Adaptive Observer for Three Phase Source Voltage Under Unbalanced Conditions

In this paper the problem of estimating amplitude, phase and frequency of the main component of three-phase line voltage under unbalanced conditions is considered. Unbalancing is a common condition and generates a so-called negative sequence in the line voltage, which may affect relevantly estimation of main components dynamics. Different adaptive schemes are proposed and analyzed. First of all, a straightforward solution derived by LTI observer with frequency adaptation is analyzed and its high sensitivity to negative sequence component is underlined. Hence, an adaptive nonlinear observer is proposed, exploiting the properties of a synchronous reference frame to represent the line voltage. Its larger robustness to negative sequence and voltage harmonics is verified by analysis and simulations. Finally, the latter solution is enhanced by adding the negative sequence model to the basic observer structure. This allows for perfect compensation if the unbalancing effects. Adaptation law for this solution is fairly different form the previous one and a completely different stability analysis is required. Simulation results are also provided to demonstrate the effectiveness of the proposed scheme even under large unbalancing.