Li-Ion Module
You can download the final simulation file here
Accurate transient battery models have become an indispensable tool for the design of battery-powered systems.
Lithium battery models with thermal effects are an essential part in the workflow for battery management system design. A battery model should capture the nonlinear dependencies associated with charge and temperature for a specific battery chemistry. Parameterization of equivalent circuit models to match real-world battery data can be a complex task. Using data from Voc-SoC measurmeents together with temperature and charge/discharge measurements, it is possible to create fast and accurate battery models.
Those battery models are based on equivalent circuits and are preferred for system-level development and controls applications due to their relative simplicity. Engineers use equivalent circuits to model the thermo-electric behavior of batteries, parameterizing their nonlinear elements with correlation techniques that combine models and experimental measurements via optimization.
In this tutorial we are going to examine the parameters for the Li-Ion module. The internal model is optimised for LiFePO4 cells. You can change the parameters so it will match the specific battery cell you have measured, or you can change the parameters such as the open circuit voltage \(V_{oc}\) and the internal resistance \(R_{total}\), as well as temperature fudge factors to match temperature relations.
The model in this tutorial is a detailed model including the growth of the SEI layer on the graphite anode, causing the internal resistance to rise during charging.
The charge and discharge process is modeled using emperic equations that were fit on Li-Ion battery measurements. Still you can adapt this model by using the fudge factors and by changing the \(V_{oc}=f(SoC)\) relation.
The open circuit voltage \(V_{oc}\) is modeled as function of the State of Charge \(SoC\) as shown below. You can change the value of \(V_{oc}\) by changing the parameters \(V_{oc}^{10\%}, V_{oc}^{40\%}, V_{oc}^{60\%}, V_{oc}^{95\%}\) and \( V_{oc}^{100\%}\). Since the \(V_{oc}=f(SoC)\) relation is very flat between \(40\%\) and \(60\%\), specify the nominal voltage at this parameters. Furthermore it is advised to enter only the \(V_{oc}\) values for a single cell, as the total voltage and \(Ah\) of a module is finally parameterized using the parameters \(N_{Parallel}\) and \(N_{Series}\).
The open circuit voltage \(V_{oc}\) also depends on the charging / discharging current of the cell. Since only one \(V_{oc}\) curve for the nominal charge /discharge current \(1C\) can be entered, the open circuit voltage \(V_{oc}\) for any other charge / discharge current is predicted by the model, based on the physics of Li-Ion material properties.
The open circuit voltage \(V_{oc}\) depends on the temperature of the cell. Since only one \(V_{oc}\) curve for the nominal temperature \(Reference-Temperature\) can be entered, the open circuit voltage \(V_{oc}\) for any other cell temperature is predicted by the model, based on the physics of Li-Ion material properties.
By changing the two Temperature Fudge Factors, you can adapt the \(V_{oc}\) curve to the measured curve. NOTE:Fudge factor 1 and 2 are interchanged!
The effects of Diffusion [Mass Transport] and the influence of the SEI layer [Electric Double Layer] are modeled by two time constants that are internally adapted depending on the State of Charge.
The resulting equivalent circuit of a battery with three distinct internal resistance with fast and slow time constants, and open circuit potential is shown below.
Battery Characterization
The first step in the development of an accurate battery model is to build and parameterize an equivalent circuit that reflects the battery's nonlinear behavior and dependencies on temperature, SOC and current. These dependencies are unique to each battery's chemistry and need to be determined using measurements performed on battery cells of exactly the same type as those for which the controller is being designed. One common application of battery models is to develop algorithms for \(SoC\) estimation. Open-circuit voltage \(V_{oc}\) measurement and current integration (coulomb counting) may give reasonable estimates for \(SoC\). However, to estimate the \(SoC\) in modern battery chemistries that have flat \(V_{oc}=f(SoC)\) discharge curve, you need to use a different approach.
