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The Transformation Of Traditional Energy Networks To Smart Grids Can Assist In Revolutionizing The Energy Industry In Terms Of Reliability, Performance And Manageability. However, Increased Connectivity Of Power Grid Assets For Bidirectional Communications Presents Severe Security Vulnerabilities. In This Letter, We Investigate Chi-square Detector And Cosine Similarity Matching Approaches For Attack Detection In Smart Grids Where Kalman Filter Estimation Is Used To Measure Any Deviation From Actual Measurements. The Cosine Similarity Matching Approach Is Found To Be Robust For Detecting False Data Injection Attacks As Well As Other Attacks In The Smart Grids. Once The Attack Is Detected, System Can Take Preventive Action And Alarm The Manager To Take Preventative Action To Limit The Risk. Numerical Results Obtained From Simulations Corroborate Our Theoretical Analysis.