1. 1 Challenges in Power Systems State Estimation Lamine Mili Virginia Tech Alexandria Research Institute

2. 2 Control Center V V : P and Q measurements n = 2 N - 1 1.5  m / n  3

3. 3 VPQI CT 0 to 5 A High voltage and high current ADC 10 k  0 to 10 V 12 bit binary data Control Center

4. 4 Types of Measurement Errors Random errors - related to the class of precision of the instrument. Intermittent errors – burst of large noise or temporary failures in the communication channels. Systematic errors – introduced by –the nonlinearity of the current transformers and capacitor coupling voltage transformers (CCVT); –Deterioration of instrument with time, temperature, weather, and other environmental causes.

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7. 7 Measurement Calibration The present practice is to perform an on-site calibration, which is rarely carried out. The measurements may be strongly biased. Develop a remote measurement calibration method that minimizes the systematic errors in the measurements.

8. 8 Power System State Estimation Provide an estimate for all metered and unmetered quantities; Filter out small errors due to model approximations and measurement inaccuracies; Detect and identify discordant measurements, the so-called bad data.

9. 9 Power System Model The system is balanced. The line parameters are perfectly known. The topology is known. No time-skew between measurements.

10. 10 Probability Distribution of Measurement Errors 3  f(x) x 0 Gaussian distibution Actual distribution

11. 11 The breakdown point is defined as the maximum fraction of contamination that an estimator can handle True value mean bias Breakdown point of least-squares estimator is   = 0 % Breakdown Point of an Estimator

12. 12 True value Breakdown point of L 1 -norm estimator is   = Breakdown Point of Sample Median median bias median

13. 13 0.10.20.30.40.5  0 0 1 2 3 Fraction of contamination Maximum Bias Maximum bias curve of the sample median

14. 14 24 0 0 2 4 6 6 z x z = a x + b Vertical outlier

15. 15 24 0 0 2 4 6 6 z x z = a x + b Bad leverage point 8 10 Critical value of x

16. 16 Leverage Points in Power Systems These are distant points (outliers) in the space spanned by the row vectors of the Jacobian matrix. They are power measurements on relatively short lines. They are power injection measurements on buses with many incident lines. Leverage measurements tend also to make the Jacobian matrix ill-conditioned.

17. 17 Leverage Point Processing Develop robust covariance method for identifying outliers in an n-dimensional point could. Minimum volume ellipsoid method is a good candidate, but it is computationally intensive. Projection methods are fast to calculate. Develop estimation methods that can handle bad leverage points.

18. 18 Topology Error Identification A topology error is induced by errors in the status of the circuit breakers of a line, a transformer, a shunt capacitor, or a bus coupler. AssumedActual

19. 19 All the measurements associated with a topology error will be seen as conforming bad data by the state estimator. The state estimator breaks down.

20. 20 Proposed Solution Develop a preprocessing method that does not assume that the topology as given. In this model, the state variables are the power flows of all the branches, be they energized or not.

21. 21 x Pi

22. 22 Topology estimator Apply a robust estimation method to estimate the flows through all the branches. Apply a statistical test to the estimated flows. If the flow is significantly different from zero, then decide that the associated branch is energized.

23. 23 Parameter estimator Take advantage of the fact that the state remains nearly unchanged over a certain period of time, typically during the late night off-peak period. Estimate the nodal voltage magnitudes and phase angles together with the parameters of the lines Extend the measurement vector by including the metered values recorded at several several snapshots.

24. 24 Research Areas Remote measurement calibration. Parameter and topology estimators. Leverage point identification and processing. Robust estimator with positive breakdown point. Measurement placement Dynamic state estimator with phasor measurements.