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PSERC ProjectPSERC Project
Power System State Estimation and Optimal Measurement Placement for Distr
ibuted Multi-Utility Operation
A. Abur and G.M. Huang (PIs) J. Lei and B. Xu (Students)
Texas A&M University
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OutlineOutline
Objectives Technical Approach Implementation Results Conclusions
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ObjectivesObjectives
Optimal Meter Placement FACTS Device Monitoring Distributed State Estimation
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Technical ApproachTechnical Approach Three step meter placement
– Choice of the minimum set– Choice of candidates– Optimal selection from candidates
FACTS device monitoring– Modeling with constraints– Incorporation into SE
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Meter Placement ProblemMeter Placement Problem Choice of Essential Measurements Set.
– If the system is observable: Factorize H matrix– Else: Run LAV estimator
Candidate Identification– Form Contingency–Measurement incidence matrix
Optimal Candidate selection– Use of integer programming
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ContingenciesContingencies
Types of Contingencies: Line Outage Measurement Loss Bus Split
Robustness Options: Against user defined contingency list Bad data Detectability All single line outages
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Graphic User InterfaceGraphic User Interface
Add injections at bus 3 and 4
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FACTS Device MonitoringFACTS Device Monitoring
UPFC Modeling: Two V-source model Four parameters Constraints
Integration into the SE: Use Hachtel’s formulation Inequality and equality constraints
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Model of UPFC Physical Model of UPFC
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Model of UPFC Steady State Model of UPFC
The constraint PB + PE = 0 implies that no real-power is exchanged between the UPFC and the system.
BBV
BZ
BZ
BI
BI
EEV 0 EB PP
EI
BI EZ
k m
kmkm jQP
kmkm jQP mkmk jQP
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MeasurementsReal and reactive power through k-m
BkB
BkEk
E
Ekkm
B
mkkm X
VV
X
VV
X
VVP ,, sinsinsin ( 1 )
BkB
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EEkm X
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XX
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2coscoscos
( 2 )
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mkmk X
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VVP ,sinsin ( 3 )
BmB
Bmmk
B
mk
B
mmk X
VV
X
VV
X
VQ ,
2
coscos ( 4 )
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ConstraintsEquality and inequality constraints of UPFC
• VB, θB, VB and θB are the control parameters of UPFC
Real Power Constraints: 0 BE PP (5)
Shunt Power Constraints: max,22
EEE TQP (6)
Series Power Constraints: max,22
BBB TQP (7)
Shunt Voltage Constraints: max,BB VV (8)
Series Voltage Constraints: max,EE VV (9)
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Hachtel’s Method
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Hachtel’s Method KKT first order optimality conditions :
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Example
From (bus) To (bus) XB XE VB,max VE,max SB,max SE,max
6 12 0.7 0.7 1.0 1.0 1.0 1.0
Parameters of the installed UPFC device
FACTS device (UPFC) is installed on line 6-12, near bus 6
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Estimation ResultsFunction of the program as an estimat
or
Function of the program as a power flow controller
• Note that PB + PE = 0 and VB < 1.0, VE < 1.0, SB < 1.0, SE < 1.0, which correctly satisfy all the constraints.
Voltages and powers of UPFC
Set power flow in line 6-12 to be 0.1 + j0.1
Voltages and powers of UPFC
VB θB PB SB VE θE PE SE
0.1099 60.07 0.0014 0.0128 1.0679 -14.31 -0.0014 0.0035
VB θB PB SB VE θE PE SE
0.1236 9.0530 0.0056 0.0159 1.0000 -14.6037 -0.0056 0.0691
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Conclusions
Optimal meter placement accounting for contingencies and loss of measurements
State estimation of systems with FACTS devices and their parameters
Setting of parameters of FACTS devices for desired power flows