From Static to Dynamic
System estimation:
The role of bus dynamics
5th Annual CMU Electricity Conference
March 11, 2009
Presented by: Ellery Blood
Advisors: Marija Ilić and Bruce Krogh
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Presentation Outline
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Static State Estimation Overview
Problems with Static State Estimation
Dynamic Estimation of Static State
DSE Implementation
Performance
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Power System State Estimation
Overview
• What our measurements are telling us
– Current flows, current injections, power flows, power
Injections, voltages
– Inaccurate & corrupted measurements
• Power System Static State
– All network measurements function of static state, δ V
– Voltage phasor magnitude angle and magnitude
• Redundant measurements
– Nmeasurements ≥ 2 x Nstates
– Filter out some of the measurement noise
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Power System State Estimation
Overview - continued
• Handle grossly inaccurate (bad) data
– Detect: Chi-square test
– Identify: Weighted residual analysis
– Remove bad data from measurement vector
• Observability Analysis
– May remove redundancy of some states
– May remove all data dependent on some states
(unobservable)
– Only try to estimate observable states
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Problems with Static Estimation
• Result entirely dependent on single snapshot of data
– Fast network transients
– Dynamically estimating network dynamics is difficult
• Observability vulnerable to
– Loss of critical measurement
– Loss of critical pair
• Accuracy vulnerable to
– Loss of redundancy
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Problems with Static Estimation
• Result entirely dependent on single snapshot of data
– Fast network transients
– Dynamically estimating network dynamics is difficult
• Observability vulnerable to
– Loss of critical measurement
– Loss of critical pair
• Accuracy vulnerable to
– Loss of redundancy
Static SE only sees the network, not what
is attached to it
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Static Estimation
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Static Estimation
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Static Estimation
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Static Estimation
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The Network
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2
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The Network
measurements
P1
P12
P2
P14
P24
P3
P34
P4
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The Network
measurements
P1
P12
P2
P14
P24
P3
P34
P4
At any time, any of the
measurements may be missing
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Dynamic State Estimation of Static State
• Time constants of attached loads and GTG systems
– Slower time constants
– Dynamic estimation of attached systems is feasible
• Effectively provide additional redundancy
– Power/current bus injections
– Comes from modeling (no extra hardware required)
– Models time behavior (correlates measurements
across snapshots)
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Dynamic Estimation
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Dynamic Estimation
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Dynamic Estimation
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Dynamic Estimation
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Dynamic Estimation
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Dynamic Estimation
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The Network
(and attached systems)
PD1
PD3
PD2
PD4
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The Network
measurements (and attached systems)
P1
P12
P2
PD1
PD2
P14
P24
P3
P34
PD3
P4
PD4
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The Network
measurements (and attached systems)
P1
P12
P2
PD1
PD2
P14
P24
P3
P34
P4
PD4
PD3
The PD measurements will persist
regardless of what telemetry data
is presently corrupt
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•
DSE Implementation
Bus dynamic system
– GTG (4 sv) Valve position, mechanical power, frequency, angle
– Load (3 or more sv) Power, frequency, angle
⎡ Δa ⎤ ⎡ − kR
⎢
⎥ ⎢
d ⎢ Δω ⎥ ⎢ 0
=
dt ⎢ΔPm ⎥ ⎢1/ Tch
⎥ ⎢
⎢
δ
⎣
⎦ ⎣ 0
•
•
k
0
0 1/ M
0 − 1/ Tch
1
0
− k − k⎤
0⎤ ⎡ Δa ⎤ ⎡ 0
⎡ΔPe ⎤
⎢
⎥
⎢
⎥
⎥
0 ⎥ ⎢ Δω ⎥ ⎢ − 1 / M 0
0 ⎥⎢
⎥
ω
+
0 ⎥
0⎥ ⎢ΔPm ⎥ ⎢ 0
0
0 ⎥⎢
⎥ ⎢⎣ L ref ⎥⎦
⎥ ⎢
⎥⎢
0⎦ ⎣ δ ⎦ ⎣ 0
0
0⎦
Network
– Bus systems coupled through the network based on voltage angle
– Pab=Bab sin(δa-δb)
State vector, x, is concatenation of bus state vectors
– E is participation matrix
– δ=E x
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Kalman Filtering
• KF minimizes the state error covariance
– Linear system with Gaussian noise
– Two steps: predict (input), correct (measurements)
• Measurements are δ, output from static estimator
• May also have information on inputs
– Load forecasts
– Info from generating facilities
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SE Performance
• Metric
–
–
–
–
SE tries to minimize state error covariance
Covariance doesn’t make sense for unobservable state
Information matrix (inverse of covariance) does
Consider trace of information matrix as metric
• Static SE has constant best case
• Dynamic SE has worst case equal to Static SE
– Improves as more measurements are collected
– Degrades but doesn’t fail when unobservable
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Three Bus Sample System
Lossless, nonlinear line flows
Pδ, QV decoupled
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Three Bus Sample System
2
1
3
2
1
3
2
1
3
PL
time
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Performance – Topology Change
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Performance – Topology Change
Topology change
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Performance – Bad Data
Bad Data
(Bus 2 unobservable)
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Conclusion
• Static state estimation
– Provides useful and reliable information to operators
– Heavily susceptible to bad data
– Some states unobservable
• Dynamic state estimation
– Provide improved accuracy over static estimation
– Reduced susceptibility to temporary unobservable
conditions
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Questions?
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