1 Challenges in Power Systems State Estimation Lamine Mili Virginia Tech Alexandria Research...
-
date post
22-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of 1 Challenges in Power Systems State Estimation Lamine Mili Virginia Tech Alexandria Research...
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
VPQI
CT0 to 5 A
High voltage and high current
ADC
10 k
0 to 10 V
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.
5
P1 P2 P3
S1 S2 S3 S4
500 KV Bus
230 KV Bus
T1 T2
6
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
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.
R j X
j C /2 j C /2
10
Probability Distribution of Measurement Errors
3
f(x)
x0
Gaussian distibutionActual
distribution
11
• 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
12
True value
Breakdown point of L1-norm estimator is =
Breakdown Point of Sample Median
medianbias
median
median
mm
/]2
1[
13
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
14
2 40
0
2
4
6
6
z
x
z = a x + b iir
min
Vertical outlier
15
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
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
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
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
pikl xP
puVV lk 1
Piklkl xX
))cos(1(2 Losses
Piklklpilk xXGxP
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.