Project 2 Thermal modeling of battery pack

For a 10 cell series lithium ion battery model, simulate the thermal effects and compare life cycle performance at various temperatures, charge & discharge rates using MATLAB.

AIM

To simulate the thermal effects and compare life cycle performance at various temperatures, charge & discharge rates for a 10 cell series lithium ion battery model, using MATLAB.

theory-

now a days lithium ion battery are mostly used in electric vehicles we must know its charge and discharge rates to operate this batterys in efficient manner and with out damage when this batterys in operation this temperature of it must be kept in limit we simulate the thermal effect of this cell , by knowing the how much temp rise take place we can provide efficient cooling to the batterys so that the life cycle of the battery increases we will see a model on this issue below and explaination as follows

cells connected in series and one of the cell is faulty so what will be thermal effect . This example shows how to simulate a battery pack consisting of multiple series-connected cells in an efficient manner. It also shows how a fault can be introduced into one of the cells to see the impact on battery performance and cell temperatures. For efficiency, identical series-connected cells are not just simply modeled by connecting cell models in series. Instead a single cell is used, and the terminal voltage scaled up by the number of cells. The fault is represented by changing the parameters for the Cell 10 Fault subsystem, reducing both capacity and open-circuit voltage, and increasing the resistance values.

circuit construction and working -

in this ckt we use li-ion cell 1 to 10 , temperature sensors ,ambient temp block , state of charge estimation scope, charge discharge profile given to ckt ,from & goto block block matlab simulink

Cell 01 to O4 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.

This block basically consists of capacitance value © table which depends 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 on an external physical signal inputs SOC and T.

Voltage value (EM) which implements the cell's main branch voltage source, and determines values for capacity (C) and state of charge (SOC). The
defining equations depend on cell temperature, T.

output of one cell is connected with the SOC estimation 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

other block which are used in lithium ion battery pack are as:

Temperature Source:

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.

This block represents an ideal energy source in a thermal network that can maintain a constant absolute temperature at the port regardless of the heat flow rate.
This block is used for ambient temperature which we can set and check results .

Battery Modelling

An accurate forecast of the remaining driving range of an electric vehicle (EV) is crucial to avoid range anxiety. Drivers need to know how much further they would travel before their vehicle batteries require a recharge. In addition, the battery management system should predict when batteries need replacement. The remaining charge calculation must be precise to utilize the battery’s full capability

The Battery (Table-Based) block represents a high-fidelity battery model. The block calculates no-load voltage as a function of charge level and optional temperature using lookup tables and includes several modeling options:

• Self-discharge
• Battery fade
• Charge dynamics
  
  

Battery Modeling Procedure followed by MATLAB

Equivalent circuit modeling is the most common approach for battery numerical analysis. For lithium cells, a one or two RC block model with no parasitic branch is a common choice. It has the advantage of being computationally simple and is easily combined with other methods such as coulomb counting with an OCV / SOC correlation for periodic recalibration during rest.

Figure 1: A general equivalent circuit model of an electrochemical cell.

The number of equivalent circuit elements results in a trade-off between fidelity and complexity. The parasitic branch can be neglected for cells with high columbic efficiencies.

Depending on the characteristics of the problem to be analyzed, the number of RC blocks typically ranges from one to two, since larger numbers increase computational effort without significantly improving model accuracy.

Figure 2: Equivalent circuit of the cell used in this model

• Thermal modeling

The value of the equivalent circuit components depends on SOC and inner cell temperature. The inner cell temperature is assumed to be uniform, and taken as the average temperature inside the cell. This cell temperature can be computed by solving the heat equation of a homogeneous body exchanging heat with the environment.

Where C_T = heat capacitance (J m-3 K-1)

T = Inner cell temperature (ºC)

Ta = ambient temperature (ºC)

R_T = convection resistance (W1 m-2 K-1)

Ps = power dissipated inside the cell (W)

Taking Laplace transform we get,

• Cell capacity and state of charge

The cell capacity (extractable charge) depends upon a number of factors, including:

1. average cell discharge current and discharge time
2. Inner cell temperature
3. Value of the end-of-discharge voltage
4. Storage time (self-discharge)
5. Number of charge-discharge cycles that the cell has undergone (aging)

For short periods of time we can restrict the list above to average cell discharge current, discharge time, and inner cell temperature.

Hence, cell capacity,

Assuming the cell to be fully charged at time t=0, the extracted charge, Qe is defined as:

Im = Current in main branch (A)

Then, the state-of-charge (SOC) is:

where C_Q is the capacity of the cell at the temperature and discharge current considered. Consequently, any SOC definition should consider the conditions under which a cell is discharged and refer to the particular discharge current and temperature under which the SOC has been evaluated.

• Equivalent circuit model parameters

Each element of the equivalent circuit of Figure 2 is a function of SOC and temperature. Specifically:

R0= R0(SOC,T)

R1=R1(SOC,T)

C1=C1(SOC,T)

Em= Em(SOC,T)

The parameter estimation routine was run for a range of discharge experiments at different temperatures. The results provide two-dimensional look-up tables each of these four equivalent circuit elements.

3.4 MODELING AND SIMULATION

The numerical analysis proposed here consisted of a parameter estimation / validation stage, and a simulation stage. During parameter estimation, a discharge profile was iteratively simulated and its results compared with experimental data. The ECM was created using SimscapeTM blocks and SimscapeTM language. The drawing shown in Figure 4 represented the circuit diagram with a single RC block. Each of the circuit elements was a subsystem consisting of custom electrical blocks, and blocks to calculate the properties of the circuit element.

Figure 3: Simscape Equivalent Circuit Model

The resistive circuit elements were modeled as variable resistors, as shown in Figure 4. These were modeled based on Ohm’s Law, though a minimum resistance value was used to prevent the differential equation solver from entering a bad state during parameter estimation or simulation. The real power of the resistive elements was also calculated for later use in simulation of thermal dynamics. The value of the resistance was provided by a lookup table with one or two inputs of SOC and temperature.

Figure 4: Resistive Circuit Element and Simscape Language

The model was validated using a single 20-minute New European Drive Cycle, which showed cell voltage accuracy within 2%. The model accounts for the inner heat generated in the cell and the corresponding thermal build-up; and predicted the cell voltage and SOC for an arbitrary current profile. The procedure also illustrates a way in which Simscape may be utilized as a numerical tool for modeling electrochemical systems using equivalent circuits, in combination with the parameter estimation functionalities of Simulink Design Optimization.

3.4.1 Modeling Battery Fade

It is generally thought that lithium deposition, electrolyte decomposition, active material dissolution, phase transition inside the insertion electrode materials, and further passive film formation on the electrode and current collectors can affect up to different degrees the capacity fade of lithium-ion batteries. Quantifying these degradation processes will not only help to improve the predictive capability of battery models but also help to elucidate the mechanism of capacity fade.

Three major causes of capacity fade including the loss of secondary material, the loss of primary material and the difference of rate capability were quantified. In each case the loss of the secondary material dominated the capacity fade of the whole cell. However, unlike the 1C-discharge-ratecycled battery, the limiting secondary material the in 3Cdischarge- rate-cycled cell was carbon. The capacity loss due to the carbon electrode material alone was 10.6% compared with the 16.9% capacity fade of the whole cell. Such a fast capacity fade for the carbon material is correlated with the increase of the internal resistance. Fitting impedance spectra for the carbon half-cell quantitatively showed that the resistance of the surface film and the resistance of the bulk carbon material increase faster for high-rate-discharged cells than for normal-rate-discharged cells.

The battery fade is modeled in MATLAB as follows.

• No load voltage change

The no load voltage across fundamental battery is modeled using the equation below.

V_0,fade = V₀ ( 1+ (dV₀ * n / 100*N))

Where,

N is the reference number of discharge cycles over which we specify percent change of various battery parameters.

dV₀ is the change in no load voltage after N discharge cycles.

