A self-commutated BTB (back-to-back) system is an AC-DC-AC power flow controller between two utility grids, and PLL (phase-locked-loop) circuits are typically used for detecting their phase information. The performance of the BTB system during line faults is strongly affected by the dynamic behavior of the PLL circuit in terms of the AC-current fluctuation, the DC-voltage fluctuation, and the DC magnetic flux deviation in the converter-transformers. However, no paper or article has been discussed explicitly on their mutual relationship. The aim of this paper is to establish a design procedure of the PLL circuit which is suitable for the BTB system. This paper also deals with the DC magnetic flux deviation in the converter-transformers under double-line-to-ground (DLG) faults.
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