EVS 24 Stavanger , Norway , May 13-16 , 2009 Internal resistance of cells of lithium battery modules with FreedomCAR model

Internal resistance is usually calculated by EIS (Electrochemical Impedance Spectroscopy) method, which gives unrealistic low internal resistance values. In this paper internal resistance will be calculated from the voltage drop with FreedomCAR method where the validation of the results is much better (99%) than EIS method[1][12]. Batteries are often tested per cell. But in most cases more than one single cell is needed for an application and the characteristics of a module of cells is not the same. In other cases the whole module is examined as one big cell, without looking on the individual cells. But the weakest cell affects the performance of the whole module. This research goes deeper than the module approach on batteries: the behavior of individual cells is examined while they are working together in a module. The battery model consists in most researches of an ideal voltage source and a simple internal resistance[2]. In this work the advanced FreedomCAR battery model, created by Idaho National Laboratories (USA), is used: the cell is represented by an ideal voltage source with two internal resistances and two capacitors. Usually batteries are tested with very low constant currents (till 5% of the nominal current value) to show a high capacity value to the customer, while the customer needs the characteristics of the battery in real conditions. Here the parameters are calculated by testing the battery packets in high pulse conditions. The matching between the predicted and the measured voltage is proportional with the quality of the model. This was 99% (+-0.9%) in the tests. This means that the model is very close to the reality. Three types of Lithium-ion battery packets with 6-7 cells were tested.

1 Introduction The evolution of the cell parameters are determined as a function of the number of cycles and as a function of SOC.The parameters are calculated at the package level and at the cell level.Three types of lithium batteries are listed in Table 1.Six (seven for type 2) cells are placed in series.

Battery model
The FreedomCAR linear battery model is shown on Fig. 1.A high pulsing current I L (Fig. 2), has to be loaded according to this model [3][4][5].Considering the model on Fig. 1, one can write: After discretisation of equation ( 1), the next simplified equation can be written: ( In (1): -V L , I L and t are measured -I p comes from (4) -OCV, OCV', R o and Rp are calculated by linear regression method Discretising and solving the differential equation ( 2), with the starting condition I p (t=0) = 0, gives for every sample i: is chosen or calibrated in the model so that the fitting between the measured and estimated voltage (Fig. 3) would be optimal.The difference between the measured and the estimated voltage V L in [%] (Fig. 3) is proportional with the quality of the model.This is around 99% in the tests.

Internal Resistance
There are 205 FreedomCar tests (Fig. 2) done on the three battery types, which corresponds to 685Ah.The temperature is kept constant at approximately 25 °C by a fan and is also measured.As mentioned in chapter 2 the voltages of the cells will be measured as well as the current and the temperature of one cell.This data is filled in in a spreadsheet, where OCV', R p , R o and OCV will be calculated.is calibrated so that the matching between the measurements and model would be optimal.
The result is shown on Table 2

Influence of SOC
The table shows that when the SOC decreases from 100 to 15% the total internal resistance R i (=R p +R o ) increases with 50-100%, especially due to R p .R p has a more dynamic character in comparison with R o which stays nearly constant.

Comparison with the datasheets
The calculated resistance is 50-100% higher than the value measured by the producer.Type 3 has the lowest internal resistance and the value provided from the producer is much closer to the one which is calculated by FreedomCar model.

Imbalance between the cells
Type 3 has the lowest internal resistance imbalance between the cells.At full SOC the variation of R i between the cells was 0,7m .For type 1 and 2 it was 13 and 10m .That means a battery management system (to balance cells) is less needed in case of type 3 than in case of type 1 or 2, which is an advantage of type 3.

Cell versus pack
Consider a pack which is capable to deliver 10Ah at 24V with only one type of cell by placing the right number of cells in parallel and/or in series, then the three types can be compared at package level (Table 3).The combination manner is written at the top of the columns.E.g. for type 1 8 cells are placed in series and form a group; there are 4 such groups placed in parallel.This is abbreviated as "8s4p" in Table 3  The internal resistance increases with approx.50% when the SOC decreases from 100% to 15% for both (10Ah and 120A) packs.The internal resistance value on the datasheets is the half of the one from the FreedomCar model.Now it is type 1 which has the lowest internal resistance value because of many parallel placed cells (4 parallel groups of cells, each containing 8 cells in series).
Putting so many cells in a pack asks for a good battery management, which is a disadvantage.OCV' (Fig. 6) is the decrease of the cell voltage per discharged As.It decreases with 40% when the SOC decreases from 100% to 33% and it increases with 15% in case when the batteries have not rested.