• Battery Capacity change

Q_nom,fade = Q_nom (1+ d_AH* sqrt(n/N)/100)

Where, Q_nom is the rating of the battery

d_AH is the change in AH rating after N cycles

• Change in Resistance

R_i,fade = R_i (1+ (d_Ri * sqrt (n/N)/100))

Where, R_i is the series resistance of the battery

d_Ri is the change in series resistance after N cycles

3.5 Selection of values for Battery pack

All the cell parameters depend upon Temperature and SOC and the values of them are given below.

Temperature_LUT(1*3) = [278.15 293.15 313.15]

SOC_LUT(7*1) = 0

0.1

0.25

0.50

0.75

0.90

1

The other parameters like No-load voltage(Em_LUT), Terminal resistance (R0_LUT), First polarization resistance (R1_LUT), and time constant(TC) are extracted from MATLAB example[5].

Figure 5: Main battery parameters

Since battery model is table based with temperature dependent, all the values have entered depending upon temperature and SOC.

Figure 6: Dynamics of battery

For simplicity of analysis, only one time constant has considered.

4. Output Analysis

4.1 Temperature Analysis

The battery performance parameters like Voltage, SOC has to be analysed at different temperatures.

Figure 7 shows the battery pack model with 10 cells connected in series. All these cells are connected such that it can transfer heat by conduction and convection. The ambient temperature can be changed to different values to analyse the battery pack performance at different temperatures.

Convective Heat Transfer:

This block models heat transfer in a thermal network by convection due to fluid motion. The rate of heat transfer is proportional to the temperature difference, heat transfer coefficient, and surface area in contact with the fluid.

this used for 1-4 cells and 6-10 cell

• from and goto blocks

The Goto block passes its input to its corresponding From blocks. The input can be a real- or complex-valued signal or vector of any data type. From and Goto blocks allow you to pass a signal from one block to another without actually connecting them.

The From block accepts a signal from a corresponding Goto block, then passes it as output. The data type of the output is the same as that of the input from the Goto block. From and Goto blocks allow you to pass a signal from one block to another without actually connecting them.

• 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 ckt estimates the battery SOC % using coulomb counting method. It takes current as the input and gives SOC% as output. Initial SOC of the battery is assumed to be 100% (1)

example shows how to simulate a battery pack consisting of multiple series-connected cells in an efficient manner. It also shows how a fault can be introduced into one of the cells to see the impact on battery performance and cell temperatures

Results

1) results at 300 k ie 26.85°C

2)results at 310 k ie 36.85°C

3 )results at 324 k ie 50.85°C

1-4 cells are normal cell 5 th cell is faulty 6-10 cell is normal cell as we are simulating thermal effect on we give Cyclic Charge/ Discharge Profile to circuit the waveform you can see above results all conditions it is same but when ckt is run on this drive cycle profile as 5th cell was faulty it will show temperature rise high than any other cell and the life cycle of cell get reduced and cell even can get damage

so as we give temp of results at 300 k ie 26.85°C the 1-4 and 6-10 cell temp is near to 316k

but 5th faulty cell temp goes to 330k ie 56.85°C and the drive cycle is shown which is Cyclic Charge/ Discharge drive cycle

In condition two we give temp 310 k ie 36.85°C and 1-4 and 6-10 cell temp is near to 326 k but 5th faulty cell temp goes to 340k ie 66.85°C and the drive cycle is shown which is Cyclic Charge/ Discharge drive cycle

In condition two we give temp 324 k ie 50.85°C and 1-4 and 6-10 cell temp is near to 340 k but 5th faulty cell temp goes to 354k ie 80.85°C and the drive cycle is shown which is Cyclic Charge/ Discharge drive cycle

terminal voltage of the battery pack decreases as the cycles proceed. This is because of the fading effect. For battery without fading effect, terminal voltage remains the same.

conclusion

Hence, the thermal effects and comparison of life cycle performance at various temperatures, charge & discharge rates using MATLAB have been simulated and graphs are also plotted.