## 3 Distribute Generation Unit Model and Lower Converter Control  
### Photovoltaic Power Generation Unit Model and Control Strategy  
The photovoltaic cell is the smallest unit of a photovoltaic array. It is a kind of semiconductor device that uses the photovoltaic effect to convert light energy into electric energy directly [20]. When the light intensity is constant, the photo-generated current is basically constant, so it can be equivalent to a constant current source. When the photo-generated current passes through the load, the terminal voltage will be formed on the load. This voltage will cause the positive-negative (PN) junction to be forward-biased and generate the dark current that is opposite to the photo-generated current. At the same time, because the material of the photovoltaic panel itself has a certain resistivity,  
Figure 2: Hierarchical control architecture of AC/DC hybrid microgrid. it is equivalent to a resistor \(R_{\rm s}\) connected in series with a constant current source. In the manufacturing process, process defects will cause leakage current of photovoltaic panels. In order to eliminate errors, parallel resistance \(R_{sh}\) is introduced [21]. Combined with the above analysis, the equivalent physical circuit model of the photovoltaic cell is shown in Figure 3.  
In practical application, it is difficult to determine some parameters in the physical circuit model shown in Figure 3. Therefore, the engineering model is generally adopted [22]. Equation (1) is shown as follow:  
\[I=I_{\rm sc}-C_{1}I_{\rm sc}\Big{[}\exp\Big{(}\frac{U}{C_{2}U_{\rm{oc}}}\Big{)} -1\Big{]}, \tag{1}\]  
where \(C_{1}\) and \(C_{2}\) are defined as:  
\[\left\{ \begin{array}{l}C_{1}=(1-\frac{I_{\rm m}}{I_{\rm sc}})\exp(-\frac{U_{ \rm m}}{C_{2}U_{\rm{oc}}})\\ C_{2}=(\frac{U_{\rm m}}{U_{\rm{oc}}}-1)\Big{[}\ln(1-\frac{I_{\rm m}}{I_{\rm sc} })\Big{]}^{-1}\end{array} \right., \tag{2}\]  
where \(I_{sc}\) is the short-circuit current of the photovoltaic cell under standard test conditions, \(U_{\rm{oc}}\) is the open-circuit voltage, \(I_{m}\) is the maximum power point current, and \(U_{m}\) is the maximum power point voltage. The voltage of a single photovoltaic cell is relatively low. So, in practice application, it is often necessary to connect multiple photovoltaic units in series to form a photovoltaic array. When the output voltage and current of the photovoltaic cell are \(U\) and \(I\), respectively, the output voltage \(U_{\rm{pv\_array}}\) and \(I_{\rm{pv\_array}}\) current of the photovoltaic array are expressed as:  
\[\left\{ \begin{array}{l}U_{\rm{pv\_array}}=N_{\rm s}U\\ I_{\rm{pv\_array}}=N_{\rm p}I\end{array} \right., \tag{3}\]  
where \(N_{\rm s}\) and \(N_{\rm p}\) are the series and parallel number of photovoltaic cells. In this paper, both photovoltaic #1 and photovoltaic #2 use perturbation and observation method (Perturbation and Observation, P&O) to realize MPPT control [23]. This method uses a fixed step size to reduce or increase the input reference voltage of the converter, thereby moving the operating point closer to the maximum power point. Compared with other MPPT methods, the P&O method requires fewer sensors, has lower calculation complexity, and is simple to implement. The control strategy of DC side photovoltaic unit photovoltaic #1 is shown in Figure 4.  
Figure 3: Physical circuit model of the photovoltaic cell.