Project 2

AIM:

Using MATLAB/simulink and  the drive cycle from the attached excel sheet, find-

1. The max heat generation of the battery 
2. The SOC of the battery at 2 *104second of the battery operation

Consider the battery resistance is 0.5 mOhm, delta time is 0.1 and entropic factor is 2

1. The max heat generation of the battery 

There are 2 heat sources for the battery heat generation

1. Joules heat 
2. Entropy heat

Heat generated = Joules Heat + Entropy Heat

Joules Heat :

From Ohms law we know that 

V = IR

when a current flowing through a resistance, there is a heat dissipated in the resistor. This heat dissipation is called Joule heating. Joule heating is also known as ohmic heating.

Power,

P = V*I = I*I*R = I^2*R 

Heat,

H = ∫P.dt with the limits of time 0 to t

H = I^2*R*t

Joule heat,

H = I^2*R*t

where. P = Power

          V = Voltage

          I = Current

          R = Resistance

          H = Heat

           t = Time

The heat Generated in the Reisitor is-

• Directly praportion to the square of the current flowing through it
• Directly praportion to the resistance
• Directly praportion to the time for which the current flows through it.

Entropy Heat:

The heat generation due to entropy change inside a battery occurs when electro chemical reactions are performed. The entropy heat is reversible heat resulting from change in open circuit voltage with respect to temperature at two Electrodes.

 Given Data:

Battery Resistance = 0.5mOhm = `0.5*10^-3`

Entropic Factor = 2

Delta Time = 0.1

Heat generated = Joules heat + Entropy heat

Case 1: Resistance = 2mOhm

The maximum current in the drive cycle is -0.896 which happens at 2 minutes(120 seconds) at step time = 1.7

I = -0.896

t = 1.7

R = 2*10^-3

Max Joule Heat = `I^2*R*t`

                =(-0.896^2) * 2*10^-3 * 1.7

Max Joule Heat =2.726mJ

Maximum Heat Generated = Max Joule heat + 2*Max Joule heat

                                            = 2.726mJ + 2*2.726mJ

Maximum Heat Generated = 8.178mJ 

Case 2: Resistance = 0.5mOhm

The maximum current in the drive cycle is -0.896 which happens at 2 minutes(120 seconds) at step time = 1.7

I = -0.896

t = 1.7

R = 0.5*10^-3

Max Joule Heat = `I^2*R*t`

                =(-0.896^2) * 0.5*10^-3 * 1.7

Max Joule Heat = 0.682mJ

Maximum Heat Generated = Max Joule heat + 2*Max Joule heat

                                            = 0.682mJ + 2*0.682mJ

                                           = 2.046mJ

Maximum Heat Generated = 2.046mJ               

b. The SOC of the battery at 2 *104second of the battery operation.

The state of charge (SOC) is a measurement of the amount of energy available in a battery at a specific point in time expressed as a percentage. The SOC provides the user with information of how much longer the battery can perform before it needs to be charged.

The SoC can be measued in different ways. Some of them are listed below

• Voltage Translation Method (VT)
• Coulomb counting method (CC)
• Combination of VT and CC

The VT and CC has its own advantages ad disadvantages so to get accurate value we have to use the Combination of VT and CC.

1. Voltage Translation Method (VT):

It is measued by Open Circut Voltge of the battery and compared it with the Data sheet of the battery and SoC is estimated. It cannot used while the battery is in operation.

2. Coulomb counting method (CC):

Estimating the SOC based on In and Out flow of current in battery pack.

It is calculated by the formula 

SOC = (Total charge input / Max capacity of the battery) * 100 

Total charge input = Charging Current * Time (H)

If the initial SOC is 50% then 

Z(t) = Z(0) - 1/Cn ∫ Ni*i(t) dt    with thw limits of 0 to t

where, Cn = Battery Nominal Capacity

           Z(t) = State of charge

           Z(0) = initial state of charge

           i(t) = Instantansous cell current

            t = time 

            Ni = Coulomb efficiency

            + for discharging 

            - for charging

3. Combination of VT and CC:

The Calibration with Voltage Translation occurs when vehicle is in idle condition during traffic etc, so there is no voltage fluctuation and CC method is used when vehicle is moving.

SIMULINK MODEL:

Blocks Used:

1. Generic Battery:

Implements a generic battery model for most popular battery types. Temperature and aging (due to cycling) effects can be specified for Lithium-Ion battery type.

The Battery Parameters selected are 7.2V 5.4Ah with initial SOC of 50%. Since the Current profile has negative value it means that the battery is charging.

2. Controlled Current Source:

This block Converts the Simulink input signal into an equivalent current source. The generated current is driven by the input signal of the block.

3. Bus Selector:

This block accepts a bus as input which can be created from a Bus Creator, Bus Selector or a block that defines its output using a bus object. The left listbox shows the elements in the input bus. Use the Select button to select the output elements. The right listbox shows the selections. Use the Up, Down, or Remove button to reorder the selections. Check 'Output as virtual bus' to output a single bus.

4. Signal Builder:

The Signal Builder block allows you to create interchangeable groups of piecewise linear signal sources and use them in a model. You can quickly switch the signal groups into and out of a model to facilitate testing. In the Signal Builder window, create signals and define the output waveforms.

Explanation:

• The above signal is given as a input to the battery block. The Excel sheet is loaded into the Signal Builder block and signal builder block ouput is given to the controlled current source.
• The Simulation stop time is 2*104 seconds ie 208Seconds.
• The Signal builder acts as a load to the battery.
• The Battery Block shows the SOC, Voltage and Current through the bus selector block.
• The output is displayed through Scope block. +ve Current represents Battery is Discharging and -ve Current represents battery is Charging.

Results:

• The above graph shows the SOC, Current and Voltage plot of Battery.
• The initial SOC is set as 50% and as current is in -ve directin so battery is charging and SOC is increased to 51% after 208seconds.
• The Voltage is also increasing as the battery is getting charged.

CONCLUSION:

The max heat generated for battery is calculated using the given drive cycle and the Battery SOC at 2*104 seconds is also calculated.