thermal_cable_model.crossing — Cable Crossings

Thermal analysis of cables crossing at an angle.

When two cable circuits cross in the ground at different depths, the deeper (or hotter) cable raises the temperature of the shallower one and vice-versa. This module computes the mutual temperature rise at the crossing point using the analytical line-source / image-source superposition method.

Reference

CIGRÉ Technical Brochure 640 (2015) – A Guide for Rating Calculations of Insulated Cables, §5.4 “Crossing cables”.

class CableCrossing[source]

Bases: object

Model for two cable systems crossing at an arbitrary angle.

Parameters:

  • cable_upper (Cable) – The two cables involved in the crossing.

  • cable_lower (Cable) – The two cables involved in the crossing.

  • depth_upper (float) – Burial depth (to centre) of each cable [m].

  • depth_lower (float) – Burial depth (to centre) of each cable [m].

  • crossing_angle_deg (float) – Angle between the cable axes projected onto the horizontal plane [°]. 90° = perpendicular crossing, 0° = parallel (degenerate case).

  • soil (ThermalMaterial) – Surrounding soil.

__init__(cable_upper, cable_lower, depth_upper, depth_lower, crossing_angle_deg, soil)[source]
Parameters:
temperature_rise_at_upper(heat_rate_lower, integration_half_length=50.0)[source]

Steady-state temperature rise at the upper cable centre-line due to the lower cable’s heat emission [°C].

Parameters:

  • heat_rate_lower (float) – Total heat output of the lower cable per unit length [W/m].

  • integration_half_length (float) – Half-length of the integration domain along the lower cable [m]. 50 m is sufficient for most practical cases.

Return type:

float

temperature_rise_at_lower(heat_rate_upper, integration_half_length=50.0)[source]

Steady-state temperature rise at the lower cable due to the upper.

Parameters:

  • heat_rate_upper (float)

  • integration_half_length (float)

Return type:

float

transient_temperature_rise_at_upper(heat_rate_lower, time_s, integration_half_length=50.0)[source]

Transient temperature rise at the upper cable [°C].

Uses the transient line-source Green’s function for a semi-infinite medium (exponential integral formulation).

Parameters:
Return type:

float

transient_temperature_rise_at_lower(heat_rate_upper, time_s, integration_half_length=50.0)[source]
Parameters:
Return type:

float

crossing_derating_factor(cable, depth, delta_T_crossing, soil)[source]

Compute the derating factor due to a crossing-induced temperature rise.

The cable’s permissible current is reduced so that the total conductor temperature (self-heating + crossing contribution) does not exceed the maximum allowed temperature.

Returns a factor in (0, 1] to multiply with the isolated cable rating.

Parameters:
Return type:

float