Real-time Algorithm for the Transformation of Multiple Harmonic Unbalanced Voltages into Symmetrical Components

The Fortescue theorem is a well-known transformation technique for parameter identification in three-phase systems. It is a valuable tool that transforms an unbalanced system into symmetrical components. This method itself can not be used in a real-time system because it needs to identify individual vectors of the voltage. The solution proposed in this paper is to combine the Fortescue theorem with a second-order generalized integrator (SOGI). The SOGI algorithm provides two functions. Firstly, it identifies voltage vectors. Secondly, it works as a band-pass filter. This means it can deal with the systems containing multiple harmonics, processing them individually. This paper evaluates the performance of the proposed algorithm, with a focus on harmonic selectivity and speed of the reaction during transients.