# TAB Series-Resonant DC-DC Converter and Multi-Phase-Shift Based Global Optimization Modulation
## 3 Global Optimization of Multiple Phase Shifts to Minimize Ohmic Loss  
For the converter, besides realizing the real-time adjustment of the transfer power, one important aspect is to reduce the power loss. In theory, there are five phase shifts that can be used to adjust the transfer power. In this section, reducing the power loss and increasing the operating efficiency in the entire voltage and power range are used as the objective to optimize the multi-phase-shift modulation. In addition, the soft-switching performance is analyzed. The power loss of the converter mainly includes the switching loss \(P_{\rm{sw}}\), the conduction loss \(P_{\rm{cond}}\), the copper loss \(P_{\rm{copp}}\), the iron loss \(P_{\rm{iron}}\), and so on. Combined with the theoretical analysis and the distribution diagram of the power loss in [24], both \(P_{\rm{cond}}\) and \(P_{\rm{copp}}\) are positively correlated with the square of the RMS value of the transformer current, thus, they are collectively called the ohmic loss \(P_{\rm{ohm}}\). \(P_{\rm{ohm}}\) has a high proportion of the total power loss in the entire power range. As the transfer power and the transformer current increase, the proportion of \(P_{\rm{ohm}}\) increases accordingly. Hence, reducing \(P_{\rm{ohm}}\) is effective to improve the converter efficiency. \(P_{\rm{ohm}}\), \(P_{\rm{cond}}\), and \(P_{\rm{copp}}\) are respectively calculated as  
\[P_{\rm{ohm}}=P_{\rm{cond}}+P_{\rm{copp}} \tag{13}\]  
\[P_{\rm{cond}}=4R_{\rm{DS1}}(\frac{{I_{\rm{r1 frms}}}}{\sqrt{2}})^{2}+4R_{\rm{DS2 }}(\frac{{I_{\rm{r2 frms}}}}{\sqrt{2}})^{2}+4R_{\rm{DS3}}(\frac{{I_{\rm{r3 frms}} }}{\sqrt{2}})^{2} \tag{14}\]  
\[P_{\rm{copp}}=R_{\rm{trans1}}{I_{\rm{r1 frms}}}^{2}+R_{\rm{trans2}}{I_{\rm{r2 frms }}}^{2}+R_{\rm{trans3}}{I_{\rm{r3 frms}}}^{2} \tag{15}\]  
where \(R_{\rm{DS1}}\), \(R_{\rm{DS2}}\), and \(R_{\rm{DS3}}\) respectively denote the on-state resistance of the power switches of each port. \(R_{\rm{trans1}}\), \(R_{\rm{trans2}}\), and \(R_{\rm{trans3}}\) respectively denote the resistance of the transformer windings of each port. \({I_{\rm{r1 frms}}}\), \({I_{\rm{r2 frms}}}\), and \({I_{\rm{r3 frms}}}\) respectively denote the RMS value of the fundamental component of the transformer current of each port. From (13)-(15), \(P_{\rm ohm}\) is closely related to \(I_{\rm r1f,rms}\), \(I_{\rm r2f,rms}\), and \(I_{\rm r3f,rms}\). The smaller the RMS value of the transformer current is, the smaller the ohmic loss will be. Therefore, the optimization objective of the modulation is equivalent to minimizing the RMS value of the transformer current. After the power is decoupled between port 1 and port 2, \(i_{\rm r1f}=i_{\rm r13f}\), and \(i_{\rm r2f}=i_{\rm r23f}\), hence, combining (6) and (7), \(I_{\rm r1f,rms}\), and \(I_{\rm r2f,rms}\) are calculated as  
\[I_{\rm r1f,\ rms}=\frac{\sqrt{8}\wp_{3}}{\pi X_{13}}\sqrt{\left(\frac{1}{k_{1} }\cos(\frac{D_{1}\pi}{2})\right)^{2}+\left(\cos(\frac{D_{3}\pi}{2})\right)^{2 }-\frac{2}{k_{1}}\cos(\frac{D_{1}\pi}{2})\cos(\frac{D_{3}\pi}{2})\cos(\varphi _{13}\pi)} \tag{16}\]  
\[I_{\rm r2f,\ rms}=\frac{\sqrt{8}\wp_{3}}{\pi X_{23}}\sqrt{\left(\frac{1}{k_{2} }\cos(\frac{D_{2}\pi}{2})\right)^{2}+\left(\cos(\frac{D_{3}\pi}{2})\right)^{2 }-\frac{2}{k_{2}}\cos(\frac{D_{2}\pi}{2})\cos(\frac{D_{3}\pi}{2})\cos(\varphi _{23}\pi)} \tag{17}\]  
The fundamental component of ir3f is composed of \(i_{\rm r1f}\) and \(i_{\rm r2f}\). The relationship of the phasors \(\stackrel{{\rightarrow}}{{I}}_{\rm r1f}\), \(\stackrel{{\rightarrow}}{{I}}_{\rm r2f}\) and \(\stackrel{{\rightarrow}}{{I}}_{\rm r3f}\) of the transformer current \(i_{\rm r1f}\), \(i_{\rm z1f}\), and \(i_{\rm r3f}\) is shown in Figure 4, where \(\varepsilon\) is the phase difference between \(\stackrel{{\rightarrow}}{{I}}_{\rm r1f}\) and \(\stackrel{{\rightarrow}}{{I}}_{\rm r2f}\).