## 2 Hybrid Microgrid Topology and Its Sub-Microgrid Control
### AC-DC Sub-Microgrid Control
#### 2.2.1 AC Sub-Microgrid Control  
In this paper, the wind power generation system adopts a permanent magnet direct-drive wind turbine and is connected to the AC bus through the back-to-back dual PWM converter AC-DC-AC three-stage conversion interface circuit, whose main circuit and control strategy are shown in Figure 2.  
In Figure 2, \(\psi_{f}\) is the rotor permanent magnet chain, \(L_{\text{d}}\) and \(L_{\text{q}}\) are the stator winding d-axis and q-axis inductances, \(\theta_{r}\) is the machine-side phase angle, \(\theta_{\text{g}}\) is the net-side phase angle, \(R_{f}\) and \(L_{f}\) are the net-side filter resistor and the net-side filter inductance, \(U_{\text{wdc}}\) is the dc bus voltage between the machine-side AC-DC converter and the net-side DC-AC converter, and \(I_{\text{wg}}\) and \(U_{\text{wg}}\) are the net-side current and voltage, respectively. Figure 1: Hybrid microgrid topology in islanding mode. First, for the control of the machine-side AC-DC converter, the given rotor angular velocity \(\omega_{\rm r}^{*}\) of the permanent magnet synchronous motor is obtained by the maximum power tracking method. The deviation value of the given rotor angular velocity \(\omega_{\rm r}^{*}\) from the actual rotor angular velocity \(\omega_{\rm r}\) is passed through the PI controller to obtain the given value of the AC-DC converter input current in q-axis \(I_{\rm wq}^{*}\). The AC-DC converter input current in d-axis is given as \(I_{\rm wd}^{*}\ =\ 0\). The given values of the current under the above dq-axis are passed through the current inner loop to obtain the modulating signal, and then the three-phase voltage modulating wave signals are obtained by coordinate transformation. Finally, the control pulse signals are obtained by SPWM [27]. For the control of the grid-side DC-AC converter, the DC-AC converter output current in q-axis is given as \(I_{\rm wgq}^{*}\ =\ 0\). The deviation of the DC voltage between the machine-side and the grid-side converters from its given value is passed through a PI controller to obtain the given value \(I_{\rm wgd}^{*}\) under the d-axis of the grid-side output current. The given values of current under the above dq-axis are passed through the current inner loop to obtain the modulating signals, and then the three-phase voltage modulating wave signals are obtained by coordinate transformation. Finally, the control pulse signals are obtained by SPWM. In this paper, two power conversion systems are controlled by droop control. The expression for the droop characteristic of PCS is shown in Equation (1). \[\left\{ \begin{aligned} & f_{\rm ac}=f_{\rm ac}^{*}-k_{\rm pi}(P_{\rm aci}-P_{ \rm aci}^{*})\\ & U_{\rm ac}=U_{\rm ac}^{*}-k_{\rm qi}(Q_{\rm aci}-Q_{\rm aci}^{*} )\end{aligned} \right., \tag{1}\]  
where the subscript \(i\) (\(i\) = 2, 3) denotes the number of DG in the AC sub-microgrid; \(P_{\rm aci}\) is the active power output from DG\({}_{i}\) in the AC sub-microgrid; \(P_{\rm aci}^{*}\) is the active power output from DG\({}_{i}\) in the AC sub-microgrid under the rated working condition; \(f_{\rm ac}^{*}\) is the rated frequency; \(f_{\rm ac}\) is the reference value for the AC sub-microgrid frequency; \(k_{\rm pi}\) is the active droop coefficient; Q\({}_{\rm aci}\) is the reactive power output from the AC sub-microgrid DG\({}_{i}\); Q\({}_{\rm aci}^{*}\) is the reactive power output from the AC sub-microgrid DG\({}_{i}\) under the rated condition; \(U_{\rm ac}^{*}\) is the rated AC voltage; \(U_{\rm ac}\) is the reference value of AC sub-microgrid AC voltage; and k\({}_{\rm qi}\) is the reactive power droop coefficient. The values of k\({}_{\rm pi}\) and k\({}_{\rm qi}\) are related to the capacity of DG. Both PCSs are three-phase DC-AC converters, with the front stage connected to the energy storage battery, which is replaced by a DC power supply in this paper, and the rear  
Figure 2: Control diagram of direct-drive wind power generation system. stage is connected to the AC bus.