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Field measurement of harmonic distortion is a fundamental requirement for monitoring, analysis, and/or control of power system harmonics. Fast and accurate estimation of time-varying harmonics is a key to realize many objectives of the smarter and cleaner grid such as harmonic source identification, improved active filter control for mitigation of harmonics, and smart meters for harmonic pollution metering. This paper presents a fast and accurate approach for real-time estimation of moderate time-varying harmonics of voltage/current signals. The proposed method is based on estimation of signal parameters via rotational invariance technique (ESPRIT)-assisted adaptive wavelet neural network (AWNN). The AWNN provides quick estimates (twice every fundamental cycle with only half-cycle data as input) of the dominant harmonics, whereas the ESPRIT complements it to handle time-varying signals with higher accuracy. The salient features of the proposed method are validated on the simulated and experimental signals of stationary and time-varying nature.