Further contributions to smart grids cyber-physical security as a malicious data attack: Proof and properties of the parameter error spreading out to the measurements and a relaxed correction model

This paper presents further contributions to smart grids cyber-physical security as a malicious data attack. The contributions are twofold. First, a formal proof of how parameter errors spread out on the measurement function having a parameter with error. The largest composed measurement error property, in its normalized form, is then demonstrated for this case of error. Second, a methodology for smart grid cyber-physical malicious data injection correction is presented. Current state of the art solutions corrects simultaneous attacks assuming measurements or parameters without error. However, how may one correct a measurement if the parameter might be simultaneously in error or the other way around? In this paper, a relaxed model strategy for such is presented. Attacks are processed simultaneously and analyzed using only the framework of measurement gross error analysis. Cyber-attack detection is made through a Chi-square (χ2) Hypothesis Testing (HT) applied to the normalized composed measurement error (CMEN). 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) in a relaxed model strategy. The proposed solution works for malicious measurement and parameter data attacks. Still, the state estimation software does not need major changes. Validation is made on the IEEE 14-bus and 57-bus systems.