## 3 The Adaptive Droop Control of the ILC
### Adaptive Bidirectional Droop Control Strategy  
The hybrid AC-DC microgrid ILC control is designed so that the side with the larger AC frequency deviation \(\Delta\)f\({}_{\rm{ac}}\) or DC voltage deviation \(\Delta\)U\({}_{\rm{dc}}\) is compensated for power on the other side. From Equations (1) and (2), it can be seen that the AC and DC sub-microgrids have droop characteristics at their ports, which can be measured by comparing the AC sub-microgrid frequency \(f_{\rm{ac}}\) and the DC sub-microgrid bus voltage \(U_{\rm{dc}}\) for absorbing or transmitting power at the ports of the AC and DC sub-microgrids. Since \(f_{\rm{ac}}\) and \(U_{\rm{dc}}\) are two parameters of different unit scales, they cannot be analyzed and compared in the same region. In order to unify the dimension and simplify the control, the AC frequency and DC voltage are normalized [15], as shown in Equation (4). \[\left\{ \begin{matrix}f_{\rm{acpu}}=\frac{f_{\rm{ac}}-0.5(f_{\rm{acma}}+f_{ \rm{acmin}})}{0.5(f_{\rm{acma}}-f_{\rm{acmin}})}\\ U_{\rm{dcpu}}=\frac{U_{\rm{dc}}-0.5(U_{\rm{dcmin}}+U_{\rm{dcmin}})}{0.5(U_{ \rm{dcma}}-U_{\rm{dcmin}})}\end{matrix} \right., \tag{4}\]  
where \(f_{\rm{acpu}}\) is the normalized AC frequency; \(U_{\rm{dcpu}}\) is the normalized DC voltage. After the normalization process of Equation (4), both the frequency and voltage of the hybrid AC-DC microgrid at a normal allowable time are unified to the variation range of [\(-\)1, 1]. In Equation (4), the normalization of AC frequency and DC voltage is performed using their respective rated operating ranges. Specifically, the AC frequency is normalized based on the standard deviation range of 49-51 Hz, and the DC voltage is normalized using a nominal window of 750-850 V. These ranges are selected based on typical allowable  
Figure 6: The topology of the ILC. variations in power system standards and practical microgrid operating conditions. If the normalization ranges are set too narrowly, minor deviations may cause overly aggressive regulation; if too wide, the system may fail to adequately respond to significant disturbances. The simulation results in Section 4.3 show that the proposed control strategy remains effective when the normalization limits are varied by \(\pm 5\%\), indicating relatively low sensitivity within a practical range. The hybrid AC-DC microgrid in islanding mode transmits power through the ILC to eliminate the difference between \(f_{\text{acpu}}\) and \(U_{\text{dcpu}}\), and the system transmission reaches an optimal steady state when \(f_{\text{acpu}}\) and \(U_{\text{dcpu}}\) are equal. The conventional normalized droop characteristic of the ILC can be expressed as shown in Equation (5). \[P_{\text{ILC}}^{*}=k(U_{\text{dcpu}}-f_{\text{acpu}}), \tag{5}\]  
where \(k\) is the droop coefficient, which can be set according to the maximum transmission power of ILC. The above traditional normalized droop control realizes the bidirectional control of active power, but based on the fixed droop coefficient, it cannot well adjust the priority of DC voltage and AC frequency response under different operating conditions. Therefore, it can be corrected by introducing the weight coefficient in Equation (5) to get Equation (6). \[P_{\text{ILC}}^{*}=k(1-\lambda)U_{\text{dcpu}}-k\lambda f_{\text{acpu}} \tag{6}\]  
The variation range of \(\lambda\) is (0, 1), and by changing the value of the droop coefficient, the ILC can coordinate the priority of the AC side and DC side power support so as to ensure the balanced compensation of the AC frequency and DC voltage during perturbation. The weight coefficient \(\lambda\) reflects the relative urgency between AC frequency and DC voltage regulation. Physically, it acts as a dynamic indicator that determines which sub-microgrid (AC or DC) requires a stronger control response at any given time. When \(\lambda\) approaches 1, the system prioritizes frequency regulation, indicating that the AC sub-microgrid is under more stress. Conversely, a value closer to 0 gives priority to DC voltage regulation.