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Challenges in Power Systems State Estimation

Lamine Mili

Virginia Tech

Alexandria Research Institute

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Control Center

V

V

: P and Q measurements

n = 2 N - 1 1.5 m / n 3

3

VPQI

CT0 to 5 A

High voltage and high current

ADC

10 k

0 to 10 V

12 bit binary data

Control Center

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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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P1 P2 P3

S1 S2 S3 S4

500 KV Bus

230 KV Bus

T1 T2

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0 50 100 150 200 250 300 1

1.01

1.02

1.03

1.04

1.05

Snap-shots (blocks)

Meter Values (treatments) in p.u.

S3

S4

S2

S1,T1,T2

6 kV

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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.

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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.

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

R j X

j C /2 j C /2

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Probability Distribution of Measurement Errors

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f(x)

x0

Gaussian distibutionActual

distribution

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• The breakdown point is defined as the maximum fraction of contamination that an estimator can handle

True value

meanbias

Breakdown point of least-squares estimator is = 0 %

Breakdown Point of an Estimator

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True value

Breakdown point of L1-norm estimator is =

Breakdown Point of Sample Median

medianbias

median

median

mm

/]2

1[

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0.1 0.2 0.3 0.4 0.5 00

1

2

3

Fraction of contamination

Maximum Bias

Maximum bias curve of the sample median

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2 40

0

2

4

6

6

z

x

z = a x + b iir

min

Vertical outlier

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2 40

0

2

4

6

6

z

x

z = a x + b i

ir

min

Bad leverage point

8 10

Critical value of x

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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.

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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.

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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.

Assumed Actual

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

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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.

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xPi

pikl xP

puVV lk 1

Piklkl xX

))cos(1(2 Losses

Piklklpilk xXGxP

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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.

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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.

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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.