air-filled pipe with objectsK.m/W
$T_{4pii}$Thermal resistance pipe wallK.m/W
$T_{4piii}$Thermal resistance pipe—ambientK.m/W
$T_{4ss}$Thermal resistance steady-stateK.m/W
$T_{4t}$Equivalent thermal resistance for tunnelK.m/W
$T_{4w}$Thermal resistance weekly load cycleK.m/W
$T_{4y}$Thermal resistance yearly load cycleK.m/W
$T_A$Thermal resistance A transient thermal circuitK.m/W
$T_a$Star thermal resistance airK.m/W
$T_{a0}$Apparent thermal resistance aK.m/W
$t_{a,1}$Thickness armour 1mm
$t_{a,2}$Thickness armour 2mm
$t_{ab}$Thickness armour beddingmm
$T_{ab}$Thermal resistance armour beddingK.m/W
$t_{ab,1}$Thickness armour bedding 1mm
$t_{ab,2}$Thickness armour bedding 2mm
$T_{air}$Absolute air temperatureK
$t_{ar}$Thickness armourmm
$T_{at}$Thermal resistance convection air—tunnelK.m/W
$T_{axial}$Axial thermal resistance due to the movement of air through the tunnelK.m/W
$T_B$Thermal resistance B transient thermal circuitK.m/W
$T_{b0}$Apparent thermal resistance bK.m/W
$T_{bulk}$Bulk temperatureK
$t_c$Thickness of hollow conductormm
$T_C$Thermal resistance C transient thermal circuitK.m/W
$t_{comp}$Thickness compartmentm
$T_{conv,ce}$Thermal resistance convection conductor—enclosureK.m/W
$T_{conv,int}$Thermal resistance convection cable—riserK.m/W
$T_{conv,sa}$Thermal resistance convection surface—airK.m/W
$t_{cs}$Thickness conductor shieldmm
$T_{cs}$Thermal resistance conductor shieldK.m/W
$t_{ct}$Thickness conductor tapemm
$T_{ct}$Thermal resistance conductor tapeK.m/W
$T_d$Internal thermal resistance for dielectric lossesK.m/W
$t_d$Thickness ductmm
$T_{dsh}$Thermal resistance corrugation fillingK.m/W
$T_e$External thermal resistance of tunnelK.m/W
$t_{EMF}$Time step to calculate current sources
$t_{encl}$Thickness enclosurem
$T_{eq}$Thermal resistance, equivalentK.m/W
$t_f$Thickness of filler/belt insulationmm
$T_{gas}$Absolute gas temperatureK
$T_{hs}$Thermal resistance heat sourceK.m/W
$t_{hsi}$Thickness pipe insulationmm
$T_{hsi}$Thermal resistance pipe insulationK.m/W
$t_{hsj}$Thickness protective jacketmm
$T_{hsj}$Thermal resistance protective jacketK.m/W
$t_{hsp}$Thickness fluid-filled pipemm
$T_{hsp}$Thermal resistance fluid-filled pipeK.m/W
$T_i$Thermal resistance insulationK.m/W
$t_i$Thickness insulationmm
$t_{ic}$Thickness core insulationmm
$t_{ins}$Thickness insulationmm
$T_{ins}$Thermal resistance insulationK.m/W
$T_{int}$Internal thermal resistance for current lossesK.m/W
$t_{is}$Thickness insulation screenmm
$T_{is}$Thermal resistance insulation screenK.m/W
$t_j$Thickness jacketmm
$T_j$Thermal resistance jacketK.m/W
$t_{jj}$Thickness of additional layer over jacketmm
$t_k$Duration of short-circuits
$T_L$Thermal resistance, longitudinalK.m/W
$T_{mh}$Mutual thermal resistance between rated and crossing object(s)K.m/W
$T_{mh,v}$Mutual thermal resistance between object(s) per sliceK.m/W
$T_o$Thermal resistance oil in the pipeK.m/W
$t_p$Thickness enclosing pipemm
$t_{prot}$Thickness protective coverm
$T_{prot}$Thermal resistance protective coverK.m/W
$T_r$Thermal resistance, totalK.m/W
$T_{rad,ce}$Thermal resistance radiation conductor—enclosureK.m/W
