Frequency Domain Modelling for Assessment of Hilbert and SOGI Based Single-Phase Synchronisation

Two different single-phase synchronisation schemes based on orthogonal system generation (OSG) are modelled in the linear, time-periodic framework. The frequency adaptive Hilbert phase locked loop (PLL) and the frequency-fixed second-order-generalised-integrator (SOGI) PLL fit smoothly into existing models for the synchronous reference frame PLL, due to the linear and decoupled nature of the orthogonal system generation. The harmonic transfer functions are established, and shown to accurately capture the frequency coupling properties of the synchronisation techniques. This modelling approach is a milestone towards the ultimate goal of assessing the impact of synchronisation on single-phase converter small-signal stability. The analytic models are compared to simulations, through use of a chirp input signal instead of the typical frequency sweeping technique. The conceptual differences between the Hilbert PLL and SOGI PLL are highlighted, yet without attempts at asserting superiority of either scheme.