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This article proposes an approach for the protection of transmission lines with flexible AC transmission systems based on artificial neural networks using the total least square estimation of signal parameters via rotational invariance technique. The required features for the proposed algorithm are extracted from the measured transient currents and voltages waveforms using the total least square estimation of signal parameters via rotational invariance technique. Since these transient waveforms are considered as a summation of damped sinusoids, the total least square estimation of signal parameters via rotational invariance technique is used to estimate different signal parameters, mainly damping factors, frequencies, and amplitudes of different modes contained in the signal. Those features are employed for fault detection and faulted phase selection using artificial neural networks. Two types of flexible AC transmission system compensated transmission lines, namely the thyristor-controlled series capacitor and static synchronous compensator, are considered. System simulation and test results indicate the feasibility of using neural networks with the total least square estimation of signal parameters via rotational invariance technique in the fault detection, classification, and faulted phase selection of flexible AC transmission system compensated transmission lines. [ABSTRACT FROM AUTHOR]