Three-phase series-connected MMC (SC-MMC) is constructed by connecting three single-phase MMC in series. Compared with conventional three-phase parallel-connected MMC, the number of semiconductor switches is reduced by one third with the assumption to withstand the same DC voltage. However, the operation of SC-MMC under unbalanced grid conditions remains a key issue. This paper derives the AC power balance equations based on stationary α-β frame, which equalizes the AC power of each phase to balance the DC-side voltages and enables to adjust the transmitted power according to the severity of AC faults. In addition, this paper presents the method based on stationary α-β frame to protect SC-MMC from over-current. Besides, the overall control scheme based on the proportional resonant controller is proposed. Finally, the SC-MMC model is established and the simulation of single-line and double-line to ground faults are both performed in PSCAD/EMTDC. The simulation result proves that SC-MMC has very good AC fault ride-through ability with the proposed control strategy. This work is supported by National Natural Science Foundation of China (No. 51507093), Natural Science Foundation of Shandong Province (No. ZR2014EEQ033), and Chinese Postdoctoral Fund (No. 2015M572029).