It describes the challenges in power system state estimation

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
V
P
Q
I
CT
0 to 5 A
High voltage and high current
ADC
10 kW
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.

5. 5
P1 P2 P3
S1 S2 S3 S4
500 KV Bus
230 KV Bus
T1 T2

6. 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. 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.
R j X
j  C /2 j  C /2

10. 10
Probability Distribution of Measurement Errors
3 s
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 e* = 0 %
Breakdown Point of an Estimator

12. 12
True value
Breakdown point of L1-norm estimator is e* =
Breakdown Point of Sample Median
median
bias
median
median
m
m
/
]
2
1
[


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

14. 14
2 4
0
0
2
4
6
6
z
x
z = a x + b 
i
i
r

min
Vertical outlier

15. 15
2 4
0
0
2
4
6
6
z
x
z = a x + b

i
i
r

min
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.
Assumed Actual

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
xPi
pi
kl x
P 
pu
V
V l
k 1


Pi
kl
kl x
X


)
)
cos(
1
(
2


 


 

Losses
Pi
kl
kl
pi
lk x
X
G
x
P 




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.