Phase synchronization and measurement digital systems of AC mains for power converters

Power converters applied to improve the AC mains quality are widely used. Usually, they need to know the phase and the amplitude of the mains voltage or current for a correct operation. Sometimes the knowledge of specific parameters (such as RMS value) is enough, spending several milliseconds of processing time in its calculation. When the power converter frequency is high, it is often necessary to know the phase and the value of the signal instantaneously with a maximum delay time of a few microseconds. This paper shows a study of the problem based on three different generic situations, intending to cover the general theory of all possible cases. The principal mathematics relationships are obtained, and practical recommendations are made for every case. This work represents a systematic study about the synchronization of power converters with AC mains and its measurement, obtained by analysis and generalization of practical results from several projects developed through more than 10 years with UPS, on-load tap changing stabilizers and active filters.