$T_{rad,int}$Thermal resistance radiation cable—riserK.m/W
$T_{rad,sa}$Thermal resistance radiation surface—airK.m/W
$T_{rad,sun}$Thermal resistance solar radiation air—surfaceK.m/W
$T_{riser}$Thermal resistance riserK.m/W
$T_s$Star thermal resistance objectK.m/W
$T_{sa}$Thermal resistance convection object—airK.m/W
$t_{sc}$Thickness screenmm
$t_{scb}$Thickness screen beddingmm
$T_{scb}$Thermal resistance screen beddingK.m/W
$t_{scs}$Thickness screen servingmm
$T_{scs}$Thermal resistance screen servingK.m/W
$t_{sh}$Thickness sheathmm
$t_{sha}$Total thickness between separate sheath and armourmm
$t_{shj}$Thickness sheath jacketmm
$T_{shj}$Thermal resistance sheath jacketK.m/W
$t_{skid}$Thickness skid wiresmm
$t_{sp}$Thickness steel pipemm
$T_{spf}$Thermal resistance steel pipe fillingK.m/W
$T_{st}$Thermal resistance radiation object—tunnelK.m/W
$T_{surf}$Absolute surface temperatureK
$t_t$Thickness wallm
$T_t$Star thermal resistance tunnelK.m/W
$T_{tot}$Thermal resistance, transientK.m/W
$T_{tr}$Thermal resistance troughK.m/W
$T_{tw}$Thermal resistance wallK.m/W
$T_{wall}$Thermal resistance pipe wallK.m/W
$\mathrm{tan} \delta_i$Loss factor insulation material
$\tau$Transient load periods
$\tau_{ar}$Armour anglerad
$\tau_L$Deep burial thermal inertia transient load periods
$\theta_{2K}$Temperature rise 2K criterion°C
$\theta_a$Ambient temperature°C
$\theta_{abs}$Absolute temperatureK
$\theta_{air}$Ambient air temperature°C
$\theta_{ar}$Temperature armour°C
$\theta_{at}$Air temperature with load°C
$\theta_{at,L}$Air temperature at outlet°C
$\theta_{at,max}$Air temperature permissible°C
$\theta_{at,z}$Air temperature z°C
$\theta_c$Temperature conductor°C
$\theta_{c,t,0}$Temperature of conductor at transient step°C
$\theta_{c,z}$Temperature conductor z°C
$\theta_{cmax}$Max. temperature conductor°C
$\theta_{cmaxeo}$Max. temperature conductor, emergency overload°C
$\theta_{cmaxsc}$Max. temperature conductor, short-circuit°C
$\theta_{cs}$Temperature conductor shield°C
$\theta_{de}$Temperature duct outer surface°C
$\theta_{di}$Temperature duct inner surface°C
$\theta_{dm}$Mean temperature medium in the duct°C
$\theta_e$External temperature object°C
$\theta_{encl}$Temperature enclosure°C
$\theta_f$Temperature filler for multi-core cables type SS with sheath°C
$\theta_{film}$Film temperature°C
$\theta_{gas}$Gas temperature°C
$\theta_{hs}$Temperature heat source°C
$\theta_{hsf}$Temperature fluid°C
$\theta_{hsi}$Temperature pipe insulation°C
$\theta_{hsj}$Temperature protective jacket°C
$\theta_{hsp}$Temperature fluid-filled pipe°C
$\theta_i$Temperature of insulation°C
$\theta_{init}$Air temperature without load°C
$\theta_{iter}$Air temperature previous iteration°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
$\theta_o$Temperature outer surface°C
$\theta_{o,L}$Temperature object surface at outlet°C
$\theta_{o,z}$Temperature object surface z°C
$\theta_{omax}$Max. temperature outer surface°C
$\theta_R$Rated current transient to steady-state ratio
$\theta_s$Temperature screen/sheath°C
$\theta_{sc}$Temperature screen°C
$\theta_{sh}$Temperature sheath°C
$\theta_{sp}$Temperature steel pipe°C
