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This paper presents a deep learning based multi-label attack detection approach for the distributed control in AC microgrids. The secondary control of AC microgrids is formulated as a constrained optimization problem with voltage and frequency as control variables which is then solved using a distributed primal-dual gradient algorithm. The normally distributed false data injection (FDI) attacks against the proposed distributed control are then designed for the distributed gener-ator's output voltage and active/reactive power measurements. In order to detect the presence of false measurements, a deep learning based attack detection strategy is further developed. The proposed attack detection is formulated as a multi-label classification problem to capture the inconsistency and co-occurrence dependencies in the power flow measurements due to the presence of FDI attacks. With this multi-label classification scheme, a single model is able to identify the presence of different attacks and load change simultaneously. Two different deep learning techniques are compared to design the attack detector, and the performance of the proposed distributed control and the attack detector is demonstrated through simulations on the modified IEEE 34-bus distribution test system.