Analysis of power system dynamics subject to stochastic power injections

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 60, Issue 12, 2013, Pages 3341-3353

  Dhople, Sairaj V ^a   Chen, Yu Christine ^b   Deville, Lee ^c   Dominguez Garcia, Alejandro D ^b  

^a University of Minnesota   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Continuous time Markov chains (CTMCs); power system dynamics; stochastic hybrid systems

Indexed keywords

ALGEBRA; CONTINUOUS TIME SYSTEMS; HYBRID SYSTEMS; LINEARIZATION; MARKOV CHAINS; ORDINARY DIFFERENTIAL EQUATIONS; SOLAR BUILDINGS; STOCHASTIC MODELS; SYSTEM THEORY;

CONTINUOUS TIME MARKOV CHAIN; DIFFERENTIAL ALGEBRAIC EQUATIONS; ELECTROMECHANICAL PHENOMENON; POWER INJECTION; POWER SYSTEM DYNAMICS; PROBABILISTIC DYNAMICS; STOCHASTIC HYBRID SYSTEMS; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS;

STOCHASTIC SYSTEMS;

EID: 84890114354     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2013.2265972     Document Type: Article

References (58)

1. A. D. Domínguez-García, "Reliability modeling of cyber-physical electric power systems: A system-theoretic framework," in Proc. IEEE Power Energy Soc. General Meeting, 2012, pp. 1-5.
2. B. Parsons, "Grid impacts of wind power variability: Recent assessments from a variety of utilities in the United States," National Renewable Energy Lab., Tech. Rep. NREL/CP-500-39955, 2006.
3. J. P. Hespanha, "Modelling and analysis of stochastic hybrid systems," IEE Proc.-Control Theory Applicat., vol. 153, no. 5, pp. 520-535, Sep. 2006. (Pubitemid 44561809)
4. P. Sauer andM. A. Pai, Power System Dynamics and Stability. Upper Saddle River, NJ, USA: Prentice-Hall, 1998.
5. P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. V. Cutsem, and V. Vittal, "Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions," IEEE Trans. Power Syst., vol. 19, no. 3, pp. 1387-1401, Aug. 2004.
6. Y. C.Chen andA.D.Domínguez-García, "Amethod to study the effect of renewable resource variability on power system dynamics," IEEE Trans. Power Syst., vol. 27, no. 4, pp. 1978-1989, Nov. 2012.
7. J. Endrenyi, Reliability Modeling in Electric Power Systems. New York, NY, USA: Wiley, 1978.
8. O. Ardakanian, S. Keshav, and C. Rosenberg, "Markovian models for home electricity consumption," in Proc. 2nd ACM SIGCOMM Workshop Green Netw., 2011, pp. 31-36.
9. Y.Manichaikul and F. C. Schweppe, "Physically based industrial electric load," IEEE Trans. Power Apparatus Syst., vol. PAS-98, no. 4, pp. 1439-1445, Jul. 1979. (Pubitemid 9476473)
10. S. Koch, J. L. Mathieu, and D. S. Callaway, "Modeling and control of aggregated heterogeneous thermostatically controlled loads for ancillary services," in Proc. Power Syst. Comput. Conf., Aug. 2011.
11. F. F. C. Véliz, C. L. T. Borges, and A. M. Rei, "A comparison of load models for composite reliability evaluation by nonsequential Monte Carlo simulation," IEEE Trans. Power Syst., vol. 25, no. 2, pp. 649-656, May 2010.
12. R. Malhamé and C. Y. Chong, "Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system," IEEE Trans. Autom. Control, vol. 30, no. 9, pp. 854-860, Sep. 1985. (Pubitemid 16494287)
13. R. Malhamé and C. Y. Chong, "Stochastic hybrid state systems for electric load modeling," in Proc. IEEE Conf. Decision Control, Dec. 1983, vol. 22, pp. 1143-1149. (Pubitemid 14514497)
14. R. Malhamé, "A jump-driven Markovian electric load model," Adv. Appl. Probab., vol. 22, no. 3, pp. 564-586, Sep. 1990.
15. C. Y. Chong and A. S. Debs, "Statistical synthesis of power system functional load models," in Proc. IEEE Conf. Decision Control including Symp. Adaptive Process., Dec. 1979, vol. 18, pp. 264-269. (Pubitemid 10451517)
16. G. Papaefthymiou and B. Klöckl, "MCMCforwind power simulation," IEEE Trans. Energy Convers., vol. 23, no. 1, pp. 234-240, Mar. 2008.
