An adaptive method for tuning process noise covariance matrix in EKF-based three-phase distribution system state estimation

Pmu-Based Real-Time Distribution System State Estimation Considering Anomaly Detection, Discrimination and Identification

“…To set the detection threshold 𝛾, we start with the assumption that measurement NIs closely follow the Gaussian distribution. The distribution of NIs is influenced by: (a) the distribution of both process and measurement noise; (b) the linearity/non-linearity of the process model (1) and measurement model (2); (c) the settings of matrices 𝑸 and 𝑹; and (d) 𝑸∕𝑹 ratio [41]. If the process and the measurement noise follow Gaussian distribution, if (1) and ( 2) are linear, if 𝑸 and 𝑹 correspond to their true values, and if 𝑸∕𝑹 is small enough, it can be expected that NIs follow standard Gaussian distribution.…”

“…For most cases, 𝑹 can be defined easier and closer to the true one (𝑹 depends on class of accuracy of measurement devices which is usually known). Then, using defined 𝑹, optimal 𝑸 for quasi-steady state operation can be defined through offline analysis of this operation mode [41].…”

“…The choice of the detection threshold 𝜸 depends on the statistical properties of the noise. For a Gaussian measurement and a process noise with known standard deviations, 𝜸 setting is still influenced by 𝑸∕𝑹 ratio [41]. Although measurement standard deviations can be known fairly, the knowledge of process noise standard deviations cannot be so reliable because process noise varies over time (even in a quasi-steady state).…”

“…The diagonal elements of 𝑹 𝑘 represent measurement variances. Standard deviation 𝝈(𝑖) for pseudo measurements of power injections and PMU measurements of voltage and current magnitudes can be assessed as [41]:…”

An interdisciplinary research perspective on the future of multi-vector energy networks

“…The M-SAT, integrated into the abovementioned FICTP, can rely on e.g. robust linear/nonlinear dynamic recursive state estimators considering the known nature of random processes characterizing the entire metering chain [46]- [50]. For example, traditionally used a) least error squares, or b) weighted least error squares estimators can be implemented under the assumption that the stochastic nature of the process and measurement noise is considered to be a non-correlated white noise.…”