# An Intelligent Control Strategy for a Highly Reliable Microgrid in Island Mode
## 2 Materials and Methods
### The Control Strategy for The Off-Grid Microgrid
#### 2.3.2 Adoptable Virtual Impedance Based on the Cloudy Model
\begin{table}
\begin{tabular}{c c} \hline \hline \(e(E_{x},\,E_{n},\,H_{ee})\) & \(ec(E_{x},\,E_{n},\,H_{ee})\) \\ \hline \(e_{NB}(-10,\,3.33,\,0.42)\) & \(ec_{NB}(-3,\,0.89,\,0.32)\) \\ \(e_{NM}(-3.82,\,2.06,\,0.26)\) & \(ec_{NM}(-1.21,\,0.61,\,0.23)\) \\ \(e_{NS}(-1.91,\,1.27,\,0.16)\) & \(ec_{NS}(-0.58,\,0.19,\,0.11)\) \\ \(e_{Z}(0,\,0.79,\,0.1)\) & \(ec_{Z}(0,\,0.40,\,0.05)\) \\ \(e_{PS}(1.91,\,1.27,\,0.16)\) & \(ec_{PS}(0.58,\,0.19,\,0.11)\) \\ \(e_{PM}(3.82,\,2.06,\,0.26)\) & \(ec_{PM}(1.21,\,0.61,\,0.23)\) \\ \(e_{PB}(10,\,3.33,\,0.42)\) & \(ec_{PB}(3,\,0.89,\,0.32)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Digital characteristics for input signals. Figure 4: The adaptive virtual impedance from the membership cloud model. The second step is that the cloud uncertainty reasoning rules are designed. Because there are two input signals \(e\) and \(ec\), the biconditional rules are needed here, which is shown in Figure 5. For example, If \(e=e_{PB}\) and \(ec=ec_{PB}\), then \(Z_{i}=L_{vPB}\). In Figure 5, \(CG_{A}\) is the forward two-dimensional cloud generator. Here cloud generator is represented as CG. It is built from three pairs of digital feature values ((\(E_{xx}\)\(E_{xxc}\)), (\(E_{ne}\)\(E_{nec}\)), (\(H_{ee}\), \(H_{exc}\))), and it satisfies:  
\[\mu(e,ec)=\exp\left(\frac{-(e-E_{xx})^{2}}{2(E_{ne}^{\prime})^{2}}+\frac{-(ec- E_{xxc})^{2}}{2(E_{nec}^{\prime})^{2}}\right), \tag{19}\]  
Here \(E_{ne}^{\prime}=R(E_{ne},H_{ee})\) and \(E_{nec}^{\prime}=R(E_{nec},H_{ee})\). \(CG_{B}\) is the reverse one-dimensional cloud generator with digital characteristic values (\(E_{xi}\), \(E_{ni}\), \(H_{ei}\)), and it satisfies:  
\[Z_{i}=E_{xi}\pm\sqrt{-2\ln[\mu(e,ec)]}E_{ni}^{\prime} \tag{20}\]  
Here \(E_{ne}^{\prime}=R(E_{ni},H_{ei})\). When the deviation \(e<E_{xx}\), the \(\pm\) in (20) takes a negative signal, otherwise it is a positive sign+. \(Z_{i}\) is the numerical output signal value. In Figure 6, it can be seen that the membership cloud model has \(i\) (\(i\) = 1, 2,..., \(n\)) biconditional rules and \(n\) = 49 here. The input signals \(e\) and \(ec\) stimulate different forward two-dimensional cloud generators \(CG_{Ai}\) to generate membership \(\mu_{Ai}\), then \(\mu_{Ai}\) pass through the reverse one-dimensional cloud generators \(CG_{BIi}\) and \(CG_{BRi}\) to generate a large number of numeric outputs \(Z_{Li}\) and \(Z_{Ri}\) to get the virtual impedance \(L_{\varphi}\) and \(R_{v}\), respectively. The final numeric outputs \(L_{\varphi}\) and \(R_{v}\) are calculated by the weighted average value of \(m\)\(Z_{Li}\) and \(Z_{Ri}\), respectively as:  
\[L_{v}=\frac{\sum\limits_{i=1}^{m}Z_{Li}\mu_{Ai}}{\sum\limits_{i=1}^{m}\mu_{Ai}}, \tag{21}\]  
\[R_{v}=\frac{\sum\limits_{i=1}^{m}Z_{Ri}\mu_{Ai}}{\sum\limits_{i=1}^{m}\mu_{ Ai}}, \tag{22}\]  
Figure 5: Biconditional rule generator. \begin{table}
\begin{tabular}{c c} \hline \(L_{V}(E_{xL}\)\(E_{nL}\)\(H_{eL}\)) & \(R_{V}(E_{xR}\)\(E_{nR}\)\(H_{eR})\) \\ \hline \(L_{V,NB}(-6\times 10^{-4},\,2\times 10^{-4},\,4.2\times 10^{-4})\) & \(R_{V,NB}(-2.5\times 10^{-2},\,8.3\times 10^{-3},\,8.4\times 10^{-4})\) \\ \(L_{V,NM}(-2.9\times 10^{-4},\,1.2\times 10^{-4},\,2.6\times 10^{-4})\) & \(R_{V,NM}(-9.5\times 10^{-3},\,5.2\times 10^{-3},\,5.2\times 10^{-4})\) \\ \(L_{V,NS}(-1.9\times 10^{-4},\,0.76\times 10^{-4},\,1.6\times 10^{-4})\) & \(R_{V,NS}(-4.8\times 10^{-3},\,3.2\times 10^{-3},\,3.2\times 10^{-4})\) \\ \(L_{V,Z}(0,0.5\times 10^{-4},\,1\times 10^{-4})\) & \(R_{V,Z}\) (0, \(2\times 10^{-3},\,2\times 10^{-4})\) \\ \(L_{V,PS}(1.9\times 10^{-4},\,0.76\times 10^{-4},\,1.6\times 10^{-4})\) & \(R_{V,PS}(4.8\times 10^{-3},\,3.2\times 10^{-3},\,3.2\times 10^{-4})\) \\ \(L_{V,PM}(2.9\times 10^{-4},\,1.2\times 10^{-4},\,2.6\times 10^{-4})\) & \(R_{V,PM}(9.5\times 10^{-3},\,5.2\times 10^{-3},\,5.2\times 10^{-4})\) \\ \(L_{V,PB}(6\times 10^{-4},\,2\times 10^{-4},\,4.2\times 10^{-4})\) & \(R_{V,PB}(2.5\times 10^{-2},\,8.3\times 10^{-3},\,8.4\times 10^{-4})\) \\ \hline \end{tabular}
\end{table} 
Table 5: Digital characteristics for output signals.