Measurement of complex RMS value of the fundamental harmonic under nonsinusoidal conditions

Two algorithms for calculating the complex RMS values of the voltage and current fundamental harmonics in the presence of harmonic distortion are given. One is based on direct calculation of the discrete Fourier transform and the other on cyclic convolution. It is shown that the algorithms reduce the number of multiplications needed to approximately one multiplication per one eliminated harmonic and need three times as many additions. at a relatively low sample rate. Therefore. the algorithms are useful for real-time applications. It is shown how to evaluate the aliasing errors.<>