This paper presents an IEEE Std. 1459 power magnitude measurement system working as a part of a power quality improvement structure. It is intended to enhance the performance of selective shunt active power compensators (SAPCs). The measurements system includes a synchronization structure to estimate the fundamental positive-sequence component of grid voltages in distorted and asymmetric three-phase systems. The synchronization signal is used by a sliding window discrete Fourier transformation (SDFT) recursive algorithm to obtain the fundamental components of the voltages and currents. This algorithm extremely reduces the computational cost compared with the classic SDFT implementation. This strategy allows for a sample-by-sample quasicontinuous calculation of all power quantities, as well as the nonefficient currents. These magnitudes had been used to generate the reference currents for an SAPC achieving a quasicontinuous compensation of the nonefficient power quantities. Simulation and experimental results demonstrate that the proposed measurements system operates correctly under all electrical power network conditions.