By analyzing the behavior of a 220 kV transmission line’s pilot direction-protection, it was found that directional element based on variation of power-frequency rejected action when single-phase line-broken earth fault happened on the line. Based on the two-port network theory, the formula of directional element is deduced in case of such fault. The results show that when the system M and N are connected by a single transmission line, the variation directional protection can properly act when such fault happens on the line; when the system M and N are connected by electrical ring, the directional element may be judged as reverse direction fault owing to the different circuit parameters. Finally, the results of PSCAD simulation further validate the principle defect that the directional element may reject action when such fault happens in electrical ring system.