naspi_march2015_poster-epri-wsu.pdf
TRANSCRIPT
-
PMU-Based Monitoring of Power System Dynamics
Guanqun Wang1, Chen-Ching Liu1, Mahendra Patel2, Evangelos Farantatos2
1. Washington State University
2. Electric Power Research Institute
Nonlinear Dynamic Observability
State Calculator and MLE
Conclusions
PMU-Based Power System Dynamics Monitoring
Goal Wide area monitoring of rotor angle stability to prevent
widespread blackouts.
Methodology State Calculator (SC).
Maximal Lyapunov Exponent (MLE).
Observability Analysis of Nonlinear Dynamic
Systems.
A dynamic system is observable if, for any time t, the current state x(t)
can be determined using only the measurements h(x(t)).
tx( )
( )
t
t
x x
l xO x
x
( )O x
0
1
0
1
1
1
( )
( )( )
( )
( )
f
f p
t
f
n
f p
L h x
L h xl x
L h x
L h x
1
21
1 2
( )
( )= ...
...
( )
f f
n
n
f x
f xh h hL h L h
x x x
f x
0
fL h h2 ( )f f fL h L L h
PMU
State Calculator
Calculation of MLEover Finite Time
Window T
Off-Line Simulation of All Credible Disturbances
Monitored State Variables (Waveforms)
Unmonitored State Variables
Time Window TCovering at Least One Cycle of the
Power Swing
t T
1, , kx x
1' , , 'kx x1, ,k nx x
1 1' , , ' , ' , , 'k k nx x x x
MLE
Spectrum Analysis
Power Swing Curves
Prediction of System Stability
Using MLE
Real Power System
Observability Analysis along
System Trajectory
Calculation of Observability
Index
The ratio of smallest and largest singular value of observabilitymatrix is chosen as an index to assess the level of system observability.
Observability indices can be tracked along system trajectory.
( ) 1,2,...,( , )
i i
i i
x f x i nh
Dynamic Model of a Power System
As the number of
PMUs increases, the
level of observability
also improves.
Developed MLE and State Calculator as effective techniques to predict
loss of synchronism in power systems.
Developed an index to quantify the level of observability for different
PMU deployment scenarios.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (s)
Obs
erva
bilit
y In
dex
14 PMU measurements
15 PMU measurements
179-Bus WECC System:
The observability indices are much higher and always above 0, but
their values differ significantly.
The observability of 15-PMU scenario is always higher than the 14-
PMU scenario.
The SC results with 15 PMUs are much closer to the simulation
results. That indicates that 15 PMUs and for that specific location
provide a sufficient level of confidence based on the system
observability.
Observability for 14 and 15 PMUs
State Calculator with 14 and 15 PMUs
PMU number
Generators with PMUs
14 1,8,9,10,15,16,17,18,19,20,21,22,24,2715 1,4,8,9,10,15,16,17,18,19,20,21,22,24,27
NASPI, March 2015, Burlingame, CA
Flowchart
Assume are observed by PMU measurements.
are estimated by
( ) = ( ) + ( ( ))
1 1( ) = ( ) + ( ( )) + ( ( ))
2 2
j j
j j
x t t x t f x t t
x t t x t t f x t f x t t
1,...,j k n
1 1( ) = ( )
( ) = ( )
observed
observed
k k
x t t x t t
x t t x t t
State Calculator
1( ), , ( )kx t x t
+1( ), , ( )k nx t x t
The Lyapunov Exponents are used tocharacterize the exponential divergence
or convergence of nearby trajectories.
( )tx
( )tx
0x
0x
Divergent trajectories: Unstable Converging trajectories: Stable
MLE is calculated by the approximation of
MLE of x(t) is calculated to monitor rotor angle stability after a disturbance. If MLE