1 challenges in power systems state estimation lamine mili virginia tech alexandria research...
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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
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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
3
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.