“…Winding deformations that may pledge to severe costly faults are detectable by various methods such as partial discharge measurement, 1 dissolved gas analysis, 2 impedance and capacitance measuring, and lately FRA method that attracted attention of researchers. [3][4][5][6] Therefore, locating the occurred faults and determining their severity in a transformer winding are Abbreviations: AOF, Augmented objective function; APDM, Acquiring parameters of the detailed model; FR, Frequency response; FRA, Frequency response analysis; HV, High voltage; LV, Low voltage; MLAPSO, Multi-level adaptive PSO; PSO, Particle swarm optimization Symbols: A n , B n , Fourier series coefficients; c, The weighting factor; g, The total number of extrema; Gbest, The best found AOF of all particles; h, The number of the i th extremum; i, The frequency point's indicator; M mes,i , The magnitude of ith measured frequency response point; M mod,i , The magnitude of ith calculated frequency response point; N, The total number of frequency points; N f , The number of Fourier coefficients; Pbest, The best found AOF of each particle; phase mes,i , The phase of ith FR point of the reference; phase mod,i , The phase of ith FR point of the obtained model; r, A uniformly distributed random number between 0 and 1; V, The velocity of each particle; w, The weighting function; X, The position of each particle; α, An arbitrary number in a defined feasible range of [0. 5 1.5] valuable tasks for enhancing their future designs and repairing procedure.…”