**1. Introduction**

There is no fluctuation of reactive power in the microgrid, and the stability of the direct current (DC) microgrid only depends on the stable operation of the bus voltage [1,2]. When the DC microgrid is operating in island mode, without the supporting of a large power grid, the instability of bus voltage will be more serious [3]. From the structural point of view, the island DC microgrid is a typical multi-source heterogeneous system containing multiple types of micro-resources and loads [4,5]. The stability is not only affected by the distributed resources, but also subjected to load, especially constant power loads (CPLs). Thus, how to eliminate the influence of the CPLs characteristics caused by the load converter and primary load is a technical challenge to ensure the stability of a DC microgrid [6].

To overcome the problem of voltage fluctuation caused by CPLs, the instability mechanism of CPLs has been widely studied and several solutions have been proposed [7,8]. In the past few years, some researchers have tried to solve such instability phenomena by a passive method [9–11]. Generally speaking, this method requires additional physical dampers. In [9], an LC (Inductive Capacitance) filter is added to the system. Although it shows a better effect, the system is based on an ideal model, which is different from the actual situation. And the response speed of the system is also affected to some extent. Based on the same idea, a physical filter containing multiple capacitors and resistors is applied to eliminate the impact of constant power loads [11]. However, the use of multiple resistors will make the power loss greater. Previous studies indicate that the power loss caused by passive damping makes it not suitable for DC microgrids. Therefore, the active control strategy gets more attention. This kind of method will not bring any additional physical dampers to the system, hence alleviating the system weight and efficiency problem. This is more in line with the requirements of efficient

energy utilization in a DC microgrid. Furthermore, because of the advantages of distributed control, droop control has been widely used as an important form of active control [12–15].

Active control method can achieve the same effect as passive control strategy, but it will not cause additional power loss. Guo et al. added a low-pass filter in series to droop control, which can increase the output impedance of the converter in the low frequency range [16]. Thus, the bus voltage fluctuation caused by CPLs can be effectively alleviated. However, this research is limited to the introduction of filter designs. Furthermore, for solving the negative effects of CPLs, Wu et al. described a virtual phase-lead impedance stability control strategy [17]. The strategy was used to adjust the output impedance of CPLs to be positive. But it was not applied to an island mode. And from the point of inertia, a corresponding virtual capacitance control strategy was established by Zhu et al. [18]. And due to the increase of inertia by virtual capacitance, the robustness of system is increased in the face of CPLs. However, because the "plug-and-play" characteristics of distributed resources, new control strategies need to be designed for the access of new micro resources, which obviously lacks flexibility. In addition, other methods are also committed to using active control methods to improve system stability [19,20]. Among various approaches investigated in the literature, there is a deficiency that the influence of transmission line is not included in these study. This is imperfect, because the transmission line is also a major factor affecting the stability of the system, especially the inductance component of the transmission line [21,22].

To address the above problem, a virtual negative inductance control strategy is proposed in this paper. On the basis of droop control, a virtual inductive is constructed, which operates as a negative inductive link and counteracts the inductive in transmission line. Thus, the negative influence of line inductance is effectively solved. This paper makes the following contributions:


The remainder of the paper is organized as follows: The configuration and modeling of the DC microgrid is introduced in Section 2, and the simplified circuit model of the system is shown. Section 3 presents the design of the virtual inductive control strategy. In Section 4, simulation results are used to verify the superiority of the strategy by comparison and different case studies. Finally, Section 5 summarizes this paper and draws conclusions.
