Low frequency oscillations following power system contingencies may cause undesirable operation of relay protections on transmission lines and enlarge the blackouts. A direct algorithm for the critical swing angle and frequency to zone 3 impedance relays is presented. The relay operation condition based on critical swing angles is quantified by the equivalent source voltages. The impacts of relay settings， source voltages and line charging on the relay performance are analyzed. With the approximately constant swing frequency， the resident time inside the protection region is found by the critical swing angles to quantify the critical swing frequency under different time settings. The feasibility and effectiveness of the algorithm are validated by the numerical results.