To effectively control and maintain the transient stability of power systems, traditionally, the extended Kalman filter (EKF) is used as the real-time state estimator (RTSE) to provide the unmeasurable state information. However, the EKF estimation may degrade or even become unstable when the measurement data are inaccurate through random sensor failures, which is a widespread problem in data-intensive power system control applications. To address this issue, this paper proposes an improved EKF that is resilient against sensor failures. This work focuses on the resilient EKF’s (REKF’s) derivation with its application to single-machine infinite-bus (SMIB) power system excitation control. The sensor failure rate is modeled as a binomial distribution with a known mean value. The performance of REKF is compared with the traditional EKF for power system observer-based control under various chances of sensor failures. Computer simulation studies have shown the efficacy and superior performance of the proposed approach in power system control applications.

References

1.
Mahmud
,
M. A.
,
Pota
,
H. R.
,
Aldeen
,
M.
, and
Hossain
,
M. J.
,
2014
, “
Partial Feedback Linearizing Excitation Controller for Multi-Machine Power Systems to Improve Transient Stability
,”
IEEE Trans. Power Syst.
,
29
(
2
), pp.
561
571
. 0885-895010.1109/TPWRS.2013.2283867
2.
Gibbard
,
M. J.
,
Martins
,
N.
,
Sanchez-Gasca
,
J. J.
,
Uchida
,
N.
,
Vittal
,
V.
, and , and
Wang
,
L.
,
2001
, “
Recent Applications of Linear Analysis Techniques
,”
IEEE Trans. Power Syst.
,
16
(
1
), pp.
154
162
. 0885-895010.1109/59.910792
3.
Kuiava
,
R.
,
Ramos
,
R. A.
, and
Pota
,
H. R
,
2013
, “
A New Method to Design Robust Power Oscillation Dampers for Distributed Synchronous Generation Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
135
(
3
), p.
031011
.10.1115/1.4023225
4.
Kumar
,
B. K.
,
Singh
,
S. N.
, and
Srivastava
,
S. C.
,
2007
, “
A Decentralized Nonlinear Feedback Controller With Prescribed Degree of Stability for Damping Power System Oscillations
,”
Electr. Power Syst. Res.
,
77
(
3–4
), pp.
204
211
. 0378-779610.1016/j.epsr.2006.02.014
5.
Gan
,
D.
,
Qu
,
Z.
, and
Cai
,
H.
,
2000
, “
Multi Machine Power System Excitation Control Design via Theories of Feedback Linearization Control and Nonlinear Robust Control
,”
Int. J. Syst. Sci.
,
31
(
4
), pp.
519
527
.10.1080/002077200291091
6.
Chang
,
J.
,
Taranto
,
G. N.
, and
Chow
,
J. H.
,
1995
, “
Dynamic State Estimation in Power System Using a Gain-Scheduled Nonlinear Observer
,”
Proceedings of the 4th IEEE Conference on Control Applications
,
IEEE
,
Albany, NY
, pp.
221
226
.
7.
Utkin
,
V.
,
Guldner
,
J.
, and
Shi
,
J.
,
1999
,
Sliding Mode Control in Electromechanical Systems
,
Taylor and Francis
,
London
.
8.
Ouassaid
,
M
,
Maarou
,
M
, and
Cherkaoui
,
M.
,
2012
, “
Observer-Based Nonlinear Control of Power System Using Sliding Mode Control Strategy
,”
Electr. Power Syst. Res.
,
84
(
1
), pp.
135
143
.10.1016/j.epsr.2011.10.014
9.
Wang
,
W.
, and
Gao
,
Z.
,
2003
, “
A Comparison Study of Advanced State Observer Design Techniques
,”
Proceedings of the American Control Conference
,
IEEE
,
Denver, CO
, pp.
4754
4759
.
10.
Leon-Morales
,
J. D.
,
Busawon
,
K.
, and
Acha-Daza
,
S.
,
2001
, “
A Robust Observer-Based Controller for Synchronous Generators
,”
Int. J. Electr. Power Energy Syst.
,
23
(
3
), pp.
195
211
.10.1016/S0142-0615(00)00058-2
11.
Gu
,
Z.
,
Yang
,
G.
,
Zhu
,
C.
, and
Shao
,
T.
,
2015
, “
Design of the Multi-Objective Constrained Nonlinear Robust Excitation Controller With Extended Kalman Filter Estimates of All State Variables
,”
Int. J. Robust Nonlinear Control
,
25
(
6
), pp.
791
808
.
12.
Fan
,
L.
, and
Wehbe
,
Y.
,
2013
, “
Extended Kalman Filtering Based Real-Time Dynamic State and Parameter Estimation Using PMU Data
,”
Electr. Power Syst. Res.
,
103
(
10
), pp.
168
177
.10.1016/j.epsr.2013.05.016
13.
Lambert
,
F.
,
Yang
,
Y.
, and
Deepakraj
,
D.
,
2007
, “
A Survey for Implementing Sensor Networks for Power Delivery Systems
,”
Proceedings of the IEEE PES General Society Meeting
,
IEEE
,
Tampa, FL
, pp.
1
8
.
14.
Luck
,
R.
,
Ray
,
A.
, and
Halevi
,
Y.
,
1992
, “
Observability Under Recurrent Loss of Data
,”
J. Guid., Control, Dyn.
,
15
(
1
), pp.
284
287
.10.2514/3.20835
15.
Savkin
,
A. V.
, and
Petersen
,
I. R.
,
1997
, “
Robust Filtering With Missing Data and a Deterministic Description of Noise and Uncertainty
,”
Int. J. Syst. Sci.
