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# Thermal behavior of three-phase busbar system under AC magnetic regime

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## Introduction

The development of high-performance electrical installation requires flexible, efficient and intelligent electrical power distribution. The busbar systems are the essential components of power stations and they define the main connection nodes for power delivery.

They are commonly used to connect high voltage equipment like in electrical switchyards, and low voltage equipment in battery banks. Generally, electrical connections, leading considerable currents between large devices in substations and industrial installations, are made from aluminum or copper busbars systems. Such type of connectors are usually air-insulated with straight rigid shapes to minimize power loss transmission.

The construction of busbar systems is typically carried out by putting together several flat rectangular bars, in a parallel arrangement for each phase in order to reduce thermal stresses and improve proximity effect. Such three-phase configuration has been proven to be the best solution to feeding the electricity structure of commercial and industrial buildings.

Figure 1 - Example of busbar system used in circuit breaker SIMENS [1]

## Problem description

The aligned arrangement of busbars carrying high current causes their resistance to rise. It is essentially due to both skin and proximity effect between busbars, which directly increases their thermal stresses. Therefore, a numerical modeling of the thermal and mechanical behavior of  a three-phase busbar system is investigated using EMS simulation tool. The AC magnetic module is used coupled to the structural analysis and steady state thermal analysis. The module is used to compute and visualize the temperature and deflection distribution for each phase.
In this analysis, the considered busbar system is made of a three-phases arrangement with a single copper conductor for each phase, separated by an equal isolation distance (D). The isometric and cross sectional view of the model are showed in the figure below.

Figure 2 - a) 3D design of busbar geometry b). Cross section view of the busbar model

The table 1 defines the dimensions of each conductor.

Table 1 - Busbar system dimensions
 Parameter Dimension (mm) Width (W) 10 Length (L) 120 Thickness (T) 1000 Distance of isolation between phases (D) 75
The studied busbar is made of Copper. The corresponding properties are detailed in Table 2.
Table 2 - Material properties
 Part Material Density (Kg/) Magnetic permeability Electrical conductivity (S/m) Thermal conductivity (W/m.K) Specific heat capacity (J/Kg.K) Elastic Modulus (Pa) Poisson ratio Conductor Copper (Cu) 8900 0.99 6 E+07 385 390 110E+9 0.37

## Boundary conditions

1- Electromagnetic input: The inductor coils are defined as solid coils. They support a maximum ampacity current of 1800 A rms under a frequency of 50 Hz for the studied busbar with a cross section dimension (3/8 in x 5 in) according to [2].
2- Thermal input:  A thermal convection is applied on the air body at ambient temperature of 25°C with a heat transfer coefficient set to 6 W/ m²C.
3- Structural boundary conditions: Fixed boundary conditions are applied to the faces corresponding to the Entry/Exit excitation ports.

## Mesh

The whole model is meshed uniformly inside EMS with a fine controlled mesh, as shown in the figure below, for more accurate results.

Figure 3 - The meshed model

## Results

The Multiphysics simulation revealed the results below. Figure 4 shows the current density distribution across each conductor for the phase . It reaches a maximum peak value of 3.83E+06 A/m²  (RMS value 2.7E+06 A/m² ), which confirms the Reference [3] results.
An unbalanced current distribution can clearly be noticed among the three conductors; this is due to the proximity effect and the 120°   dephasing.

(a)

(b)
Figure 4 - a) Cross section view of the current density distribution at  b) Current density animation versus phase.

The attained temperature, generated by the induced current from proximity and skin effects with dephasing, is shown in the figure 5. It achieves an average value of 330K for each conductor of the busbar system.

Figure 5 - Temperature distribution in the 3-phase busbar system a)- whole model b)-cross sectional view.

A comparison between EMS and Reference [3] results, regarding the busbar losses, shows a good coincidence for each single conductor.

Table 3 - Comparative table between EMS and Reference results:
 Conductor A B C Reference [3] losses results (W) 51.58 51.22 51.24 EMS losses results (W) 51.55 51.2 51.29

The mechanical displacement of the busbar conductors generated by thermal stress, is also evaluated under AC regime. It reaches maximum values within the lateral faces of the busbar conductors. The figure below shows the resultant displacement plot across the busbar system.

(b)
Figure 6 - a)-Displacement resultant plot b)- Displacement animation

## Conclusion

The numerical model of three-phase busbar system, using EMS software, allowed to investigate its thermal and mechanical behavior in steady-state regime. Such type of multiphysics numerical simulation is a crucial step for the dimensioning phase; which allows the prediction of critical thermal stresses location that occurs across busbars.

During the above carried out simulation, Joule and Eddy losses were computed using the frequency domain module of EMS and transferred to the thermal solver where the resultant temperature is predicted. Thermal results were also fed to the structural solver where the thermal stress is calculated.

## Reference

[1]. http://www.directindustry.com/prod/siemens-low-voltage-products/product-25580-1704961.html
[2]. https://www.copper.org/applications/electrical/busbar/bus_table1.html
[3]- Popa, Ioan C., and Alin-Iulian Dolan. "Numerical modeling of three-phase busbar systems: Calculation of the thermal field and electrodynamic forces." Applied and Theoretical Electricity (ICATE), 2016 International Conference on. IEEE, 2016.