Project 2 Thermal modeling of battery pack
BATTERY PACK MODELING WITH TEMPERATURE AND LIFE CYCLE EFFECTS
1.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.
2.Objective
To analyze temperature andlife cycle parameters of the 10 cell series battery pack.
• Connect 10 cells in series analyze the response to a cyclic charge and discharge source.
• Change the ambient temperatures of the battery pack and compare the performances.
• Add the fading parameters of the battery and analyse the performance after each
charge/discharge cycles.
3.Simulink Modelling of Battery pack
3.1 Need of 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 state of charge (SOC) of a battery or pack
of batteries is analogous to a fuel gauge of a conventional vehicle.
3.2 Battery Modelling
The Battery modeling procedure followed in the MATLAB is explained below. The MATLAB
model is available from the library given below.
Battery (Table-Based)
Library:
Simscape / Electrical / Sources
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
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 that does not output battery charge level
and simulates at a fixed temperature. This modeling variant is the default.
• Uninstrumented | Show thermal port - Model with exposed thermal port. This model does
not output internal charge level of the battery.
• Instrumented I No thermal port I Model with exposed charge output port. This model uses
a fixed temperature throughout the simulation.
• Instrumented | Show thermal port - Model that lets you output internal charge level of the
battery. Both the thermal port and the charge output port are exposed.
The instrumented variants have an extra physical signal port that outputs the internal state
of charge. Use this functionality to change load behavior as 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 made up of the fundamental battery model, the self-
discharge resistance SD, the charge dynamics model, and the series resistance RO.
3.3 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.
dT
Cr at
-
T-Ta + P.
RT
Where Cr = heat capacitance (J m-3 K-1)
T = Inner cell temperature (°C)
Ta = ambient temperature (°C)
RT = convection resistance (WI m-2 K-1)
PS = power dissipated inside the cell (W)
Taking Laplace transform we get,
P,R, + Ta
T(s).
=
1+ R,C-s
• Cell capacity and state of charge
The cell capacity (extradiable 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 averade cell discharge current,discharge time,and inner cell temperature
Hence, cell capacity,
CO = Co (I, D)
Assuming the cell to be fully charged at time t=0, the extracted charge, Qe is defined as:
A
Im = Current in main branch (A)
Then, the state-of-charge (SOC) is:
SOC = 1 - 0 / Co
where Co 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:
RO= RO(SOC,T)
RI=RI(SOC,T)
CI=CI(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 CM 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 IC-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.
Vorade = Vo (1+ (dVo * n / 100*N))
Where,
N is the reference number of discharge cycles over which we specify percent change of
various battery parameters.
dVo is the change in no load voltage after N discharge cycles
• Battery Capacity change
Qnom,fade = Qnom (1+ dAH* sqrt(n/N)/100)
Where, Qnom is the rating of the battery
dAH is the change in AH rating after N cycles
• Change in Resistance
Rifade = R; (1+ (dpi * sart (n/N)/100))
Where, R is the series resistance of the battery
dRi 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
The other parameters like No-load voltage(Em_LUT), Terminal resistance (RO_LUT), First
polarization resistance (RI_ 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.
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 IC rate.
For the comparison to be more specific, simulation ran 3 times by changing the ambient
temperature values 273k (0 degc), 298k (25 degc), 313k (40 degC). These output results
stored in workspace in out _TO, out_TI, 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 11: SOC of Cell at different ambient temperatures
For comparison purpose only SOC of celll has considered. Since the cells are connected in
series, there will be some difference in charging/ discharging of each cell.
In figure12, cell 1 temperature plotted at different ambient temperatures. We can see that
after 10,000sec, the temperatures are settling to ambient temperature.
Figure 12: Temperature of cell at different ambient temperatures
4.2 Life cycle Analysis
Figure 13 shows the Simulink model of battery pack for lifecycle analysis is shown below.
From [2 and [3, we know that the terminal voltage and capacity of the battery will
decrease and internal resistance will increase after specified number of cycles.
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%
For comparison of analysis, simulation ran 2 times and saved the data in 'out_fade' and
'out_ nofade' variables. In first simulation, all the cells are entered with fade parameters as
shown in figure 14 and saved the output in out_fade variable in WS. In second simulation,all the cells fade parameters made to zero as shown in figure 15 and saved the output in out nofade variable in WS
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 to the deterioration of capacity of the battery we added in fade parameters. As
the life cycle increases, battery maximum charge and maximum discharge varies as
shown in the above plot.
Figure 17: Terminal voltage of battery pack by adding fading parameters and removing it
To obtain the terminal voltage of battery pack without fading effect, all the fading
parameters set to zero and the output of simulation was saved in WS.
In figure 17, 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.
5.Conclusion
MATLAB library model parameters were evaluated for its life cycle and thermal effects
parameters. A battery pack with 10 cells connected in series also made with a source of
charging and discharging cycle.
The thermal effects of battery pack at different ambient temperatures for cycling
charging/ discharging has been analysed and plotted. The life cycle performance also
evaluated for individual cells and overall battery pack.
6.Future Scope
In this model, individupil cells were connected in series to make the battery pack. The
thermal and life cycle performance of individual cells are different from battery pack.
In future we can consider the battery pack parameters to analyse the performance.
Also there are different associated components that contribute the temperature increase
such as charger, connectors, wire resistances etc. In future, all these parameters have to be
considered while analysing thermal behaviour.
7.References
1. 'High Fidelity Electrical Model with Thermal Dependence for Characterization and
Simulation of High Power Lithium Battery Cells', Tarn Huria, Massimo Ceraolo, Javier
Gazzarri, Robyn Jackey
2. 'Mathematical modeling of the capacity fade of Li-ion cells', P. Ramadass, Bala Haran,
Ralph White, Branko N. Popov
3. Capacity fade study of lithium-ion batteries cycled at high discharge rates, Gang Ning,
Bala Haran, Branko N. Popov
4. MATLAB help-› Battery (Table-based)
5. https://www.mathworks.com/help/physmod/simscape/ug/lithium-ion-battery-pack-
with-fault.html
Attachments
1.simulink model file of battery pack
2.workspace file with variable declaration