Power system transient stability simulation under uncertainty based on Taylor model arithmetic

Abstract

The Taylor model arithmetic is introduced to deal with uncertainty. The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model (TM). Thus, time domain simulation under uncertainty is transformed to the integration of TM-based differential equations. In this paper, the Taylor series method is employed to compute differential equations; moreover, power system time domain simulation under uncertainty based on Taylor model method is presented. This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation. It is computationally fast compared with the Monte Carlo method, which is another technique for uncertainty analysis. The proposed method has been tested on the 39-bus New England system. The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

Keywords

interval arithmetic / power systems / Taylor series expansion / Taylor model / time domain simulation / transient stability / uncertainty

References

[1] Kosterev D N, Tylor C W, Mittelstadt W A. Model validation for the August 10, 1996 WSCC system outage. IEEE Transactions on Power Systems, 1999, 14(3): 967–979

[2] Dopazo J F, Klitin O A, Sasson A M. Stochastic load flows. IEEE Transactions on Power Apparatus and Systems, 1975, 94(2): 299–309

[3] Allan R N, Billinton R, Breipohl A M, Grigg C H. Bibliography on the application of probability methods in power system reliability evaluation 1992-1996. IEEE Transactions on Power Systems, 1999, 14(1): 51–57

[4] Timko K J, Bose A, Anderson P M. Monte Carlo simulation of power system stability. IEEE Transactions on Power Apparatus and Systems, 1983, PAS-102(10): 3453–3459

[5] Anderson P M, Bose A. A probabilistic approach to power system stability analysis. IEEE Transactions on Power Apparatus and Systems, 1983, PAS-102(8): 2430–2439

[6] Wu F F, Tsai Y K. Probabilistic dynamic security assessment of power systems I: basic model. IEEE Transactions on Circuits and Systems, 1983, 30(3): 148–159

[7] Hiskens I A, Pai M A, Nguyen T B. Bounding uncertainty in power system dynamic simulations. In: Proceedings of IEEE Power Engineering Society Winter Meeting, Singapore. 2000, 2: 1533–1537

[8] Hockenberry J R, Lesieutre B C. Evaluation of uncertainty in dynamic simulations of power system models: the probabilistic collocation method. IEEE Transactions on Power Systems, 2004, 19(3): 1483–1491

[9] Moore R E. Interval arithmetic and automatic error analysis in digital computing. Dissertation for the Doctoral Degree. Stanford: Stanford University, 1962

[10] Alefeld G, Mayer G. Interval analysis: theory and applications. Journal of Computational and Applied Mathematics, 2000, 121(1-2): 421–464

[11] Hickey T, Ju Q, Van Emden M H. Interval arithmetic: from principles to implementation. Journal of the ACM, 2001, 48(5): 1038–1068

[12] Wang Z, Alvarado F L. Interval arithmetic in power flow analysis. IEEE Transactions on Power Systems, 1992, 7(3): 1341–1349

[13] Das B. Radial distribution system power flow using interval arithmetic. International Journal of Electrical Power & Energy Systems, 2002, 24(10): 827–836

[14] Sarić A T, Stanković A M. An application of interval analysis and optimization to electric energy markets. IEEE Transactions on Power Systems, 2006, 21(2): 515–523

[15] Chaturvedi A, Prasad K, Ranjan R. Use of interval arithmetic to incorporate the uncertainty of load demand for radial distribution system analysis. IEEE Transactions on Power Delivery, 2006, 21(2): 1019–1021

[16] Berz M, Hoffstatter G. Computation and application of Taylor polynomials with interval remainder bounds. Reliable Computing, 1998, 4(1): 83–97

[17] Makino K. Rigorous Analysis of nonlinear motion in particle accelerators. Dissertation for the Doctoral Degree. East Lansing: Michigan State University, 1998

[18] Neumaier A. Taylor forms–use and limits. Reliable Computing, 2003, 9(1): 43–79

[19] Revol N, Makino K, Berz M. Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY. Journal of Logic and Algebraic Programming, 2005, 64(1): 135–154

[20] Makino K, Berz M. Taylor models and other validated functional inclusion methods. International Journal of Pure and Applied Mathematics, 2003, 4(4): 379–456

[21] Barrio R. Performance of the Taylor series method for ODEs/DAEs. Applied Mathematics and Computation, 2005, 163(2): 525–545

[22] Pai M A. Energy Function Analysis for Power System Stability. Norwell, MA: Kluwer Academic Publishers, 1989

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Higher Education Press and Springer-Verlag Berlin Heidelberg