Development of Active Filters with Spiral Vector Theory

The paper develops active filters according to spiral vector theory that has a definition of instantaneous reactive power in single-phase networks. At first, the paper obtains rms active and reactive power with integral method and shows that they are the same in a steady state condition and in a transient state condition, then it obtains the system voltage with least square method and the system current that has a sinusoidal waveform. The harmonic currents are equal to the load current minus the system current and it used as the output of an active filter.