17. A. P. Leite, C. L. T. Borges, and D. M. Falcão, "Probabilistic wind farms generation model for reliability studies applied to Brazilian sites," IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1493-1501, Nov. 2006. (Pubitemid 46357746)
18. P. S. Perez, J. Driesen, and R. Belmans, "Characterization of the solar power impact in the grid," in Proc. Int. Conf. Clean Electrical Power, May 2007, pp. 366-371. (Pubitemid 47592341)
19. R. J. Aguiar, M. Collares-Pereira, and J. P. Conde, "Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices," Solar Energy, vol. 40, no. 3, pp. 269-279, 1988. (Pubitemid 18575073)
20. H. A. Pulgar-Painemal, "Wind farm model for power system stability analysis," Ph.D. dissertation, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA, 2010.
21. H. A. Pulgar-Painemal, "Towards a wind farm reduced-order model," Elect. Power Syst. Res., vol. 81, no. 8, pp. 1688-1695, 2011.
22. D. L. King, W. E. Boyson, and J. A. Kratochvil, "Photovoltaic array performance model," Sandia National Laboratories, Tech. Rep., Aug. 2004.
23. D. L. King, S. Gonzalez, G. M. Galbraith, and W. E. Boyson, "Performance model for grid-connected photovoltaic inverters," Sandia National Laboratories, Tech. Rep., Sept. 2007.
24. I. A. Hiskens and M. A. Pai, "Trajectory sensitivity analysis of hybrid systems," IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat., vol. 47, no. 2, pp. 204-220, Feb. 2000. (Pubitemid 30580897)
25. I. A. Hiskens and M. A. Pai, "Hybrid systems view of power system modelling," in Proc. IEEE Int. Symp. Circuits Syst., 2000, vol. 2, pp. 228-231.
26. I. A. Hiskens, "Power system modeling for inverse problems," IEEE Trans. Circuits Syst. I: Reg. Papers, vol. 51, no. 3, pp. 539-551, Mar. 2004.
27. Y. Susuki, H. Ebina, and T. Hikihara, "Application of hybrid system theory to power system stability analysis," in Proc. Int. Symp. Nonlinear Theory its Applicat., 2005, pp. 202-205.
28. G. K. Fourlas, K. J. Kyriakopoulos, and C. D. Vournas, "Hybrid systems modeling for power systems," IEEE Circuits Syst. Mag., vol. 4, no. 3, pp. 16-23, Third Quarter, 2004.
29. F. F. Wu and Y.-K. Tsai, "Probabilistic dynamic security assessment of power systems-I: Basic model," IEEE Trans. Circuits Syst., vol. 30, no. 3, pp. 148-159, Mar. 1983.
30. K. Loparo and G. Blankenship, "A probabilistic mechanism for small disturbance instabilities in electric power systems," IEEE Trans. Circuits Syst., vol. CS-32, no. 2, pp. 177-184, Feb. 1985. (Pubitemid 15454928)
31. C. O. Nwankpa and S. M. Shahidehpour, "Stochastic model for power system planning studies," IEE Proc.-C, Generation, Transmiss. Distrib., vol. 138, no. 4, pp. 307-320, Jul. 1991. (Pubitemid 21680640)
32. C. O. Nwankpa, S. M. Shahidehpour, and Z. Schuss, "A stochastic approach to small disturbance stability analysis," IEEE Trans. Power Syst., vol. 7, no. 4, pp. 1519-1528, Nov. 1992. (Pubitemid 23568722)
33. H. Mohammed and C. O. Nwankpa, "Stochastic analysis and simulation of grid-connected wind energy conversion system," IEEE Trans. Energy Convers., vol. 15, no. 1, pp. 85-90, Mar. 2000.
34. K. Wang and M. L. Crow, "Numerical simulation of stochastic differential algebraic equations for power system transient stability with random loads," in Proc. IEEE Power Energy Soc. General Meeting, Jul. 2011, pp. 1-8.
35. T.Odun-Ayo and M. L. Crow, "Structure-preserved power system transient stability using stochastic energy functions," IEEE Trans. Power Syst., vol. 27, no. 3, pp. 1450-1458, Aug. 2012.
36. Z. Y. Dong, J. H. Zhao, and D. J. Hill, "Numerical simulation for stochastic transient stability assessment," IEEE Trans. Power Syst., vol. 27, no. 4, pp. 1741-1749, Nov. 2012.
