# PSERC Project Power System State Estimation and Optimal by alicejenny

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```									         PSERC Project
Power System State Estimation
and Optimal Measurement Placement for
Distributed Multi-Utility Operation

A. Abur and G.M. Huang (PIs) J. Lei and B. Xu
(Students)

Texas A&M University
Outline
 Objectives
 Technical Approach
 Implementation
 Results
 Conclusions
Objectives

 Optimal  Meter Placement
 FACTS Device Monitoring
 Distributed State Estimation
Technical 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
Meter 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
Contingencies
Types of Contingencies:
   Line Outage
   Measurement Loss
   Bus Split

Robustness Options:
   Against user defined contingency list
   All single line outages
Graphic User Interface

Add injections at bus 3 and 4
FACTS Device Monitoring
UPFC Modeling:
   Two V-source model
   Four parameters
   Constraints

Integration into the SE:
   Use Hachtel’s formulation
   Inequality and equality constraints
Model of UPFC
 Physical Model of UPFC
Model of UPFC
 Steady State Model of UPFC
VB  B
Pkm  jQkm                             ZB       Pmk  jQmk
Pkm  jQkm                             ZB
k                                                                       m
IE
ZE                                  IB
IB
IB
PB  PE  0
V E  E

The constraint PB + PE = 0 implies that no real-power is exchanged between
the UPFC and the system.
Measurements
 Real and reactive power through k-m

Vk Vm                 Vk V E                   Vk V B
Pkm             sin  km             sin  k , E                 sin  k , B   (1)
XB                    XE                         XB
XE  XE      Vk Vm            Vk V E               Vk V B
Q km          Vk        cos  km         cos  k , E         cos  k , B
2
(2)
XBXE         XB               XE                   XB
Vk Vm                 Vm V B
Pmk             sin  mk              sin  m , B                               (3)
XB                     XB
2
Vm           Vk Vm               Vm V B
Qmk                         cos mk                  cos m , B                 (4)
XB           XB                    XB
Constraints
 Equality and inequality constraints of UPFC

Real Power Constraints:                P E P B  0             (5)

PE  Q E  TE ,m ax
2         2
Shunt Power Constraints:                                        (6)

PB  Q B  TB ,m ax
2        2
Series Power Constraints:                                       (7)

Shunt Voltage Constraints:             V B  V B ,m ax          (8)

V E  V E ,max
Series Voltage Constraints:                                     (9)

• VB, θB, VB and θB are the control parameters of UPFC
Hachtel’s Method

1 T 1
min         r R r
2
s.t       f ( x)  s    0
c( x)       0
r  z  h( x )  0
s         0
Hachtel’s Method
 KKT first order optimality conditions :

D         0       0      F       f (xk ) 
0         0       0          
G      g(x )  k 
                                 
0        0       R       H      z  h( x k ) 
 T                                            
F       G T
H T
0  x      0        

Example
 FACTS device
(UPFC) is installed
on line 6-12, near
bus 6

Parameters of the installed UPFC device

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
Estimation Results
 Function of the program as an estimator
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

• Note that PB + PE = 0 and VB < 1.0, VE < 1.0, SB < 1.0, SE < 1.0, which correctly
satisfy all the constraints.

 Function of the program as a power flow controller
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
0.1236     9.0530     0.0056   0.0159   1.0000   -14.6037    -0.0056    0.0691
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

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