Computing Power System Steady-state Stability Using Synchrophasor Data Karl Reinhard ECE Power and...
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Computing Power System Steady-state Stability Using Synchrophasor Data Karl Reinhard ECE Power and Energy Group Colloquium 29 Oct 12 work with Peter Sauer
Computing Power System Steady-state Stability Using
Synchrophasor Data Karl Reinhard ECE Power and Energy Group
Colloquium 29 Oct 12 work with Peter Sauer and Alejandro
Domnguez-Garca
Slide 2
Conjecture Collect synchrophasor measurements at 2 buses
directly connected by transmission Line Compute model parameters
for a pair of Thevenin sources Connect Thevenin sources by the
transmission line 2
Slide 3
Conjecture Collect synchrophasor measurements at 2 buses
directly connected by transmission Line Compute model parameters
for a pair of Thevenin sources Connect Thevenin sources by the
transmission line Resulting Thevenin source angle difference
(AnglxSys) indicates system stability stress Largest AnglxSys of
all directly connected buses is proposed as an indicator of the
risk of losing system stability 3
Slide 4
Purpose To report progress investigating this conjecture to
date 4 Take Aways Synchrophasor data is not suitable for some
Thevenin equivalent formulations equations poorly conditioned with
field measurements A reduced Thevenin equivalent system meeting
expected power system physical constraints can be calculated
Importance of verifying that computed values are consistent with
power system physics and model at each iteration
Slide 5
Stability Limits to Power System Operation 5 easy to assess
from measurements. Thermal short term and long term typically
measured in Amps or Power (MW or MVA) easy to assess from
measurements. easy to assess from measurements Voltage plus or
minus 5% of nominal easy to assess from measurements. difficult to
assess. Stability voltage collapse, steady-state stability,
transient stability, bifurcations margins to each critical point
difficult to assess. Thermal Voltage Stability
Slide 6
Stability Limits to Power System Operation 6 69 KV 12 MW 138 KV
50 MW 230 KV 140 MW 345 KV 400 MW 500 KV 1000 MW 765 KV 2000 MW
Thermal Voltage Stability 1.0 SIL = power delivered by a lossless
line to a load resistance equal to the surge (characteristic)
impedance Voltage and current are in phase along entire line VARS
into line from shunt charging are exactly equal to the total line
VAR series losses Flat voltage profile along entire line
Slide 7
Estimating Thevenin Equivalents w/ SPD (SynchroPhasor Data)
7
Slide 8
Estimating Thevenin Equivalents w/ SPD 8
Slide 9
9
Slide 10
Condition No. Analysis Exact Soln 10 Condition Number
Slide 11
Condition No. Analysis 11 Condition Number
Slide 12
Condition No. Analysis 12 Condition Number
Slide 13
Condition No. Analysis Least Squares Estimate (m x n matrix)
13
Slide 14
Estimating Reduced Thevenin Equivalent w/ SPD 14
Slide 15
Estimating Reduced Thevenin Equivalent w/ SPD Real Power Eqn
15
Slide 16
Estimating Reduced Thevenin Equivalent w/ SPD 16
Slide 17
Estimating Reduced Thevenin Equivalent w/ SPD 17
Slide 18
Estimating Reduced Thevenin Equivalent w/ SPD 18
Slide 19
RECAP Purpose: To report progress investigating the conjecture
that a Thevenin Equivalent from Synchrophasor data indicates system
stress 19 Take Aways Synchrophasor data is not suitable for some
Thevenin equivalent formulations equations poorly conditioned with
field measurements A reduced Thevenin equivalent system meeting
expected power system physical constraints can be calculated
Importance of verifying that computed values are consistent with
power system physics and model at each iteration Next Does AnglxSys
indicate system stress?? Simulation using MATLAB and Power
World
GPS Timing Data 22 2 Satellite Signals Intersection Circle 3
Satellite Signals Intersection 2 Points 4th Satellite Timing Signal
Correction Satellite 4 Receiver Due to Clock errors, Unlikely 4th
satellites sphere will intersect either of 2 intersection points
Distance from the valid GPS receiver position estimate to the 4 th
satellite sphere surface enables timing error determination /
correction: Satellite 3 da