,
28
(
4
), pp.
373
378
.10.1080/00207729708929397
16.
Savkin
,
A. V.
,
Petersen
,
I. R.
, and
Moheimani
,
S. O. R.
,
1999
, “
Model Validation and State Estimation for Uncertain Continuous-Time Systems With Missing Discrete-Continuous Data
,”
Comput. Electr. Eng.
,
25
(
1
), pp.
29
43
.10.1016/S0045-7906(98)00024-X
17.
Smith
,
S.
, and
Seiler
,
P.
,
2003
, “
Estimation With Lossy Measurements: Jump Estimators for Jump Systems
,”
IEEE Trans. Autom. Control
,
48
(
12
), pp.
2163
2171
.10.1109/TAC.2003.820140
18.
Wang
,
Z.
,
Ho
,
D.
, and
Liu
,
X.
,
2003
, “
Variance-Constrained Filtering for Uncertain Stochastic Systems With Missing Measurements
,”
IEEE Trans. Autom. Control
,
48
(
7
), pp.
1254
1258
.10.1109/TAC.2003.814272
19.
Wang
,
Z.
,
Yang
,
F.
,
Ho
,
D. W. C.
, and
Liu
,
X.
,
2005
, “
Robust Finite Horizon Filtering for Stochastic Systems With Missing Measurements
,”
IEEE Signal Process. Lett.
,
12
(
6
), pp.
437
440
.10.1109/LSP.2005.847890
20.
Sinopoli
,
B.
,
Schenato
,
L.
,
Franceschetti
,
M.
,
Poolla
,
K.
,
Jordan
,
M. I.
, and
Sastry
,
S. S.
,
2004
, “
Kalman Filtering With Intermittent Observations
,”
IEEE Trans. Autom. Control
,
49
(
9
), pp.
1453
1464
.10.1109/TAC.2004.834121
21.
Matveev
,
A. S.
, and
Savkin
,
A. V.
,
2003
, “
The Problem of State Estimation via Asynchronous Communication Channels With Irregular Transmission Times
,”
IEEE Trans. Autom. Control
,
48
(
4
), pp.
670
676
.10.1109/TAC.2003.809771
22.
Hounkpevi
,
F. O.
, and
Yaz
,
E. E.
,
2007
, “
Robust and Resilient Minimum Variance Linear State Estimators for Multiple Sensors With Different Failure Rates
,”
Automatica
,
43
(
7
), pp.
1274
1280
. 0005-109810.1016/j.automatica.2006.12.025
23.
Jeong
,
C. S.
,
Yaz
,
E. E.
, and
Yaz
,
Y. I.
,
2011
, “
Lyapunov-Based Design of Resilient Mixed MSE-Dissipative Type State Observers for a Class of Nonlinear Systems and General Performance Criteria
,”
Int. J. Syst. Sci.
,
42
(
5
), pp.
789
800
.10.1080/00207721.2010.547634
24.
NaNacara
,
W.
, and
Yaz
,
E. E.
,
1997
, “
Recursive Estimator for Linear and Nonlinear Systems With Uncertain Observations
,”
Signal Process.
,
62
(
2
), pp.
215
228
.
25.
Hu
,
J.
,
Wang
,
Z.
,
Gao
,
H.
, and
Stergioulas
,
L. K.
,
2012
, “
Extended Kalman Filtering With Stochastic Non-Linearities and Multiple Missing Measurement
,”
Automatica
,
48
(
9
), pp.
2007
2015
. 0005-109810.1016/j.automatica.2012.03.027
26.
Mahmud
,
M. A.
,
2014
, “
An Alternative LQR-Based Excitation Controller Design for Power Systems to Enhance Small-Signal Stability
,”
Electr. Power Energy Syst.
,
63
(
12
), pp.
1
7
.10.1016/j.ijepes.2014.05.045
27.
Kundur
,
P.
,
1994
,
Power System Stability and Control
,
McGraw-Hill
,
New York
.
28.
Lahdhiri
,
T.
, and
Alouani
,
A. T.
,
1995
, “
Nonlinear Stabilizing Controller for a Single Machine Infinite-Bus Power System
,”
Proceedings of the 4th IEEE Conference on Control Applications
,
IEEE
,
Albany, NY
, pp.
1014
1019
.
29.
Reif
,
K.
,
Gunther
,
S.
,
Yaz
,
E.
, and
Unbehauen
,
R.
,
1999
, “
Stochastic Stability of the Discrete-Time Extended Kalman Filter
,”
IEEE Trans. Autom. Control
,
44
(
4
), pp.
714
728
.10.1109/9.754809
30.
Reif
,
K.
,
Gunther
,
S.
,
Yaz
,
E.
, and
Unbehauen
,
R.
,
2000
, “
Stochastic Stability of the Continuous-Time Extended Kalman Filter
,”
IEE Proc.—Control Theory Appl.
,
147
(
1
), pp.
45
52
.10.1049/ip-cta:20000125
31.
Wang
,
X.
, and
Gu
,
P.
,
2015
, “
Single Machine Infinite Bus Power System Control with Resilient Extended Kalman Filter
,”
Proceedings of the ASME International Mechanical Engineering Congress
,
ASME
,
Houston, TX
, IMECE2015-50289.
32.
Wang
,
X.
, and
Yaz
,
E.
,
2016
, “
Smart Power Grid Synchronization With Fault Tolerant Nonlinear Estimation
,”
IEEE Trans. Power Syst.
33.
Horn
,
R. A.
, and
Johnson
,
C. A.
,
1991
,
Topics in Matrix Analysis
,
Cambridge University Press
,
Cambridge, UK
.
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