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This paper proposes a new method to determine the optimal allocation pattern of multiple phase shifting transformers (PSTs) for unwinding parallel flows. In the proposed method, the concept of co-tree in graph theory is used to determine the minimum number of PSTs required for the independent modulation of individual loop flows. Moreover, eigenanalysis is applied to find out the correlation between each allocation patterns of PSTs and corresponding power flow profiles. Consequently, the sensitivity of flow alteration vector to the input angle vector of PSTs can be characterized into a matrix. Whereas, by the sensitive matrix, the required control angles of each PST for unwinding parallel flows can be found precisely. As a result of the proposal, the optimal allocation pattern of PSTs is determined as which can unwind the specific parallel flows by minimum control angles against other patterns. The validity of the proposed method is confirmed through the simulation studies.