Set Invariance Based Localization of Kalman Filter Estimation Error in Automatic Generation Control

Non-conservative set-based characterization of Kalman filter state estimation error under the influence of bounded disturbances acting on the system under consideration is needed to analyze the corresponding control system performance comprehensively. One important newly rising application of such error characterization is also in cyber-attack detection. This work outlines how the estimation error set characterization is performed by relying on set-theoretic methods in control. In particular, minimal robust positively invariant sets correspond to the smallest such sets and thus represent their least conservative characterization. The procedure is applied to the automatic generation control problem in an exemplary electrical transmission grid configuration with two control areas. A simulation study is performed under a random sequence of bounded disturbances of production-consumption mismatch and frequency/power measurement noises to demonstrate the correct and non-conservative estimation error localization.