By Mladen Kezunovic, Sakis Meliopoulos, Vaithianathan Venkatasubramanian, Vijay Vittal (auth.)
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Extra resources for Application of Time-Synchronized Measurements in Power System Transmission Networks
Compute the state estimate xˆ in the weighted least squares sense. m m i =1 i =1 Step 2. Compute the value ζ = ∑ si2 ( xˆ ) = ∑ ( hi ( xˆ ) − bi σi 2 ). Step 3. “Read” the probability Pr χ 2 ≤ ζ = Pr (ζ , v ) from the chi-square probability distribution function. Step 4. 0 − Pr (ζ , v ). Above probability is the probability that measurements fit the model of the system. This can be also expressed as a confidence level. , data that do not fit the model. , low value indicates presence of bad data.
The results are presented in terms of the magnitude and phase residuals. The displayed residuals are amplified by a factor of 50; the actual maximum values of the residuals are also given for reference. 16 the residuals for phase A are relatively very small. 18. It is clear that without actual phase B and phase C measurements, the residuals for these phases are relatively large. The magnitude depends on the system imbalance. This system has relatively small imbalance, but yet the results clearly show a deterioration of the state estimator performance for the unmeasured phases.
The state estimation is solved using the weighted least squares approach. 12) where η = z − h ( x, y ) and W is a diagonal matrix, whose nonzero entries are equal to the inverse of the variance of the measurement errors: 1 W = diag 2 . 14) where x refers to the best estimate of the state vector, and H is the Jacobian matrix of the measurement equations. , it becomes a LSE. 7 Performance Metrics The accuracy of the state estimate is quantified via the standard chi-square test and the statistical properties of the state estimator.
Application of Time-Synchronized Measurements in Power System Transmission Networks by Mladen Kezunovic, Sakis Meliopoulos, Vaithianathan Venkatasubramanian, Vijay Vittal (auth.)