# An Intelligent Control Strategy for a Highly Reliable Microgrid in Island Mode
## 2 Materials and Methods
### The Control Strategy for The Off-Grid Microgrid  
#### 2.3.1 The Circulating Currents Analysis  
In the off-grid microgrid shown in Figure 1, if the parameters between the two inverters are not completely consistent, the amplitude and phase of the output voltages are different, and the line impedances are unequal. The circulating currents between the parallel systems will be generated, resulting in the microgrid produces large losses, which will cause the inverter power switching devices to burn out in serious cases, and affect the stable operation of the entire microgrid. This section analyzes the circulating currents between the two inverters in Figure 1 to design the circulating current suppression strategy to make the microgrid operation safer and more stable. Figure 3 is a schematic diagram of the circulating currents between the inverter 1 and the inverter 2 after reconstruction. Figure 3: The circulating currents. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **First Fault** & **Second Fault** & \(\mathbf{J_{ao}}\) & \(\mathbf{J_{bo}}\) & \(\mathbf{J_{co}}\) & **On** \\ \hline
2–1 & \(\mathrm{V_{1}}\) & \(\mathrm{V_{4}}\) & \(Z\) & \(P\) & \(Z\) & \(\mathrm{TR_{2}}\) \\
2–2 & \(\mathrm{V_{1}}\) & \(\mathrm{V_{6}}\) & \(Z\) & \(Z\) & \(P\) & \(\mathrm{TR_{1}}\) \\
2–3 & \(\mathrm{V_{2}}\) & \(\mathrm{V_{3}}\) & \(Z\) & \(N\) & \(Z\) & \(\mathrm{TR_{2}}\) \\
2–4 & \(\mathrm{V_{2}}\) & \(\mathrm{V_{5}}\) & \(Z\) & \(Z\) & \(N\) & \(\mathrm{TR_{1}}\) \\
2–5 & \(\mathrm{V_{3}}\) & \(\mathrm{V_{2}}\) & \(N\) & \(P\) & \(Z\) & \(\mathrm{TR_{2}}\) \\
2–6 & \(\mathrm{V_{3}}\) & \(\mathrm{V_{4}}\) & \(Z\) & \(P\) & \(Z\) & / \\
2–7 & \(\mathrm{V_{4}}\) & \(\mathrm{V_{1}}\) & \(P\) & \(Z\) & \(Z\) & \(\mathrm{TR_{2}}\) \\
2–8 & \(\mathrm{V_{4}}\) & \(\mathrm{V_{3}}\) & \(Z\) & \(N\) & \(Z\) & / \\
2–9 & \(\mathrm{V_{5}}\) & \(\mathrm{V_{2}}\) & \(P\) & \(Z\) & \(Z\) & \(\mathrm{TR_{1}}\) \\
2–10 & \(\mathrm{V_{5}}\) & \(\mathrm{V_{6}}\) & \(Z\) & \(Z\) & \(P\) & / \\
2–11 & \(\mathrm{V_{6}}\) & \(\mathrm{V_{1}}\) & \(N\) & \(Z\) & \(Z\) & \(\mathrm{TR_{1}}\) \\
2–12 & \(\mathrm{V_{6}}\) & \(\mathrm{V_{5}}\) & \(Z\) & \(Z\) & \(N\) & / \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Second fault diagnosis and reconfiguration. From Figure 3, the output currents of inverter 1 and inverter 2 can be obtained as:  
\[\left\{ \begin{array}{l}i_{\text{e1}}=\frac{u_{dc}(2S_{a}-S_{b}-\frac{1}{2})-3u_{ PCC}}{32u_{\text{e1}}}\\ i_{\text{b1}}=\frac{u_{dc}(-S_{a}+2S_{b}-\frac{1}{2})-3u_{ PCC}}{32u_{\text{e1}}}\\ i_{\text{c1}}=\frac{u_{dc}(-S_{a}-S_{b}+1)-3u_{ PCC}}{32u_{\text{e1}}}\\ \end{array} \right., \tag{11}\]  
\[\left\{ \begin{array}{l}i_{a2}=\frac{u_{dc}(2S_{a}-S_{b}-\frac{1}{2})-u_{ PCC}}{32u_{\text{e2}}}\\ i_{b2}=\frac{u_{dc}(-S_{a}+2S_{b}-S_{c})-u_{ PCC}}{32u_{\text{e2}}}\\ i_{\text{c2}}=\frac{u_{dc}(-S_{a}-S_{b}+2S_{c})-u_{ PCC}}{32u_{\text{e2}}}\\ \end{array} \right., \tag{12}\]  
Among them, \(u_{\text{PCC}}\) is the voltage at the PCC point. The formula for calculating the circulating current between the two inverters is as follows:  
\[i_{Hx}=\frac{i_{x2}-i_{x1}}{2}, \tag{13}\]  
where, \(i_{x1}\) and \(i_{x2}\) are the output currents of the two inverters respectively, \(x=a\), \(b\), \(c\). Assuming that the equivalent output impedances of the two inverters in the microgrid with reconfigurable inverters are equal, that is \(Z_{eq1}=Z_{eq2}=Z_{eq}\). The circulating current of each phase between the reconstructed inverter 1 and inverter 2 is:  
\[\left\{ \begin{array}{l}i_{Ha}=\frac{u_{dc}(-4S_{a}+2S_{b}+3S_{c}-\frac{1}{2} )}{6Z_{eq}}\\ i_{Hb}=\frac{u_{dc}(2S_{a}-4S_{b}+3S_{c}-\frac{1}{2})}{6Z_{eq}}\\ i_{Hc}=\frac{u_{dc}(2S_{a}+2S_{b}-8S_{c}+1)}{6Z_{eq}}\\ \end{array} \right., \tag{14}\]  
It can be seen from the above equation that when the equivalent output impedances of the two inverters are the same, the magnitude of the circulating currents generated between the two inverters are affected by the modulation of the switching function.