This paper studies asymmetrical voltage sags caused by single phase short circuits appearing in power grids. Research defines the worst case fault conditions and shows their impact on stability of high voltage synchronous motors. Calculations done within the research take into account the distribution of voltage and current symmetrical components in power-supply system elements. Power supply system model was developed in the Matlab program in order to study stability of synchronous motors during voltage sags. The motor in the model is equipped with static exciter that enables us to account the impact of sag on motors excitation winding. The paper also shows fault appearance time (initial point on wave influence) as one of the worst case fault conditions. Finally research proposes the methodology developed to assess synchronous motor stability (calculation of the fault critical duration) under discovered worst case fault conditions. Results of the research could be used to calibrate protective relays used in power supply grids of oil and gas transportation systems equipped with powerful synchronous motors.