## 3 Control Strategy
### Power Coordinated Control  
The PET should be able to offer coordinated control for power flows of all ports when the power demand of the output stage changes, in order to ensure safe and stable operations of the AC/DC hybrid distribution system. It can be seen from Figure 2 that the DC side of the input stage and the input side of the isolation stage are connected in parallel, and the input sides of ISOS and ISOP are connected in series. Since the DC side voltage of the input stage is necessarily controlled to remain consistent, it is able to adjust the input side voltages of ISOS and ISOP at the isolation stage to change the power flow and fulfill the power demand of the ports at the output stage.  
In order to facilitate the analysis, the average model of each stage is developed and shown in Figure 9, where \(R_{\mathrm{L1}}\) and \(R_{\mathrm{L2}}\) represent the equivalent loads.  
Figure 8: Input-series output-parallel (ISOP) connection: (**a**) Topology; (**b**) Block diagram.  
Figure 9: \(Cont.\)  
Set the input power of the input stage MMC to \(P\), and the output power of the AC and DC output port to \(P_{1}\) and \(P_{2}\), respectively. Equations (17)-(19) can be obtained when the PET operates stably and the circuit loss is negligible:  
\[P=P_{1}+P_{2} \tag{17}\]  
\[U_{\mathrm{dc}}=U_{\mathrm{dc1}}+U_{\mathrm{dc2}} \tag{18}\]  
\[\frac{P_{1}}{P_{2}}=\frac{U_{\mathrm{dc1}}}{U_{\mathrm{dc2}}} \tag{19}\]  
Since \(U_{\mathrm{dc}}\) is controlled by the input stage to remain at a set value, and the output powers (\(P_{1}\), \(P_{2}\)) of AC and DC output ports are given, Equations (20)-(21) can be derived from Equations (17)-(19):  
\[U_{\mathrm{dc1}}=U_{\mathrm{dc}}\frac{P_{1}}{P_{1}+P_{2}} \tag{20}\]  
\[U_{\mathrm{dc2}}=U_{\mathrm{dc}}\frac{P_{2}}{P_{1}+P_{2}} \tag{21}\]  
When the power demand of the output ports changes, PET will be unable to stably operate if the adjusting is not made to the input side voltage of the isolation stage. Hence, assuming variations of the power demand of AC output port and DC output port are \(\Delta P_{1}\) and \(\Delta P_{2}\), respectively, \(U_{\mathrm{dc1}}\) and \(U_{\mathrm{dc2}}\) should be adjusted to \(U^{\prime}_{\mathrm{dc1}}\) and \(U^{\prime}_{\mathrm{dc2}}\) as shown in Equations (22)-(23) to meet the power demand.  
\[U^{\prime}_{\mathrm{dc1}}=U_{\mathrm{dc}}\frac{P_{1}+\Delta P_{1}}{P_{1}+ \Delta P_{1}+P_{2}+\Delta P_{2}} \tag{22}\]  
\[U^{\prime}_{\mathrm{dc2}}=U_{\mathrm{dc}}\frac{P_{2}+\Delta P_{2}}{P_{1}+ \Delta P_{1}+P_{2}+\Delta P_{2}} \tag{23}\]  
The correlations between voltage adjustments (\(\Delta U_{\mathrm{dc1}}\), \(\Delta U_{\mathrm{dc2}}\)) and power variations (\(\Delta P_{1}\), \(\Delta P_{2}\)) can be derived through Equations (20)-(23) and are given by Equations (24)-(25):  
\[\Delta U_{\mathrm{dc1}}=U_{\mathrm{dc}}\bigg{(}\frac{P_{1}+\Delta P_{1}}{P_{1 }+\Delta P_{1}+P_{2}+\Delta P_{2}}-\frac{P_{1}}{P_{1}+P_{2}}\bigg{)} \tag{24}\]  
\[\Delta U_{\mathrm{dc2}}=U_{\mathrm{dc}}\bigg{(}\frac{P_{2}+\Delta P_{2}}{P_{1 }+\Delta P_{1}+P_{2}+\Delta P_{2}}-\frac{P_{2}}{P_{1}+P_{2}}\bigg{)} \tag{25}\]  
Based on the above discussion, a control strategy is proposed that when the power demands of the AC/DC output ports changes, stabilizing \(U_{\mathrm{dc}}\) and adjusting \(U_{\mathrm{dc2}}\) according to Equation (24)  
Figure 9: Average model: (**a**) Input stage MMC; (**b**) isolation stage and output stage.  
can effectuate the power coordinated control. It is worth mentioning that the control strategy is also applicable for multiple AC/DC output ports.