Optimizing of sampling in a low-cost single-phase instantaneous AC-grid synchronization unit with discrete calculation of derivative function

This paper deals with single-phase grid synchronization unit suitable for integration in interface converters of distributed renewable energy sources. A well known problem of the second orthogonal component for Park transformation of a phase-locked loop is successfully solved with a help of the approximate derivative function for the first time. Optimal sampling times for finding this derivative function are calculated with highest accuracy. It is shown that the implementation of approximate derivative function can reduce start-up time of the synchronization unit. The method is implemented in a low-cost microcontroller and successfully experimentally verified with a physical model of the grid, as well as with a real voltage sensor.