**4. Simulation Verification 4. Simulation Verification**

In this section, simulation results in Matlab/Simulink are shown to validate the proposed control strategy. The changes in bus voltage, inductor current, and output current of the DC microgrid before and after the application of the control strategy are shown in Figure 8. Initially, the traditional droop control was applied. Due to the influence of CPLs, the system suffers oscillation. At t = 0.5s, the control strategy is switched from the traditional droop control to the proposed control strategy. Obviously, the DC microgrid bus voltage can quickly be restored to a stable state. Compared with the virtual capacitance control strategy based on droop control (the gray curve in In this section, simulation results in Matlab/Simulink are shown to validate the proposed control strategy. The changes in bus voltage, inductor current, and output current of the DC microgrid before and after the application of the control strategy are shown in Figure 8. Initially, the traditional droop control was applied. Due to the influence of CPLs, the system suffers oscillation. At t = 0.5s, the control strategy is switched from the traditional droop control to the proposed control strategy. Obviously, the DC microgrid bus voltage can quickly be restored to a stable state. Compared with the virtual

tests are carried out with the change of droop coefficients, line lengths, and operating points.

the figure) in [18], the proposed control strategy in this paper can reduce the adjustment time and

voltage fluctuation during the regulation process. Overall, this strategy will have more advantages in improving stability. To further verify the effectiveness of the proposed strategy, the following capacitance control strategy based on droop control (the gray curve in the figure) in [18], the proposed control strategy in this paper can reduce the adjustment time and make the system reach the balance faster. In addition, the control strategy can reduce the bus voltage fluctuation during the regulation process. Overall, this strategy will have more advantages in improving stability. To further verify the effectiveness of the proposed strategy, the following tests are carried out with the change of droop coefficients, line lengths, and operating points. *Appl. Sci.* **2019**, *9*, x FOR PEER REVIEW 10 of 15

**Figure 8.** Simulation results of a DC microgrid system with the proposed control strategy.

### **Figure 8.** Simulation results of a DC microgrid system with the proposed control strategy. *4.1. Change of Droop Coe*ffi*cients*

under different droop coefficients.

*4.1. Change of Droop Coefficients*  DC microgrids can coordinate the output of resources by adjusting the droop coefficient, which means that the system may operate under different droop coefficients due to different requirements [29]. Therefore, the stable operation of the system under different droop coefficients must be ensured. Figure 9 shows the simulation result of the proposed control strategy under different droop coefficients. It can be seen that the system remained stable whether the droop coefficient was switched to 0.3 or 0.7. Thus, it is evident that the control strategy can ensure the system stability DC microgrids can coordinate the output of resources by adjusting the droop coefficient, which means that the system may operate under different droop coefficients due to different requirements [29]. Therefore, the stable operation of the system under different droop coefficients must be ensured. Figure 9 shows the simulation result of the proposed control strategy under different droop coefficients. It can be seen that the system remained stable whether the droop coefficient was switched to 0.3 or 0.7. Thus, it is evident that the control strategy can ensure the system stability under different droop coefficients.

**Figure 9.** Simulation results of DC microgrid system with the change droop coefficient. *4.2. Change of Line Lengths* 

### **Figure 9.** Simulation results of DC microgrid system with the change droop coefficient. *4.2. Change of Line Lengths* The system needs to meet the energy requirements of the load, but the distance between

The system needs to meet the energy requirements of the load, but the distance between different loads and the bus are different. It is generally considered that the value of the droop coefficient is much larger than the line resistance and only the inductive component in the line is considered in this paper. The inductance of the line is proportional to the length. Hence, the variable considered in this section is the line length. As shown in Figure 10, the line length varies following the sequence of 1.070 km, 0.535 km and 0.749 km. It can be seen that no matter the length of the line increases or decreases, the DC microgrid can keep stable after applying the proposed control strategy. Thus, the effectiveness of the proposed stabilization strategy is proved when the system line length varies. different loads and the bus are different. It is generally considered that the value of the droop coefficient is much larger than the line resistance and only the inductive component in the line is considered in this paper. The inductance of the line is proportional to the length. Hence, the variable considered in this section is the line length. As shown in Figure 10, the line length varies following the sequence of 1.070 km, 0.535 km and 0.749 km. It can be seen that no matter the length of the line increases or decreases, the DC microgrid can keep stable after applying the proposed control strategy. Thus, the effectiveness of the proposed stabilization strategy is proved when the system line length varies.

