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This paper proposes a novel approach to identify the deviations of power flows which are controlled by multiple phase-shifting transformers (PSTs). In order to control the power flows of each loop independently, at the first, the minimum need of PST sets is determined as the number of co-trees to the entire network. For the reason that the co-tree patterns are not unique, there are many PST allocations that exist and can be found as the co-tree patterns. In this paper, since the correlation between power-flow deviations to the control angles of PSTs allocating in one co-tree pattern can be characterized into one matrix, the features of the controllable area of power flows corresponding to all PSTs allocation candidates can be extracted by the eigenanalysis of those matrices. By which, the features of the controllable area of power flows corresponding to all of the PST's allocation candidates can be extracted by the eigenanalysis of the matrix. Finally, judging from the power-flow profiles, the optimal allocation to the specific control target can be found. From the viewpoint of the flexible power-flow control in an open-access network, the proposal should contribute to find out the optimal PST's allocation for power-flow control. The effectiveness of the proposed method is confirmed by the simulation studies of two model systems.