**4. Improved SOC Control Strategy**

Based on the disadvantages of the traditional control strategy, an improved control strategy is proposed herein based on the compound converter structure with an isolated soft-switching symmetric half-bridge two-way converter as the protection structure. As shown in Figure 12, speed and SC SOC control are added to the controller as influencing factors, thereby forming a four-dimensional space vector control strategy.

**Figure 12.** SOC control structure.

According to the above discussion, the driving cycle has an important influence on the control effect. Therefore, the new strategy adjusts SC SOC to the optimal state by analyzing the relationship between SC SOC, speed and power demand. During the electric vehicle is running, the SC provides peak power and the battery provides average power. Considering the kinetic energy theorem, the following relationship can be obtained (excluding power losses):

$$\frac{1}{2}mv\_{\text{max}}^2 - \frac{1}{2}mv^2 = \frac{1}{2}cu\_{\text{sc}}^2 - \frac{1}{2}c(0.5\overline{u\_{\text{sc}}})^2 + p\_{\text{bat}}t\_0\tag{1}$$

$$
\dot{\nu}\_{\text{bat}} = \mu\_{\text{bat}} \dot{\imath}\_{\text{bat}} \tag{2}
$$

*Energies* **2020**, *13*, 5297

Here, *v* is the current vehicle speed, *v*max is the maximum vehicle speed, *m* is the vehicle total mass, *<sup>c</sup>* is the SC system capacitance, *usc* is the current voltage of the SC end, \_ *usc* is the rated voltage of the SC, *Pbat* is the rated power of the battery, *t*<sup>0</sup> is the time for battery to release energy, *ubat* is the battery nominal voltage, and *ibat* is the battery nominal current. From (1) and (2), the optimal SC SOC is given by:

$$q\_{\rm sc}^{\*} = \sqrt{\frac{m\upsilon\_{\rm max}^{2} - m\upsilon^{2} - 2\mu\_{\rm but}i\_{\rm bat}t\_{0}}{c\overline{u\_{\rm sc}}^{2}} + 0.25} \tag{3}$$

where, *q* is the SOC of the ultracapacitor, and *q*\* is the ideal SOC of the SC. To verify the performance of the optimized power distribution strategy, experimental tests were performed under different conditions. The results of the current distribution are shown in Figure 13. Unlike the traditional control strategy, the battery transfers charge to SC at a constant speed driving and stopping stage, and the current frequency is higher than that of the traditional control strategy. At the end of the acceleration process (380–500 s), the SC provides approximately four times higher *ibat* peak current than the conventional mode. Based on the comparison between traditional control strategy and the SOC control strategy, the SOC control strategy is concluded to be more conducive to EV acceleration performance. The SOC curve of the SC is shown in Figure 14.

**Figure 13.** Charge and discharge current distribution of supercapacitors and batteries under SOC control strategy.

**Figure 14.** SOC curve of the supercapacitor under the control strategy.

The SOC value of SC is 0.97. In the acceleration and braking stages, the actual SC SOC deviates from the expected value owing to the drastic change in SC charging and discharging current. The SC SOC approaches the optimal curve when EVs continue to operate. Compared with the SOC changes of SC shown in Figure 10, the SOC control strategy is more ideal. Under the optimized control strategy, the SOC of the SC has a small decrease, which can meet the energy output requirement.

The acceleration test of the system is shown in Figure 15a. The acceleration performance under the SOC control is approximately 50% higher than that of the pure battery, and approximately 25% higher than that of the conventional control. The energy loss test under EDUC, NYCC, 1050 and CSHVR is shown in Figure 15b. The energy loss under SOC control is approximately 4%, which is 23% lower than that of conventional control and 69% lower than that of the pure battery. The test parameters of the EV are shown in Table 2. The EV with the SOC control strategy has the shortest acceleration time and the lowest energy consumption. The SOC control strategy proposed herein is superior to the traditional control strategy in terms of acceleration performance and power distribution.

**Figure 15.** Acceleration and power tests: (**a**) Acceleration tests; (**b**) Power tests.


**Table 2.** Vehicle, Battery and SC Parameters.

#### **5. Conclusions**

The ordered mesoporous carbon electrode SC prepared herein exhibits good performance under high current conditions through charge and discharge experiments. Using the prepared SC, an optimized hybrid energy distribution method was proposed for the HESS. A hybrid converter with an isolated soft-switching symmetric half-bridge bidirectional converter is used as the protection structure to accurately control the charging/discharging of the SC and battery. Through the optimized power distribution method, the SC energy can be quickly supplemented when stopping and driving at a constant speed; this makes up for the shortcomings of the traditional control strategy. On the other hand, by controlling the SOC of the SC via the speed of EV enables the energy storage system to have better flexibility and adaptability, thereby enhancing the demand for the acceleration performance and energy variation of EVs. The experimental results demonstrate that the optimized SOC control strategy proposed herein can meet the peak power demand and energy loss, shorten the acceleration time of EVs but reduce the energy loss, improve the performance of EVs and extend the service life of the battery.

**Author Contributions:** Conceptualization, K.W. and L.L.; methodology, K.W.; software, W.W.; validation, W.W. and L.W.; formal analysis, K.W.; investigation, L.W.; resources, L.L.; data curation, L.L.; writing—original draft preparation, K.W.; writing—review and editing, W.W.; visualization, K.W.; supervision, K.W.; project administration, L.L.; funding acquisition, L.L. All authors have read and agree to the published version of the manuscript.

**Funding:** The work was supported by the Scientific Research Development Plan of Shandong Higher Education Institutions (No. J18KA316), the Development Plan of Shandong Province (No. 2019GGX104019), and Guangdong Basic and Applied Basic Research Foundation (2019A1515110706).

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