Measurement-Based Voltage Stability
Application: Methodology and Initial
Experience
Scott G. Ghiocel & Joe H. Chow
Rensselaer Polytechnic Institute
Topics
• The new AQ bus type for voltage stability analysis
• Voltage stability analysis for

New York power system – central New York (PMU data)

BPA wind hub (SCADA data, future PMU data)

Southern California Edison (SCE) (PMU data)
• Future work on voltage stability analysis
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May 2014 SGG & JHC
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The AQ Bus Type
• Specify the voltage angle for the load bus (remove 1 unknown)
• Remove load P equation (load power not enforced)
• Instead, control the angle separation to indirectly adjust P
Removed
P equation
Specified bus angle
Reduced Jacobian
• The size of the resulting reduced Jacobian is reduced by 1
• No load parameter required
• This reduced Jacobian matrix is nonsingular at the
maximum loading point [1]
[1] Ghiocel, S.G.; Chow, J.H., "A Power Flow Method Using a New Bus
Type for Computing Steady-State Voltage Stability Margins," IEEE
Transactions on Power Systems, vol.29, no.2, pp.958-965, March 2014
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A New, Nonsingular Jacobian
• At the point of maximum power transfer, the reduced
Jacobian is nonsingular
Conventional Jacobian
Singularity
0
5
4.5
-0.2
Reduced
Jacobian
4
-0.4
3
2.5
-0.6
2
Power Transfer (p.u.)
Determinant of Jacobian
3.5
1.5
-0.8
1
Jacobian determinant
Reduced Jacobian determinant
Power Transfer
-1
0
10
20
30
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40
50
Load bus angle (deg)
60
70
80
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0.5
0
90
4
NPCC System: Contingency Analysis
Swing bus
AQ bus
50
C
A
B
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36
D E
16
4 15
30
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PV Curves & Contingency Analysis
Line Trip Contingency Analysis based on PV Curves
1
0.95
Base case
AQ-bus (Bus 16) voltage magnitude (pu)
AQ Bus voltage magnitude (pu)
1.05
0.9
0.85
0.8
B
0.75
C
A
0.7
D
Base Case
Line 73--74 (72 MW)
Line 8-73 (97 MW)
Line 2--37 (53 MW)
Line 3--2 (295 MW)
Line 3--18 (50 MW)
0.65
0
2
4
6
8
Active power loading margin at AQ-bus (Bus 16) (pu)
E
10
12
14
Active power margin (ΔP) at AQ Bus (pu)
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PV Curve with a Var-Limited Nose Point
• Reduced some generator var limits on the NPCC system
• Maximum power transfer becomes a var limit (corner)
• No convergence issues at the nose point with the AQ-bus method
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Chateauguay
Hybrid VSA Example:
Central NY
Massena
Moses
• Phasor data from 6 PMUs
provided by New York Power
Authority (NYPA)
• 13-bus observable subnetwork
Oswego
Complex
• Pseudo PMU data calculated
on the non-PMU buses using a
phasor-only state estimator
(PSE) – phase biases and
Volney
current scaling correction
Clay
• Power flows from West and
Marcy South
Interface
North towards NYC
• Critical power transfer
interfaces
• Weaker ties to ISO-New
Oakdale
England and other neighboring
control areas
230 kV
345 kV
PMU Location
765 kV
Est. Location
Unmeasured Current
Marcy 765
Scott Ghiocel – Rensselaer Polytechnic Institute
Central East
Interface
Marcy 345
New
Scotland
CSC
New England
Interface
Edic
Alps
Gilboa
Leeds
Fraser
Pleasant
Valley
Coopers
Corners
Total East
Interface
Rensselaer Polytechnic Institute
NYS TRANSMISSION SYSTEM
(with synchrophasors shown)
Rock
Tavern
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Roseton
E. Fishkill
8
Computed PV Curves (Event 1)
• Computed transfer limit agrees with operational
guidelines
• Includes SVC
equipment
limits
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Computed PV Curves (Event 2)
PV Curves for Event 2
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Close-up of PMU data
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Voltage Issues at a BPA Wind Hub
Wind Farm Response (at point of connection)
2.2
2
P
P (p.u.)
• 2-sec resolution data
from a 600 MW wind
interconnection
• Huge voltage variations
1.8
1.6
Wind plant
curtailment
1.4
1.2

