Defining and measuring AC quantities based on symmetry principles

This paper defines and measures the AC quantities of single-tone signals based on symmetry principles. After defining the frequency associated with a rotation phase angle in a sampling time interval, the author discovers two symmetry groups to calculate gauge voltage and gauge difference voltage according to group theory. Then, they are used to obtain the rotation phase angle, thus frequency and amplitude are obtained simultaneously. Furthermore, the author discovers two symmetry groups to calculate gauge active power and gauge reactive power. Then, they are used to obtain active power and reactive power respectively. At last, three numerical examples show that the novel method is effective for measuring the AC quantities.