As converter based renewable energy systems continue to penetrate the electric power grid, regulatory standards for grid interconnection continue to evolve. One of the most challenging requirements for generative systems is the injection of valuable reactive currents during Low-Voltage Ride-Through (LVRT) events, especially during unbalanced LVRT situations. As state-of-the-art, Phase Looked Loops (PLLs) are used to determine the corresponding amplitudes and phases of positive- and negative-sequence voltages. Such widely used PLLs are well developed, however, they show an inherent limited dynamic response during LVRT events. Therefore, this paper proposes an estimation algorithm for the positive- and negative-sequence systems that is based on the online elliptical approximation of the voltage space vector trajectory. The algorithm shows enhanced dynamic performance with regard to grid transients and grid faults compared to PLL based methods. To be able to perform the required computing resources and the required computing power for solving the related nonlinear equation system, the algorithm is implemented and tested on a novel Field Programmable Gate Array (FPGA) based platform. The enhanced transient performance of the proposed algorithm is shown by direct comparison to the common PLL methods Complex-Coefficient Filter (CCF)-PLL and the Dual Second Order Generalized Integrator (DSOGI)-PLL in simulations as well in Hardware-in-the-Loop (HiL) tests. The proposed algorithm clears the way to provide a fast and supporting current injection from renewable energy sources during LVRT events without the settling times of common PLLs. This work is an outcome of a collaborative research project between a research institute and a company partner.