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Fault detection plays an indispensable role in ensuring the security of smart grid systems. Based on the dynamics of the generators, we show the time evolution of the smart grid system can be modeled by a discrete-time linear state space model. We focus on faults that can be described by changes in system matrices of the state space model. Newly developed locally optimum tests are discussed and utilized to improve the performance for detecting small changes. Numerical results are provided which demonstrate the superiority of the new approaches when compared to existing methods, especially in the detection of small changes.