Influence of current
Changing the load profile does increase the internal resistance of a battery, even if the new profile is less heavy than the previous one.Fig. 7 shows R p for type 3.The FreedomCar tests are done at 120A until 509Ah, also written in red on the figure.From 509 Ah to 556 Ah the tests are done at 60A.From 556 Ah on the tests are done at 40A.

Influence on discharge time 4.1 Influence of exchanged capacity on discharge time
When the exchanged capacity increases, the battery can deliver the maximum current for shorter time (Fig. 8).

Influence of SOC on discharge time
When the SOC of the battery decreases, the battery provides the requested current during a shorter time (Fig. 9).Fig. 11 shows that the decrease of the capacity at high discharge currents is not only due to the high current but also due to the high temperature, which increases up to 45°C [6].The fan was not sufficient to cool the battery when it was discharging with 80A CC until he was empty.The temperature increased till 45°C.No ageing test were performed neither was the influence of temperature analysed at the moments.This will be carried out in future work.But the producer did a ageing test for type 1 (Fig. 12).6 Energy and efficiency 6.1 Energy Fig. 13 show the energy imbalance between the cells for type 3 cells.Cell 5 and 3 got the lowest energy input because of their little higher internal resistance in comparison with other cells.The efficiency of cell 3 and 5 is also low on Fig. 15.

Efficiency
Fig. 14 and Fig. 15 show the efficiency of type 1 and type 3 cells.The efficiency of type 3 cell is much higher at reasonable currents.

Voltage imbalance
Voltage imbalance between the cells is maximum 0,2V (Fig. 19).It decreases when the cells are charged with a low current.

CONCLUSION
The internal resistance is 50-100% higher than the value on the producers' datasheet.Moreover it increases with 50-100% when the battery gets empty.Furthermore it increases with 20% when the cells have not rested for long time.
Type 3 cell has the lowest internal resistance and shows also that the producers can provide the realistic value for internal resistance.
The internal resistance imbalance is lowest for type 3 cell.This can be correlated with the voltage imbalance.If the voltage imbalance is low, then there is less need for a battery management or the energy system is less dependent from a battery management system.
Decreasing the load current increases the internal resistance for few cycles.After few cycles the internal resistance drops down to the original value.So it is only the change of the load profile that increases the internal resistance in this case.
The temperature only increases with 2°C during one FreedomCar test.
The energy loss is calculated from the internal resistance value.
The efficiency of the cells are around 88%.

Fig. 4 ,Fig. 5 :Fig. 6 :
Fig. 4, Fig. 5 and Fig. 6 show R p , R o and OCV' of type 1 as a function of SOC in case when the cells

Fig. 7 :
Fig. 7: Rp as a function of the exchanged capacity When the cycle profile changes for the first time from 120A to 60A R p increases with 25%.But after a few cycles it comes back to the original value.

Fig. 8 :
Fig. 8: Discharge time as a function of the exchanged capacity

Fig. 14 :Fig. 15 :
Fig. 14: Charge and discharge energy and efficiency of type 1 cell as a function of current

Fig. 16 ,
Fig.16, Fig.17and Fig.18show the capacity for the three cell types.They are in the order of what is written on the datasheet, except type 2. It has a lower capacity than on the datasheet because the cells were charged to 3.55V instead of 3.65V in order to be safe.

Fig. 18 :
Fig. 18: Charge and discharge capacity of type 3 cell as a function of current Fig. 18 shows the capacity decrease as a function of the current for type 3.

Table 1 :
Datasheet of the batteries

Table 3 :
Internal resistance of a pack: calculated from

Table 4 :
Energy loss in [kWs] and in [%] for packs