## 3 Virtual Inductive Control Strategy
### Virtual Inductance Control Strategy  
Voltage and current double closed-loop control is a common control method [12; 18]. And transfer function of voltage and current double closed-loop control of DC microgrid given by  
\[G_{CLi}(s)=\frac{\left(k_{pi}s+k_{ii}\right)V_{0}}{Ls^{2}+k_{pi}V_{0}s+k_{ii}V _{0}}, \tag{13}\]  
\[G_{CLv}(s)=\frac{\left(k_{pi}s+k_{ii}\right)(1-D)}{Cs^{2}+k_{pi}(1-D)s+k_{iv}( s)}, \tag{14}\]  
\(k_{pi},k_{ii}\) are the proportional and integral parameters of current loop, respectively. And \(k_{pi},k_{iv}\) are the proportional and integral parameters of voltage loop, respectively. According to the selection rules of controller parameters in [16], the specific PI controller parameters of this paper given in Table 1. The dynamic characteristics of the current inner loop can be equivalent to proportional gain one when calculating the voltage outer loop transfer function. The small signal block diagram of the droop control strategy can be derived, as illustrated in Figure 5 [28].  
where \(Z_{d}\) is the droop control, \(\Delta v_{o},\Delta v_{ref}\), \(\Delta i_{o},\Delta i_{ref}\) are the perturbation of the output voltage, the reference voltage, output current, and the output reference current of double closed-loop controller, respectively. \(G_{PIv}(s)\) is the voltage control loop transfer function and \(G_{c}(s)\) is the current inner loop controller closed-loop transfer function. The output voltage perturbation \(varDelta_{o}\) can be given by:  
\[varDelta_{o}= \frac{G_{PIv}(s)G_{c(s)}}{Cs+G_{PIv}(s)G_{C}(s)}varDelta_{ref}- \frac{1+Z_{d}G_{PIv}(s)G_{c}(s)}{Cs+G_{PIv}(s)G_{c}(s)}varDelta_{o}, \tag{15}\]  
In (15), the change of \(varDelta_{ref}\) and \(varDelta_{0}\) have an effect on the bus voltage. It is generally considered that the reference voltage of the system is unique and the fluctuation of the output voltage  
Figure 5: Small signal control block diagram of droop control.  
is determined by the change of the output current. Therefore, reasonable design of control strategy can reduce the influence of the latter. The definition is as follows  
\[1+Z_{d}G_{Pt_{0}}(s)G_{c}(s)=0, \tag{16}\]  
And \(Z_{d}\) can be rewritten as  
\[Z_{d}=-L_{d}s\frac{1}{Ts+1}, \tag{17}\]  
where \(L_{d}=1/k_{iv}\), and \(T=k_{pu}/k_{iv}\). Formula (18) can be considered as a form of multiplication of a coefficient \(-L_{d}\) differential link with a low-pass filter. According to the actual situation, the value of \(-L_{d}\) is chosen as shown in Table 1. On the basis of the traditional droop control, the control form is expressed as follows  
\[Z_{d}=R_{d}-L_{d}s, \tag{18}\]  
And an improved droop controller block diagram is depicted in Figure 6.  
As shown in Figure 7, with the proposed control strategy, an equivalent virtual control link is added between the source and the transmission line, which is equivalent to a negative inductance link in the system, helps to offset the influence of the line inductance in the system.  
The control parameters of system are shown in Table 1. Where the value of droop coefficient depends on the maximum voltage deviation  
\(varDeltav_{max}\) and the rated output current \(i_{0}\). The maximum allowable voltage deviation is \(\pm 5\%\) of the rated bus voltage. \(R_{d}\) can be derived as:  
\[R_{d}=\frac{varDeltav_{0 max}}{i_{0}}, \tag{19}\]