Documentation

 Symbol Name Unit A $a_0$ Coefficient a for partial transient temperature rise 1/s $a_{12}$ Distance between phase 1 and 2 mm $a_{23}$ Distance between phase 2 and 3 mm $a_{31}$ Distance between phase 3 and 1 mm $A_{ab}$ Cross-sectional area of armour bedding mm$^2$ $A_{ar}$ Cross-sectional area of armour mm$^2$ $A_c$ Cross-sectional area of conductor mm$^2$ $a_c$ Skin and proximity effect coefficient a for PAC/GIL conductor $A_{comp}$ Cross-sectional area of compartment m$^2$ $A_d$ Cross-sectional area of duct wall mm$^2$ $A_{d,fill}$ Free cross-sectional area inside duct mm$^2$ $A_{di}$ Surface of duct inner wall m$^2$ $A_{do}$ Surface of duct outer wall m$^2$ $A_e$ Surface of object m$^2$ $A_{encl}$ Cross-sectional area of enclosure mm$^2$ $a_{encl}$ Skin and proximity effect coefficient a for PAC/GIL enclosure $A_{er}$ Surface of object m$^2$ $A_f$ Cross-sectional area of filler mm$^2$ $A_{fluid}$ Cross-sectional area of fluid mm$^2$ $A_i$ Cross-sectional area of insulation mm$^2$ $A_{it}$ Cross-sectional area of insulation (IEC 60853) mm² $A_j$ Cross-sectional area of jacket mm$^2$ $A_k$ Thermal property constant A mm/s$^{1/2}$ $a_m$ Mean distance between the phases mm $A_{pipe}$ Cross-sectional area of fluid-filled pipe mm$^2$ $A_{prot}$ Cross-sectional area of protective cover mm$^2$ $a_{S1}$ 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 screen mm$^2$ $A_{scb}$ Cross-sectional area of screen beddig mm$^2$ $A_{scs}$ Cross-sectional area of screen serving mm$^2$ $A_{sh}$ Cross-sectional area of sheath mm$^2$ $A_{shj}$ Cross-sectional area of sheath jacket mm$^2$ $a_{shj}$ Factor $a_{shj}$ for jacket around each core $A_{skid}$ Cross-sectional area of skid wires mm$^2$ $A_{sp}$ Cross-sectional area of steel pipe mm$^2$ $A_t$ Cross-sectional area of the tunnel m$^2$ $A_{tape}$ Cross-sectional area of bedding/serving tapes mm$^2$ $a_{type}$ Construction of armour $\alpha_0$ Constant depending on the burial depth $\alpha_{ar}$ Temperature coefficient of armour material 1/K $\alpha_{at}$ Heat transfer coefficient to channel wall W/(K.m$^2$) $\alpha_c$ Temperature coefficient of conductor material 1/K $\alpha_{encl}$ Temperature coefficient of enclosure material 1/K $\alpha_f$ Phase shift ° $\alpha_{gas}$ Thermal diffusivity for gas m$^2$/s $\alpha_M$ Factor $\alpha_M$ $\alpha_{sa}$ Heat transfer coefficient for convection W/(K.m$^2$) $\alpha_{sc}$ Temperature coefficient of screen material 1/K $\alpha_{sh}$ Temperature coefficient of sheath material 1/K $\alpha_{skid}$ Temperature coefficient of skid wire material 1/K $\alpha_{sp}$ Temperature coefficient of steel pipe material 1/K $\alpha_{st}$ Heat transfer coefficient for radiation W/(K.m$^2$) $\alpha_{sys}$ Inclination angle in degrees ° $\alpha_t$ Conductor to surface attainment factor B $B$ Susceptance S/m $b_0$ Coefficient b for partial transient temperature rise 1/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 B mm$^2$/s $b_{Nu,r}$ Factor b $b_{shj}$ Factor $b_{shj}$ for jacket around each core $b_x$ Shorter side of backfill mm $b_y$ Longer side of backfill mm $\beta_0$ 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 material K $\beta_b$ Angle of exposed wetted surface of pipe rad $\beta_c$ Reciprocal of temperature coefficient of conductor material K $\beta_{encl}$ Reciprocal of temperature coefficient of enclosure material K $\beta_{gas}$ Volumetric thermal expansion coefficient for gas 1/K $\beta_k$ Reciprocal of temperature coefficient of resistance K $\beta_M$ Factor $\beta_M$ $\beta_{sc}$ Reciprocal of temperature coefficient of screen material K $\beta_{sh}$ Reciprocal of temperature coefficient of sheath material K $\beta_{skid}$ Reciprocal of temperature coefficient of skid wire material K $\beta_{sp}$ Reciprocal of temperature coefficient of steel pipe material K $\beta_t$ 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 flow W/K $C_b$ Capacitance of insulation F/m $C_{bq}$ Constants $C_1$ - $C_7$ of multi-layer backfill $c_c$ Distance between the axis of a conductor and the cable center mm $C_{c1}$ Thermal capacitance, 1st loop J/m.K $C_{c2}$ Thermal capacitance, 2nd loop J/m.K $C_{c3}$ Thermal capacitance, 3rd loop J/m.K $C_{c4}$ Thermal capacitance, 4th loop J/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 pressure J/kg.K $c_{p,soil}$ Specific heat capacity of soil J/kg.K $c_{p,w}$ Specific heat capacity at constant pressure J/kg.K $c_{shj}$ Factor $c_{shj}$ for jacket around each core $c_{SI}$ Surge velocity of propagation km/s $c_{type}$ Construction of conductor $c_{v,gas}$ Specific heat