37. F. F.Wu and S. Kumagai, "Steady-state security regions of power systems," IEEE Trans. Circuits Syst., vol. CS-29, no. 11, pp. 703-711, Nov. 1982. (Pubitemid 13491292)
38. R. Kaye and F. F. Wu, "Dynamic security regions of power systems," IEEE Trans. Circuits Syst., vol. 29, no. 9, pp. 612-623, Sep. 1982. (Pubitemid 13506604)
39. V. A. Ugrinovskii and H. R. Pota, "Decentralized control of power systems via robust control of uncertain Markov jump parameter systems," in Proc. IEEE Conf. Decision Control, Dec. 2004, vol. 4, pp. 3503-3508. (Pubitemid 40286950)
40. V. A. Ugrinovskii and H. R. Pota, "Decentralized control of power systems via robust control of uncertainMarkov jump parameter systems," Int. J. Control, vol. 78, no. 9, pp. 662-677, Jun. 2005. (Pubitemid 41657402)
41. L. Li, V. A. Ugrinovskii, and R. Orsi, "Decentralized robust control of uncertain Markov jump parameter systems via output feedback," Automatica, vol. 43, no. 11, pp. 1932-1944, Nov. 2007. (Pubitemid 47576047)
42. X. Ge, S. Parise, and P. Smyth, "Clustering Markov states into equivalence classes using SVD and heuristic search algorithms," in Proc. Int. Workshop Artif. Intell. Statist., 2003.
43. K. Deng, P. G. Mehta, and S. P. Meyn, "A simulation-based method for aggregatingMarkov chains," in Proc. IEEE Conf. Decision Control, Dec. 2009, pp. 4710-4716.
44. G. Kotsalis and M. Dahleh, "Model reduction of irreducible Markov chains," in Proc. IEEE Conf. Decision Control, Dec. 2003, vol. 6, pp. 5727-5728.
45. G. Kotsalis, A.Megretski, andM. A. Dahleh, "Model reduction of discrete-timeMarkov jump linear systems," in Proc. Amer. Control Conf., Jun. 2006, pp. 454-459. (Pubitemid 46530853)
46. J. P. Hespanha, "A model for stochastic hybrid systems with application to communication networks," Nonlinear Anal., vol. 62, no. 8, pp. 1353-1383, Sep. 2005, Special Iss. on Hybrid Syst. (Pubitemid 41252306)
47. S. V. Dhople, L. DeVille, and A. D. Domínguez-García, "A stochastic hybrid systems framework for analysis of Markov reward models," Univ. of Illinois at Urbana-Champaign, Coordinated Science Laboratory Tech. Rep. UILU-ENG-13-2205, Jun. 2013.
48. M. H. A. Davis, Markov Models and Optimization. London, U.K.: Chapman & Hall, 1993, Boundary Row.
49. J. R. Norris,Markov Chains. New York, NY, USA: Cambridge Univ. Press, 1997.
50. K. Steliga and D. Szynal, "On Markov-type inequalities," Int. J. Pure Appl. Math., vol. 58, no. 2, pp. 137-152, 2010.
51. P. Billingsley, Probability and Measure, ser. Wiley Series in Probability and Mathematical Statistics, 3rd ed. New York, NY, USA: Wiley, 1995.
52. R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems. New York, NY, USA: Springer, 1996.
53. A. D. Domínguez-García, "Models for impact assessment of windbased power generation on frequency control," in Control and Optimization Methods for Electric Smart Grids, A. Chakrabortty and M. Ili?, Eds. Berlin, Germany: Springer-Verlag, 2012.
54. Univ. of Washington, Oct. 2012, Power system test case archive, [Online]. Available: http://www.ee.washington.edu/research/pstca/
55. Power System Toolbox, [Online]. Available: http://www.eps.ee.kth.se/ personal/vanfretti/pst
56. Y. Zhang, W. Huang, Z. Liu, J. Yang, X. Cai, and J. Zhang, "Research on the relationship of the singular point for load flow jacobian matrix and the critical point of voltage collapse," in IEEE Power Eng. Soc. General Meeting, Jun. 2005, pp. 2939-2943. (Pubitemid 41497472)
57. Y.Wang, L. da Silva, and X.Wilsun, "Investigation of the relationship between ill-conditioned power flowand voltage collapse," IEEE Power Eng. Rev., vol. 20, no. 7, pp. 43-45, July 2000.
58. P. W. Sauer and M. A. Pai, "Power system steady-state stability and the load-flow Jacobian," IEEE Trans. Power Syst., vol. 5, no. 4, pp. 1374-1383, Nov. 1990.