$\theta_{spf}$Mean temperature medium in the steel pipe°C
$\theta_{surf}$Surface temperature°C
$\theta_t$Temperature wall (inner)°C
$\theta_{t,L}$Temperature wall at outlet°C
$\theta_{t,z}$Temperature wall z°C
$\theta_{tm}$Mean temperature between surface and air in tunnel or trough°C
$\theta_{to}$Temperature wall (outer)°C
$\theta_{to,z}$Temperature wall (outer) z°C
$\theta_w$Temperature water°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 pipe fully buriedW/(K.m$^2$)
$U_d$Constant U for cables in ductsK.m/W
$U_e$Line-to-ground voltageV
$U_{exposed}$OHTC part of pipe in contact with waterW/(K.m$^2$)
$U_{ground}$OHTC part of pipe in contact with groundW/(K.m$^2$)
$U_{inwall}$OHTC inside film + pipe wallW/(K.m$^2$)
$U_k$Induced shield voltageV/m
$U_m$Highest voltage for equipmentkV
$U_n$Rated line-to-line voltagekV
$U_o$Operating voltagekV
$U_{OHTC}$Overall heat transfer coefficientW/(K.m$^2$)
$u_p$Substitution coefficient u
$U_p$Constant U for air-filled pipe with objectsK.m/W
$U_{partially}$OHTC pipe partially buriedW/(K.m$^2$)
$U_{spf}$Constant U pipe-type cableK.m/W
$U_{sr}$Reference voltage shunt reactorkV
$U_{ti}$Circumference of inner rectangular tunnel wallm
$U_{wall}$OHTC pipe wallW/(K.m$^2$)
V$v_4$Ratio thermal resistivity dry/moist soil
$V_{ab}$Voltages between shields/sheaths at the cross-bonding points phases a — bV
$V_{ac}$Voltages between shields/sheaths at the cross-bonding points phases a — cV
$V_{air}$Air velocitym/s
$V_{air,min}$Air velocity required to remove all heat by ventilationm/s
$V_{bc}$Voltages between shields/sheaths at the cross-bonding points phases b — cV
$V_{comp}$Gas volumem$^3$
$V_d$Constant V for cables in ductsK.m/W
$V_{drop}$Voltage dropV/(A.m)
$V_{fluid}$Velocity of fluidcm/s
$V_{gas}$Volume percentage of second gas$\%$
$V_{mol}$Molar volumem$^3$/mol
$V_p$Constant V for air-filled pipe with objectsK.m/W
$v_{prop}$Velocity of propagationkm/s
$V_{spf}$Constant V pipe-type cablesK.m/W
$V_w$Velocity watercm/s
W$w_{a,1}$Width of flat wires armour 1mm
$w_{a,2}$Width of flat wires armour 2mm
$W_{a,L}$Heat removed by air at outletW/m
$W_{a,z}$Heat removed by air zW/m
$W_{ar}$Armour losses (phase)W/m
$w_{ar}$Width armourmm
$w_b$Width backfillmm
$w_{b4}$Distance to lateral edge multi-layer backfillm
$W_c$Conductor losses (phase)W/m
$W_{conv,ce}$Convective heat transfer conductor→enclosureW/m
$W_{conv,ext}$Convective heat transfer riser—airW/m
$W_{conv,gd}$Convective heat transfer gas—ductW/m
$W_{conv,int}$Convective heat transfer cable→riserW/m
$W_{conv,og}$Convective heat transfer cable→gasW/m
$W_{conv,sa}$Convective heat transfer, surface→airW/m
$W_d$Dielectric losses (phase)W/m
$w_d$Volumetric density of dielectric lossesW/m$^3$
$W_{d,DC}$Dielectric losses in HVDC cablesW/m
$W_{de}$Losses outside of riserW/m
$W_{di}$Losses between cable and riserW/m
$W_{duct}$Duct lossesW/m
$W_{encl}$Ohmic losses enclosureW/m
$W_h$Heat generated by external objectW/m
$W_{hs}$Heat dissipation heat sourceW/m
$W_I$Ohmic losses (phase)W/m
$W_{rad,ce}$Radiation heat transfer conductor→enclosureW/m
$W_{rad,ext}$Radiation heat transfer riser—airW/m
