Real-time adaptive stochastic control of smart grid data traffic for security purposes

Abstract Smart grid data traffic behaves in a similar way to computer network data traffic and they are vulnerable to the same security risks. This paper presents a methodology for the real-time determination of adaptive estimates of router traffic-rate demand every five-minutes, as well as for the evolution of the estimated demand starting from zero during a five-minute interval using a Modified Mean Reverting Stochastic Process (M-MRSP). The determination of real-time adaptive estimates is based on an autoregressive model (AR(n)), which uses a window-size of past real-time router traffic-rate data with coefficients determined by a Kalman Filter (KF). The benefit of this technique is that potential monitoring tools could be provided with future knowledge of one 5-minute interval ahead. The methodology simulations show that the range of RMS error between the KF prediction and the internet service provider (ISP) measurements is of the order of 0.03, whereas the range of RMS error between the KF prediction and the M-MRSP values is of the order of 0.07. The synthetic time-series is a combination of M-MRSP and KF methodologies and maintains all the characteristics of a real traffic-rate time-series, such as non-stationarity, non-normality, long-range dependency (LRD), self-similarity and multimodality.