QuickField, enforced by ActiveField technology may be effectively used for multi-physics analysis of various engineering tasks. This analysis could be highly automated.
This document displays the results of cable analysis based on specific modeling parameters. Pictures, tables and graphs below have been automatically calculated by QuickField, controlled by VBA code implemented as Microsoft Word macros.
Geometry This high-voltage tetra-core cable has three triangle sectors with phase conductors and round neutral conductor in the lesser area of the cross-section above. All the conductors are made of aluminum. Each conductor is insulated and the cable as a whole has a three-layered insulation. The cable insulation consists of inner and outer insulators and a protective braiding (steel tape). The sharp corners of the phase conductors are chamfered to reduce the field crown. The corners of the conductors are rounded. Empty space between conductors is filled with some insulator, possibly with an air.
Conductors' geometric parameters
Phase conductor area
120 mm²
Neutral conductor area
35 mm²
Thread rounding radius (R)
2 mm
Insulator geometric parameters
Cable-core insulation thickness
2 mm
Inner cable insulation thickness
1 mm
Protective steel braiding thickness
1 mm
Outer cable isolation thickness
3 mm
Given
Conductors' loading
Current amplitude
200 A
Voltage amplitude (electrostatics)
6500 V
Frequency
50 Hz
Conductors' physical properties
Conductivity
36 MS/m
Thermal conductivity
140 W/K-m
Young's modulo
69 GPa
Poisson's ratio
0.33
Coefficient of thermal expansion
2.33·10-5 1/K
Specific density
2700 kg/m³
Conductors' physical properties
Relative permeability
1000
Conductivity
6 MS/m.
Thermal conductivity
85 W/K-m
Young's modulo
200 GPa
Poisson's ratio
0.3
Coefficient of thermal expansion
0.000012 1/K
Specific density
7870 kg/m³
Insulator physical properties
Core
Inner
Outer
Relative electric permittivity
2.5
2.5
2.5
Thermal conductivity, W/K-m
0.04
0.04
0.04
Young's modulo, MPa
10
10
10
Poisson's ratio
0.3
0.3
0.3
Coefficient of thermal expansion, 1/K
0.0001
0.0001
0.0001
Specific density, kg/m³
900
900
1050
Solution Cable linear weight per meter is calculated from geometrical parameters and specific densities of the cable components. The whole cable specific density is a total density calculated by taking into account all cable components.
Cable physical parameters
Cable outer diameter
42.8 mm
Weight (per meter)
2.74 kg
Cable specific density
1900 kg/m²
Results Conductors' capacitance table holds self- and mutual- capacitances of the cable conductors.
Conductors' capacitance, pF/m
Conductor1
Conductor2
Conductor3
Null-cord
Conductor1
170
66.1
9.47
36.8
Conductor2
169
66.3
0.413
Conductor3
170
36.8
Neutral cord
64.5
Conductors' inductances are calculated using the flux linkage approach by the formula: Lij = Φj / Ii. The table diagonal elements represent the self-inductance values.
Conductors' inductance, uH/m
Magnetostatics
AC magnetics
C-1
C-2
C-3
0-cord
C-1
C-2
C-3
0-cord
Conductor1
11.5
11.2
11.1
11.3
8.73
8.47
8.41
8.51
Conductor2
11.5
11.2
11.1
8.73
8.47
8.38
Conductor3
11.5
11.3
8.73
8.51
Neutral cord
117
8.87
In the magnetostatics problem the conductor's impedance (equal to the resistance) per meter is calculated by the formula: R = l / (ρ·S)
Joule heat per meter in magnetostatics problem is calculated by the formula: P = I² · R, where I is the root-mean-square current and R is the conductor impedance.
The conductors' impedances in AC magnetics problem are calculated using the Ohm's law as a complex ratio of the conductor's average potential divided by the conductor total current. The real part of this ratio represents the resistance, imaginary part represents the reactance and the modulus represents the impedance. The Joule heat in the AC magnetic problem is calculated using the corresponding QuickField integral.
Conductors' impedance
Magnetostatics
AC magnetics
Conductor
Null cord
Conductor1
Conductor2
Conductor3
Impedance, Ω/m
2.31e-04
7.94e-04
2.40e-04
2.55e-04
2.80e-04
Resistance, Ω/m
2.31e-04
7.94e-04
2.15e-04
2.37e-04
2.59e-04
Reactance, Ω/m
-
-
1.08e-04
9.41e-05
1.06e-04
Joule heat, W/m
4.63
0
4.71
4.74
4.71
The generated heat field is exported from the AC magnetics problem into the heat transfer problem. As a result of QuickField simulation you can see the cable exterior surface average temperature, heat flow from the cable surface and the average temperatures of all conductors. Average temperatures are relative numbers presented in Celsius assumed that ambient space temperature is 20 °C.
Cable heat parameters
Exterior surface average temperature
23.5°C
Heat flow
14.2 W
Conductors average temperature, °C
Conductor1
Conductor2
Conductor3
Null-cord
45.9
46.8
45.9
39.3
Stress analysis problem is the utmost one that imports the temperature field from the heat transfer problem and the magnetic forces from the AC magnetic problem. Due to this magnetic and thermal loading the cable components become deformed.