capacity at constant volume J/kg.K $C_{v,soil}$ Volumetric heat capacity of soil J/K.m$^3$ $c_{v,w}$ Specific heat capacity at constant volume J/kg.K $C_{vair}$ Volumetric heat capacity of air J/K.m$^3$ $CC$ Charging capacity kvar/km $CC_{pull}$ Conduit clearance mm $CF_{pull}$ Conduit fill $\%$ $CJ_{pull}$ Conduit jamming ratio $\mathrm{cos}\varphi$ Power factor $CR_{pull}$ Conduit ratio $cuw$ Standard copper wires mm D $D_{ab}$ Diameter over armour bedding mm $D_{ar}$ External diameter of armour mm $d_{ar}$ Mean diameter of armour mm $d_b$ Diameter of the backfill mm $d_{b3}$ Distance c of multi-layer backfill m $d_{b4}$ Distance d of multi-layer backfill m $d_c$ External diameter of conductor mm $D_c$ Diameter of conductor m $d_{ci}$ Internal diameter of conductor mm $D_{comp}$ Diameter of compartment (metric) m $d_{comp}$ Diameter of compartment mm $d_{ct}$ External diameter of conductor for transient calculations mm $D_{di}$ Inner diameter of duct m $D_{do}$ Outer diameter of duct m $D_{dry}$ Diameter of drying zone m $D_e$ External diameter of object mm $d_e$ Equivalent diameter of screen/sheath and armour mm $d_{encl}$ Outer diameter of enclosure mm $D_{encl}$ Outer diameter of enclosure (metric) m $D_{eq}$ Equivalent diameter of a group of round objects mm $D_{ext}$ Overall outer diameter of pipe m $D_f$ External diameter of the filler mm $d_f$ Spacing from hottest object in group m $D_i$ Diameter over insulation mm $d_{im}$ Imaginary layer of soil m $D_{in}$ Inner diameter of pipe m $D_{ins}$ Diameter over insulation without insulation screen mm $d_{ins}$ Diameter of insulation around pipe mm $D_{it}$ Diameter over insulation for transient calculations mm $d_j$ Diameter below jacket mm $D_j$ Diameter over jacket mm $D_o$ Outer diameter m $d_{pk1}$ Distance to mirrored buried object mm $d_{pk2}$ Distance between buried objects mm $d_{prot}$ Diameter of protective cover mm $d_{psc}$ Point source correction m $D_{ref}$ Reference diameter for determination of OHTC m $d_s$ Equivalent diameter of screen and sheath mm $D_{sc}$ Diameter over screen mm $d_{sc}$ Mean diameter of screen mm $D_{scb}$ Diameter over screen bedding mm $D_{scs}$ Diameter over screen serving mm $D_{sh}$ Diameter over sheath mm $d_{sh}$ Mean diameter of sheath mm $D_{shb}$ Diameter below sheath mm $D_{shj}$ Diameter of sheath jacket mm $D_{soil}$ Outer diameter of soil layer m $d_t$ Channel covering m $d_w$ Depth under water m $D_{wall}$ Outer diameter of steel pipe m $d_x$ Equivalent diameter of a conductor mm $D_x$ Characteristic diameter mm $D_{x,w}$ Characteristic diameter for weekly load mm $D_{x,y}$ Characteristic diameter for yearly load mm $\Delta_1$ Substitution coefficient $\Delta_1$ for eddy-currents $\delta_1$ Thickness of screening layer mm $\Delta_2$ Substitution coefficient $\Delta_2$ for eddy-currents $\delta_{ar}$ Equivalent thickness of armour mm $\delta_d$ Distance between cable and duct m $\delta_k$ Thickness of screen, sheath or armour mm $\delta_{soil}$ Soil thermal diffusivity m$^2$/s $\Delta d_{sh}$ Depth of corrugation mm $\Delta H_c$ Heat of combustion coefficient MJ/kg $\Delta t$ Length of time step s $\Delta \theta_{0t}$ Air temperature in tunnel increase K $\Delta \theta_{0x}$ Temperature rise by crossing heat sources K $\Delta \theta_{0x,1}$ Temperature rise of the conductor, first estimate K $\Delta \theta_{0x,h}$ Temperature rise of the conductor by source h K $\Delta \theta_{a,t}$ Corrected transient temperature rise of conductor K $\Delta \theta_{air}$ Temperature increase of air K $\Delta \theta_c$ Temperature rise of conductor K $\delta \theta_c$ Ohmic steady-state temperature rise K $\Delta \theta_{c,t}$ Transient temperature rise of conductor by ohmic losses K $\Delta \theta_{ce}$ Temperature difference, conductor to surface K $\Delta \theta_d$ Temperature rise by dielectric losses K $\Delta \theta_{e,t}$ Transient temperature rise of outer surface K $\Delta \theta_{gas}$ Temperature difference, conductor to enclosure °C $\Delta \theta_{kp}$ Temperature rise by buried object k K $\Delta \theta_{max}$ Maximum permissible conductor temperature rise K $\Delta \theta_p$ Temperature rise by other buried objects K $\Delta \theta_R$ Conductor temperature rise above ambient temperature K $\Delta \theta_{R,\infty}$ Maximum permissible conductor temperature rise °C $\Delta \theta_s$ Temperature difference surface to ambient K $\delta \theta_{SPK}$ Peak cyclic temperature rise K $\Delta \theta_{sun}$ Temperature rise by solar radiation K $\Delta \theta_t$ Transient temperature rise of conductor K $\Delta \theta_{t,\infty}$ Steady-state temperature rise of conductor K $\Delta \theta_x$ Critical soil temperature rise K $\Delta \theta_{x0}$ VDE soil temperature rise K $\Delta W$ Incremental heat generated W $\Delta z$ Length of the interval m $Di_d$ Inner diameter of duct mm $di_{pipe}$ Internal diameter of fluid-filled pipe mm $Di_{sp}$ Inner diameter of steel pipe mm $Di_t$ Tunnel inner diameter m $Do_d$ Outer diameter of duct mm $do_{pipe}$ External pipe diameter mm $Do_{sp}$ Outer diameter of steel pipe mm $Do_t$ Tunnel/trough outer diameter m E $E_{bs}$ Installation constant E $e_{hor}$ Horizontal clearance mm $e_{limit}$ Limit of thickness of soil layer m $e_{soil}$ Thickness of soil layer m $E_{stress}$ Electrical field strength kV/mm $e_{ver}$ Vertical clearance mm $e_{wall}$ Clearance to wall mm $EEC$ Embodied energy and carbon MJ/kg $\epsilon_0$ Vacuum permittivity F/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 gas Pa.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 gas Pa.s $\eta_w$ Dynamic viscosity of water Pa.s F $f$ System frequency Hz $F_{\alpha}$ Inclination derating factor p.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 force N/m $F_{ij}$ View factor object-object $F_k$ Imperfect contact thermal factor $F_{lay}$ Effective length per unit lay length of armour mm $F_m$ Radiation coefficient mutual $F_{mh}$ Mutual heating coefficient $f_{ppc}$ Factor of permissible pull N/mm$^2$ $F_{ppc}$ Permissible pull force N $F_{pt}$ Function of pressure and temperature $F_{pull}$ Pulling force N $f_{rad}$ Sidewall bearing pressure factor N/m $F_{rad}$ Sidewall bearing pressure N/m $F_{red}$ Reduction factor for the permissible current rating $F_{T10,1}$ Factor Table 10, single cables p.u. $F_{T10,3}$ Factor Table 10, trefoil groups p.u. $F_{T11,s}$ Factor Table 11, first part p.u. $F_{T11,t}$ Factor Table 11, second part p.u. $F_{T12}$ Factor Table 12 p.u. $F_{T13}$ Factor Table 13 p.u. $f_{wc}$ Weight correction factor $F_x$ Geometrical distance factor for multi-core cables G $g$ Standard acceleration of gravity m/s$^2$ $G$ Conductance S/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 soil p.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 diameter p.u. $\gamma_{bessel}$ Bessel constant p.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 constant m/s$^2$ $\gamma_t$ Attainment factor for groups of cables $\gamma_X$ Attenuation factor for crossing 1/m $GMD$ Geometric mean distance mm $GMR$ Geometric mean radius mm $\mathrm{Gr}_c$ 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 ground m $H_1$ Component of inductance $H_1$ of armour H/m $h_1$ Factor $h_1$ for emergency load $H_2$ Component of inductance $H_2$ of armour H/m $H_3$ Component of inductance $H_3$ of armour H/m $h_{amb}$ Pseudo film coefficient of ambient fluid at ground level W/(K.m$^2$) $h_{atm}$ Height above sea level m $h_b$ Height of the backfill mm $h_{bs}$ Heat dissipation coefficient for black surfaces in free air W/m$^2$/K$^{5/4}$ $h_{buried}$ Heat transfer coefficient wall to soil W/(K.m$^2$) $H_c$ Heat energy content MJ/m $h_{conv,c}$ Convection heat transfer coefficient, conductor to gas W/(K.m$^2$) $h_{conv,da}$ Convection heat transfer coefficient, duct to air W/(K.m$^2$) $h_{conv,encl}$ Convection heat transfer coefficient, gas to enclosure W/m2.K $h_{conv,gd}$ Convection heat transfer coefficient, gas to duct W/(K.m$^2$) $h_{conv,od}$ Convection heat transfer coefficient, object to duct W/(K.m$^2$) $h_{conv,og}$ Convection heat transfer coefficient, object to gas W/(K.m$^2$) $h_{conv,sa}$ Convection heat transfer coefficient, surface to air W/(K.m$^2$) $h_{era}$ Convection heat transfer coefficient acc. ERA W/(K.m$^2$) $h_{ext}$ External heat transfer coefficient W/(K.m$^2$) $h_{ground}$ Heat transfer coefficient buried part of wall to soil W/(K.m$^2$) $h_{in}$ Heat transfer coefficient inside W/(K.m$^2$) $h_{lg}$ Ratio of heat dissipation coefficients $h_{rad,ce}$ Radiation heat transfer coefficient, conductor to enclosure W/(K.m$^2$) $h_{rad,da}$ Radiation heat transfer coefficient, duct to air W/(K.m$^2$) $h_{rad,od}$ Radiation heat transfer coefficient, object to duct W/(K.m$^2$) $h_{rad,sa}$ Radiation heat transfer coefficient, surface to air W/(K.m$^2$) $H_s$ Sheath conductance H/m $h_{soil}$ Heat transfer coefficient wall-soil W/(K.m$^2$) $H_{sun}$ Intensity of solar radiation W/m$^2$ $h_t$ Inner height m $h_{T4}$ Ratio of thermal resistance to ambient $H_{tc}$ Parameter H for trough $h_{tr}$ Heat transfer coefficient W/(K.m$^2$) $H_{ts}$ Parameter H depending on air velocity $H_x$ Magnetic field