Mapping matrices against vectorial frame in the instantaneous reactive power compensation

The original instantaneous reactive power or p–q theory has been used in a systematic way in the control of active power filters (APFs).When the APF is switched in parallel to a nonlinear and unbalanced load, the application of p–q theory allows a constant power compensation strategy. This means that after the APF connection, the supply instantaneous power is constant and presents the same value as the load average power. The use of other compensation strategies such as unity power factor, sinusoidal or balanced supply currents, among others, is also possible, as the development of another compensation strategy is possible within the p–q theory frame. A p–q theory reformulation without using mapping matrices is presented, which makes obtaining compensation currents easier. Finally, an exhaustive analysis of practical cases has been carried out at simulation and experimental levels through a laboratory prototype that has allowed verification of the proposed approach.