This paper presents new fault-tolerant control strategies for field-oriented control of 7-phase non-sinusoidal permanent magnet (PM) machines supplied by voltage source inverters (VSI). Single phase open-circuit fault is considered. The proposed strategies aim at finding waveforms of current references in natural frame in the way that post-fault currents create the same rotational magnetomotive force (MMF) as in healthy mode. Therefore, in the faulty mode, average torque can be maintained if no current limits are set. The proposed strategies are validated and compared to a previous strategy by numerical results in terms of joule losses, maximum RMS and peak phase currents, maximum phase voltage as well as their controllability with PI controllers.