“Observability analysis and bad date processing of state estimation using Hachtel's augmented matrix method”Authors: Felix F. Wu, Wen-Hsiung E. Liu, Lars Holten, Anders Gjelsvik and Sverre AamAffiliation: University of Berkeley, Norwegian State Power Board (Statkraft), The Norwegian Research Institute of Electricity Supply (EFI, now SINTEF Energy Research) Reference: 1988, Vol 9, No 3, pp. 109-128. |
|
Keywords: Electric power system, static state estimation, error covariance sparse matrices, least squares, numerical methods
Abstract: The triangular-factorization-based observability analysis and the normalized residual-based bad data processing are extended to state estimation using Hachtel's augmented matrix method. This method is numerically robust, computationally efficient, and has a reasonable extra storage requirement. In this paper it is shown that the observability analysis can be carried out in the process of triangular factorization of the augmented coefficient matrix used in Hachtel's method. Moreover, the normalized residuals are shown to be obtainable using the sparse inverse of this augmented matrix. The algorithms have been successfully incorporated in the state estimation program developed at Norwegian State Power Board (Statkraft). Test results on the IEEE 14 bus system and a 99-bus system consisting of the main grid of southern Norway are presented. Hachtel's approach to state estimation provides an attractive alternative to the standard normal equations approach.
PDF (1858 Kb)
DOI: 10.4173/mic.1988.3.1
Currently no DOI forward links to this article
References:
[1] ASCHMONEIT, F.C., PETERSON, N.M., and ADRIAN, E.C. (1977). State estimation with equality constraints, Tenth PICA Conference Proceedings, May 1977, Toronto, pp. 427-430.
[2] BJORCK, A. (1967). Iterative refinement of linear least square solutions, BIT,7, 257-278, doi:10.1007/BF01939321
[3] BROUSSOLLE, F. (1978). State estimation in power systems: detecting bad data through the sparse inverse matrix method, IEEE Trans. Power App. and Syst., 97, 678-682, doi:10.1109/TPAS.1978.354538
[4] CLEMENTS, K.A. and DAVIS, P.W. (1985). Multiple bad data detectability and identitiability: a geometric approach, Proc. 1985 PICA Conference, San Francisco, May 6-10, 1985, pp. 461-466.
[5] CLEMENTS, K.A., KRUMPHOLZ, G.R., and DAVIS, P.W. (1983). Power system state estimation with measurement deficiency: an observability measurement placement algorithm, IEEE Trans. Power App. and Syst., 102, 2012-2020, doi:10.1109/TPAS.1983.318187
[6] DUFF, I.S. and REID, J.K. (1976). A comparison of some methods for the solution of sparse overdetermined systems of linear equations, J. Inst. Math. Appl., 17, 267-280, doi:10.1093/imamat/17.3.267
[7] DUFF, I.S. and REID, J.K. (1983). Multifrontal solution of indefinite sparse symmetric linear systems, ACM Trans. on Mathematical Software, 9, No. 3., 302-325, doi:10.1145/356044.356047
[8] DUFF, I.S., REID, J.K., MUNKSGAARD, N., and NIELSEN, H.B. (1979). Direct solution of sets of linear equations whose matrix is sparse, symmetric, and indefinite, J. Inst. Maths. Applies, 23, 1979, 235-250, doi:10.1093/imamat/23.2.235
[9] GJELSVIK, A., AAM, S., and HOLTEN, L. (1985). Hachtel's augmented matrix method - A rapid method improving numerical stability in power system static state estimation, IEEE Trans. Power App. and Syst., 104, 2987-2993, doi:10.1109/TPAS.1985.318939
[10] GOLUB, G.H. and VAN LOAN, C.F. (1983). Matrix Computations (Johns Hopkins University Press, Baltimore, Maryland.)
[11] GU, J.W., CLEMENTS, K.A., KRUMPHOLZ, G.R., and DAVIS, P.W. (1983). The solution of ill-conditioned power System state estimation problems via the method of Peters and Wilkinson, PICA Conference Proceedings, pp. 239-246, 1983.
[12] HANDSCHIN, E., SCHWEPPE, F.C., KOHLAS, J., and FIECHTER, A. (1975). Bad data analysis for power systems state estimation, IEEE Trans. Power App. and Syst., 94, 329-337, doi:10.1109/T-PAS.1975.31858
[13] KRUMPHOLZ, G.R., CLEMENTS, K.A., and DAVIS, P.W. (1980). Power system observability: a practical algorithm using network topology, IEEE Trans. Power App. and Syst., 99, 1534-1542, doi:10.1109/TPAS.1980.319578
[14] LIU, W.-H. E., WU, F. F., HOLTEN, L, GJELSVIK, A., and AAM, S. (1987). Computational issues in the Hachtel's augmented matrix method for power system state estimation, presented at the 1987 Power System Computation Conference, Cascais, Portugal, 30 August - 4 September 1987.
