Kalman filtering and statistical decision making for detection of attacks against power grid sensors

Kalman Filtering and statistical decision making criteria are used to develop a systematic method for the detection of attacks against sensors of the power grid. To emulate the functioning of the grid's sensors in the fault-free mode, the Kalman Filter is used as a virtual sensor. By comparing the output of the Kalman Filter against the output of the real sensors, the resulting differences generate the residuals' sequence. By weighting the square of the residuals' vector with the inverse of the associated covariance matrix a random variable is defined which is shown to follow the χ2distribution. This variable provides a statistical test about the deviation of the sensors functioning from the normal mode. Moreover, by exploiting the properties of the χ2distribution and by using the confidence intervals approach, one can define thresholds against which the value of the statistical test is compared. In case that these thresholds are exceeded by the value of the statistical test then it can be inferred that the sensors' functioning is abnormal. Additionally, sections of the power grid which have been exposed to the attack can be identified by applying the statistical test on clusters of sensors. Actually, by applying the statistical test at each individual sensor one can isolate the compromised sensors. Finally, one can estimate the additive disturbance inputs that affect the sensors by redesigning the Kalman Filter as a disturbance observer. This may provide an indication on whether the deviation of the sensors functioning from normal has been the result of an attack to the grid by intruders.