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Controlled interruption of short circuit currents in medium- and high-voltage systems by means of point-on-wave control has not been feasible so far for technical reasons. The determination of the optimal tripping moment to achieve minimal contact wear should not take more time than the protection relay takes to indicate the fault, which makes it a difficult problem. As a solution, a so-called safe-point algorithm was developed, which overcomes the problem by an approximation of sufficient accuracy and with a time request of not much more than half a cycle of the power frequency. Computer simulations demonstrate that the mean I2t can be reduced significantly. The method provides the foundation for implementing controlled switching of fault currents.