5.2.2. Experiment 2

To validate the compatibility of adaptive control scheme in an EV level's voltage, a 50.4 V battery pack was applied in Experiment 2. The working voltage, current, and estimating error are shown in Figure 8a. The estimating error has converged to near zero in 150 s. The trajectories of the estimating parameters are listed in Figure 8b, the steady parameters, θˆ 1,θˆ 2, θˆ 3, and θˆ <sup>4</sup> converge to 0.078 Ω, 7.45 F−1, 99.55 S−1, and 4950 V−1, respectively. The target parameters of *Rs*, *Rt*, and OCV are plotted in Figure 8c.

(**b**)

**Figure 8.** *Cont.*

**Figure 8.** (**a**) Terminal voltage, discharge current, and estimating error; (**b**) estimating model parameters, θˆ*i*, i = 1~4; (**c**) estimated Rs, Rt, and voc in Experiment 2.

For checking online battery management for a battery, an offline numerical model based on a schematic method [16] was established, and is shown in Figure 9. From sudden voltage drop and voltage rise in one discharge, it is possible to roughly estimate *Rs*, *Rt*, and *Ct* in the figure. Then, the analytical solution of voltage drop can be derived, as listed in Figure 9. In experiment 2, battery discharges 5 A for 12 min and rests for 1 h, then repeats this pattern for 12 h, as shown in Figure 10a. In Figure 10b, the red and blue lines represent the offline numerical and online estimated results, respectively. Trends of estimating OCV and IRs estimation are close to the offline numerical model. The deviation of OCV is roughly within 2%. Furthermore, the battery pack is composed of continuous discharging patterns, as shown in Figure 11a. For OCV, the estimated values, in the green line, are compared with offline numerical results, in the red line, as shown in Figure 11b. The deviation between online and offline values in the left-hand side of Figure 11b might be due to the heat accumulated in the battery, but the trend is identical. In this study, the algorithm of OCV and internal resistance assumes the battery pack is well-ventilated and isothermal. Temperature is not considered in the calculation. As for *Rt*, the online values are almost overlapped with offline results, as expected.

**Figure 9.** An offline numerical model based on the schematic method [16] (Id: discharge current; td: discharge time).

**Figure 10.** (**a**) Voltage drop and discharge current; (**b**) comparison of online estimating open-circuit voltage (OCV) and internal resistances (IRs) with the offline numerical model.

(**b**)

**Figure 11.** (**a**) Voltage drop and discharge current; (**b**) comparison of online estimating OCV and Rt with the offline numerical model.

### **6. Conclusions**

In this study, an in-house BMS is developed for RLIB. Additional enhanced battery management is established. Adaptive control schemes in the BMS are established for estimating a battery's IRs and OCV relative to key parameters of RLIB, e.g., SOC and SOH, respectively. Here, IRs and OCV of a battery pack are accurately extracted from working voltage and discharge current in two experiments in this study. An offline numerical model using the schematic method is applied to verify the results of the online proposed scheme. In experiment 2, results of online estimations regarding OCV and IRs show good agreement with offline numerical model. The deviation of OCV is roughly within 2%. Furthermore, a hybrid battery pack using a UC is proposed to share peak power of RLIB by adjusting the duty ratio in the BMS. It shows more constrained voltage drops of battery when increasing the duty ratio of UC. The UC effectively reduces the voltage drop and decreases the DOD of the battery in the life extension test. It is shown that enhancing battery management for an RLIB can properly estimate OCV and IRs, and actively extend the life of the battery. For a new battery, offline estimation of parameters such as OCV and IRs meet the requirement. However, enhancing online management is indispensable on safety. This study proves the achievability of this managing solution for RLIBs. In the next phase, an RLIB integrated with this in-house BMS will be arranged, for storage of the intermittent renewable energies in site, in order to evaluate the performance.

**Author Contributions:** Conceptualization: W.-Y.S. and Y.-H.C.; methodology: Y.-H.C.; software: W.-P.Y.; validation: W.-P.Y., W.-Y.S., and Y.-H.C.; formal analysis: W.-P.Y., W.-Y.S., and Y.-H.C.; writing—original draft preparation: W.-P.Y.; writing—review and editing: W.-Y.S. and S.-M.J.; supervision: Y.-H.C. and S.-M.J.; project administration: W.-Y.S.; funding acquisition: W.-Y.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was financially supported by the Chung Yuan Christian University (Project No: 109609432).

**Conflicts of Interest:** The authors declare no conflicts of interest.