x-component mH $H_y$ Magnetic field y-component mH I $I_1$ Steady-state current before transient A $I_2$ Emergency load current A $I_c$ Conductor current A $I_C$ Capacitive load current A/km $I_{c,max}$ Highest current load of line A $I_{c,peak}$ Permissible peak cyclic load current A $I_{Ce}$ Capacitive earth short-circuit current A/km $I_{EMF}$ Phase current for EMF calculation A $I_k$ Permissible short-circuit current kA $I_{k1}$ Phase-to-ground short-circuit current kA $I_{k2}$ Phase-to-phase short-circuit current kA $I_{k3}$ Three-phase symmetric short-circuit current kA $I_{kAD}$ Short-circuit current (adiabatic) kA $I_{kSC}$ Effective short-circuit current kA $I_{method}$ Current calculation method $I_R$ Transient conductor current A $inst_{air}$ 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 soil W/(m.K) $K_A$ Coefficient K to calculate in air $k_{air}$ Thermal conductivity of air W/(m.K) $k_{ar}$ Thermal conductivity of armour material W/(m.K) $K_{BICC}$ Constant relating to conductor formation $k_{Boltzmann}$ Boltzmann constant J/K $k_c$ Thermal conductivity of conductor material W/(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 enclosure W/(m.K) $k_{fluid}$ Thermal conductivity of fluid W/(m.K) $k_{gas}$ Thermal conductivity for gas W/(m.K) $K_{GMR}$ Geometric mean radius factor $k_H$ Heinhold characteristic diameter coefficient $k_{ins}$ Thermal conductivity of insulation W/(m.K) $K_k$ Specific short-circuit parameter A.s$^{1/2}$/mm$^2$ $k_l$ Temperature rise factor in air $k_{LF}$ Load loss constant coefficient p.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 pipe W/(m.K) $k_{prot}$ Thermal conductivity of protective cover W/(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 material W/(m.K) $k_{sh}$ Thermal conductivity of sheath material W/(m.K) $k_{skid}$ Thermal conductivity of skid wires $k_t$ Temperature rise ratio p.u. $K_t$ Effective emissivity of surface $K_{vermeer}$ Vermeer constant for convection heat transfer $k_w$ Thermal conductivity of water W/(m.K) $K_x$ Factor for fictitious diameter by Neher $k_X$ Number of heat sources crossing L $L_0$ Reference length of the tunnel m $L_1$ Inductance of phase 1 H/m $L_2$ Inductance of phase 2 H/m $L_3$ Inductance of phase 3 H/m $L_b$ Vertical center of backfill mm $L_{b4}$ Trench depth of multi-layer backfill m $L_c$ Depth of laying of sources mm $L_{char}$ Characteristic length earth surface $L_{cm}$ Depth of laying m $L_{crit}$ Critical system length km $L_d$ Length of duct m $L_{deep}$ Equivalent depth for deep burial m $L_{dry}$ Depth of characteristic diameter of drying zone m $L_{dw}$ Length of duct in water m $L_{earth}$ Equivalent depth of earth return path mm $L_h$ Depth of laying of crossing element mm $L_{leg}$ Length of a section m $L_r$ Depth of laying of the rated object mm $L_{sys}$ System length km $L_T$ Length of the tunnel m $\\lambda_0$ 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 factor p.u. $LF_w$ Weekly load factor p.u. $LF_y$ Yearly load factor p.u. $LME$ London Metal Exchange USD/mt M $M$ Cyclic rating factor p.u. $m_0$ Substitution coefficient $m_0$ for eddy-currents Hz.m/$\Omega$ $M_0$ Coefficient M for partial transient temperature rise s $M_1$ Corrected cyclic rating factor K $M_{ab}$ Material of armour bedding $m_{ab}$ Mass of armour bedding kg/km $M_{ar}$ Material of armour $m_{ar}$ Mass of armour kg/km $M_c$ Material of conductor $m_c$ Mass of conductor kg/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 filler kg/km $M_{fluid}$ Fluid material $M_{gas}$ Gas and gas-mixtures $m_{hollow}$ Mass of hollow cable kg/km $M_i$ Material of insulation $m_i$ Mass of insulation kg/km $M_{IEEE}$ Materials acc. IEEE 442 $M_{ins}$ Material of insulation around pipe $M_j$ Material of jacket $m_j$ Mass of jacket kg/km $M_k$ Thermal contact factor s$^{1/2}$ $m_{metal}$ Mass of the metallic parts kg/km $M_{mol}$ Molar mass g/mol $m_{mol}$ Molecular mass mol $m_{Nu,L}$ 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 screen kg/km $M_{seabed}$ Material of seabed $M_{sh}$ Material of sheath $m_{sh}$ Mass of metallic sheath kg/km $M_{shj}$ Material of sheath jacket $m_{shj}$ Mass of jacket over each core kg/km $M_{skid}$ Material of skid wires $m_{skid}$ Mass of skid wires kg/km $M_{soil}$ Type of soils $M_{sp}$ Material of containment for pipe-type cables $m_{sp}$ Mass of steel pipe kg/km $M_{spf}$ Steel pipe filling medium $m_{tape}$ Mass of tapes kg/km $m_{tot}$ Mass of cable kg/km $\mu$ Loss factor p.u. $\mu_0$ Vacuum permeability H/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 variation