# A Three-Port Power Electronic Transformer Based on Magnetic Integration
## 2 Description of the Proposed PET Topology  
The schematic of the proposed PET is depicted in Figure 2a. Based on a typical MMC, in each phase, the arm inductors are incorporated into the same core of HF transformer to  
Figure 1: Application of the proposed three-port PET. form an integrated transformer. The integrated transformer consists of a primary winding with center tap and a secondary winding. The primary winding also acts as arm inductors and its center tap is connected to the MVAC port by the transformer leakage inductance \(L_{\text{g}}\). Meanwhile, the secondary winding is connected to LVDC port through leakage inductance \(L_{\sigma}\) and an H-bridge. In addition, an MMC DC bus is connected to the MVDC port via a small \(LC\) filter. In this structure, six arm inductors and a large number of transformers in traditional MMC-based PET [7] are simplified to three integrated transformers, which reduces the core material [14]. Moreover, an LVDC port can be obtained on the secondary side with only three H-bridges. Thus, the proposed PET enables a compact design that reduces the number of magnetic components and power cells (its economic benefits have been demonstrated in Section 6). The basic principle of the proposed PET is to control MVDC, MVAC, and LVDC ports, respectively, by using DC, low-frequency (LF), and HF components of MMC. Then the upper and lower arm voltages \(u_{\text{P}x}\) and \(u_{\text{N}x}\), and the upper and lower arm currents \(i_{\text{P}x}\) and \(i_{\text{N}x}\) of \"\(x\)\" phase (\(x=\text{a}\), \(\text{b}\), \(\text{c}\)) are  
\[ \begin{cases}u_{\text{P}x}=\frac{1}{2}u_{\text{MVDC}}-u_{x}-u_{\text{mx}}\\ u_{\text{N}x}=\frac{1}{2}u_{\text{MVDC}}+u_{x}-u_{\text{mx}}\end{cases} , \begin{cases}i_{\text{P}x}=\frac{1}{2}i_{\text{MVDC}}+\frac{1}{2}i_{x}+i_{ \text{mx}}\\ i_{\text{N}x}=\frac{1}{2}i_{\text{MVDC}}-\frac{1}{2}i_{x}+i_{\text{mx}}\end{cases}  \tag{1}\]  
Figure 2: The proposed three-port PET: (**a**) circuit topology; (**b**) equivalent circuit of “\(x\)” phase (the blue line indicates the HF loop). where \(\frac{1}{2}u_{\text{MVDC}}\), \(u_{x}\) and \(u_{\text{mx}}\) are the DC, LF, and HF voltage components, respectively, \({}^{1}/\dot{y}_{\text{MVDC}}\), \(\frac{1}{2}\dot{t}_{x}\) and \(i_{\text{mx}}\) are DC, LF and HF current components, respectively. Note that the HF voltage \(u_{\text{mx}}\) is applied on the primary windings of the integrated transformer, and there is another HF voltage \(u_{\text{xx}}\) generated by the H-bridge on secondary side. By adjusting the phase shift angle \(\varphi\) between \(u_{\text{mx}}\) and \(u_{\text{xx}}\), the LVDC port power can be controlled (similarly to DAB). The DC, LF and HF current components all flow through the primary winding of the integrated transformer and they are separable, which is the basis for achieving three ports. For the DC component, it flows through the primary winding and enters the MVDC port with no effects on MVAC and LVDC ports. For LF current component, it never enters the MVDC port but flows into the MVAC port via the center tap, where the currents split in the primary winding and have an inverse direction. Thus, the magnetic fluxes (marked as red in Figure 2a) excited by LF currents are cancelled, without affecting the secondary LVDC port. For the HF current component, it has the same direction in the split primary windings thus obtaining a mutually intensified magnetic flux (marked as blue in Figure 2a), which transfers power to the secondary side LVDC port. Note that HF current also flows through the primary winding and enters the MVDC bus. Fortunately, a small filter capacitor \(C_{\text{f}}\) can provide low-impedance return path for the HF current. To sum up, the three current components correspond to the three-port power transfer, respectively. According to the DC, LF and HF components, the three port equivalent circuit loops, namely DC loop, LF loop and HF loop can be extracted, individually, as shown in Figure 2b.