$W_{rad,int}$Radiation heat transfer cable—riserW/m
$W_{rad,sa}$Radiation heat transfer surface—airW/m
$W_s$Screen/sheath losses (phase)W/m
$W_{sar}$Total loss in shield and magnetic armour (phase)W/m
$w_{sc}$Width flat screen wiresmm
$W_{sp}$Steel pipe losses (phase)W/m
$W_{sum}$Sum of total losses of all systemsW/m
$W_{sun}$Heat transfer solar radiation air→surfaceW/m
$W_{sys}$Total losses (system)W/m
$W_t$Total losses (phase)W/m
$w_t$Width (inner)m
$W_{tot}$Total losses (object)W/m
X$X$Reactance matrix$\Omega$/m
$X_1$Positive sequence reactance$\Omega$/m
$X_a$Self reactance conductor$\Omega$/m
$X_{ap}$Equivalent mutual reactance between conductors$\Omega$/m
$X_{ar}$Self reactance armour$\Omega$/m
$x_b$Horizontal center backfillmm
$X_c$Mutual reactance between middle and outer cables in flat formation with earth return$\Omega$/m
$X_{cp}$Zero-sequence reactance steel pipe$\Omega$/m
$X_d$Reactance steel pipe$\Omega$/m
$X_e$Self reactance screen/sheath$\Omega$/m
$X_G$Factor $X_G$
$X_{G2}$Factor $X_{G2}$
$X_h$Reactance link$\Omega$/m
$X_{ij}$Mutual reactance between conductors i + j$\Omega$/m
$X_K$Factor $X_K$
$X_L$Mutual reactance between outer cables in flat formation$\Omega$/m
$X_m$Mutual reactance between conductors flat formation without transposition$\Omega$/m
$X_{mut}$Mutual reactance$\Omega$/m
$x_p$Factor for proximity effect of conductors
$x_{pos}$Horizontal position x multi-layer backfillm
$x_s$Factor for skin effect on conductor
$X_s$Self reactance 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
$X_{sw}$Reactance skywire$\Omega$/m
$\xi_X$Parameter $\xi$ calculation of loss factor
Y$Y$Admittance matrixS/m
$Y_1$Positive sequence admittanceS/m
$y_{2K}$Depth 2K criterionmm
$Y_{ag}$Admittance armour - groundS/m
$y_c$Skin and proximity effect factor y PAC/GIL conductor
$Y_{cs}$Admittance conductor - shieldS/m
$Y_d$Constant Y for cables in ductsK.m/W
$y_{encl}$Skin and proximity effect factor y 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 conductor
$Y_p$Constant Y for air-filled pipe with objectsK.m/W
$y_s$Skin effect factor conductor
$Y_{sa}$Admittance shield - armourS/m
$Y_{sg}$Admittance shield - groundS/m
$Y_{spf}$Constant Y pipe-type cablesK.m/W
Z$Z$Impedance matrix$\Omega$/m
$Z_1$Positive sequence impedance$\Omega$/m
$Z_2$Negative sequence impedance$\Omega$/m
$Z_a$Self impedance of phase conductor with earth return$\Omega$/m
$Z_{as}$Impedance at transition overhead line to underground cable$\Omega$/m
$Z_{bs}$Installation constant Z
$Z_c$Mutual inductance between middle and outer cables in flat formation with earth return$\Omega$/m
$Z_C$Surge impedance$\Omega$
$z_c$Factor z to calculate skin effect coefficients for conductor
$Z_{ch}$Surge impedance$\Omega$
$Z_{ct}$Self impedance earth continuity conductor$\Omega$/m
$Z_d$Positive sequence impedance$\Omega$/m
$z_{encl}$Factor z to calculate skin effect coefficients for enclosure
$z_h$Location of the heat sourcem
$Z_h$Zero-sequence impedance$\Omega$/m
$Z_{ij}$Mutual impedance between cables with earth return$\Omega$/m
$Z_K$Factor $Z_K$
$Z_{kp}$Impedance between cable k and p in ground$\Omega$/m
