Power system state estimation via feasible point pursuit: Algorithms and Cramér-rao bound

Gang Wang, Ahmed S. Zamzam, Georgios B. Giannakis, Nicholas D. Sidiropoulos

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Accurately monitoring the system's operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cramér-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss-Newton iterations and SDR approaches.

Original languageEnglish (US)
Article number8253864
Pages (from-to)1649-1658
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume66
Issue number6
DOIs
StatePublished - Mar 15 2018

Fingerprint

State estimation
Quadratic programming
Electric potential
Computational complexity
Economics
Monitoring

Keywords

  • Power flow analysis
  • autonomous energy grid
  • feasible point pursuit
  • nonconvex quadratically constrained quadratic programming
  • state estimation

Cite this

Power system state estimation via feasible point pursuit : Algorithms and Cramér-rao bound. / Wang, Gang; Zamzam, Ahmed S.; Giannakis, Georgios B.; Sidiropoulos, Nicholas D.

In: IEEE Transactions on Signal Processing, Vol. 66, No. 6, 8253864, 15.03.2018, p. 1649-1658.

Research output: Contribution to journalArticle

@article{2b9287f2d2134909b49711fafb849fa4,
title = "Power system state estimation via feasible point pursuit: Algorithms and Cram{\'e}r-rao bound",
abstract = "Accurately monitoring the system's operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cram{\'e}r-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss-Newton iterations and SDR approaches.",
keywords = "Power flow analysis, autonomous energy grid, feasible point pursuit, nonconvex quadratically constrained quadratic programming, state estimation",
author = "Gang Wang and Zamzam, {Ahmed S.} and Giannakis, {Georgios B.} and Sidiropoulos, {Nicholas D.}",
year = "2018",
month = "3",
day = "15",
doi = "10.1109/TSP.2018.2791977",
language = "English (US)",
volume = "66",
pages = "1649--1658",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",

}

TY - JOUR

T1 - Power system state estimation via feasible point pursuit

T2 - Algorithms and Cramér-rao bound

AU - Wang, Gang

AU - Zamzam, Ahmed S.

AU - Giannakis, Georgios B.

AU - Sidiropoulos, Nicholas D.

PY - 2018/3/15

Y1 - 2018/3/15

N2 - Accurately monitoring the system's operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cramér-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss-Newton iterations and SDR approaches.

AB - Accurately monitoring the system's operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cramér-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss-Newton iterations and SDR approaches.

KW - Power flow analysis

KW - autonomous energy grid

KW - feasible point pursuit

KW - nonconvex quadratically constrained quadratic programming

KW - state estimation

UR - http://www.scopus.com/inward/record.url?scp=85041200149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041200149&partnerID=8YFLogxK

U2 - 10.1109/TSP.2018.2791977

DO - 10.1109/TSP.2018.2791977

M3 - Article

AN - SCOPUS:85041200149

VL - 66

SP - 1649

EP - 1658

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 6

M1 - 8253864

ER -