In this paper, power swing detection is studied in terms of blocking distance relay responses which lead to wrong breaker operation. A new power swing detection method based on k-NN algorithm is proposed which uses areas of triangles constituted by phase angles of instantaneous power phasors calculated by Discrete Fourier Transform (DFT). Triangles corresponding to harmonic components from 1st to 9th are processed for generating the learning database. The performance of the method is compared with four conventional power swing detection methods on a test system in 30 cases for only symmetrical faults. The results show that the proposed method has better performance than the four conventional methods in total for the cases created in this work.