*5.2.2. Battery balancing validation*

To validate the balancing method, the initial SOC is set to 93%, 88%, 88%, and 80% for the four cells, respectively. In this scenario, the energy is balanced from *C*1 to *C*4. UDDS current profiles will be utilized to test the battery string and the balancing processes are performed according to the SOC-based balancing strategy simultaneously, as shown in Figure 18. The estimated SOC is denoted as rSOC, while the reference SOC is as eSOC in the figure.

Since the balancing process is based on SOC, the SOCs of the four cells should be first known. But these actual SOCs are not known to the SOC estimator. Initially, the SOC estimator assumes that the initial eSOC is 90% for all four cells. However, after a few sampling cycles of 50 to 100 s for example, the eSOC of each cell converges to the rSOC and the SOC differences of the cells can be observer by the balancing algorithm. With the eSOC obtained, the SOC-based balancing algorithms start to work efficiently, as shown in the figure. Eventually, the four cells are balanced according to the SOC in about 4000 s.

With the operation of the balancing procedures (as shown in Figure 18a), the SOC of *C*<sup>4</sup> and *C*1 converge to the average SOC of cells, and finally the SOC of the four cells are almost the same, which could be considered as balanced. The voltage results of the balancing processes are also shown in Figure 18b. The voltages of the four cells are a lot different when the experiment starts, as shown in the first subplot of Figure 18b. After the balancing procedures, the voltages of the four cells converge to almost the same at the end of the experiment as shown in the second subplot of Figure 18b, which is another proof of the effectiveness of the balancing processes.

**Figure 18.** The results of battery balancing experiment: (a) SOC results for the balancing experiment. (b) Voltage results for the balancing experiment.
