# Busbars Modelling

In the vehicle model, the power needed (Pt) to propel the vehicle with a mass mv, at a vehicle speed V, and up a slope of angle θ is calculated from the sum of force (Ft) that is used to overcome the vehicle aerodynamic drag (Fa), rolling resistance (Fr), the component of vehicle’s weight over a slope (Fg), and vehicle acceleration (Facc). The calculations of Fa, Fr, Fg, Facc, Ft and then Pt are given by equations adapted from.

Vehicle specifications used in the present study is based on a series hybrid electric sports car, designed and built by the Association des Entreprises du Pole de la Performance Nevers Magny-Cours (PPNMC). This hybrid sports car is equipped with an electric motor of 90 kW nominal output power, a small 3-cylinder 1 litre ICE engine, and three lithium-ion batteries (144 cells) with a total capacity of 20 kWh. This small innovative hybrid sports car is capable to reach the maximum top speeds of 200 km/h

The electrical part of the battery model is based on the model proposed Erdinc et Al. The battery output voltage can be calculated using equation

Vbat = Voc(SOC) – Ibat·R

Where Voc(SOC) is the battery open-circuit voltage in the function of SOC and Ibat is the battery current. Battery open circuit voltage is calculated using an equation as a function of battery SOC. SOC is depending on the battery initial SOC condition (SOCinitial), current (Ibat) and battery capacity (C). With Cinitial is the initial battery capacity, so SOC can be expressed as:

SOC = SOCinit – ʃ(Ibat/Cusable) dt

The battery current can be calculated from the terminal power. P [Watt] is the power required to move the vehicle as explained in the vehicle model’s section.

Ibat = Pt /Vbat

Usable battery capacity, Cusable [Ah] is depending on the initial capacity, Cinitial and the capacity correction factor, CCF that takes into consideration the capacity fading effect which integrates the calendar life losses and cycles life losses.

Battery heat generation can be modelled from power lost due to internal resistance and electrochemical reaction. However, in this project, the effect of electrochemical reaction will be neglected, because of its complexity and it is less important than internal resistance power losses. The power losses due to internal resistance are:

Plosses = I2 ·R

While the energy generated from these power losses, Q is:

Q = ʃPlosses·dt

This energy is transferred into heat energy which can be expressed as:

Q = m·Cp·ΔT

Where ΔT is the temperature change in the battery, m is the mass of the battery cell and Cp specific heat capacity

As for the heat generation during charging, the modelled is based on the battery heat loss during discharge as proposed by Eddaheck et al. Eddaheck et al. present the experimental result of the difference of the heat generated during charge and discharge at several current rates (Crate). It shows that the heat generation during charge is less than during discharge, but the heat generation during charging becomes more significant as the current rates increase. Equations are used to link the power losses during charge and discharge through different Crate using the percentage of power losses %Plosses

a·Crate + b = %Plosses

With, a and b is a constant, Plosses(disc) is the power losses during discharge, and the Plosses(chrg) is the power losses during charge.

The generated heat is transferred to the surrounding through forced convection process. The amount of transferred heat can be calculated by:

Qt = A.h (Tbatt – T)

With, Qt is heat transferred to the surrounding, A is the battery surface area, h is the convective heat transfer coefficient, Tbatt is the battery temperature, and T is the surrounding temperature. The amount of transferred heat depends on the cooling air temperature and velocity. A constant cooling air temperature and velocity are used in the modelling.

### Bus Bar Design :

Before designing the busbar, it was necessary to decide how the connections needed to be made. It was decided to use bolted connections rather than welding for ease of assembly and maintenance. For a bolted connection, it was decided to bend the cell tabs to overlap on each other and be clamped together by busbars. The tabs would be overlapped and clamped between two metal plates by bolting the plates together besides the cell tabs. It was decided to avoid drilling the cell tabs to avoid damaging the cell tabs.

Material Selection: To achieve a long and reliable service life at the lowest cost, the conductor material needed to exhibit the following properties:

• Low electrical and thermal resistance
• High mechanical strength in tension, compression and shear
• High resistance to fatigue failure
• The low electrical resistance of surface films
• High resistance to corrosion

As seen from the table, the electrical conductivity of copper is higher than aluminium, so an equivalent resistant conductor for aluminium would have a cross-sectional area greater than copper. However, the greater hardness of aluminium gives it more resistance to mechanical damage during its range of service. Even though the thermal conductivity of copper is higher than aluminium, the convective heat transfer of aluminium is better than copper, that is, heat dissipation of aluminium is better than copper. Also, the weight of aluminium is nearly three times less than copper.

To keep the specific resistance of the bus bars equal to that of the copper wire, the following calculations can be done. The cross-sectional area of the bus bar should be varied. From the data provided in the data, we can calculate the area of the bus bars for a copper wire diameter of 25mm2

A = Area of cross-section

ρcopper  = 0.0171 Ohm · mm²/m

ρaluminium =  0.0238 Ohm · mm²/m

Hence for Acopper  = 50 mm2

AAluminium  =  70mm2

Hence we chose a bus bar of the cross-section area of 4.3 mm x 8mm.

As most of the current would directly flow through the direct contact of the cell tabs (as cells tabs are made of nickel-plated copper) due to overlapping of cell tabs, and the need for better heat dissipation due to high discharge rates, the material selected for busbars is aluminium. The heat rejected away from the cells was assumed to be mainly due to forced convection from the busbar. So, it is necessary for maximizing the surface area of the busbar so as to allow maximum contact area with the incoming airflow.

The dimensions were restricted due to packaging constraints. Busbars were designed to have high thermal mass as possible and provide a maximum surface area at the same time. Making solid busbars increased weight but it was negligible as compared to making busbar with fins.

Busbar consists of two parts: -upper and lower which were to be bolted together. Bolting the busbar was chosen instead of clamping or bolting the tabs together because tabs were 0.2mm thin and we didn’t want to damage the tabs. The lower busbar was to be made as thin and rigid as possible to provide high thermal resistance on the lower part of the tabs.

Hence analysis was done to make sure that the temperature of a single bus bar doesn’t cross 60 deg Celsius. This was done on Ansys. Eventually, the airflow analysis should be done on any CFD software to simulate the heat flowing through the accumulator.

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