**Figure 10.** Simulation results of DC microgrid system with the change of line length.

### **Figure 10.** Simulation results of DC microgrid system with the change of line length. *4.3. Change of Operating Points*

*4.3. Change of Operating Points* The load in the DC microgrid is an important part of the system and one of the main factors affecting the stability of the system. Instability problems are more likely to occur when load changes The load in the DC microgrid is an important part of the system and one of the main factors affecting the stability of the system. Instability problems are more likely to occur when load changes [30,31]. Thus, the effectiveness of the proposed control strategy was verified by changing the power of CPLs.

It proves that the control strategy can improve the system robustness in case of load variation.

[30,31]. Thus, the effectiveness of the proposed control strategy was verified by changing the power

The load doubled at 0.5 s, tripled at 0.7 s, and recovered to the initial at 0.9 s, as illustrated in Figure 11. It can be seen that the system operates steadily whether the power increases or decreases. It proves that the control strategy can improve the system robustness in case of load variation. *Appl. Sci.* **2019**, *9*, x FOR PEER REVIEW 13 of 15

**Figure 11.** Simulation results of a DC microgrid system with the change of operation points.

### **Figure 11.** Simulation results of a DC microgrid system with the change of operation points. **5. Conclusions**

acquisition, G.M.

(18A470015,18A470017, and 19A120012).

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

**5. Conclusions** A virtual negative inductance control strategy for DC microgrids with constant power loads is proposed in this paper. The particular is that this strategy improves the stability of the system from A virtual negative inductance control strategy for DC microgrids with constant power loads is proposed in this paper. The particular is that this strategy improves the stability of the system from the point of line inductance. And the main contributions of this paper lie in the following:


regulation process when compared with the virtual capacitance strategy. In this paper, the stability of a single DC microgrid is studied. For future work, the stability of a DC microgrid group will be of concern. The power generation variation of renewable energy based distributed generators will also be considered. And more detailed research will be carried out by considering more detailed transient models of distributed generation and load. Besides, we also In this paper, the stability of a single DC microgrid is studied. For future work, the stability of a DC microgrid group will be of concern. The power generation variation of renewable energy based distributed generators will also be considered. And more detailed research will be carried out by considering more detailed transient models of distributed generation and load. Besides, we also intend to extend the proposed control strategy to a hybrid alternating current (AC)/DC microgrid.

**Funding:** This work was supported by the National Natural Science Foundation of China (61803343), the China

intend to extend the proposed control strategy to a hybrid alternating current (AC)/DC microgrid. **Author Contributions:** Conceptualization, Z.C. and G.M.; methodology, G.M. and Z.L.; software, Z.C., G.M. and Z.L.; validation, Z.C. and G.M. and J.G.; formal analysis, Z.C. and G.M.; investigation, G.M.; resources, Z.L.; data curation, J.G.; writing—original draft preparation, G.M.; writing—review and editing, Z.C. and G.M.; visualization, Z.C. and G.M.; supervision, J.G., Z.L. and J.S.; project administration, Z.L.; and funding **Author Contributions:** Conceptualization, Z.C. and M.G.; methodology, G.M. and Z.L.; software, Z.C., M.G. and Z.L.; validation, Z.C. and M.G. and J.G.; formal analysis, Z.C. and M.G.; investigation, M.G.; resources, Z.L.; data curation, J.G.; writing—original draft preparation, M.G.; writing—review and editing, Z.C. and M.G.; visualization, Z.C. and M.G.; supervision, J.G., Z.L. and J.S.; project administration, Z.L.; and funding acquisition, M.G.

**Funding:** This work was supported by the National Natural Science Foundation of China (61803343), the China Postdoctoral Science Foundation (2018M630835), and the Key Projects of Higher Education of Henan Province (18A470015,18A470017, and 19A120012).

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