Parallel Cable Installations

When multiple cables are buried near each other, each cable raises the soil temperature in its vicinity, increasing the operating temperature of its neighbours. Thermal Cable Model accounts for this mutual heating automatically when multiple cables are added to a CableInstallation.

Setting up parallel cables

Add cables at different horizontal positions (x) and burial depths:

from thermal_cable_model import Cable, CableInstallation, ThermalSimulation, LoadProfile
from thermal_cable_model.materials import SOIL_STANDARD

cable = Cable.single_core_xlpe_cu(240, voltage_class="MV")

inst = CableInstallation(soil=SOIL_STANDARD)
inst.add_cable(cable, x=-0.3, depth=1.0, load=LoadProfile.constant(450, 48*3600))
inst.add_cable(cable, x=0.0,  depth=1.0, load=LoadProfile.constant(400, 48*3600))
inst.add_cable(cable, x=0.3,  depth=1.0, load=LoadProfile.constant(350, 48*3600))

sim = ThermalSimulation(inst)
result = sim.run_transient(dt=600, duration=48 * 3600)

for i in range(3):
    print(f"Cable {i}: max conductor = {result.max_conductor_temp(i):.1f} °C")

Image method for mutual heating

The mutual thermal resistance between cables i and j is computed using the image method for a semi-infinite conducting half-space with an isothermal ground surface:

\[\Delta T_{4,ij} = \frac{\rho_\text{soil}}{2\pi} \ln\!\left(\frac{d'_{ij}}{d_{ij}}\right)\]

where:

• \(d_{ij}\) is the real distance between cables i and j

• \(d'_{ij}\) is the distance from cable i to the image of cable j (reflected about the ground surface)

The temperature rise at cable i due to heat from all other cables is:

\[\Delta T_{\text{mutual},i} = \sum_{j \ne i} W_j \cdot \Delta T_{4,ij}\]

This coupling is included in the forcing vector of the thermal network at every time step, so the mutual heating evolves dynamically with the changing cable currents.

Different load profiles

Each cable can carry a different load profile — this is useful for modelling cables from different circuits (industrial, residential, constant base load) sharing the same trench:

load_industrial = LoadProfile.cyclic(500, 100, 8*3600, 0.6, 6)
load_base       = LoadProfile.constant(450, 48*3600)
load_residential = LoadProfile.daily_pattern(hourly_currents, n_days=2)

inst.add_cable(cable, x=-0.3, depth=1.0, load=load_industrial)
inst.add_cable(cable, x=0.0,  depth=1.0, load=load_base)
inst.add_cable(cable, x=0.3,  depth=1.0, load=load_residential)

Cross-section visualisation

Use plot_cross_section() to visualise the cable arrangement and annotate temperatures:

from thermal_cable_model.visualization import plot_cross_section

fig = plot_cross_section(
    positions_x=[-0.3, 0.0, 0.3],
    depths=[1.0, 1.0, 1.0],
    outer_radii=[cable.outer_radius] * 3,
    temperatures=[result.max_conductor_temp(i) for i in range(3)],
    cable_names=["Left", "Centre", "Right"],
)
fig.savefig("parallel_cross_section.png", dpi=150)