Project 2 Thermal modeling of battery pack

Introduction:

      A default MATLAB Simulink Model of Battery Pack Which it Used 10 cell battery pack thermal Modelling.

       A detail design of MATLAB Simulink model for thermal Modelling is given as

Cell 01 to 04 Subsystem:

• Cell subsystem basically consist of a Thermal Model and Lithium cell 1RC block which calculate the temperature and thermal effect for cells and overall calculate for the battery pack.
• The block which are inside the cell subsystem are PS gain block which multiplies the input signal by a constant i.e, y = u*gain. Another block are voltage sensor and Current Voltage Source.
• The voltage sensor block represents an ideal voltage sensor, that is a device that convert voltage measured between any electrical connections into a physical signal proportional to the voltage.
• Current Voltage source represent an ideal voltage source that is powerful enough to maintain the specified voltage at its output regardless of the current passing through it. The output voltage is V=Vs, where Vs is the numerical value presented at the physical signal port.

                                

Thermal Model Subsystem:

The important block which is inside the thermal model subsystem are:

Thermal Reference:

       The Thermal Reference block represents a thermal reference point, that is, a point with an absolute zero temperature, with respect to which all the temperatures in the system are determined.

Controlled Heat Flow Rate:

• The Controlled Heat Flow Rate Source block represents an ideal source of thermal energy that is powerful enough to maintain specified heat flow at its outlet regardless of the temperature difference across the source.
• Connections A and B are thermal conserving ports corresponding to the source inlet and outlet, respectively. Port S is a physical signal port, through which the control signal that drives the source is applied. You can use the entire variety of Simulink signal sources to generate the desired heat flow variation profile. The heat flow through the source is directly proportional to the signal at the control port S.
• The block positive direction is from port A to port B. This means that positive signal at port S generates heat flow in the direction from A to B.

 

Temperature Sensor:

• The Temperature Sensor block represents an ideal temperature sensor, that is, a device that determines the temperature differential measured between two points without drawing any heat.
• Connections A and B are thermal conserving ports that connect to the two points where temperature is being monitored. Port T is a physical signal port that outputs the temperature differential value.
• The block positive direction is from port A to port B. The measured temperature is determined as T = T_A – T_B.

 

Thermal Mass:

        The Thermal Mass block represents a thermal mass, which reflects the ability of a material or a combination of materials to store internal energy. The property is characterized by mass of the material and its specific heat. The thermal mass is described with the following equation:

    where

         The block has one thermal conserving port. The block positive direction is from its port towards the block. This means that the heat flow is positive if it flows into the block.

                                   

Lithium cell 1RC Subsystem:

• The block basically consists of capacitance value at table which depend on an external physical signal inputs SOC and T. It is assumed that the Capacitance value is slowly Varying with time and hence the equation i = c*dv/dt holds.
• Resistance value (R) table which depends an an external Physical signal inputs SOC and T.
• Voltage Value(EM) Which implements the cells main branch Voltage Source, and determines Values for Capacity (c) and state of Charge(SOC) .The defining equation depend on cell temperature T.
• 

Thermal Behaviour and Fault setup:

        Lithium Ion cell one RC- Branch equivalent circuit detail for 10 cells.

            

For cell 01 to 04

• Number of series connected cells are 4
• Initial Temperature is 2991.K
• For cell 05(fault setup). In this cell I have done some changes in Electrical system of cell so that we can see the fault.
• Number of series connected cells are 4
• Initial Temperature is 2991.K
• Capacity(A*hr)= Capacity_LUT*0.95
• Em open-circuit Voltage(volts) = Em_LUT*0.9
• R0 terminal resistance (ohms)=R0_LUT*5
• R1 cell resistance(ohms)= R1_LUT*5
• C1 Capacitance(farads) = C1_LUT*0.95

For cell 06 to 10

• Number of series connected cells are 4
• Initial Temperature is 2991.K
• 

Here the output of one cell is connected with the SOC calculation Whereas other output is connected with AC Current source for cyclic charge/discharge profile.

The peak amplitudes set to 50 A for cyclic charge and discharge . A basic parameter of AC current source is as

AC Current Source : 

     The AC Current Source block represents an ideal current source that maintains sinusoidal current through it, independent of the voltage across its terminals.

The output current is defined by the following equation:

where

The positive direction of the current flow is indicated by the arrow.

Temperature  Source:

The Convective Heat Transfer block represents a heat transfer by convection between two bodies by means of fluid motion. The transfer is governed by the Newton law of cooling and is described with the following equation:

where

Connections A and B are thermal conserving ports associated with the points between which the heat transfer by convection takes place. The block positive direction is from port A to port B. This means that the heat flow is positive if it flows from A to B.

 

Conductive Heat Transfer:

The Conductive Heat Transfer block represents a heat transfer by conduction between two layers of the same material. The transfer is governed by the Fourier law and is described with the following equation:

where

Connections A and B are thermal conserving ports associated with material layers. The block positive direction is from port A to port B. This means that the heat flow is positive if it flows from A to B.

