This paper discusses a critical study of fault detection and fault time analysis in a Unified Power Flow Controller (UPFC) transmission line. Here the Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT) approach are used for processing the faulty current signal to obtain fundamental current signal. The extracted fault current signals from the current transformer are fed to DWT and DFT approach for computing spectral energy (SE). The differential spectral energy (DSE) of phase currents are evaluated by taking the difference of SE obtained at sending and receiving end. The DSE is the key factor for deciding the fault in any of the phase or not. The Daubechy mother wavelet (db4) is used here because of its high accuracy of detection with less processing time. The novelty of the scheme is that it can accurately detect the critical fault variation of the line. Number of simulations are validated at the extreme condition of the line and compared to other conventional existing scheme. Multi-phase fault in double circuit line, CT saturation, UPFC operating condition (series voltage and angle), UPFC location and wind speed variation including wind farm simulation are validated to verify the performance of the scheme. The advantages of the scheme is that it works effectively to detect the fault at any stage of critical condition of the line and fault detection time remains within 20 msec (less than one cycle period). This scheme protects both internal and external zone including parameter variation of the line.