# Application of MMC-RPC in High-Speed Railway Traction Power Supply System Based on Energy Storage
## 2 Principle of MMC-RPC
\right., \tag{4}\]  
According to Equations (2)-(4), the relationship between bridge leg current and voltage can be obtained: \(i_{\mathrm{qp}}=i_{\mathrm{bnr}}\), \(i_{\mathrm{an}}=i_{\mathrm{bp}}\), \(u_{\mathrm{ap}}=u_{\mathrm{bn}}\), and \(u_{\mathrm{an}}=u_{\mathrm{bp}}\). Since the output of the MMC-RPC is a single intersection flow and has only a single degree of freedom, it cannot separate the instantaneous active power and reactive power through Park transformation such as the three-phase MMC. Therefore, with the help of SOGI, this study constructs a virtual component orthogonal to the actual quantity, to delay the phase of the single-phase component by 90 degrees. The transfer function of SOGI is [10]:  
\[G(s)=\frac{\omega s}{\omega^{2}+s^{2}}, \tag{5}\]  
After constructing the orthogonal virtual component, equations of AC quantities in dq coordinate system can be obtained in (6), and the active and reactive power of single phase system can be extracted in (7) [10]:  
\[\left\{ \begin{array}{l}u_{\mathrm{jd}}=u_{\mathrm{skd}}-2R_{\mathrm{s}}i_{ \mathrm{sd}}-2L_{\mathrm{s}}\frac{di_{\mathrm{jd}}}{dt}\\ u_{\mathrm{jq}}=u_{\mathrm{skd}}-2R_{\mathrm{s}}i_{\mathrm{sq}}-2L_{\mathrm{s}} \frac{di_{\mathrm{sdq}}}{dt}\end{array} \right., \tag{6}\]  
\[\left[ \begin{array}{l}p\\ q\end{array} \right]=\frac{1}{2} \begin{bmatrix}u_{\mathrm{d}}&u_{\mathrm{q}} \\ u_{\mathrm{q}}&-u_{\mathrm{d}}\end{bmatrix}\begin{bmatrix}i_{\mathrm{d}}\\ i_{\mathrm{q}}\end{bmatrix} , \tag{7}\]  
Through the above single-phase instantaneous power calculation method, the active power \(P_{\mathrm{L}}\), \(P_{\mathrm{R}}\), reactive power \(Q_{\mathrm{L}}\), \(Q_{\mathrm{R}}\) of the load fundamental wave on the left and right power supply arms can be obtained, realizing active power balance, reactive power compensation and harmonic power suppression. Figure 2 shows the power compensation diagram under heavy load on the left arm and light load on the right arm of the traction network. \(U_{\mathrm{A}}\), \(U_{\mathrm{B}}\) and \(U_{\mathrm{C}}\) are the three-phase voltages of the power grid. \(P_{\mathrm{Lref}}\), \(P_{\mathrm{Rref}}\), \(Q_{\mathrm{Lref}}\) and \(Q_{\mathrm{Rref}}\) are the active power and reactive power compensation reference quantities of the traction power supply arms. In order to achieve active power balance, MMC-RPC needs to transfer \(0.5\!\mid\!P_{\mathrm{L}}-P_{\mathrm{R}}\!\mid\) power from the right power supply arm to the left arm with the heavy load, to obtain the expected power \(P_{\mathrm{L}}\!^{\prime}=P_{\mathrm{R}}\!^{\prime}\) for two power supply arms. Secondly, considering the relationship between the primary and secondary sides of the traction transformer in Figure 2, the left and right power supply arms compensate \(P_{\mathrm{L}}\!^{\prime}\mathrm{tan30^{\circ}}+Q_{\mathrm{L}}\) and \(P_{\mathrm{R}}\!^{\prime}\mathrm{tan30^{\circ}}-Q_{\mathrm{R}}\) reactive power, respectively, to realize the three-phase current balance on the primary side of the \(V/v\) traction transformer, and eliminate the negative sequence current. Finally, according to  
the distorted current existing in the system in the actual simulation, the power reference components \(P_{\text{LH}}\), \(P_{\text{RH}}\), \(Q_{\text{LH}}\) and \(Q_{\text{RH}}\) of harmonic suppression are superimposed to obtain the references:  
\[P_{\text{Rref}}=\frac{P_{\text{R}}-P_{\text{L}}}{2}-P_{\text{RH}}, \tag{8}\]  
\[P_{\text{Lref}}=\frac{P_{\text{L}}-P_{\text{R}}}{2}-P_{\text{LH}}, \tag{9}\]  
\[Q_{\text{Rref}}=-Q_{\text{R}}+P_{\text{R}}^{\prime}\tan\frac{\pi}{6}-Q_{\text {RH}}, \tag{10}\]  
\[Q_{\text{Lref}}=Q_{\text{L}}+P_{\text{L}}^{\prime}\tan\frac{\pi}{6}-Q_{\text{ LH}}, \tag{11}\]