Challenges in Power Systems State Estimation

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

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

3. High voltage and high current CT 0 to 5 A I Q P V 10 kW 0 to 10 V ADC 12 bit binary data Control Center

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.

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

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

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

12. Breakdown Point of Sample Median True value median median bias median Breakdown point of L1-norm estimator is e* =

13. Maximum bias curve of the sample median Maximum Bias 3 2 1 0  0 0.1 0.2 0.3 0.4 0.5 Fraction of contamination

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

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

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. 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. Assumed Actual 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.

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. 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. xPi

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. 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. 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.