This paper presents an alternative approach for real time measurement of all electrical quantities in a power system signal based on a new least squares algorithm. The advantage of this approach is that the least squares algorithm is an easy to understand, fast and cheap method that can be applied to track changes in power system quantities rapidly. The technique can be used to accurately evaluate the rms voltage and rms current magnitudes and phase angle of each harmonic component directly from single measurements of the voltage and current. Once these values have been evaluated all other quantities such as average power and power factor can be readily calculated. Computer simulation is used to evaluate the algorithm's accuracy. The results confirm the structural robustness of the proposed algorithm with respect to noise and distortions in the waveforms being measured.