(327f) Estimation of State of Charge of a Lithium-Ion Battery Pack

The high energy density of lithium-ion batteries make them the preferred candidate for portable and mobile applications. Many manufacturers of electric vehicles combine lithium-ion cells into a battery pack to fulfill the requirement of large energy in a small space. When many cells are integrated into a single pack, it poses a challenge of maintenance and safety. The battery pack may face failure due to overcharging, increasing internal pressure, a short circuit, or a drop in the state of charge (SOC) of an individual cell in the pack. To maintain the battery pack in a good state of health, it is important to maintain the SOC of each cell in the pack, so the prediction of the SOCs is essential.

The energy stored in the battery pack is governed by the cell having highest percentage of SOC, as this cell will reach the cutoff voltage earlier than the other cells in the pack. If charging of the pack is continued then the cell with higher percentage of SOC will overcharge and lead to thermal runaway and cause a failure of the battery pack. If any cell of the battery pack enters into thermal runaway, then the internal pressure will build up, leading the battery pack even to explode. In fact, there are many cases of Li-ion batteries going into thermal runaway in laptops leading to recalls by major brands and manufacturers.

In a battery pack, direct measurement of SOC is not possible and the only measurement is the terminal voltage of the battery pack. It is evident that the voltage obtained from the battery pack essentially depends on the SOC of the cells of the pack. During the charging and discharging cycles, each cell in the battery pack undergoes different forms of capacity fade and aging mechanisms due to different profiles across the pack and hence significantly differ from each other in their SOC even though they were started at the same initial conditions. This makes the estimation of SOC with cycle number a challenging task. Several techniques have been proposed for SOC estimation, such as model-based observers and black-box methods [1-3]. The accuracy reached is about 2% [4]. The probable reason for this accuracy is the use of a simple model for prediction of SOC. This motivates the use of a reformulated model [5] for the lithium-ion battery that reduces the computational burden while keeping accurately describing the battery dynamics.

In this work we estimate the SOC of the battery pack consisting of 16 cells in series as needed for a battery pack produced by Tesla [6]. The technique involves predicting the terminal voltage of each cell in the battery pack with initial guesses for the values of SOC for each cell and summing the cell voltages to obtain a predicted terminal voltage of the battery pack to be compared with the measured value in real time. Minimizing a suitable norm of the error between the measured and predicted terminal cell voltage using numerical optimization methods [7, 8] enables the fast and accurate estimation of the SOC of each cell. The mathematical representation of the objective function is

Figure 1 is an example result comparing the measured and estimated terminal voltage of two cells in a battery pack. These two cells are maintained as 0% and 50% SOC. Figure 1 shows that the presented approach predicts the SOC of each cell in the battery pack reasonably well. Table 1 show that the SOC of each cell can be estimated within ±1% error with a small computational time. The computation time for estimation of SOC for two cells is very much less than the charging time of the pack. The presentation will show results for 4, 8, and 16 cells per pack and for varying disturbances and nonidealities in the model.

Figure 1: Comparison of predicted discharge curve with measured discharge curve.

Table 1: Percentage error and CPU time for the SOC estimation

Acknowledgements

The authors acknowledge partial financial support by the National Science Foundation under contract numbers CBET-1008692, CBET- and CBET-0828123, I-CARES (WUSTL) and the United States Government.

References

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