# Application of MMC-RPC in High-Speed Railway Traction Power Supply System Based on Energy Storage
## 2 Principle of MMC-RPC  
The ES type MMC-RPC and its application in the traction power supply system are shown in Figure 1. The topology is mainly composed of back-to-back modular multilevel converters (MMCs) and SC-type ES units. In the traction power supply system, the 220 kV three-phase voltage is transformed to the value of \(2\times 27.5\) kV through the traction transformer. And the MMC-RPC system is directly connected to the traction power supply arm. Through the MMC-RPC system, energy integration and power quality management of two arms are realized. Finally, SCs are connected in parallel with the DC link support capacitor of the submodule to utilize regenerative braking energy through the DC/DC converter. Figure 1 also shows the single-phase MMC (SM) topology structure on the inverter side of the MMC-RPC system, and the MMC submodule structure is shown in the lower right corner. The SM structure is composed of left and right bridge legs, and each bridge leg is composed of submodules, bridge-leg inductance and resistance. The bridge-leg inductance has three functions: (1) Suppress the charging current on the bridge leg when the converter is started. (2) During the normal operation of the converter, the circulating current in the bridge leg is suppressed. (3) When the DC-link short-circuit fault occurs in the converter, the short-circuit current is suppressed. The topological structure of MMC-RPC can be obtained from Figure 1; it is defined that the left and right power supply arms are \(\alpha\) and \(\beta\) phases, respectively. Since the structure of each phase and each bridge leg of MMC-RPC are the same, a and b are defined as the left and right bridge legs in one phase, and \(p\) and n represent the upper and lower parts of one bridge leg, respectively, where:  
\(u_{\text{sk}}\) (\(k=\alpha\), \(\beta\)) is the AC voltage of each phase;  
\(i_{\text{sk}}\) is the AC current of two power supply arms;  
\(u_{\text{kjp}}\) and \(u_{\text{kjn}}\) (\(j=\) a or b) are the voltages of the upper and lower bridge legs of each phase;  
\(i_{\text{kjp}}\) and \(i_{\text{kjn}}\) are the currents of the upper and lower bridge legs of each phase;  
\(u_{\text{kj}}\) (\(j=\) a or b) is the ground reference voltage of the AC port of the bridge leg;  
\(R_{0}\) and \(L_{0}\) are the equivalent resistance and inductance of the bridge leg in Figure 1, respectively;  
\(R_{\text{S}}\) and \(L_{\text{S}}\) are the equivalent resistance and inductance at the AC side;  
\(i_{\text{dc}}\) and \(u_{\text{dc}}\) are the DC-link current and voltage, respectively. Figure 1: Topology of MMC-RPC. According to Figure 1, [PERSON]'s voltage law is used to analyze the AC side and DC side circuits of the MMC-RPC, and the port equations on the AC side and DC side of the MMC-RPC are [15]:  
\[u_{j}=u_{\mathrm{ka}}-u_{\mathrm{kb}}=u_{\mathrm{sk}}-2R_{\mathrm{s}}i_{\mathrm{ s}}-2L_{\mathrm{s}}\frac{di_{\mathrm{sk}}}{dt}, \tag{1}\]  
\[\left\{ \begin{array}{l}0.5u_{\mathrm{dc}}=u_{kjp}+L_{\mathrm{S}}\frac{di_{ \mathrm{kip}}}{dt}+R_{\mathrm{S}}i_{\mathrm{kjp}}+u_{j}\\ 0.5u_{\mathrm{dc}}=u_{kjn}+L_{\mathrm{S}}\frac{di_{\mathrm{kjn}}}{dt}+R_{ \mathrm{S}}i_{kjn}-u_{j}\end{array} \right., \tag{2}\]  
By solving Equation (2), the voltage on the AC side and DC side of the MMC-RPC can be obtained [15]:  
\[\left\{ \begin{array}{l}u_{j}\!=\!0.5\!\left(u_{kjn}-u_{kjp}\right)\!+\!0.5L_ {\mathrm{S}}\frac{d\left(i_{\mathrm{kjn}}\!-\!i_{kjp}\right)}{dt}\!+\!0.5R_{ \mathrm{S}}\!\left(i_{kjn}-i_{kjp}\right)\\ u_{\mathrm{dc}}=\left(u_{kjn}+u_{kjp}\right)+L_{\mathrm{S}}\frac{d\left(i_{ \mathrm{kjn}}\!+\!i_{kjp}\right)}{dt}\!+\!0.5R_{\mathrm{S}}\!\left(i_{kjn}-i_{ kjp}\right)\end{array} \right., \tag{3}\]  
According to [PERSON]'s theorem, we have:  
\[\left\{ \begin{array}{l}i_{\mathrm{kap}}\!=\!-i_{\mathrm{dc}}/2\!-\!i_{ \mathrm{S}},i_{\mathrm{kan}}\!=\!-i_{\mathrm{dc}}/2\!+\!i_{\mathrm{S}}\\ i_{\mathrm{kbp}}\!=\!-i_{\mathrm{dc}}/2\!+\!i_{\mathrm{S}},i_{\mathrm{kbn}}\!= \!-i_{\mathrm{dc}}/2\!-\!i_{\mathrm{S}}\end{array}