Batteries are currently the most common form of mobile energy storage for low carbon vehicles. Lead acid, along with Nickel and Lithium-based chemistries, are the most common. Early electric vehicles, such as the GM EV1, utilised lead acid batteries, but this chemistry was considered too heavy [102]. Nickel Metal Hydride (NiMH) has been used for production in vehicles such as the Toyota Prius and the Honda Insight [103; 104].
However, it is acknowledged that Lithium-based batteries provide the best power and energy density to weight (compared to the other chemistries), with cell costs declining in recent years [12]. Other battery technologies, such as Nickel-Chloride, Lithium-Air, and REDOX were considered in several publications, but were mostly deemed unfeasible for automotive applications [12; 103; 105]. Therefore, the battery model will be narrowed down to Lithium-based batteries, and this research will be based on this chemistry.
For modelling purposes, the internal resistance of the battery can be approximated as a resistor in series with an Equivalent Electrical Circuit (EEC) model [106]. The advantage of the EEC battery model is that it provides good balance between accuracy, complexity, and runtime performance for automotive simulation applications [107]. The battery model was created based on the work by Tremblay et al. [108]. The schematic representation of a single Li-ion cell within the battery model is shown in Equation (3-19) and consists of the open circuit voltage, UOCV(cell), connected in series with a
single resistor, R0. To calculate the cell terminal voltage, UL(cell), the following equation
is used
𝑈𝐿(𝑐𝑒𝑙𝑙)= 𝑈𝑂𝐶𝑉(𝑐𝑒𝑙𝑙)− 𝐼𝐿𝑅0 (3-19)
where IL is the current flowing through the battery. This relatively simple layout, also
known as the “Rint” battery model [109], was adopted because the higher transient characteristics of the battery (< 1 Hz) was not captured, given the comparatively large sampling rate when measuring the battery data from the Smart ED. This negates the necessity to include capacitive elements (such as those found in the Thevenin and PNGV battery models [109]), and hence reduces the overall simulation time. Figure 26 shows the schematic diagram of the Rint battery model.
Data for parameterisation of the battery model was also obtained from the CAN interface of the Smart ED. The Open Circuit Voltage (OCV) was estimated based on the battery terminal voltage, temperature, and State-of-Charge (SOC). Figure 27 shows the relationship between the OCV, SOC, and temperature.
Figure 26: The “Rint” battery model
Figure 27: The battery OCV map derived from the Smart ED
3.2.1.1 Battery Model Scaling
The battery pack in the Smart ED is rated at 16.5 kWh and contains Panasonic NCR18650 cells [94]. According to the datasheet supplied by Panasonic, each cell has a capacity of 2.9Ah and mass of approximately 45g [110]. Each parallel string of cells has a capacity of approximately 1kWh. Therefore, a battery pack rated at 20kWh, for example, contains approximately 20 strings in parallel. It is estimated that each string contains 94 cells in series, after dividing the measured battery pack voltage from the Smart ED with the published cell voltage from Panasonic.
During simulation runtime, the SOC is quantified using the generic method of coulomb counting, in which SOCinit defines the initial condition of the battery SOC and Qb the
capacity of the battery expressed in Ah:
𝑆𝑂𝐶(𝑡) =𝑆𝑂𝐶𝑖𝑛𝑖𝑡∙ 𝑄𝑏∙ 3600 − ∫ 𝐼𝑏∙ 𝑑𝑡 𝑡 0 𝑄𝑏∙ 3600
(3-20)
where Ib is the current flowing through the battery pack.
Figure 28 shows an example of the arrangement of cells in series and in parallel within a battery pack. In this example, there are two cells in series and three strings of cells in parallel. Referring to this example, and continuing on from Equation (3-19), the sum of the electrical currents in each string is shown in Equation (3-21), where I1, I2, and I3 are
the electrical currents passing through each string respectively.
Figure 28: Example of cell arrangements in a battery pack
𝐼𝐿 = 𝐼1+ 𝐼2+ 𝐼3 (3-21)
The electrical current passing through each string of cells (two per string in this example) can then be calculated as shown in (3-22), where Ustring is the potential
difference for each string of cells. 𝐼1,2,3=
𝑈𝑠𝑡𝑟𝑖𝑛𝑔 2𝑅0
(3-22)
Expanding further to three strings in parallel, the following equation applies: 𝐼𝐿 = 3 (𝑈𝑠𝑡𝑟𝑖𝑛𝑔
2𝑅0 )
(3-23)
Given that Rb, the total internal resistance of the battery, is based on the following,
𝑅𝑏= 𝑈𝑠𝑡𝑟𝑖𝑛𝑔 𝐼𝐿
(3-24)
𝑅𝑏 = 𝑅0
2 ∙ 𝑈𝑠𝑡𝑟𝑖𝑛𝑔 3 ∙ 𝑈𝑠𝑡𝑟𝑖𝑛𝑔
(3-25)
Replacing “2” and “3” with ns (number of cells in series) and np (number of strings in
parallel) respectively the following generalised equation is obtained: 𝑅𝑏 = 𝑅0∙
𝑛𝑠 𝑛𝑝
(3-26)
Equations (3-26) to (3-28) present how the battery is scaled by altering the number of parallel strings, np. This set of equations is executed to create the OCV map. The
number of cells in series, ns, is fixed during simulation to maintain the bus voltage. In
these equations, Rb is the battery internal resistance, UOCV(batt) is the battery OCV, and
Qcell is the capacity of each cell.
𝑈𝑂𝐶𝑉(𝑏𝑎𝑡𝑡) = 𝑈𝑂𝐶𝑉(𝑐𝑒𝑙𝑙)∙ 𝑛𝑠 (3-27)
𝑄𝑏 = 𝑄𝑐𝑒𝑙𝑙 ∙ 𝑛𝑝 (3-28)
The value of Rb will be discussed in Section 3.2.1.2. The cells within the battery pack
are assumed to be homogeneous in operation, which allowed for scaling the battery pack size by changing the number of parallel strings. In reality, temperature gradient and disproportionate aging may affect the performance of individual cells [111].
3.2.1.2 Battery Model Verification
The value of the battery pack internal resistance, Rb, was estimated so that it performed
as close as possible to the recorded SOC trajectory from the vehicle, during a charge- depleting cycle. This is similar to the approach shown by Rodrigues et al., for measuring impedance of a Li-ion battery [112]. Using an optimisation routine, the value of Rb was identified, such that the SOC trajectory of the battery model and the measured
data was as close as possible. A comparison of the measured SOC and the estimated SOC (from the battery model) is shown in Figure 29.
Figure 29: Comparison of measured and estimated battery SOC
Based on this optimisation routine, the value for Rb was identified to be 0.43 ohms. The
author acknowledges that variations in the resistance under charge and discharge conditions, as well as in different thermal operating conditions, were inherently averaged using this approach. Furthermore, any additional resistances from the battery contactors have also been lumped using this approach. However, without a controlled test environment on a battery test rig, it was difficult to extract the specific resistance values. Future work could investigate on improving this area.