## 2 Analysis of the Principle of FMSS Promoting the Consumption of DG
### Analysis of Consumption Capacity of DG after FMSS Is Connected  
With the continuous increase of the permeability of DG, it is difficult to regulate the power flow of the traditional distribution network by traditional means. The power flow of each branch may exceed the limit of the feeder power flow, and the voltage of each node in the system can also greatly deviate from the nominal voltage of the system and exceed the allowable value of the voltage deviation. By virtue of its flexible and fast power flow regulation ability, FMSS optimizes the power flow distribution under the condition of high permeability of DG and inhibits the off-limit of the branch power flow and node voltage deviation to improve the consumption ability of DG in the distribution network.  
The following is an example of the simple double-feeder distribution network model shown in Figure 2 to introduce the principle of FMSS to improve the consumption capacity of DG in the distribution network.  
In the simple distribution network shown in Figure 2, the two feeder ends are connected by FMSS. According to the operating constraints of FMSS, the active and reactive power relationship of the two ports is shown in (6).  
\[\left\{\begin{aligned}  P_{1}+P_{2}&=0\\ -\sqrt{S_{1}^{2}-P_{1}^{2}}&\leq Q_{1}& \leq\sqrt{S_{1}^{2}-P_{1}^{2}}\\ -\sqrt{S_{2}^{2}-P_{2}^{2}}&\leq Q_{2}& \leq\sqrt{S_{2}^{2}-P_{2}^{2}}\end{aligned}\right. \tag{6}\]  
The access DG is at \(j_{1}\), end node of feeder 1. According to (5), the maximum capacity of DG that node \(j\) can access is \(S_{DG,max}=P_{DG}+\text{j}\mathcal{Q}_{DG}\). At this point, the node voltage deviation is shown in (7). If the DG access capacity exceeds this value, the voltage deviation of node \(j_{1}\) exceeds the allowable voltage offset value.  
\[\Delta U_{\text{j1 max}}=\Delta U_{\text{j1}}=\frac{(P_{\text{DG}}-P_{\text{j1 }})R+(Q_{\text{DG}}-Q_{\text{j1}})X}{U_{\text{N}}}>0 \tag{7}\]  
Figure 2: Simple uniform distribution network system with DG.  
when FMSS is connected, the voltage at node \(j_{1}\) changes to:  
\[\Delta U_{j1}^{\prime}=\frac{(P_{\text{DG}}-P_{1}-P_{j1})R+(Q_{\text{DG}}-Q_{1}- Q_{j1})X}{U_{\text{N}}}\leq\Delta U_{j1\text{max}} \tag{8}\]  
Meanwhile, the voltage change at the end node \(j_{2}\) on feeder 2 is:  
\[\Delta U_{j2}^{\prime}=\frac{(-P_{2}-P_{j2})R+(-Q_{2}-Q_{j2})X}{U_{\text{N}}} =\frac{(P_{1}-P_{j2})R+(-Q_{2}-Q_{j2})X}{U_{\text{N}}} \tag{9}\]  
In the low-voltage distribution network, there is little difference between the resistance and inductance, and the influence of resistance cannot be ignored. Therefore, both active power and reactive power have some influence on the voltage offset. By type (8), when FMSS absorbs active power from feeder 1 and transfers it to the end of feeder 2, the node voltage offset caused by the active power of DG at node \(j_{1}\) can reduce. If FMSS simultaneously absorbs inductive power from feeder 1, the voltage offset caused by DG can further reduce, therefore, the digestible DG capacity at node \(j_{1}\) increases. At the same time, Equation (9) shows that since feeder 2 receives the active power transferred from feeder 1 by FMSS, the terminal node voltage increases and the offset also decreases. If FMSS absorbs capacitive reactive power here, the terminal node voltage will further increase. It can be seen that FMSS can increase the consumption capacity of distribution network to the DG by regulating the active power flow between feeders and the reactive power at the port, and at the same time, achieve the effect of feed load balance and overall reduction of node voltage deviation.