Parameters
The parameters in the Li-Ion module are:
- Ah (battery capacity: ampere-hour)
Default = 1 (maximum charge of the battery) - Fast Time constant
Default = 5 second (The time constant related to the SEI grow of the electric double layer. It is much smaller than slow time constant and mostly in the order of several seconds.) - Lseries
Default = 1uH (series inductance of the battery due to the wiring inside the battery) - Mass
Default = 1e6 kg (the mass of the battery)
Why is the "mass" parameter up to 10^6 kg? Well, the reason is following: The model is mostly used without thermal model. In order to keep the initial temperature constant if no thermal model is added, the size of the thermal capacitor in the thermal model is simply increased, as it has an initial temperature of 25 degrees. Using this large value for the mass, it ensures that the temperature remains constant. If a thermal model is added, the correct mass of the module should be specified. - Nparallel
Default = 1 (number of cells connected in parallel inside the battery module) (Notices that all the parameters in other fields are specified for a single cell.) - Nseries
Default = 1 (number of cells connected in series inside the battery module) (Notices that all the parameters in other fields are specified for a single cell.) - Reference Temperature
Default = 25 °C (These Voc values and Rtotal in this dialogue block are specified in datasheet at this reference temperature.) - Rthermal
Default = 1e-3 K/W (thermal resistance between battery cells and the thermal connection of the battery module) - Rtotal
Default = 125m ohm (total series resistance of this battery module) - SoC(time=0)
Default = 100% (initial state of charge of this battery) (100 stands for a fully loaded battery or any other value between 0 and 100 for a partially discharged battery) - SpecificHeat
Default = 1 J/Kg/K (the self heating of the battery) (a value close to 1 is averagely a default value for many battery materials) - TemperatureFudgeFactor1
Default = 500 (temperature fudge factor for making the Voc table relates to the decrease of state of charge) - TemperatureFudgeFactor2
Default = -5.7 (temperature fudge factor for making the Voc table relates to the decrease of series resistance) - Tslow
Default = 180 seconds (Slow time constant related to the mass transport inside the battery. Mostly in the order of several tens of seconds to minutes.) - Voc10
Default = 2.874 volts (Voc while SoC = 10%) - Voc40
Default = 3.288 (Voc while SoC = 40% for no load current) - Voc60
Default = 3.312 (Voc while SoC = 60% for no load current) - Voc95
Default = 3.372 (Voc while SoC = 95% for no load current) - Voc100
Default = 3.6 (Voc while SoC = 100% for no load current)
Voc
The open circuit voltage \(V_{oc}\) is shown for the discharging over a constant load. Scope1 shows the open circuit voltage \(V_{oc}\) over time, Scope shows the State of Charge \(SoC\) and Scope 3 shows the open circuit voltage \(V_{oc}\) as functon of the State of Charge \(SoC\). Notice that in Scope3, the coordinate X axis is from zero to maximum charge.
Discharging
Discharging the Li-Ion module will show you how the open circuit voltage \(V_{oc}\) decreases over time, depending on the discharging current.
Animation of SoC
If the animation is enabled, you will see the \(SoC\) as an indicator on the Li-Ion module.
Nseries and Nparallel
Using the parameters \(N_{Parallel}\) and \(N_{Series}\), you can create any combination of cells in the Module.
Initial SoC
The initial \(SoC\) can be specified, to model ful or empty modules.
Capacity Ah
The capacity in \(Ah\) can be specified. The value of \(kWh\) is simply calculated as \(kWh=V_{nom} \cdot Ah\)
Temperature dependency
As the LiFePO4 temperature increases, the internal resistance decreases.
Detail of Scope3:
Temperature Fudge Factor 1
Using Temperature Fudge Factor 1 you can change the value of the flat region of the open circuit voltage (V_{oc}\) dependency on temperature.
Detail of Scope3:
Temperature Fudge Factor 2
Using Temperature Fudge Factor 2 you can change the value of the knee of the curve.
Internal series resistance
The nominal open circuit voltage \(V_{nom}\) at \(SoC=60\%\) equals \(3.312\) volt in the following example. At a constant discharge current of \(I_{discharge}=1\) Ampere, the open circuit voltage \(V_{oc}\) is smaller than the nominal open circuit voltage \(V_{nom}\) by \[ V_{oc} = V_{Nom}^{60\%} - I_{discharge} \cdot R_{total} \]
Time response during discharging pulse
When the Li-Ion cell is discharged, it first shows a transient response. There are two time constants (slow and fast) and constant voltage drop. First the open circuit voltage \(V_{oc}\) drops because of the voltage drop over the internal resistance and secondly the time delays due to the SEI layer and Diffusion are visible.
After the voltage drop because of the internal resistance, the time constant for the stored charge at the SEI layer is visible in the decrease of the open circuit voltage \(V_{oc}\). After that the diffusion time constant for the mass transport is visible in the decrease of the open circuit voltage \(V_{oc}\).
The discharge pulse is only for 100seconds. When the discharge current is again zero, the open circuit voltage \(V_{oc}\) first rises with the constant voltage drop over the internal reistance, secondly it rises with the fast time constant because of the SEI layer and third, it rises slowly to the nominal open circuit voltage \(V_{oc}\) with the diffusion timem constant of the mass transport. The simulation shows the difference in open circuit voltage \(V_{oc}\) for different time constants.
Time response during a charging pulse
When a charge pulse is applied, the opposite as with a discharge pulse is occuring, but now the open circuit voltage \(V_{oc}\) first rises and after the charging, the open circuit voltage \(V_{oc}\) falls back to the nominal open circuit voltage \(V_{oc}\). The simulation shows the difference in open circuit voltage \(V_{oc}\) for different time constants.
Temperature dependent discharge transient
In contrary to the dependency of resistance of metals, the internal resistance in a Li-Ion cell changes in the opposite direction. As the LiFePO4 temperature decreases, the internal resistance increases. Therefore cold Li-Ion cells show more losses. In general the temperature of the Li-Ion cell should be kept around \(25\) degrees for efficient operation. If the temperature gets too high, overheating of the internal cell can occur with with fire as a result.
Temperature dependent charge transient
During charging of a cold Li-Ion cell, there are more losses and a higher external chaging voltage is required to charge the cell.
Discharge/Charge cycle
A complete discharge following a complete charge of the Li-Ion module is simulated. One module is at \(25\) degrees above zero and the second module is at 25 degrees below zero. The effect of the temperture on the total capacity is visible as the colder module is discharged faster.
The Charge-Discharge cycle shows clearly that loop for the colder module is larger and shows a larger difference for the open circuit voltage \(V_{oc}\).
