Power cable parameters calculation

power cable capacitance calculation, power cable impedance calculation, power cable Joule losses calculation

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 Professional Edition, controlled by VBA code implemented as Microsoft Word macros.

Model description
Input parameters
Calculated cable parameters
Field pictures

1. Model description.

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.

It is often required to design a cable according to parameters of the conductor section areas. Conductor section areas are defined in the Table 1. The tables 2 to 7 describe other input parameters.

2. Input parameters.

Table 1. Conductors' geometric parameters.

Phase conductor area	120	mm²
Neutral conductor area	35	mm²
Thread rounding radius (R)	2	mm

Table 2. 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

Table 3. The precision.

Areas calculation reasonable error

0.001

mm².

Table 4. Conductors' loading.

Current amplitude	200	A
Voltage amplitude (electrostatics)	6500	V
Frequency	50	Hz
Current phase (for static problems)	0	deg

Table 5. Conductors' physical properties.

Relative permeability	1
Conductivity	36000000	S/m
Thermal conductivity	140	W/K-m
Young's modulo	6.9e+10	N/m²
Poisson's ratio	0.33
Coefficient of thermal expansion	2.33·10^-5	1/K
Specific density	2700	kg/m³

Table 6. Steel braiding physical properties.

Relative permeability	1000
Conductivity	6000000	S/m.
Thermal conductivity	85	W/K-m
Young's modulo	2·10¹¹	N/m²
Poisson's ratio	0.3
Coefficient of thermal expansion	0.000012	1/K
Specific density	7870	kg/m³

Table 7. Insulator physical properties.

	Core	Inner	Outer
Relative permeability	1	1	1
Conductivity	0	0	0	S/m
Relative electric permittivity	2.5	2.5	2.5
Thermal conductivity	0.04	0.04	0.04	W/K-m
Young's modulo	10000000	10000000	10000000	N/m²
Poisson's ratio	0.3	0.3	0.3
Coefficient of thermal expansion	0.0001	0.0001	0.0001	1/K
Specific density	900	900	1050	kg/m³

3. Calculated cable parameters.

Cable physical parameters are presented in the next table.

Cable outer diameter is calculated using conductor and insulator geometrical parameters put into Table 1 and Table 2. 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.

Table 8. Cable physical parameters

Cable outer diameter	42.8	mm
Weight (per meter)	2.74	kg
Cable specific density	1.90e+03	kg/m²

"Conductors' capacitance" table holds self- and mutual-capacitances of the cable conductors. These values are calculated in the QuickField electrostatics problem.

q₁ = c₁₁ * (U₁ - 0) + c₁₂ * (U₁ - U₂) + ... + c_1n * (U₁ - U_n)
q₂ = c₂₁ * (U₂ - U₁) + c₂₂ * (U₂ - 0) + ... + c_2n * (U₂ - U_n)
......
q_n = c_n1 * (U_n - U₁) + c_n2 * (U_n - U₂) + ... + c_nn * (U_n - 0)

Table 9. Conductors' capacitance, pF/m (lumped capacitance)

	Conductor1	Conductor2	Conductor3	Null-cord
Conductor1	170	66.1	9.47	36.8
Conductor2	66.3	169	66.3	0.413
Conductor3	9.45	66.1	170	36.8
Neutral cord	37.0	0.534	37.0	64.5

Conductors' inductances are represented in the Table 10. Values in the columns 2-5 are calculated in the magnetostatics problem at the phase defined in the Table 4. Values in the columns 6-9 are calculated in AC magnetic problem. All values are calculated using the flux linkage approach by the formula: L_ij = F_j / I_i. The table diagonal elements represent the self-inductance values.

Table 10. Conductors' inductance, uH/m

	In magnetostatic problem				In AC magnetic problem
	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	11.2	11.5	11.2	11.1	8.47	8.73	8.47	8.38
Conductor3	11.1	11.2	11.5	11.3	8.41	8.47	8.73	8.51
Neutral cord	11.3	11.1	11.3	117	8.51	8.38	8.51	8.87

Table 11 includes the impedance and impedance-like values. 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 = I_A² · R, where I_A 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 density. The real part of this ratio represents the resistance, imaginary part - reactance and the modulus - impedance. The Joule heat in the AC magnetic problem is calculated using the corresponding QuickField integral.

Table 11. Conductors' impedance.

	In electrostatics problem		In AC magnetic problem
	Conductors	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	0.00	0.00	1.08e-04	9.41e-05	1.06e-04
Joule heat, W/m	4.63	0.00	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.

Table 12. 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. The numerical values of these deformations are presented in the next table.

Table 13. Stress analysis problem results.

Maximal displacement	5.14e-02	Mm
Maximal Mohr criteria value	8.16e+07	N/m²

The strength value is important for the cable fault analysis.

Table 14. The strength.

Maximal peak strength value

8.78e+03

A/m

The "Strength" field is shown on a figure below as well as the "Total current density", "Energy density", "Momentary flux density", "Temperature" and "Displacement" field pictures.

4. Field pictures.

Current density in the cable