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The static VAR generator (SVG) is an important device in flexible AC transmission systems (FACTS) for the development of smart grids. Based on the basis principle of SVG and instantaneous reactive power theory, the conventional ip-iq and dq methods have a certain error when the three phase voltages are unbalanced. In this paper, the current detection algorithm is improved in cases of three-phase power asymmetry by using the fundamental positive-sequence reactive current instead of the voltage as the input of phase locked loop (PLL). So the problems caused by unbalanced three-phase voltages could be avoided. In addition, a moving average filter is designed to improve the performance of the detection accuracy and dynamic response. Experiments verify the correctness and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]