$Z_L$Mutual inductance between outer cables in flat formation with earth return$\Omega$/m
$Z_m$Mutual impedance between phase conductor and metal screen with earth return$\Omega$/m
$z_{max}$Logitudinal thermal limit distancem
$Z_{mt}$Equivalent mutual impedance between earth continuity conductor and any cable$\Omega$/m
$Z_{oig}$Mutual impedance between shields/sheaths of inner and outer cables with ground return$\Omega$/m
$Z_{oog}$Mutual impedance between shields/sheaths of outer cables with ground return$\Omega$/m
$z_r$Location of the hottest pointm
$Z_s$Self impedance of metal screen with earth return$\Omega$/m
$Z_{sg}$Mutual impedance of shield/sheath with ground return$\Omega$/m
$Z_{ss}$Self impedance of the shield/sheath with ground return$\Omega$/m
$Z_{sw}$Self impedance skywire$\Omega$/m
$Z_x$Equivalent mutual impedance between cables with earth return$\Omega$/m
$\zeta_{ab}$Density armour bedding materialg/cm$^3$
$\zeta_{ar}$Density armour materialg/cm$^3$
$\zeta_c$Density conductor materialg/cm$^3$
$\zeta_{er}$Radiation shape factor touching cables
$\zeta_f$Density filler materialg/cm$^3$
$\zeta_i$Density insulation materialg/cm$^3$
$\zeta_j$Density jacket materialg/cm$^3$
$\zeta_M$Density cable materialg/cm$^3$
$\zeta_{sc}$Density metallic screen materialg/cm$^3$
$\zeta_{sh}$Density sheath materialg/cm$^3$
$\zeta_{shj}$Density of jacket material over each coreg/cm$^3$
$\zeta_{skid}$Density skid wire materialg/cm$^3$
$\zeta_{soil}$Density soil materialkg/m$^3$
$\zeta_{sp}$Density steel pipe materialg/cm$^3$
$\zeta_{tape}$Density tape materialg/cm$^3$
$\zeta_w$Density waterkg/m$^3$
$\mathscr{z}_1$Impedance conductor outer surface$\Omega$/m
$\mathscr{z}_2$Impedance insulation conductor—screen$\Omega$/m
$\mathscr{z}_3$Impedance shield inner surface$\Omega$/m
$\mathscr{z}_{34}$Impedance insulation shield—armour$\Omega$/m
$\mathscr{z}_{3,s}$Impedance shield inner surface$\Omega$/m
$\mathscr{z}_{3,sc}$Impedance screen inner surface$\Omega$/m
$\mathscr{z}_{3,sh}$Impedance sheath inner surface$\Omega$/m
$\mathscr{z}_4$Mutual impedance shield$\Omega$/m
$\mathscr{z}_{4,s}$Mutual impedance shield$\Omega$/m
$\mathscr{z}_{4,sc}$Mutual impedance screen$\Omega$/m
$\mathscr{z}_{4,sh}$Mutual impedance sheath$\Omega$/m
$\mathscr{z}_5$Impedance shield outer surface$\Omega$/m
$\mathscr{z}_{56}$Impedance jacket$\Omega$/m
$\mathscr{z}_{5,s}$Impedance shield outer surface$\Omega$/m
$\mathscr{z}_{5,sc}$Impedance screen outer surface$\Omega$/m
$\mathscr{z}_{5,sh}$Impedance sheath outer surface$\Omega$/m
$\mathscr{z}_6$Impedance insulation screen—sheath$\Omega$/m
$\mathscr{z}_{cc}$Impedance conductor$\Omega$/m
$\mathscr{z}_{cs}$Impedance conductor—screen$\Omega$/m
$\mathscr{z}_g$Impedance earth return in ground$\Omega$/m
$\mathscr{z}_{gm}$Impedance mutual earth return in ground$\Omega$/m
$\mathscr{z}_{int}$Impedance cable, internal$\Omega$/m
$\mathscr{z}_{os}$Impedance outersheath$\Omega$/m
$\mathscr{z}_{pin}$Impedance armour inner surface$\Omega$/m
$\mathscr{z}_{pmut}$Mutual impedance armour$\Omega$/m
$\mathscr{z}_{pout}$Impedance armour outer surface$\Omega$/m
$\mathscr{z}_{ss}$Impedance cable, external$\Omega$/m