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 and life 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 | No thermal port — 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 RSD, the charge dynamics model, and the series resistance R0.

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.

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.

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.

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.

SIMULINK Model of 10 Batteries connected in series:

Battery (Table-Based):

Description

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

Note
The block can use linear or nearest interpolation and extrapolation for all the table based parameters. For rows and columns, it follows the row-column convention, whereas rows are indexed first and, subsequently, columns.

The plot shows a battery whose performance varies with temperature and state of charge changes, as typically found on a datasheet.

Use this block to parameterize batteries with complex no-load voltage behavior from datasheets or experimental results. For a simpler representation of a battery, see the Battery block.

The Battery (Table-Based) block has four modeling variants, accessible by double click on block and keep EXPOSE SOC MEASUREMENT to YES

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.

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 = TA – TB.

Ports
The block has the following ports:

A
Thermal conserving port associated with the sensor positive probe.

B
Thermal conserving port associated with the sensor negative probe.

T
Physical signal output port for temperature.

Temperature Source:

The Temperature Source block represents an ideal source of thermal energy that is powerful enough to maintain specified temperature at its outlet regardless of the heat flow consumed by the system.

The source generates constant absolute temperature, defined by the Temperature parameter value.

Convective Heat Transfer:

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

Q Heat flow
k Convection heat transfer coefficient
A Surface area
TA,TB Temperatures of the bodies
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.

SOC Estimation through Coulomb counting:

Coulomb counting gives a relative change in SoC and not an absolute SoC. If you measure the current over a given time step you have a measure of the number of Ah that have left or been received by the battery.

where:

• SoC(t) = estimated State of Charge at time, t
• SoC(t-1) = previous State of Charge at time t-1
• I(t) = charging or discharging current at time, t
• Q_n = battery cell capacity
• Δt = time step between t-1 and t

NOW SIMULATING THE SYSTEM WITH TEMPERATURE SOURCE AS 350K AT 0.1 m^2 AREA