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This paper presents an analytical methodology for smart grids cyber-physical security based on gross error analysis. The presented methodology is built on the Weighted Least Square (WLS) state estimator (SE) formulation. Although cyber-physical security is a wide subject, in this paper Cyber-Attacks are modeled as bad data. Detection, identification and correction of multiple and simultaneous cyber-attacks on power grid's SCADA system, or network database, are investigated. Cyber-attack detection is made through a Chi-square ( χ 2 ) Hypothesis Testing (HT) applied to the composed measurement error ( CME ). Composed errors are estimated with measurements’ innovation index ( II ). Cyber-attack identification is made through the Largest Normalized Error Test property. Cyber-attack correction is made considering cyber-attack type and using the composed normalized error ( CNE ). One important advantage of the presented method is it does not require a previous knowledge of how the attack was performed, as far as it is restricted to a change of measurements, parameters or topology, since the error is estimated and then the bad data is corrected. A significant advantage of this correction is that it avoids potential local or global unobservable conditions, since it does not delete any measurement of the measurement set. Validation of the proposed methodology is made on the IEEE 14-bus and 57-bus systems. Simulations show the reliability and robustness of the proposed methodology even when the cyber-attack occurs simultaneously on SCADA data and network database. [ABSTRACT FROM AUTHOR]