This paper presents a method for online detection of symmetrical components of arbitrarily distorted and biased three-phase input signals. This method is based on Second-Order Generalized Integrators (SOGIs), for which a new tuning based on a gradient search is presented to achieve the fastest possible estimation. Frequency estimation is achieved by a Frequency Locked Loop (FLL) with Gain Normalization (GN) for which an Output Saturation (OS) is applied; this OS guarantees stability of the overall system. Offset detection is implemented by a combination of High-Pass Filter (HPF) and HPF-Amplitude Phase Correction (APC); the HPF filters out any offset, where the APC reconstructs the original offset-free signal. An identical method (APC) can be used for the implemented Low-Pass Filter (LPF) used for noise filtering. The resulting estimates are then used for Harmonic Sequence Detection (HSD) of each harmonic. For the overall system, stability is proven. The estimation performances of the proposed overall system are verified by simulation results. The improvements in tuning and offset detection are compared to standard approaches.