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The impact of exponentially decaying direct component on the Fourier algorithm is theoretically investigated first in this paper. A new algorithm to eliminate the error caused by this decaying component in the Fourier algorithm has been proposed. Furthermore, three simplified methods are proposed to alleviate the computation burden. The performance of the Fourier algorithm improved with these methods along with the least error squares algorithm is evaluated using a simple network and a real power system modeled by EMTP. The evaluation results are presented and discussed.