p.u. $\mu_y$ Loss factor for yearly load variation p.u. N $N_0$ Coefficient N for partial transient temperature rise s$^2$ $n_{a,1}$ 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 constant 1/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 air m$^2$/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 gas m$^2$/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 water m$^2$/s O $\omega$ Angular frequency rad/s P $p_{a,1}$ Length of lay of 1st armour mm $p_{a,2}$ Length of lay of 2nd armour mm $p_{ab}$ Factor apportioning the armour bedding $p_{ar}$ Length of lay of armour mm $p_{atm}$ Atmospheric air pressure hPa $p_{cb}$ Minor ratio of section lengths $p_{comp}$ Gas pressure in compartment bar $p_{gas}$ Gas pressure Pa $p_i$ Factor apportioning the insulation $p_j$ Factor apportioning the jacket $P_L$ Active power at load receptor kW $p_{Nu,r}$ Factor p $p_{shj}$ Factor apportioning the sheath jacket $p_{soil}$ Depth of image source $p_{tr}$ Effective perimeter of trough m $p_w$ Water pressure bar $P_X$ Substitution coefficient P to calculate loss factor by circulating currents $\Phi_{air}$ Relative humidity of air $\%$ $\phi_{ar}$ Angle between armour and cable axis rad $\phi_{arc}$ Angle of a bend rad $\phi_{el}$ Angle to the plane of a section rad $\phi_{tr}$ 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 circuit J/m.K $Q_{ab}$ Thermal capacitance of armour bedding J/m.K $Q_{ar}$ Thermal capacitance of armour J/m.K $q_{ar}$ Ratio of losses armour $Q_B$ Element B of two-part thermal circuit J/m.K $Q_{B,ab}$ Element B of two-part thermal circuit of armour bedding J/m.K $Q_{B,d}$ Element B of two-part thermal circuit, duct J/m.K $Q_{B,f}$ Element B of two-part thermal circuit, filler J/m.K $Q_{B,i}$ Element B of two-part thermal circuit, insulation J/m.K $Q_{B,j}$ Element B of two-part thermal circuit, jacket J/m.K $Q_{B,s}$ Element B of two-part thermal circuit, screen/sheath J/m.K $Q_c$ Thermal capacitance of conductor J/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 wall J/m.K $Q_{d,fill}$ Thermal capacitance of duct filling J/m.K $Q_f$ Thermal capacitance of filler J/m.K $q_f$ Ratio of losses affecting the filler $Q_i$ Thermal capacitance of insulation J/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 jacket J/m.K $Q_s$ Thermal capacitance of screen+sheath J/m.K $q_s$ Ratio of losses screen/sheath $Q_{sc}$ Thermal capacitance of screen J/m.K $Q_{scb}$ Thermal capacitance of screen bedding J/m.K $Q_{scs}$ Thermal capacitance of screen serving J/m.K $Q_{sh}$ Thermal capacitance of sheath J/m.K $Q_{shj}$ Thermal capacitance of sheath jacket J/m.K $Q_{sp}$ Thermal capacitance of steel pipe J/m.K $Q_{tot}$ Total thermal capacitance, transient J/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 conductors mm $R_1$ Resistance of conductor before emergency rating $\Omega$/m $R_{ar}$ Electrical resistance of armour $\Omega$/m $r_{arc}$ Radius of a bend m $r_b$ Equivalent radius of backfill mm $r_c$ Radius of conductor mm $R_c$ Electrical resistance of conductor $\Omega$/m $R_{c1}$ Thermal resistance, 1st loop K.m/W $R_{c2}$ Thermal resistance, 2nd loop K.m/W $R_{c20}$ DC resistance of conductor at 20°C $\Omega$/m $R_{c3}$ Thermal resistance, 3rd loop K.m/W $R_{c4}$ Thermal resistance, 4th loop K.m/W $R_{cDC}$ Electrical DC resistance of conductor $\Omega$/m $R_{CG}$ Thermal resistance of multi-layer backfill K.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 path p.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 insulation mm $R_{gas}$ Specific gas constant J/kg.K $R_{gas0}$ Universal molar gas constant $r_I$ Radius of the insulation mm $r_{ij}$ Coefficient r for view factor $R_{max}$ Resistance of conductor at emergency rating $\Omega$/m $r_{mbi}$ Minimal bending radius for installation m $r_{mbif}$ Factor of minimal installation bending radius $r_{mbp}$ Minimal bending radius during cable pulling m $r_{mbpf}$ Factor of minimal pulling bending radius $r_o$ Radius of object m $R_{q11}$ Thermal resistance 11 of multi-layer backfill K.m/W $R_{q12}$ Thermal resistance 12 of multi-layer backfill K.m/W $R_{q13}$ Thermal resistance 13 of multi-layer backfill K.m/W $R_{q21}$ Thermal resistance 21 of multi-layer backfill K.m/W $R_{q22}$ Thermal resistance 22 of multi-layer backfill K.m/W $R_{q31}$ Thermal resistance 31 of multi-layer backfill K.m/W $R_{q32}$ Thermal resistance 32 of multi-layer backfill K.