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Estimating the amplitude of the grid voltage is important for low-voltage ride-through (LVRT) operation in single-phase systems. It requires fast dynamics and is typically achieved through a phase-locked loop (PLL). This paper proposes a fast amplitude estimation (FAE) method without a PLL structure. The grid voltage is formulated as a vector sum of sine and cosine functions, resulting in an algebraic model with two unknown parameters. The proposed FAE identifies the two parameters, and thus achieving a fast fault detection (i.e., the amplitude estimation). Experimental results verify the performance of the proposed method in terms of fast dynamics.