Empirical criteria for avoiding thermal runaway and predicting steady state conductor temperature in EHVDC cables

The criterion was derived from many full model cable calculations on different HVDC cable designs operated at different conditions and with varying insulation material properties.

The full model considers the heat generation in the conductor by the load current and by the leakage current through the insulation layer, the radial temperature profile inside the cable, the electrical field gradient in the insulation layer, the conductivity of the insulation layer as function of the temperature and the electrical field and the heat transfer from conductor to ambient.

The empirical approach followed here differs from other studies in which runaway conditions are derived from fundamental considerations on the Maxwell–Heaviside and the energy conservation equations.

The heat generation in the insulation due to dielectric losses sufficient for igniting a runaway:

W!,#$ , follows from 𝑅%& : the overall thermal resistance between the cable conductor and its surroundings and α: the exponential coefficient for the temperature dependence of the DC conductivity of the insulation.

𝐖𝑰,𝑹𝑨 = 0.79 ∗ 𝑹𝒕𝒉 ,𝟏.𝟑𝟔 ∗ 𝛂,𝟎.𝟗

Together with relations

𝑽𝟐 ∗ 𝝈𝑹𝑨 ∗ 𝟐𝝅

𝐖𝑰,𝑹𝑨 =

𝒓

𝒍𝒏 2𝒓𝟐 4

𝟏

𝝈𝑹𝑨 = 𝝈𝟎 𝒆𝜶𝑻𝑪,𝑹𝑨 6𝜷|𝑬| the combination of the DC voltage and the design conductor temperature at which runaway is initiated can be determined.

As the steady state conductor temperature close to the ‘mathematical’ runaway condition can already be much above the design conductor temperature also a relation was developed for limiting the difference between the conductor steady state and the design conductor temperature.

The heat generation in the insulation due to dielectric losses at the design conductor temperature for a specific difference between the steady state and design conductor temperature, W!,∆;%% , depends on this difference, ΔT<< , and the overall thermal resistance between the cable conductor and its surroundings.

(1)

𝐖𝑰,∆𝑻𝒔𝒔 = 𝚫𝐓𝐒𝐒 ∗ 𝑹𝒕𝒉 ,𝟏.𝟐𝟒 2

As an example, it is demonstrated that an underground XLPE insulated 3000 mm conductor 525kV design HVDC cable with a design conductor temperature of 90°C cables is sufficiently far removed from runaway even at type test voltage and that at 525kV operating voltage the steady state conductor temperature will be less than 1 °C above the design temperature.