In order to solve the frequency estimation problem in unbalanced three-phase power systems, the Complex-valued DFE (CDFE)algorithm is analyzed and improved.The CDFE algorithm is based on the linear prediction of sinusoidal signal, in which the instantaneous squared value of the error function is first defined, and its first derivative is used to track the frequency of the unbalanced three-phase power system.Furthermore, variable step-size CDFE (VSS-CDFE)algorithm is also derived based on the CDFE algorithm by using the steepest descent method.The experimental results show that CDFE algorithm is able to accurately track the frequency in the unbalanced power systems that based on complex-model under white Gaussian measurement noise, and the estimated mean square error (MSE)is also consistent with that obtained by the theoretical analysis.Compared with the traditional CDFE algorithm, the VSS-CDFE algorithm has smaller estimated variance at the same convergence rate.On the other hand, its convergence rate is faster than the conventional CDFE algorithm for a predefined variance requirement.Both algorithms provide unbiased and robust frequency estimates and the VSS-CDFE algorithm is more superior in terms of estimation variances.