# An Intelligent Control Strategy for a Highly Reliable Microgrid in Island Mode
## 2 Materials and Methods
### Open-Circuit Fault Diagnosis and Reconfiguration for Inverter 1
Similarly, the polarity of the midpoint voltage of other bridges can be also obtained when other power switch faults occur. After the faulty power switch is diagnosed, the inverter can be reconfigured to operate in the fault-tolerant state. The results of the first fault diagnosis and reconstruction according to the polarity of the midpoint voltage difference of the bridge are shown in Table 2. The polarities \(J_{ao}\), \(J_{bo}\) and \(J_{co}\) of the midpoint voltage of the bridges \(a\), \(b\) and \(c\). \(Z\), \(N\), and \(P\) represent zero, negative, and positive, respectively. \"No\" means it isn't reconfigured. \(N\)-\(P\) presents the polarity of the midpoint voltage difference negative when the faulty switch is in the upper bridge and positive when the faulty switch is in the lower bridge. Take case 1-1 as example. If V\({}_{1}\) is detected as faulty, the polarities \(J_{ao}\) is negative and \(J_{bo}\) and \(J_{co}\) are positive. Then the inverter 1 is reconfigured after the first fault so that the inverter 1 can operate fault-tolerantly. Some power switches can still be used after the reconfiguration in some fault cases. For example, when the faulty V\({}_{1}\) is removed, V\({}_{2}\) is still normal. Therefore, V\({}_{2}\) can be used for the second reconfiguration when the other power switch in the inverter is detected as faulty. The primary reconfigured inverter as shown in Figure 2d is diagnosed for the second time. Then power switch V4 is taken as an example. We can see from Figure 2d, when V4 has no fault, the voltage of the midpoint of the bridge can be expressed as:  
\[u_{boN2}=\left\{ \begin{array}{cc}\frac{u_{dc}}{2}\ S_{b}=1\\ -\frac{u_{dc}}{2}\ S_{b}=-1\end{array} \right., \tag{7}\]  
when V4 has an open-circuit fault and \(S_{b}=-1\), V3 and V4 are both disconnected, then point b is suspended and \(i_{b}=0\). Potential \(b\) is the same as potential \(n\). That is \(u_{boF}=u_{noF}\). According to Figure 2d, when \(S_{a}=1\) and \(S_{b}=-1\), there is the midpoint voltage \(u_{boF}\) after the second fault as:  
\[u_{boF2}=u_{noF2}=\frac{u_{dc}}{2\times 2Z}\times Z=\frac{u_{dc}}{4}, \tag{8}\]  
when \(S_{a}=-1\) and \(S_{b}=-1\), there is:  
\[u_{boF2}=u_{noF2}=-\frac{u_{dc}}{2\times 2Z}\times Z=-\frac{u_{dc}}{4}, \tag{9}\]  
Finally, considering Equations (7)-(9), there is:  
\[J_{bo2}=J\big{[}u_{noF2}-u_{noN2}\big{]}=P, \tag{10}\]  
That is to say, when an open-circuit fault occurs at V4, the polarity \(J_{bo2}\) of the midpoint voltage difference of the bridge \(b\) is positive. The second reconfiguring process is shown in Figure 2c after the fault of V4. V4 is removed. TR4 is triggered on and the pulse signal of V4 is sent to V2. The phase \(c\) is still replaced by the DC-side capacitors. The inverter can be still reconstructed into the TPFS structure which is shown in Figure 2d. The second fault diagnosis and reconfiguration are finished. Similarly, the polarity of the midpoint voltage difference of other bridge can be obtained when other power switches fail. The results of the second fault diagnosis and reconfiguration are shown in Table 3. \"/\" means no need to let any other triacs be on. In Table 3, take case 2-1 as example. The inverter 1 is already reconfigured as TPFS when  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **First Fault** & \(\mathbf{J_{ao}}\) & \(\mathbf{J_{bo}}\) & \(\mathbf{J_{co}}\) & **On** \\ \hline
1–1 & Normal & Z & Z & Z & TR3 \\
1–2 & V1 & N & Z & Z & TR4 \\
1–3 & V2 & P & Z & Z & TR4 \\
1–  
\(\mathrm{V_{1}}\) is detected faulty. The polarities \(J_{bo}\) is positive. \(\mathrm{TR_{4}}\) and \(\mathrm{TR_{2}}\) are triggered on and the pulse signal of \(\mathrm{V_{4}}\) is sent to \(\mathrm{V_{2}}\). The phase \(c\) is still replaced by the DC-side capacitors. The inverter 1 can be reconstructed into the TPFS again. The secondary reconfiguration enables the inverter to continue operating in fault-tolerant mode and the fault tolerant space is greatly improved to make the system more reliable.