# Design of a Power Converter for Solar Energy Storage System
## 3 Design and Experimental Results  
### Specifications and Parameter Design  
Table 1 lists the electric component parameters used in the experiment. The rated conversion power was 1 kW, and the switching frequency of the power switches was fixed at 100 kHz. In addition to emphasizing the performance of the bidirectional isolated DC-to-DC converter, matching a practical solar panel with an appropriate energy storage battery was a serious challenge. Figure 8: Circuit diagram for R2D mode. Figure 9: Theoretical waveforms for R2D mode. The parameter values for the main components of the power converter designed in this study are described below. (1)  
Inductor design for boost converter \(L_{1}\) and \(L_{2}\)  
In this scenario, an interleaved boost converter is used. The input has two inductors sharing the input current. Thus, the input current is composed of \(i_{L1}\) and \(i_{L2}\). Under optimal conditions, \(i_{L1}\) is equal to \(i_{L2}\). The relationship between the input power and inductance can be derived from the inductor current and input voltage. Therefore, the inductance value must be obtained. To ensure that the converter can operate when renewable energy is charged to the battery, \(L_{1}\), \(L_{2}\), and the parasitic capacitor \(C_{OSS}\) can form a resonant circuit to achieve zero voltage switching(ZVS) for four switches at the primary side. The inductor current must be designed in discontinuous conduction mode (DCM), and all switches must meet the condition in Equation (12) to achieve ZVS easily. \[i_{min}=\sqrt{\frac{(2\cdot C_{OSS})\cdot{V_{bat}}^{2}}{L_{lk}}} \tag{11}\]  
\[ \begin{cases}-ids1=i_{L1,max}-i_{p}>i_{min},\ for\ S_{1}\\ ids2=i_{L1,min}-i_{p}<i_{min},\ for\ S_{2}\\ -ids3=i_{L2,max}-i_{p}>i_{min},\ for\ S_{3}\\ ids4=i_{L2,min}-i_{p}<i_{min},\ for\ S_{4}\end{cases}  \tag{12}\]  
According to voltage-second balancing theory, the average voltage \(v_{L}\) is 0 during a complete switching period. The discharging time of the inductor is derived as follows:  
\[(1-D)T=DT\cdot\frac{V_{reg}}{V_{bat}-V_{reg}} \tag{13}\]  
The average inductor current \(i_{L,\text{avg}}\) in a switching period is related to \(V_{reg}\), \(V_{bat}\), and the duty cycle \(D\) and is expressed as follows:  
\[i_{L,avg}=\frac{V_{reg}}{2L}\times DT\times(D+D\cdot\frac{V_{reg}}{V_{bat}-V_{ reg}}) \tag{14}\]  
This circuit has two inductors sharing the input current. The input current \(I_{reg}\) is the sum of \(i_{L1,\text{avg}}\) and \(i_{L2,\text{avg}}\). Under optimal conditions, \(i_{L1,\text{avg}}=i_{L2,\text{avg}}=i_{L,\text{avg}}\). Hence, as expressed in Equation (15), \(I_{reg}\) can be set to twice the value of \(i_{L,\text{avg}}\). As expressed in Equation (16), the average power of the converter can be derived by summarizing Equations (13)-(15). In addition, the inductance of \(L_{1}\) and \(L_{2}\) can be determined. As expressed in Equation (17), the inductance \(L\) is approximately 87.6 \(\upmu\)H. To ensure that the switches achieve ZVS, the practical inductance is 81 \(\upmu\)H.  
\[I_{reg}=2\times I_{L,avg} \tag{15}\]  
\[P_{reg}=\frac{{V_{reg}}^{2}\times D^{2}}{L\times f_{s}}\times(1+\frac{V_{reg}} {V_{bat}-V_{reg}}) \tag{16}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Renewable energy port voltage \(V_{reg}\) & 140–170 V \\ Energy storage port voltage \(V_{bat}\) & 240–296 V \\ DC grid voltage \(V_{DC,Grid}\) & 400 V \\ Maximum conversion power \(P\) & 1000 W \\ Power switch switching frequency \(f_{s}\) & 100 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Converter circuit specifications. \[L=\frac{{V_{\text{r}eg}}^{2}\times D^{2}\times\eta}{{P_{bat}\times f_{s}}}\times(1+ \frac{{V_{r\text{g}}}}{{V_{bat}-V_{r\text{g}}}}) \tag{17}\]  
(2) Design of \(C_{\text{bat}}\)  
Equation (18) shows the relationship between \(C_{\text{bat}}\) and \(\Delta v_{\text{Cbat}}\). According to this equation, \(C_{\text{bat}}\) is approximately 85.7 \(\mu\)F. The proposed converter is suitable for use with batteries or high-capacity storage equipment.