## 3 The Adaptive Droop Control of the ILC
### Adaptive Bidirectional Droop Control Strategy
By continuously adapting to real-time deviations, \(\lambda\) allows the interlinking converter to allocate control efforts dynamically, which improves system stability and prevents overcompensation. The simulation results in Section 4.2 further demonstrate that this adaptive mechanism ensures robust performance under load disturbances and unbalanced conditions. In order to facilitate the subsequent calculation and analysis, Equation (6) can be rewritten as  
\[P_{\text{ILC}}^{*}=k(1-\lambda)U_{\text{pu0}}-k\lambda f_{\text{pu0}}, \tag{7}\]  
where  
\[\left\{ \begin{aligned} & U_{\text{pu0}}=U_{\text{dcpu}}+1\\ & f_{\text{pu0}}=f_{\text{acpu}}+1\end{aligned} \right., \tag{8}\]  
where \(U_{\text{pu0}}\) and \(f_{\text{pu0}}\) operate in the range of [0, 2]. When \(U_{\text{pu0}}<f_{\text{pu0}}\) indicates that the degree of AC sub-microgrid power surplus is higher than the degree of power surplus of the DC sub-microgrid, at this time, the power is prioritized to be transmitted from AC to the DC sub-microgrid to regulate the DC voltage. Conversely, when \(U_{\text{pu0}}>f_{\text{pu0}}\) indicates that the degree of power surplus of the DC sub-microgrid is higher than that of the AC sub-microgrid, then the power is preferentially transmitted from the DC to AC sub-microgrid to regulate AC frequency. Therefore, the weight coefficient is positively related to \(f_{\text{pu0}}\)and negatively related to \(U_{\text{pu0}}\). From the above analysis, the weight coefficient can be defined as  
\[\lambda=\left\{ \begin{array}{ll}\frac{f_{\text{pu0}}{}^{n}}{U_{\text{pu0}}{}^{ \alpha}+f_{\text{pu0}}{}^{\alpha}},&|f_{\text{pu0}}-1|>\varepsilon\ \cup|U_{\text{pu0}}-1|>\varepsilon\\ 0.1,&|f_{\text{pu0}}-1|<\varepsilon\ \cap|U_{\text{pu0}}-1|<\varepsilon\end{array}  \right., \tag{9}\]  
where \(\varepsilon\) is a very small value, which can be selected according to the microgrid operation requirements; this paper takes a value of 0.05. When the deviation of the normalized AC frequency and DC voltage is within 5% without adjusting the weight of the bidirectional droop control, at this time, \(\lambda\) takes 0.1. When \(n\) takes different values, the changes are shown in Figure 7.  
From Figure 7, it can be seen that when \(n\) is taken as 1, \(\lambda\) changes slowly, which indicates that the transmission power is not sensitive to the changes in \(U_{\text{pu0}}\) and \(f_{\text{pu0}}\), and it is not possible to fully realize the support mutual aid between the AC and DC micro-networks; when \(n\) is taken as 5, \(\lambda\) changes too fast, and the transmission power is too sensitive to the changes in \(U_{\text{pu0}}\) and \(f_{\text{pu0}}\), making it easy to produce the oscillation instability. When \(n\) is taken as 3, \(\lambda\) can respond appropriately to the changes in \(U_{\text{pu0}}\) and \(f_{\text{pu0}}\) but will not be too sensitive to cause system oscillation and instability. In order to adjust the value of \(\lambda\) according to the changes in \(U_{\text{pu0}}\) and \(f_{\text{pu0}}\) in real time, and to ensure that the system can stably and effectively support the power mutual aid between the microgrids, \(n\) is taken to be 3 in Equation (9), and the weight coefficients shown in Equation (10) are obtained. \[\lambda=\left\{ \begin{array}{ll}\frac{f_{\text{pu0}}{}^{3}}{U_{\text{pu0}}{}^ {\alpha}+f_{\text{pu0}}{}^{\alpha}},&|f_{\text{pu0}}-1|>\varepsilon\ \cup|U_{\text{pu0}}-1|>\varepsilon\\ 0.1,&|f_{\text{pu0}}-1|<\varepsilon\ \cap|U_{\text{pu0}}-1|<\varepsilon\end{array} \right. \tag{10}\]  
By substituting Equation (10) into Equation (7), the adaptive bidirectional droop control equation can be obtained, as shown in Equation (11). \[P_{\text{ILC}}^{*}=\left\{ \begin{array}{ll}\frac{U_{\text{pu0}}{}^{\alpha}- f_{\text{pu0}}{}^{\alpha}}{U_{\text{pu0}}{}^{3}+f_{\text{pu0}}{}^{3}}k,&|f_{ \text{pu0}}-1|>\varepsilon\ \cup|U_{\text{pu0}}-1|>\varepsilon\\ \frac{1}{10}(U_{\text{pu0}}-f_{\text{pu0}})k,&|f_{\text{pu0}}-1|<\varepsilon\ \cap|U_{\text{pu0}}-1|< \varepsilon\end{array} \right.