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This research addresses the special requirements of phase locked loops (PLLs) for a typical application with FACTS elements. A new PLL system that uses adaptation algorithms is developed with the aim of improving speed of responses, robustness to AC voltage depressions, and harmonic rejection. The adaptive PLL consists of the three control units that individually control frequency, phase angle, and voltage magnitude. The voltage controller output is used to compensate for reduced gain caused by the AC voltage magnitude depressions. The output phase angle and its derivative, the frequency signal, are controlled in two independent control systems in order to enable elimination of frequency and phase error without compromising transient responses. The simulation results are compared with a PLL available with the PSB MATLAB block-set and noticeable improvements are demonstrated. In particular, settling time and overshooting are significantly lower with conditions of reduced AC voltage magnitude.