Sequences Detection of an Unbalanced Sinusoidal Voltage of Unknown Frequency Using a Reduced-Order Observer

This paper presents a globally convergent nonlinear observer capable of recovering the positive and negative sequences of an unbalanced grid voltage. The proposed algorithm has frequency adaptation, and is therefore, in steady state, immune to grid frequency variations. Another feature is that since it is a reduced-order observer, only three states are needed to implement it. The validity of the proposed scheme is verified through mathematical analysis, simulation, and experimental results.