In order to extend the speed range and reduce power electronics devices of the permanent-magnet linear motor traction system, a half-centralized open-end winding topology is studied in this article, in which two movers are supplied by three voltage-source-inverters (VSIs). All these VSIs share a common dc-bus voltage, and the zero-sequence current becomes a challenge. In order to solve cope with this challenge, two phase model predictive voltage controls (PMPVCs) are proposed. Referring to the traditional finite-control-set MPVC (FCS-MPVC), an FCS-PMPVC scheme is proposed and the optimal phase voltage group is determined by minimizing three independent phase cost functions. For FCS-PMPVC, 21 phase voltage group are evaluated while the evaluation number of the traditional FCS-MPVC is 512. In order to reduce the computation burden furthermore, a new concept phase voltage vector (PVV) is defined, and the optimal PVV is directly determined by the nearest distance principle instead of the time-consuming evaluation. The second PMPVC is named as geometrical-location PMPVC (GL-PMPVC). Both PMPVCs have same performances while the computation burden of GL-PMPVC is nearly 47% of that of FCS-PMPVC. The effectiveness of the proposed PMPVCs have been verified by experimental results.