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 insulation mm $\mathrm{Ra}_c$ 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 soil K.m/W $\rho_{4d}$ Thermal resistivity of dry soil K.m/W $\rho_{ab}$ Thermal resistivity of armour bedding K.m/W $\rho_{ab,1}$ Thermal resistivity of 1st armour bedding K.m/W $\rho_{ab,2}$ Thermal resistivity of 2nd armour bedding K.m/W $\rho_{ar}$ Specific electrical resistivity of armour material $\Omega$.m $\rho_b$ Thermal resistivity backfill K.m/W $\rho_{b1}$ Thermal resistivity of surface layer K.m/W $\rho_{b2}$ Thermal resistivity of middle layer K.m/W $\rho_c$ Electrical resistivity of conductor material $\Omega$.m $\rho_{corr}$ Thermal resistivity of corrugation filling K.m/W $\rho_{cr}$ Thermal resistivity of conductor material K.m/W $\rho_d$ Thermal resistivity of duct material K.m/W $\rho_{d,fill}$ Thermal resistivity of bentonite filling K.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 filler K.m/W $\rho_{gas}$ Gas density kg/m$^3$ $\rho_i$ Thermal resistivity of insulation K.m/W $\rho_j$ Thermal resistivity of jacket material K.m/W $\rho_{k2}$ Thermal resistivity of the layer located above K.m/W $\rho_{k20}$ Electrical resistivity of metallic component $\Omega$.m $\rho_{k3}$ Thermal resistivity of the layer located below K.m/W $\rho_{ki}$ Thermal resistivity of adjacent material K.m/W $\rho_{sc}$ Specific electrical resistivity of screen material $\Omega$.m $\rho_{scb}$ Thermal resistivity of screen bedding K.m/W $\rho_{scs}$ Thermal resistivity of screen serving K.m/W $\rho_{sh}$ Specific electrical resistivity of sheath material $\Omega$.m $\rho_{shj}$ Thermal resistivity of sheath jacket material K.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 wall K.m/W S $s_{air}$ Axial spacing between objects m $s_{b1}$ Thickness of surface layer m $s_{b2}$ Thickness of middle layer m $s_{b3}$ Thickness from object to top of bedding layer m $s_{b4}$ Thickness from object to bottom of bedding layer m $s_c$ Separation of conductors in a system mm $s_{cm}$ Separation of conductors in a system m $S_G$ Apparent power at injecting point kVA $S_{gas}$ Sutherland's constant K $s_{ij}$ Spacing between object i and j $S_k$ Cross-sectional area of current carrying component mm$^2$ $s_{S1}$ Spacing between phases in 1st section p.u. $s_{S2}$ Spacing between phases in 2nd section p.u. $s_{S3}$ Spacing between phases in 3rd section p.u. $SI$ Surge Impedance $\Omega$ $\sigma$ Stefan Boltzmann constant W/m$^2$K$^4$ $\sigma_{ab}$ Volumetric heat capacity of armour bedding J/K.m$^3$ $\sigma_{ab,1}$ Volumetric heat capacity of 1st armour bedding J/K.m$^3$ $\sigma_{ab,2}$ Volumetric heat capacity of 2nd armour bedding J/K.m$^3$ $\sigma_{ar}$ Volumetric heat capacity of armour material J/K.m$^3$ $\sigma_c$ Volumetric heat capacity of conductor material J/K.m$^3$ $\sigma_d$ Volumetric heat capacity of duct material J/K.m$^3$ $\sigma_{d,fill}$ Volumetric heat capacity of duct filling J/K.m$^3$ $\sigma_{encl}$ Volumetric heat capacity of enclosure material J/K.m$^3$ $\sigma_f$ Volumetric heat capacity of filler J/K.m$^3$ $\sigma_{fluid}$ Volumetric heat capacity of fluid J/K.m$^3$ $\sigma_i$ Volumetric heat capacity of insulation material J/K.m$^3$ $\sigma_{ins}$ Volumetric heat capacity of insulation J/K.m$^3$ $\sigma_j$ Volumetric heat capacity of jacket material J/K.m$^3$ $\sigma_{k2}$ Specific isobaric volumetric heat capacity of layer located below J/K.m$^3$ $\sigma_{k3}$ Volumetric heat capacity of layer located above J/K.m$^3$ $\sigma_{kc}$ Volumetric heat capacity of metallic component J/K.m$^3$ $\sigma_{ki}$ Volumetric heat capacity of adjacent material J/K.m$^3$ $\sigma_{pipe}$ Volumetric heat capacity of fluid-filled pipe J/K.m$^3$ $\sigma_{prot}$ Specific isobaric volumetric heat capacity of protective cover J/K.m$^3$ $\sigma_{sc}$ Volumetric heat capacity of screen material J/K.m$^3$ $\sigma_{scb}$ Volumetric heat capacity of screen bedding J/K.m$^3$ $\sigma_{scs}$ Volumetric heat capacity of screen serving J/K.m$^3$ $\sigma_{sh}$ Volumetric heat capacity of sheath material J/K.m$^3$ $\sigma_{shj}$ Volumetric heat capacity of sheath jacket material J/K.m$^3$ $\sigma_{skid}$ Volumetric heat capacity of skid wires J/K.m$^3$ $\sigma_{sp}$ Volumetric heat capacity of steel pipe material J/K.m$^3$ $\sigma_{sun}$ Absorption coefficient of solar radiation T $T0_{gas}$ Gas reference temperature K $T_1$ Thermal resistance between one conductor and sheath K.m/W $t_1$ Thickness of insulation to sheath mm $t_{1t}$ Thickness of insulation to sheath, transient mm $T_2$ Thermal resistance of armour bedding K.m/W $t_2$ Thickness of bedding under armour mm $t_{2i}$ Thickness of insulation between conductors mm $T_3$ Thermal resistance of jacket K.m/W $t_3$ Thickness of serving over armour mm $T_{4d}$ Transient thermal resistance for daily load K.m/W $T_{4db}$ Correction of thermal resistance for backfill K.m/W $T_{4i}$ Thermal resistance of medium in the duct K.m/W $T_{4ii}$ Thermal resistance of the duct wall K.m/W $T_{4iii}$ Thermal resistance to ambient K.m/W $T_{4mu}$ Thermal resistance to ambient K.m/W $T_{4ss}$ Steady-state thermal resistance K.m/W $T_{4t}$ Equivalent thermal resistance for tunnel K.m/W $T_{4w}$ Transient thermal resistance for weekly load K.m/W $T_{4y}$ Transient thermal resistance for yearly load K.m/W $T_A$ Element A of equivalent thermal circuit K.m/W $T_a$ Star thermal resistance of air K.m/W $T_{a0}$ Apparent thermal resistance a K.m/W $t_{a,1}$ Thickness of 1st armour mm $t_{a,2}$ Thickness of 2nd armour mm $t_{ab}$ Thickness of armour bedding mm $T_{ab}$ Thermal resistance of armour bedding K.m/W $t_{ab,1}$ Thickness of 1st armour bedding mm $t_{ab,2}$ Thickness of 2nd armour bedding mm $T_{air}$ Absolute air temperature K $t_{ar}$ Thickness of armour mm $T_{at}$ Thermal resistance by convection, air to tunnel K.m/W $T_{axial}$ Axial thermal resistance due to the movement of air through the tunnel K.m/W $T_B$ Element B of equivalent thermal circuit K.m/W $T_{b0}$ Apparent thermal resistance b K.m/W $T_{bulk}$ Bulk temperature K $t_c$ Thickness of hollow conductor mm $T_C$ Element C of equivalent thermal circuit K.m/W $t_{comp}$ Thickness of compartment mm $T_{conv,ce}$ Thermal resistance by convection, conductor to enclosure K.m/W $T_{conv,od}$ Thermal resistance by convection, object to duct K.m/W $T_{conv,sa}$ Thermal resistance by convection, surface to air K.m/W $t_{corr}$ Thickness of corrugation filling mm $t_{cs}$ Thickness of conductor shield mm $t_{ct}$ Thickness of conductor tape mm $T_d$ Internal thermal resistance for dielectric losses K.m/W $t_d$ Thickness of duct mm $T_e$ External thermal resistance of tunnel K.m/W $t_{EMF}$ Time step to calculate current source s $t_{encl}$ Thickness of enclosure mm $T_{eq}$ Equivalent thermal resistance K.m/W $t_f$ Thickness of filler/belt insulation mm $T_{gas}$ Absolute gas temperature K $T_i$ Thermal resistance of insulation K.m/W $t_i$ Thickness of insulation mm $t_{icore}$ Thickness of core insulation mm $t_{ins}$ Thickness of insulation mm $T_{ins}$ Thermal resistance of insulation K.m/W $T_{int}$ Internal thermal resistance for current losses K.m/W $t_{is}$ Thickness of insulation screen mm $T_{is}$ Thermal resistance of insulation screen K.m/W $t_j$ Thickness of jacket mm $T_j$ Thermal resistance of jacket K.m/W $t_{jj}$ Thickness of additional layer over jacket mm $t_k$ Duration of short-circuit s $T_L$ Thermal longitudinal resistance K.m/W $T_{mh}$ Mutual thermal resistance between rated and crossing object K.m/W $T_{mh,v}$ Mutual thermal resistance per slice K.m/W $T_o$ Thermal resistance of the oil in the pipe K.m/W $t_{prot}$ Thickness of protective cover mm $T_{prot}$ Thermal resistance of protective cover K.m/W $T_r$ Total thermal resistance K.m/W $T_{rad,ce}$ Radiation thermal resistance, conductor to enclosure K.m/W $T_{rad,od}$ Radiation thermal resistance, object to duct K.m/W $T_{rad,sa}$ Radiation thermal resistance, surface to air K.m/W $T_{rad,sun}$ Solar radiation thermal resistance K.m/W $T_{riser}$ Thermal resistance of riser/J-tubes in air/water K.m/W $T_s$ Star thermal resistance of object K.m/W $T_{sa}$ Thermal resistance by convection, surface to air K.m/W $t_{sc}$ Thickness of the screen mm $t_{scb}$ Thickness of screen bedding mm $T_{scb}$ Thermal resistance of screen bedding K.m/W $t_{scs}$ Thickness of screen serving mm $T_{scs}$ Thermal resistance of screen bedding K.m/W $t_{sh}$ Thickness of the sheath mm $t_{sha}$ Total thickness between separate sheath and armour mm $t_{shj}$ Thickness of sheath jacket mm $T_{shj}$ Thermal resistance of sheath jacket K.m/W $t_{skid}$ Thickness of skid wires mm $t_{sp}$ Thickness of steel pipe mm $T_{st}$ Radiation thermal resistance, surface to tunnel K.m/W $T_{surf}$ Absolute surface temperature K $t_t$ Wall thickness m $T_t$ Star thermal resistance of tunnel K.m/W $T_{tot}$ Total thermal resistance, transient K.m/W $T_{tr}$ Thermal resistance of trough K.m/W $T_{tw}$ Thermal resistance of tunnel wall K.m/W $T_{wall}$ Thermal resistance of pipe wall K.m/W $\mathrm{tan} \delta_i$ Loss factor of insulation $\tau$ Transient load period s $\tau_{ar}$ Armour angle rad $\tau_L$ Transient load period for deep burial s $\theta_{2K}$ Temperature rise for 2K criterion °C $\theta_a$ Ambient temperature °C $\theta_{abs}$ Absolute temperature K $\theta_{air}$ 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 constant s U $u$ Substitution coefficient u $U_0$ Base voltage for tests kV $u_b$ Substitution coefficient u $U_{buried}$ OHTC of fully buried pipe W/(K.m$^2$) $U_d$ Constant U for cables in ducts K.m/W $U_e$ Line-to-ground voltage kV $U_{exposed}$ OHTC of part of pipe in contact with water W/(K.m$^2$) $U_{ground}$ OHTC of part of pipe in contact with ground W/(K.m$^2$) $U_{inwall}$ OHTC of inside film and pipe wall W/(K.m$^2$) $U_m$ Highest voltage for equipment kV $U_n$ Rated line-to-line voltage kV $U_o$ Operating voltage kV $U_{OHTC}$ Overall heat transfer coefficient W/(K.m$^2$) $U_{partially}$ OHTC of partially buried pipe W/(K.m$^2$) $U_{spf}$ Constant U for pipe-type cables K.m/W $U_{ti}$ Circumference of inner rectangular tunnel wall m $U_{wall}$ OHTC of pipe wall W/(K.m$^2$) V $v_4$ Ratio thermal resistivity dry/moist soil $V_{air}$ Air velocity m/s $V_{comp}$ Gas volume m$^3$ $V_d$ Constant V for cables in ducts K.m/W $V_{drop}$ Voltage drop V/A/km $V_{fluid}$ Velocity of fluid cm/s $V_{gas}$ Volume percentage of second gas $\%$ $V_{spf}$ Constant V for pipe-type cables K.m/W $V_w$ Velocity of water cm/s W $w_{a,1}$ Width of flat wires of 1st armour mm $w_{a,2}$ Width of flat wires of 2nd armour mm $W_{a,L}$ Heat removed by air at outlet W/m $W_{a,z}$ Heat removed by air at z W/m $W_{ar}$ Armour losses W/m $w_{ar}$ Width of armour mm $w_b$ Width of the backfill mm $w_{b4}$ Distance to lateral edge of multi-layer backfill m $W_c$ Conductor losses W/m $W_{conv,ce}$ Convection heat transfer, conductor to enclosure W/m $W_{conv,da}$ Convection heat transfer, duct to air W/m $W_{conv,gd}$ Convection heat transfer, gas to duct W/m $W_{conv,od}$ Convection heat transfer, object to duct W/m $W_{conv,og}$ Convection heat transfer, object to gas W/m $W_{conv,sa}$ Convection heat transfer, surface to air W/m $W_d$ Dielectric losses W/m $W_{de}$ Losses outside of riser/J-tube W/m $W_{di}$ Losses between cable and riser/J-tube W/m $W_{duct}$ Losses in duct W/m $W_{encl}$ Enclosure losses W/m $W_h$ Heat generated by external object W/m $W_{hs}$ Heat dissipation of heat source W/m $W_I$ Ohmic losses per phase W/m $W_{rad,ce}$ Radiation heat transfer, conductor to enclosure W/m $W_{rad,da}$ Radiation heat transfer, duct to air W/m $W_{rad,od}$ Radiation heat transfer, object to duct W/m $W_{rad,sa}$ Radiation heat transfer, surface to air W/m $W_s$ Screen and sheath losses W/m $W_{sar}$ Total loss in shield and magnetic armour W/m $w_{sc}$ Width of flat screen wire mm $W_{sp}$ Losses in steel pipe W/m $W_{sum}$ Sum of total losses of all systems W/m $W_{sun}$ Solar radiation heat transfer to surface W/m $W_{sys}$ Total losses of the system W/m $W_t$ Total losses per phase W/m $w_t$ Inner width m $W_{tot}$ Total losses per object W/m X $X_0$ Zero sequence reactance $\Omega$/m $x_b$ Horizontal center of backfill mm $X_c$ 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 backfill m $x_s$ 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 $Y$ Admittance S/m $y_{2K}$ Depth for 2K criterion mm $y_c$ Skin and proximity effect factor for PAC/GIL conductor $Y_d$ Constant Y for cables in ducts K.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 cycle p.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 cables K.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 source m $Z_K$ Factor $Z_K$ $Z_m$ Mutual impedance between conductor and metal screen $\Omega$/m $z_{max}$ Logitudinal thermal limit distance m $Z_{neg}$ Negative sequence impedance $\Omega$/m $Z_{pos}$ Positive sequence impedance $\Omega$/m $z_r$ Location of the hottest point m $Z_s$ Self impedance of metal screen $\Omega$/m $Z_x$ Equivalent mutual impedance between cables $\Omega$/m $\zeta_{ab}$ Density of armour bedding material g/cm$^3$ $\zeta_{ar}$ Density of armour material g/cm$^3$ $\zeta_c$ Density of conductor material g/cm$^3$ $\zeta_f$ Density of filler material g/cm$^3$ $\zeta_i$ Density of insulation material g/cm$^3$ $\zeta_j$ Density of jacket material g/cm$^3$ $\zeta_M$ Density of material g/cm$^3$ $\zeta_{od}$ Radiation shape factor for touching cables $\zeta_{sc}$ Density of metallic screen material g/cm$^3$ $\zeta_{sh}$ Density of metallic sheath material g/cm$^3$ $\zeta_{shj}$ Density of jacket material over each core g/cm$^3$ $\zeta_{skid}$ Density of metallic skid wire material g/cm$^3$ $\zeta_{soil}$ Density of soil kg/m$^3$ $\zeta_{sp}$ Density of steel pipe g/cm$^3$ $\zeta_{tape}$ Density of tapes g/cm$^3$ $\zeta_w$ Density of water kg/m$^3$