# 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  
When one of or two of power switches in inverter 1 are faulty, the topology of the inverter 1 will be reconfigured as a three phases four switches (TPFS) structure to keep operating. The corresponding triacs are connected. For example, one of two reconfiguring processes of inverter 1 is shown in Figure 2. Figure 2a is the equivalent circuit for the reconfigurable inverter 1. When V\({}_{1}\) is in open circuit faulty, TR\({}_{4}\) is on and stop trigger V\({}_{2}\). The DC link takes the place of phase \(c\). Then inverter 1 is reconfigured as TPFS as shown in Figure 2d and runs continuously. The first reconfiguration is finished, which is shown in Figure 2b. If V\({}_{4}\) is in open circuit faulty for the reconfigured inverter 1, TR\({}_{4}\) is still on, TR\({}_{2}\) on and V\({}_{2}\) takes the place of V\({}_{4}\). The second reconfiguration is finished as shown in Figure 2c and the inverter 1 is reconfigured as TPFS again. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Nodes** & **Inverter 1** & **Inverter 2** \\ \hline
1 & Normal & Normal \\
2 & Normal & Removed \\
3 & TPFS & Removed \\
4 & TPFS & Normal \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Four operating modes. Figure 1: Topology of the off-grid microgrid with the reconfigurable inverter 1. Figure 2: The one of two reconfiguring processes of inverter 1. (**a**)The equivalent circuit; (**b**) The first reconfiguring process; (**c**) The second reconfiguring process; (**d**) The reconfigured result as TPFS. In Figure 2a, \(u_{ao}\), \(u_{bo}\), and \(u_{co}\) are the midpoint voltages between the midpoint of the three phase bridge arms and the midpoint of the DC side. The fault characteristics of the midpoint voltages are analyzed after an open-circuit fault occurs in the reconfigurable inverter 1. Then these features are used for fault diagnosis. The fault diagnosis can be used in TPFS and TPSS structures. The bridge switch function \(S_{x}\) is set as:  
\[S_{x}=\left\{ \begin{array}{ll}1\ \ \text{upper}\ \ \text{bridge}\ \ \text{on}\\ -1\ \ \text{lower}\ \ \text{bridge}\ \ \text{on}\ \ \text{,}\end{array} \right. \tag{1}\]  
Here phase \(x=(a,b,c)\). The midpoint voltage \(u_{xo}\) without fault can be obtained from Figure 2a as:  
\[u_{xo}=\frac{u_{dc}}{2}S_{x}, \tag{2}\]  
when V\({}_{1}\) is in an open-circuit fault and \(S_{c}=1\), V\({}_{1}\) and V\({}_{2}\) are both disconnected, and \(c\) is suspended, then \(i_{c}=0\). The potential of point \(c\) is equal to that of point \(n\) and there is \(u_{coF1}=u_{n01}\). The midpoint voltage \(u_{coF1}\) after the first fault can be obtained:  
\[u_{coF1}=u_{n01}=\frac{u_{ao1}+u_{b01}}{3}=\frac{u_{dc}}{3}(S_{a}+S_{b})-u_{ dc}, \tag{3}\]  
Then different \(S_{a}\) and \(S_{b}\) are substituted into the Equation (3), the midpoint voltage of the faulty bridge is obtained as:  
\[u_{coF1}<\frac{u_{dc}}{2}, \tag{4}\]  
The polarity \(J_{xo}\) of the midpoint voltage of the bridge \(x\) is defined as:  
\[J_{xo}=J[u_{coF1}-u_{xoN}], \tag{5}\]  
where \(u_{xoF}\) denotes the midpoint voltage after one power switch is fault at phase \(x\). \(u_{xoN}\) is the normal midpoint voltage at phase \(x\). \(x=(a,b,c)\). When V\({}_{1}\) is in an open-circuit fault and \(S_{c}=1\), according to Equations (2) and (4), there is the polarity \(J_{co}\) of the midpoint voltage of the bridge \(c\):  
\[J_{co1}=J[u_{coF1}-u_{coN1}]=N, \tag{6}\]  
The difference of the midpoint voltage of the bridge before and after fault is less than 0. That is to say, this polarity of the voltage difference is negative \(N\). The reconfiguration process after the fault of inverter 1. V\({}_{1}\) is removed is shown in Figure 2b. TR\({}_{4}\) is triggered on and stops sending triggering pulses to V\({}_{2}\). The phase \(c\) is replaced by the DC-side capacitors. The inverter can be reconstructed into the TPFS structure which is shown in Figure 2d. The first fault diagnosis and reconfiguration are finished.