ABSTRACT This PhD thesis deals with shunt active power compensation systems used to improve power quality and efficiency in low voltage electric power networks. In this work, a new active power filter with selective capabilities has been developed. Some power quantities defined in the IEEE Std. 1459-2010 have inconsistencies when are resolved. These inconsistencies are corrected with a new approach developed in this work. The new approach propose new expressions of the effective current (Ie), and the effective voltage (Ve). With the new expressions of Ve and Ie, some IEEE Std. 1459-2010 power quantities are recalculated. The instantaneous power theory is proposed to explain phenomena in electrical systems. This theory can provide a simultaneous common base for the measurement and quantification of the power magnitudes, and for dynamic compensation. This theory can also be used to detect the sources of waveform distortion. Analysing the instantaneous power flow, the positive-sequence active power P1+ is the unique power considered ussefull. The currents used for active power filters are deduced for global compensation when the filter has the capacity to compensate all inefficient currents that the load demands. These currents are based on IEEE Std. 1459-2010 and the proposed instantaneous power theory. As all electrical or electronical devices, the active power filters have limits in its output power. In these case, all inefficient currents can not be compensated and the maximum output power limit in the active filter is reached. Under this operating conditions, the currents for the filter are also deduced and the filter works in a selective compensation mode. Selectivity criteria are proposed to reduce the usseles powers in the supply. With these criteria the transfer of useful power is more efficient, the use of the active power filter is optimized, the power losses and nocive effects are reduced, and the operation cost are minimized. Both simulated and experimental results of the proposed selective active power filter, including all proposed compensation strategies, are presented. The results demonstrate not only that the proposed system improves the electrical power quality but also the excellent behaviour of the selective compensation strategies. Finally conclusions, contributions, future research areas, and publications product of these Phd thesis are presented.