Power swing conditions in power systems make distance relays take the wrong breaker action in some cases. In this context, power swing blocking and power swing deblocking are two important functions in distance relays so as to distinguish power swing froma fault, which maintains stability of system and continuity of the power supply. In this paper, a sample estimation and error calculation method based on Taylor Series expansion is proposed for improving power swing detection performance of the relay. Performance of the method is compared with four conventional methods and a novel method in literature. Analyses are carried out in two systems: single machine-infinite bus system with parallel lines and 68-bus New England test-New York power system for fault, power swing, and fault during power swing scenarios. Simulations and performance analyses are carried out by using EMTDC/PSCAD and MATLAB, respectively. According to the results, when performances in correct operation, algorithm response times, clarity of outputs, and time passed for program execution on processor are considered, the proposed method has the best performance overall. It is found that by using the proposed method, distance relay performance in correct operation and speed for taking power swing blocking and deblocking actions are improved.