Nowadays with increasing use of numerous nonlinear loads, voltage and current HARMONICS in power systems are one of the most important problems power engineers encounter.Many of these nonlinear loads, because of their dynamic natures, inject TIME-VARYING HARMONICS into power system. Common techniques applied for HARMONICS measurement and assessment such as FFT have significant errors in present of TIME-VARYING HARMONICS due to the TIME-windows applied. In this paper, a Kalman filter-based algorithm is developed and implemented for measuring TIME-VARYING HARMONICS. The efficiency of the proposed algorithm has been successfully tested in off-line mode by various computer simulations. Based on this algorithm, a prototype harmonic analyzer has been designed, fabricated and used for on-line harmonic monitoring and assessment studies. To assess the severity of TIME-VARYING HARMONICS, cumulative TIME indices that are computed in real-TIME using the output of the analyzer are proposed. In addition, new cumulative TIME curves for total harmonic distortion and individual harmonic distortions are presented.Also, an auto-synchronization algorithm is proposed to accompany the Kalman filter algorithm in order to eliminate the errors occurred due to the variations in the incoming signal frequency.