## 2 Analysis of the Principle of FMSS Promoting the Consumption of DG  
### Analysis of the Capacity of Traditional Distribution Network to Consume DG  
When analyzing the consumption capacity of the distribution network DG, the permitted access capacity of DG is firstly analyzed on the premise that the voltage of the access point of DG does not exceed the limit [19]. In this paper, the DG is equivalent to a special load with negative power. In the calculation of the system power flow distribution and voltage analysis, the access node of DG can be equivalent to PQ node. A method based on the short-circuit capacity of the access point can be used to determine the maximum access capacity of DG.  
The equivalent circuit of Thevenin of Figure 1 is an example for analysis. \(E\) is the power supply voltage of the equivalent circuit, \(Z_{S}\) is the equivalent impedance between the access point and the system power supply, and \(U\) is the voltage at the access point of DG. Assuming the corresponding current change on the line caused by the output of DG is \(\Delta I\), the voltage change of the access point value as shown in (1).  
\[\Delta U=(R+jX)(\Delta I_{p}+j\Delta I_{q})=|Z_{s}||\Delta I|[(\cos\phi\cos \theta-\sin\phi\sin\theta)+j(\sin\phi\cos\theta+\cos\phi\sin\theta)] \tag{1}\]  
where \(\phi\) is the impedance angle, \(\theta\) is the angle of the DG output current leading the voltage, that is, the negative value of the power factor angle.  
The short-circuit capacity of the DG access point is calculated as shown in (2)  
\[S_{k}=\frac{U^{2}}{|Z_{S}|} \tag{2}\]  
where \(S_{k}\) is the short circuit capacity of the distributed power supply access point. \(Z_{S}\) is the equivalent impedance between the access point and the system power supply, and \(U\) is the voltage at the access point of DG.  
Combined with Equations (1) and (2), and as the distribution network analyzed in this paper is of voltage grade below 110 kV, the phase displacement at both ends of the line is not large. Therefore, the lateral component of the voltage variation can be ignored, thus, the relationship between the voltage variation of the access point of DG and the short-circuit capacity of the access point can be obtained as shown in (3):  
\[\Delta U=\frac{U^{2}}{S_{\rm K}}\frac{|\Delta S_{\rm n}|}{U}(\cos\phi\cos \theta-\sin\phi\sin\theta)=\frac{U^{2}}{S_{\rm K}}\frac{|\Delta S_{\rm n}|}{U }\cos(\phi+\theta) \tag{3}\]  
where \(\Delta S_{\rm n}\) is DG access apparent power size, namely \(\Delta S_{\rm n}=P_{\rm DG}+j\Omega_{\rm DG}\).  
Therefore, the relationship between the voltage deviation of the access point and access capacity of DG is:  
\[d\%=\frac{\Delta U}{U}=\frac{|\Delta S_{\rm n}|\cos(\phi+\theta)}{S_{\rm K} }\times 100\% \tag{4}\]  
Figure 1: Thevenin equivalent circuit of the distributed generation (DG) access point.  
According to Equation (4), when the allowable upper limit \(d_{max}\) of distribution network voltage deviation is known, the maximum allowable access capacity of DG at this access location can be obtained according to Equation (4), as shown in (5).  
\[S_{\text{DGmax}}\approx\frac{S_{\text{K}}d_{\text{max}}\%}{100\cos(\phi+\theta)} (cos\theta+\text{j}\sin\theta) \tag{5}\]  
For the traditional distribution network, the maximum capacity of the accessible DG depends on the maximum allowable voltage deviation of the distribution network. This occurs when the impedance angle between the power supply and the access point of DG, and the power factor of the access of DG and the short-circuit capacity at the input node have been determined.