thermal_cable_model.thermal_network — Thermal Network
IEC 60287 / IEC 60853 thermal resistance and capacitance network.
Builds a lumped-parameter thermal circuit for each cable, including the cable-internal resistances T1–T3 and the external (soil) resistance T4. Mutual heating between parallel cables is computed via the image method.
- class InternalThermalResistances[source]
Bases:
objectPer-unit-length thermal resistances of the cable layers [K·m/W].
- classmethod from_cable(cable)[source]
Compute T1–T3 by summing layer thermal resistances.
The first insulation layer is T1, intermediate layers form T2, and the outermost jacket is T3. This mapping follows IEC 60287-2-1 conventions for typical cable constructions.
- Parameters:
cable (Cable)
- Return type:
- class InternalThermalCapacitances[source]
Bases:
objectPer-unit-length thermal capacitances [J/(m·K)].
- external_thermal_resistance(depth, cable_outer_radius, soil)[source]
T4 for a single isolated cable buried at depth [m].
- IEC 60287-2-1 §2.2.7:
T4 = (ρ_soil / 2π) · ln(2L / D_e)
where L = burial depth to cable centre, D_e = external diameter.
- Parameters:
depth (float)
cable_outer_radius (float)
soil (ThermalMaterial)
- Return type:
- mutual_heating_resistance(xi, yi, xj, yj, soil)[source]
Temperature rise at cable i due to unit heat from cable j.
Uses the image method for a semi-infinite conducting half-space with isothermal surface (ground level at y = 0, cables at y < 0 i.e. depth is positive downward so yi, yj > 0).
Returns ΔT4_ij = ρ_soil/(2π) · ln(d’_ij / d_ij)
d_ij = real distance between cables i and j d’_ij = distance from cable i to the image of cable j
- cylindrical_shell_thermal_resistance(thermal_resistivity, inner_radius, outer_radius)[source]
Radial thermal resistance [K·m/W] of a homogeneous cylindrical shell.
Same physics as
thermal_cable_model.cable.CableLayerwith constant ρ_th (IEC 60287-2-1 §4.1 cylindrical layer).
- cylindrical_shell_thermal_resistance_diameters(thermal_resistivity, inner_diameter, outer_diameter)[source]
Thermal resistance [K·m/W] from ρ/(2π)·ln(D_out/D_in).
inner_diameter and outer_diameter may be in any consistent unit.
- plastic_duct_air_gap_thermal_resistance(cable_outer_diameter_mm, theta_max_celsius, u_constant=1.87, v_constant=0.312, y_constant=0.0037)[source]
Thermal resistance of the air space between cable and plastic duct [K·m/W].
IEC 60287-2-1 Table 4 (plastic duct), as implemented in CIGRE TB880 case 2 (touching trefoil in HDPE ducts).
- external_buried_duct_thermal_resistance_tb880_form(burial_depth_to_axis, duct_outer_diameter, soil_thermal_resistivity)[source]
External thermal resistance of a buried duct [K·m/W], TB880 notebook form.
Uses T4‴ = ρ/(2π)·(ln(2u) + 2·ln(u)) with u = 2L/D, where L is depth to the duct axis and D is the duct outer diameter. All length inputs must share the same unit (e.g. mm or m).
This is not identical to
external_thermal_resistance()for a solid cable (IEC 60287-2-1 §2.2.7 / acosh formulation).
- class CableThermalNetwork[source]
Bases:
objectState-space thermal circuit for one or more parallel cables.
For N cables the state vector has N × 6 entries. The network is represented as
C · dθ/dt + G · θ = P(t)
where C is the (diagonal) capacitance matrix, G the conductance matrix, and P the forcing vector (heat sources + boundary coupling).
Nodes per cable (6-node model) ────────────────────────────── 0 : conductor θ_c 1 : insulation mid-point θ_i (Van Wormer split of T1) 2 : sheath / screen θ_sh (boundary between T1 and T2) 3 : armour θ_a (boundary between T2 and T3) 4 : cable surface θ_s (outer jacket) 5 : soil node θ_soil (near cable)
Thermal resistance chain:
θ_c ─[p·T1]─ θ_i ─[(1−p)·T1]─ θ_sh ─[T2]─ θ_a ─[T3]─ θ_s ─[T4/2]─ θ_soil ─[T4/2]─ T_amb
Coupling to ambient (ground temperature) is through T4 from node 5.
- NODES_PER_CABLE = 6
- forcing_vector(currents, conductor_temps, ambient_temps)[source]
Build the right-hand-side vector P.
- Parameters:
currents (per-cable RMS current [A])
conductor_temps (current conductor temperatures for R(T) [°C])
ambient_temps (per-cable ambient ground temperature [°C])
- Return type: