Project 2 Thermal modeling of battery pack

BATTERY PACK MODELING WITH TEMPERATURE AND LIFE CYCLE EFFECTS

1.AIM

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

2.Objective

To analyze temperature life cycle parameters 10 cell series battery pack.

• Connect 10 cells series analyze to cyclic charge and discharge source.
• Change ambient temperatures battery pack  compare performances.
• Add  parameters battery and analyse performance each charge/discharge cycles.

3.Simulink Modelling of Battery pack

3.1 Need of Battery Modelling

An accurate driving range of electric vehicle (EV) to avoid range anxiety. Drivers  they travel  vehicle battery recharge management system batteries need replacement. The charge calculation utilize the battery’s full capability. The state of charge (SOC) of a battery or pack a fuel gauge of a conventional vehicle.

3.2 Battery Modelling

The Battery modeling in the MATLAB is explained below available from the library given below.

Battery (Table-Based)

Library:

Simscape / Electrical / Sources

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

• Self-discharge
• Battery fade
• Charge dynamics

The Battery (Table-Based) block has four modeling variants, accessible by right-clicking the block in your block diagram and then selecting the appropriate option from the context menu, under Simscape > Block choices:

• Uninstrumented No thermal port — Basic model does not output battery charge level simulates fixed temperature. This modeling variant is the default.
• Uninstrumented  thermal port — Model exposed thermal port output internal charge level of the battery.
• Instrumented | No thermal port — Model exposed charge output port. This model fixed temperature simulation.
• Instrumented | Show thermal port — Model that lets you output internal charge level of the battery. Both the thermal port and charge output port are exposed.

The instrumented variants an extra physical signal port outputs internal state of charge. Use this functionality change load behavior a function of state of charge, without the complexity of building a charge state estimator.

The thermal port variants expose a thermal port, which represents the battery thermal mass.

The battery equivalent circuit is fundamental battery model self-discharge resistance RSD, charge dynamics model series resistance R0.

3.3 Battery Modeling Procedure followed by MATLAB

Equivalent circuit modeling battery numerical analysis.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  coulomb counting OCV / SOC correlation 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 characteristics of problem analyzed 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 equivalent circuit components depends on SOC inner cell temperature. T is assumed uniform the average temperature inside the cell. This cell temperature  computed by solving heat equation homogeneous body exchanging heat with  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 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)

 short periods of time restrict list above average cell discharge current, discharge time, inner cell temperature.

Hence, cell capacity,

 the cell fully charged at time t=0, the extracted charge, Qe as:

Im = Current in main branch (A)

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

where C_Q is capacity of cell at temperature and discharge current  Consequently SOC definition  conditions under cell is discharged current and temperature SOC has 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 run 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

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

Figure 3: Simscape Equivalent Circuit Model

The resistive circuit elements variable resistors, as shown in Figure 4. modeled based  Ohm’s Law minimum resistance value 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 usingsingle 20-minute Drive Cycle cell voltage accuracy 2%.  inner heat generated cell corresponding thermal build-up predicted cell voltage  SOC  current profile inSimscape utilized as numerical tool for modeling electrochemical systems equivalent circuits combination with parameter estimation functionalities of Simulink Design Optimization.

3.4.1 Modeling Battery Fade

It lithium deposition electrolyte decomposition active material dissolution, phase transition inside insertion electrode materials further passive film formation on the electrode  current collectors can affect different degrees 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 10 cells connected in series. All these cells are connected it transfer heat conduction and convection. The ambient temperature changed to different values analyse  battery pack performance at different temperatures.

Figure 7: Simulink model of 10 cell connected in series for temperature analysis

Figure 8: Cyclic charge/discharge profile

An AC source has been connected to analyse the cyclic charge and discharge performance. The positive cycle will charge the battery and negative cycle will discharge the battery. Peak Amplitude has given 3A so that the charging/ discharging doesn’t go beyond 1C rate.

Figure 9: Terminal voltage of battery pack at different temperatures

For the comparison more specific, simulation ran 3 times changing ambient temperature values 273K (0 degC), 298K (25 degC), 313K (40 degC). These output results stored in workspace in out_T0, out_T1, out_T2 respectively as shown in figure 10.

The terminal voltage of the battery pack has been plotted in figure 9. From the above plot we can see that battery pack voltage will be maximum at 273K (0 degC). As the temperature increases, the battery pack voltage reduces.

The performance of the battery at 273K is such that it is going to peak voltage and lowest voltage. From SOC plot in figure 11, we can see that at zero SOC, terminal voltage falls below the cut off voltage which is not desirable.

Figure 10: Workspace variables

Figure 11: SOC of Cell1 at different ambient temperatures

For comparison purpose SOC cell1 are connected in series, there will be some difference in charging/ discharging of cell.

In figure12, cell 1 temperature plotted at different ambient temperatures. We see 10,000sec, temperatures settling ambient temperature.

Figure 12: Temperature of cell1 at different ambient temperatures

4.2 Life cycle Analysis

Figure 13  Simulink model battery pack for lifecycle analysis  From [2] and [3] terminal voltage and capacity of battery will decrease, internal resistance will increase after specified number of cycles.

Figure 13: Simulink model of battery pack to analyse battery fading

Figure 14: Fade parameters of battery

For the fade data I’ve just given some arbitrary values for the purpose of simulation analysis. In actual case, battery fading happens after 2000-5000 cycles depending upon battery type. But to analyse the performance in simulation, 100 cycles have given.

1. Change in no-load voltage = -2% (This indicates that the no load voltage will reduce 2% after N cycles)
2. Change in terminal resistance = 2% (The terminal resistance will increase by 2%)
3. Change in AH rating = -3% (Ampere hour decrease by 3% after N cycles)
4. Change in first polarization resistance = 3% (First polarization resistance increase by 3%

Figure 15: Making the fade parameters to zero to compare performance

For comparison of analysis, simulation ran 2 times saved the data in ‘out_fade’ and ‘out_nofade’ variables. In first all the cells entered fade parameters  saved the output in out_fade variable in WS. In second simulation, all cells fade parameters made to zero as shown in figure 15 and saved the output in out_nofade variable in WS.

Figure 16: SOC of cell1 comparison plot

In figure 16, we can see that the SOC is a bit higher for battery with fading effect(Blue plot) that without fading plot (Pink plot).

This is due deterioration capacity battery added in fade parameters. As life cycle increases, battery maximum charge and discharge varies as shown in above plot.

Figure 17: Terminal voltage of battery pack by adding fading parameters and removing it

 the terminal voltage battery pack without fading effect the fading parameters set to zero output  simulation saved in WS.

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

5.Conclusion

MATLAB library model parameters life cycle thermal effects parameters. A battery pack 10 cells connected in series also source of charging and discharging cycle.

The thermal effects of battery pack different ambient temperatures for cycling charging/discharging analysed and plotted. The life cycle performance also evaluated individual cells overall battery pack.

6.Future Scope

In this  individual cells connected in series to make battery pack.thermal life cycle performance individual cells are different from battery pack.

In future the battery pack parameters to analyse the performance.

 components contribute temperature increase such as charger, connectors, wire resistances etc. In future, parameters analysing thermal behaviour