5.3.2. Keep the Load Resistance and Change the Constant Power Load

The constant load power was changed during the simulation; that is, CPL rose from 6 W to 8 W at 0.04 s and then dropped to 6 W at 0.08 s.

As can be seen from the output voltage response curve in Figure 17a, Method 1 not only minimizes the voltage drop but also minimizes the recovery time. Although Method 2 can also keep the system stable, it sacrifices control performance to some extent. From the inductor current curve in Figure 17b, it can be seen that the recovery speed of the Method 1 curve is significantly faster than that of Method 2. As shown in the controller output of Figure 17c, the response and convergence speed of the controller output, u, of Method 1 are higher than those of Method 2.

As shown in Figure 18, the convergence time of the observer pairs and estimates are 0.015 s and 0.007 s, respectively. At 0.08 s, the power of the constant power load decreases from 8 W to 6 W, and the convergence time of the observer is 0.014 s and 0.007 s, respectively. The GPI observer can quickly track the value of the disturbance and make accurate estimates of and match the disturbance.

**Figure 17.** Comparison of output responses under CPL variation: (**a**) output voltage, (**b**) inductive current, and (**c**) control input.

**Figure 18.** Estimate of the observer under CPL variation: (**a**) estimation of unmatched perturbations, d1; and (**b**) estimation of matching perturbations, d2.

In short, from the comparison results in Table 5, it can be seen that the converter under the control of Method 1 has a faster output voltage response, better transient performance, and greater anti-disturbance ability.


**Table 5.** Comparison of dynamic response of the proposed controller under CPL changes.

### **6. Conclusions**

Aiming at the precise power control of three-phase interleaved bidirectional converters in a DC microgrid under the variation of supply voltage and constant power load, a GPI observer sliding-mode control method based on a super-twisting algorithm was proposed. The proposed high-order sliding-mode control strategy can stabilize the output voltage at the expected CPL power value and generate errors between the inductance current and the output voltage of the converter on the sliding-mode surface. By combining the interference estimations, smaller switching gains can be achieved without sacrificing interference suppression, thus ensuring the stability of the output voltage.

Finally, the effectiveness of the control algorithm was verified by comparing the simulation results of the proposed control method with the classical method. The transient recovery index and anti-interference capability of the controller were further improved. The results show that the proposed method can ensure that the output voltage of the system converges to the reference voltage, and this controller further improves the transient recovery index, anti-interference ability, and vibration-reduction performance of the system. The advantage of the controller is that it can quickly improve the rate of convergence of the system state, which is the disadvantage of the traditional observer.

**Author Contributions:** Y.J. and D.W. described the proposed framework and wrote the whole manuscript; Y.L. implemented the simulation experiments; G.S. and K.S. collected data; Y.J. and Y.N. revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is supported in part by the Natural Science Foundation of China, under Grant 52077027 Study, and in part by the Liaoning Province Science and Technology Major Project No. 2022021000014.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available upon request from the corresponding author.

**Acknowledgments:** The authors thank the chief editor and the reviewers for their valuable comments on how to improve the manuscript.

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