[15] MONTICELLI, A. and GARCIA, A. (1983). Reliable bad data processing for real-time state estimation, IEEE Trans. Power App. and Syst., 102, 1126-1139, doi:10.1109/TPAS.1983.318053
[16] MONTICELLI, A., MURARI C.A.F., and WU, F.F. (1985). A Hybrid State Estimator: Solving Normal Equations by Orthogonal Transformations, IEEE Trans. Power App. and Syst., 105, 3460-3468, doi:10.1109/TPAS.1985.318896
[17] MONTICELLI, A. and WU, F.F. (1985a). Network observability: theory, IEEE Trans. Power App. and Syst., 104, 1042-1048, doi:10.1109/TPAS.1985.323454
[18] MONTICELLI, A. and WU, F.F. (1985b). Network observability: identification of observable islands and measurement placement, IEEE Trans. Power App. and Syst., 104, 1035-1041, doi:10.1109/TPAS.1985.323453
[19] MONTICELLI, A. and WU, F.F. (1986). Observability analysis for orthogonal transformation based state estimation, IEEE Trans. Power Syst., 1, 201-208, doi:10.1109/TPWRS.1986.4334870
[20] MONTICELLI, A., WU, F.F., and YEN, M. (1986). Multiple bad data identification for state estimation by combinatorial optimization, IEEE Trans. Power Delivery, 1, 361-369, doi:10.1109/TPWRD.1986.4308016
[21] QUINTANA, V.H., SIMOES-COSTA, A., and MANDEL, A. (1982). Power system observability using a direct graph-theoretic approach, IEEE Trans. Power App. and Sys:., 101, 617-626, doi:10.1109/TPAS.1982.317275
[22] SCHWEPPE, F.C. and HANDSCHIN, E.J. (1974). Static state estimation in electric power systems, Proc. IEEE, 62, 972-983, doi:10.1109/PROC.1974.9549
[23] SIEGEL, I.H. (1965). Deferment of computation in the method of least squares, Math. Comp., 19, 329-331, doi:10.2307/2003361
[24] SIMOES-COSTA, A. and QUINTANA, V.H. (1981a). A robust numerical technique for power system state estimation, IEEE Trans. Power App. and Syst.,100, 691-698, doi:10.1109/TPAS.1981.316920
[25] SIMOES-COSTA, A. and QUINTANA, V.H. (1981b). An orthogonal row processing algorithm for power system sequential state estimation, IEEE Trans. Power App. and Syst., 100, 3791-3800, doi:10.1109/TPAS.1981.317022
[26] TINNEY, W.F., BRANDWAIN, V., and CHAN, S.M. (1985). Sparse vector methods, IEEE Trans. Power App. and Syst., 104, 295-301, doi:10.1109/TPAS.1985.319043
[27] U.S. DEPARTMENI OF ENERGY, (1984). Contribution to power system state estimation and transient stability analysis, prepared by ESCA Corporation, DOE/ET/29362-1, February 1984.
[28] VAN CUTSEM, Th. (1985). "Power system observability and related functions - derivation of appropriate strategies and algorithms", Int. Journal of Electric Power and Energy Systems, Vol. 7, pp. 175-187, doi:10.1016/0142-0615(85)90047-X
[29] WANG, J.W. and QUINTANA, V.H. (1984). A decoupled orthogonal row processing algorithm for power state estimation, IEEE Trans. Power App. and Syst., 103, 2337-2344, doi:10.1109/TPAS.1984.318550
[30] WU, F.F., LIU, W.-H. E., and LUN, S.-M. (1987). Observability analysis and bad data processing for state estimation with equality constraints, Paper No. 87WM103-5 presented at IEEE PES Winter Meeting, New Orleans LA, Feb. 1987.
[31] WU, F.F. and MONTICELLI, A. (1986). Recent Progress in Real-Time Network Security Analysis, Proc. IFAC Symp. on Power Systems and Power Plant Control, August 12-15, 1986, Beijing, China, pp. 10-16.
BibTeX:
@article{MIC-1988-3-1,
title={{Observability analysis and bad date processing of state estimation using Hachtel's augmented matrix method}},
author={Wu, Felix F. and Liu, Wen-Hsiung E. and Holten, Lars and Gjelsvik, Anders and Aam, Sverre},
journal={Modeling, Identification and Control},
volume={9},
number={3},
pages={109--128},
year={1988},
doi={10.4173/mic.1988.3.1},
publisher={Norwegian Society of Automatic Control}
};
