This paper presents a hybrid data-driven physics model-based framework for real time monitoring in smart grids. As the power grid transitions to the use of smart grid technology, it's real time monitoring becomes more vulnerable to cyber attacks like false data injections (FDI). Although smart grids cyber-physical security has an extensive scope, this paper focuses on FDI attacks, which are modeled as bad data. State of the art strategies for FDI detection in real time monitoring rely on physics model-based weighted least squares state estimation solution and statistical tests. This strategy is inherently vulnerable by the linear approximation and the companion statistical modeling error, which means it can be exploited by a coordinated FDI attack. In order to enhance the robustness of FDI detection, this paper presents a framework which explores the use of data-driven anomaly detection methods in conjunction with physics model-based bad data detection via data fusion. Multiple anomaly detection methods working at both the system level and distributed local detection level are fused. The fusion takes into consideration the confidence of the various anomaly detection methods to provide the best overall detection results. Validation considers tests on the IEEE 118 bus system.