State of Charge Estimation:

The Coulomb Counting Method measures the discharging Current of a battery and integrates the discharging current over time in order to estimate SOC

This Subsystem takes current as input and gives the battery SOC% as output. A current Sensor block is used and connected for SOC estimation.

This circuit estimates the battery SOC% Using Coulomb Counting method. It takes current as the input and gives gives SOC as Output. Initial SOC of the battery is assumed to be 100%

For the study, we have some observation where we getting results for different cell temperature.

Here we have set ambient temperature is to 299.1k or 25c

 

 

Results:

To check the conduction, convection and charge and discharge rate plot we used the simscape results option.

1)For Test-1

Graphs:

a) Cell temperature:

All the three cell having the same temperature at the same temperature at the start which is at 299.1k but in beginning few seconds of simulation cell no 5 oscllates with more the cell 4 and 10 because its design with fault and ranging to higher temperature then cell 4 and 10 after a time period of around 1300 sec both the cells getting are unfollowing the temperature line which was following the same temperature rate, cell no 4 and 10 having approximately 315 sec at the end of the simulation and the cell no 5 achieving the higher temperature of around 328k.

b)Soc: 

The SOC graph following the sinusoidal waveform structure and fluctuating after 297 seconds and this waveform achieving the value of more than 100.06 soc

C) Conduction:

Conduction is basically heat flow rate(Q) and temperature difference with respect to time

For Cell 04-05

Cell no 04-05 and having a high amplitude of waveform (for heat flow and temperature difference) Which are oscillating at a pretty high rate Which is Starting from Zero and dropping into the negative zone at the end of the simulation.

The heat transfer coefficient is -21.32W/(m2k)

Thermal Conductivity -10.66W/m K

For cell 05-06:

For cell no 05-06 both the waveform oscillating at a high rate but in a positive zone which are increasing initially and maintaining a certain range.

The heat Transfer Coefficient is 20.12

Thermal conductivity 10.06

d) Convection:

Convection is the process of heat transfer by the bulk movement of molecules within fluids such as gases and liquids

For cell 01-04:

For cell no 01-04 the oscillation are pretty low and dropping into the negative Zone at the end of the Simulation.The final Values for

The heat transfer coefficient is -71.63 

Thermal conductivity -15.76

For cell 05:

For cell no 5 they are starting from 0 and falling into the negative zone the oscillation having high amplitude because of the faulty cell at the end of the Simulation

The heat transfer coefficient is -13.39

Thermal conductivity -26.92

For cell 06-10:

For cell no 06-10 the falling from zero to the negative zone the oscillation are less at the end of the simulation

The heat transfer coefficient is -82.63

Thermal Conductivity -16.36

e) Charge and Discharge profiles:

In the charge and discharge rate graph the voltage and current oscillating from pretty highly where current is ranging from -50 to 50A and voltage is ranging from 30 to 43 volts

The final value at the end of the Simulation for 

Current = 1.4695e^-13A

Voltage = 36.334 volt

 

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Test case 2:

a) Cell Temperature:

Here the cell no 04 and cell no 10 starting from a temp 310k at start of simulation and cell no 5 from 299.1k with higher oscillation as compared to the other cells because of faulty design at the end of the simulation the cells 04 and 10 having the final temp of nearby 315k and cell no 5 achieving the temp of 328k.

b) SOC:

For cell 04-05:

The heat flow rate plot starts from 20 and falls into the negative zone and the temperature difference plot starts from 10 and falls into the negative zone and oscillate at the end of the simulation the final value fot 

The heat transfer coefficient is -21.32

Thermal Conductivity -10.66

For cell 05-06:

For cell no 05-06 plot initiate from negative zone and at the end settle down in the positive zone where the final values for,

The heat transfer coefficient is 20.12

Thermal Conductivity 10.06

Convection:

For cell no 01-04 the plot remain in the negative zone throughout the simulation with pretty low oscillation with falling nature and the final values at the end of the simulation are

The heat transfer coefficient is -71.63

Thermal Conductivity -15.62

For cell 05

For cell no 5 the initial values are 0 and falling into the negative side with high oscillation because of the fault and the final values are

The heat transfer coefficient is -13.66

Thermal Conductivity -26.28

For cell 06-10

For cell no 06-10 the plot remains on the negative side and falling at the end of the simulation the final values are

The heat transfer coefficient is -82.64

Thermal Conductivity -16.36

e) Charge and Discharge profile:

Charge and discharge rate profile the plot for current is ranging in between -50 to 50A and the voltage 30 to 43 volt and the final values for

I(current) = 1.4695e^-13A

V(volt)=36.33 V

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Test case 3:

a) Cell Temperature:

