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Increment of volumetric density of dielectric losses in HVDC cables

Symbol
$\Delta w_d$
Unit
W/m$^3$
Formulae
$\left(\frac{r}{r_{osc}}\right)^{2\left(\delta_i-1\right)} e^{\alpha_i \left(a_i \left(r^2-{r_{isc}}^2\right)+\frac{\Delta \theta_i-a_i \left({r_{isc}}^2-{r_{osc}}^2\right)}{r_{isc}-r_{osc}} \left(r-r_{isc}\right)+\theta_c\right)+\gamma_i \frac{{\delta_i}^2 {U_o}^2 \left(\frac{r}{r_{osc}}\right)^{\delta_i-1}}{r_{osc} \left(1-\left(\frac{r_{isc}}{r_{osc}}\right)^{\delta_i}\right)}}$
Related
$a_i$
Parameter a for radial derivative of dielectric losses
$\alpha_i$
Temperature coefficient of conductivity of insulation material [1/K]
$\delta_i$
Electrical thickness of insulation material [m]
$\Delta \theta_i$
Temperature difference across insulation [K]
$\gamma_i$
Electrical field coefficient of insulation material [mm/kV]
$r_{isc}$
Radius above the inner semi-conducting layer [mm]
$r_{osc}$
Radius over capacitive insulation layers [mm]
$\theta_c$
Temperature of conductor [°C]
$U_o$
Operating voltage [kV]
$w_d$
Volumetric density of dielectric losses [W/m$^3$]
Used in
$W_{d,DC}$
Dielectric losses in HVDC cables [W/m]