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In this study, a time-domain methodology for the harmonic state estimation (HSE) assessment of power networks is proposed. The time domain HSE solution is based on the application of the Kalman filter, Poincaré map and extrapolation to the limit cycle using a numerical differentiation procedure. The noisy state variables measurements to be used for HSE are taken from a simulation of the network harmonics propagation. The estimated harmonic magnitudes are obtained applying the discrete Fourier transform. The results obtained with the proposed time-domain HSE methodology are validated against the actual system response and against the solution obtained with the power systems computer aided design/electromagnetic transients including direct current (PSCAD/EMTDC) simulator, widely accepted by the power industry, a close agreement between the results is obtained.