The initial temperature for cell no 04 is 310k cell no 5 is 320k and cell no 10 is 330k, but after some point cell no 04 and cell no 10 started following the same temperature rate, and cell no 5 starts oscillating with high value because of fault, the final value for cell no 04 and 10 is around 316k and pro cell no 5 is 328k because of its fault design.

b)SOC:

C) Conduction

For cell 04-05

For cell 04-05 the plot starts from the negative side and drops and then again increases and maintains throughout  the simulation negative zone. The final values at the end of the Simulation are

The heat transfer coefficient is -21.32

Thermal Conductivity -10.66

For cell 05-06

For cell no 05-06 both the plot starts from the negative side and then entered into the positive side and the final value at the end of Simulation are

The heat transfer coefficient is 20.97

Thermal Conductivity 10.06

d) Convection:

For cell 01-04

 

For cell no 01-04 the final values at the end of the simulation are

The heat transfer coefficient is -71.64

Thermal Conductivity -15.75

For cell 05

For cell no 5 the final values at the end of the simulation are

The heat transfer coefficient is -13.39

Thermal Conductivity -26.28

For cell 06-10

For cell no 06-10 the final values at the end of the simulation are

The heat transfer coefficient is -83.30

Thermal Conductivity -16.34

e) Charge and Discharge Profile:

Charge and discharge profile rate the plot for current is ranging in between -50 to 50A and the voltage 30 to 43 volt and the final values for

I(current)=1.4695e^-13A

V(Volt) = 36.33 V.

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Test Case:4

a) Cell Temperature:

For cell no 04 the initial temperature is 350k, cell no 10 is 305k and for cell no 5 the temperature is 325k both the temperature of cell no 04 and 10 started following the Same temperature rate after the Time period of 2000 sec and on the other hand, the cell bo 5 is designed for fault oscillates with high temperature the end temperature of cell no 04 and 10 are near about 315k and for cell no 5 having temperature at the end is 328k

b) SOC:

C)Conduction:

For cell 04-05

For cell no 04-05 the final values at the end of the simulation are

The heat transfer coefficient is -21.32

Thermal conductivity -10.66

For cell 05-06:

For cell no 05-06 the final values at the end of the simulation are

The heat transfer coefficient is 20.84

Thermal conductivity 10.06

d)Convection:

For cell 01-04

For cell no 01-04 the final values at the end of the simulation are

The heat transfer coefficient is -72.13

Thermal conductivity -15.62

For cell 05:

For cell no 05 the final values at the end of the simulation are

The heat transfer coefficient is -13.39

Thermal conductivity -26.28

For cell 06-10:

For cell no 06-10  the final values at the end of the simulation are

The heat transfer coefficient is -83.20

Thermal conductivity-16.22

e) Charge and Discharge Profiles:

Charge and Discharge rate profile the plot for current is ranging in between -50 to 50A and the Voltage 30 to 43 volt and the final Values of

I=1.4695e^13A

V = 36.33V

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Test Case 5:

a) Cell Temperature:

For cell no 04 and 10 having the same initial temperature is 310k, and having the same temperature rate throughout the Simulation, Just small difference is cell no 10 is having a high temperature than cell no 4 because the no of cells is different and cell no 5 which is design for fault having an initial temperature of 350k with high Oscillation. Cells no 04 and 10 having temperature value at the end of the simulation around 315k and the cell no 05 having a temperature of 325k at the end of the simulation.

b) SOC:

C) Conduction:

For cell 04-05:

For cell no 04-05 the final values at the end of the simulation are

The heat transfer coefficient is -21.32

Thermal conductivity -10.66

For cell no 05-06 the final values at the end of the simulation are

The heat transfer coefficient is 20.12

Thermal conductivity 10.06

d) Convection:

For cell 01-04:

 

For cell no 01-04 the final values at the end of the simulation are

The heat transfer coefficient is -71.64

Thermal conductivity -15.62

For cell 05:

 

For cell no 5 the values at the end of the Simulation are

The heat transfer coefficient is -13.68

Thermal conductivity -26.28

For cell 06-10

 

For cell 06-10 the values at the end of the simulation are

The heat transfer coefficient is -83.32

Thermal conductivity -16.22

e) Charge and Discharge Profile:

Charge and Discharge rate profile the plot for current is ranging in between -50 to 50A and the Voltage 30 to 43 volt and the final Values of

I=1.4695e^13A

V = 36.33V

CONCLUSIONS:

1. As the difference in temperature we can observe the changes in heat flow rate by conduction and convection
2. There are Slight changes in cyclic charge and discharge as I fixed peak amplitude at 50A.
3. SOC for all the temperature remains the same so there is no difference in SOC graphs
4. Cell no 5 had higher oscillation and we can observe that in every graph because we design that cell for Fault.

 

REFERENCE:

For base model: https://www.mathworks.com/help/physmod/simscape/ug/lithium-ion-battery-pack-with-fault.html