This paper deals with a fundamental aspect in the control of grid-connected power converters, i.e., the detection of the positive-sequence component at fundamental frequency of the utilityvoltage under unbalanced and distorted conditions. Accurate and fast detection of this voltagecomponent under grid faults is essential to keep the control over the power exchange with thegrid avoiding to trip the converter protections and allowing the ride-through of the transient fault. In this paper, the systematic use of well known techniques conducts to a new positive-sequencevoltage detection system which exhibits a fast, precise, and frequency-adaptive response underfaulty grid conditions. Three fundamental functional blocks make up the proposed detector, these are: i) the quadrature-signals generator (QSG), ii) the positive-sequence calculator (PSC), and iii) the phase-locked loop (PLL). A key innovation of the proposed system is the use of a dual second order generalized integrator (DSOGI) to implement the QSG. For this reason, the proposed positive-sequence detector is called DSOGI-PLL. A detailed study of the DSOGI-PLL and verification by simulation are performed in this paper. From the obtained results, it can be concluded that the DSOGI-PLL is a very suitable technique for characterizing the positive-sequence voltage under grid faults.