~12% within 10 min
Q (p.u.)
• Weak system / line outage
• Wind plant curtailment
• Shunt capacitor issues
Q
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
3000
4000
5000
Time (s)
6000
7000
8000
9000
0.05
0
-0.05
-0.1
-0.15
-0.2
1
0.9
0.8
0.7
0.6
1.06
0.5
1.04
0.4
1.02
V
0.3
V (p.u.)
Power (p.u.)
-0.25
WP 1
WP 2
WP 3
WP 4
WP 5
WP 6
1
0.2
0.98
0.1
0.96
0
0.94
0
~14%
variation
0
100
200
300
Time (min)
400
500
1000
2000
600
Time (s)
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BPA Wind Hub Diagram
G
Thévenin equiv.
(swing bus)
G
Measurements
Edge of the
observable
network
AQ bus
PQ
PQ
PV
PQ
PQ
PV
Unobservable
Credit: E. Heredia, D. Kosterev, M. Donnelly, “Wind Hub Reactive Resource
Coordination and Voltage Control Study by Sequence Power Flow, 2013 IEEE PES
General Meeting, July 2013.
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Estimating Wind Plant Models and Shunts
• Separation of shunt compensation from wind turbine output
• Online characterization of Type 2 wind plants using steady-state PQ
models (polynomial approximation)
PQ curve for Wind Plant 1
PQ curve for Wind Plant 2
0.05
-0.05
WT Reactive Power (p.u.)
WT Reactive Power (p.u.)
0
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
Measurements
Measurements w/ est. shunt Q removed
PQ model
-0.4
-0.45
0
0.2
0.4
0.6
0
-0.05
Shunt action
-0.1
-0.15
-0.2
Measurements
Measurements w/ est. shunt Q removed
PQ model
-0.25
0.8
WT Active Power (p.u.)
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1
0
0.2
0.4
0.6
0.8
1
WT Active Power (p.u.)
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Creating the Hybrid Model
• Thévenin equivalents (West and East systems)

Calculate Eʹ and Xʹ using a least-squares fit
• Calculate power flow sensitivities

Incremental power output from the wind plants is split between the West
and East systems
• Estimate shunt status

Detect jumps in Q flow that are not caused by the wind turbines (WT):
• Estimate wind plant status and PQ-equivalent models

3rd order polynomial fit using adjusted Q output:
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PV Curves using the Hybrid Model
Wind Hub
West
East
1.03
1.025
1.02
1.015
1.01
1.005
1
0.995
West
Measured
VS Calculation
0.99
0.985
1.06
1.06
1.04
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
1
2
3
4
5
East Voltage Magnitude (p.u.)
Wind Hub Voltage Magnitude (p.u.)
West Voltage Magnitude (p.u.)
1.035
Wind Hub
Measured
VS Calculation
1
Wind Hub Power (p.u.)
2
3
4
5
1.02
1
0.98
0.96
0.94
0.92
0.9
Wind Hub Power (p.u.)
East
1
2
3
4
5
Wind Hub Power (p.u.)
Can also analyze weak or strong connection only configuration
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Ongoing Analysis: Southern California
• New wind generation north
of Los Angeles
Local voltage
issues
• LA is a load area with
multiple in-feeds
• Reactive power support
and series compensation
on high-voltage lines
New wind
plants
• Local voltage issues
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PV Curves from PMU Data
1.05
1.03
1.04
1.02
1.03
1.01
1.02
1
1.01
0.99
1
0.98
0.99
0.97
0.98
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Rensselaer Polytechnic Institute
-0.5
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0
0.5
1
17
Real-Time Implementation
• Installation and testing to begin at BPA in June
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Future Research: Voltage Stability
• Ongoing project work with Southern California Edison and BPA


Real-time prototype implementation
Demonstration at NASPI VSA workshop in October
• Interest in AQ-bus method from a commercial power system
simulation software vendor
• Continuation of DoE/CERTS funding on PMU-based VS



Extend to system-wide voltage stability analysis
Multiple voltage collapse scenarios and cascading failures
Decision support for system operators considering high renewable
penetration and demand response (remedial action schemes)
• Wind turbine PMU data from NY North Country from NYPA
(NYSERDA project)
• Sensitivity of the maximum loadability to wind turbine type
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Acknowledgements
This work was supported by the Lawrence Berkeley National Lab
(LBL) and CERTS, the ERC Program of the National Science
Foundation and DOE under NSF Award Number EEC-1041877, and
the CURENT Industry Partner Program.
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