SVSM calculation of power system with high wind-power penetration

SVSM calculation of power system with high wind-power penetration

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Calculation of the static voltage stability margin (SVSM) of power system with high wind-power penetration must consider the uncertain fluctuation of power output from wind farms (WFs). On the basis of a continuous power flow (CPF) and improved affine interval (IAI) algorithm that considers quadratic terms, a new method to calculate the SVSM interval of a power system that considers the uncertain fluctuation intervals of WF output is proposed. Considering the high penetration of wind power, the power variation of the active load, and wind-power fluctuation are assigned by all conventional generators, except the swing generator in the CPF calculation model. In the proposed IAI algorithm, the non-linear second-order sensitivities are considered to obtain a more accurate SVSM interval. With the correlation of different WF output intervals described by relative angles, as well as the independent intervals obtained by decorrelation of the correlated WF output intervals, the SVSM interval is calculated by the CPF and IAI algorithms. Take the IEEE 39-bus system and an actual 964-bus provincial power grid as examples, and compared with Monte Carlo method, the results show that the SVSM interval calculated by the proposed method is more accurate, and the computation time is significantly reduced.


    1. 1)
      • 1. Vittal, E., O'Malley, M., Keane, A.: ‘A steady-state voltage stability analysis of power systems with high penetrations of wind’, IEEE Trans. Power Syst., 2010, 25, (1), pp. 433442.
    2. 2)
      • 2. Hemmatpour, M.H., Mohammadian, M., Gharaveisi, A.-A.: ‘Simple and efficient method for steady-state voltage stability analysis of islanded microgrids with considering wind turbine generation and frequency deviation’, IET J. Mag., 2016, 10, (7), pp. 16911702.
    3. 3)
      • 3. Ajjarapu, V.: ‘The continuation power flow: a tool for steady state voltage stability’, IEEE Trans. Power Syst., 1992, 7, (1), pp. 416423.
    4. 4)
      • 4. Xu, X., Yan, Z.: ‘Probabilistic load flow evaluation considering correlated input random variables’, Int. Trans. Electr. Energy Syst., 2016, 26, (3), pp. 555572.
    5. 5)
      • 5. Qin, Z., Li, W., Xiong, X.: ‘Estimating wind speed probability distribution using kernel density method’, Electr. Power Syst. Res., 2011, 81, (12), pp. 21392146.
    6. 6)
      • 6. Papaefthymiou, G., Schavemaker, P.H., Sluis, L.V.D., et al: ‘Integration of stochastic generation in power systems’, Int. J. Electr. Power Energy Syst., 2006, 28, (9), pp. 655667.
    7. 7)
      • 7. Ran, X., Miao, S.: ‘Probabilistic evaluation for static voltage stability for unbalanced three-phase distribution system’, IET Gener. Trans. Distrib., 2015, 9, (14), pp. 20502059.
    8. 8)
      • 8. Wang, H., Xu, X., Yan, Z., et al: ‘Probabilistic static voltage stability analysis considering the correlation of wind power’. Int. Conf. Probabilistic Methods Applied to Power Systems (PMAPS), Beijing, China, 2016, pp. 16.
    9. 9)
      • 9. Silva, A.M.L.D., Coutinho, I.P., Souza, A.C.Z.D., et al: ‘Voltage collapse risk assessment’, Electr. Power Syst. Res., 2000, 54, (3), pp. 221227.
    10. 10)
      • 10. Rodrigues, A.B., Prada, R.B., Silva, M.D.G.D.: ‘Voltage stability probabilistic assessment in composite systems: modeling unsolvability and controllability loss’, IEEE Trans. Power Syst., 2010, 25, (3), pp. 15751588.
    11. 11)
      • 11. Deng, W., Zhang, B., Ding, H.: ‘The risk-based assessment of static voltage stability issues with consideration of load and wind power uncertainties’. Clemson University Power Systems Conf. (PSC), Clemson, SC, USA, 2015, pp. 14.
    12. 12)
      • 12. Tang, F., Zhou, S., Zhang, Q., et al: ‘A static voltage stability assessment scheme of power systems considering charging state of electric vehicles and load fluctuation limits’, IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 2017, pp. 15.
    13. 13)
      • 13. Kumar, S.S., Raj, A.D.V.: ‘Fuzzy logic based stability index power system voltage stability enhancement’, Int. J. Comput. Electr. Eng., 2010, 2, (1), pp. 2431.
    14. 14)
      • 14. Zhang, J., Guo, Y., Yang, M.: ‘Assessment of voltage stability for real-time operation’. IEEE Power India Conf., New Delhi, India, 2006, pp. 15.
    15. 15)
      • 15. Wang, Y., Chiang, H.D., Wang, T.: ‘A two-stage method for assessment of voltage stability in power system with renewable energy’. IEEE Electrical Power & Energy Conf., Halifax, Canada, 2014, pp. 16.
    16. 16)
      • 16. Haesen, E., Bastiaensen, C., Driesen, J., et al: ‘A probabilistic formulation of load margins in power systems with stochastic generation’, IEEE Trans. Power Syst., 2009, 24, (2), pp. 951958.
    17. 17)
      • 17. Schellenberg, A., Rosehart, W., Aguado, J.A.: ‘Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems’, IEEE Trans. Power Syst., 2006, 21, (2), pp. 579585.
    18. 18)
      • 18. Liu, K.-Y, Sheng, W., Hu, L., et al: ‘Simplified probabilistic voltage stability evaluation considering variable renewable distributed generation in distribution systems’, IET Gener. Transm. Distrib., 2015, 9, (12), pp. 14641473.
    19. 19)
      • 19. Liu, K.-Y, Hu, L., Sheng, W.: ‘Probabilistic evaluation of static voltage stability taking account of the variation of load and stochastic distributed generations’. Int. Conf. Electrical Machines and Systems (ICEMS), Busan, South Korea, 2013, pp. 418421.
    20. 20)
      • 20. Muñoz, J., Cañizares, C.A., Bhattacharya, K., et al: ‘An affine arithmetic-based method for voltage stability assessment of power systems with intermittent generation sources’, IEEE Trans. Power Syst., 2013, 28, (4), pp. 44754487.
    21. 21)
      • 21. Adusumilli, B.S., Kumar, B.K.: ‘Modified affine arithmetic based continuation power flow analysis for voltage stability assessment under uncertainty’, IET Gener. Transm. Distrib., 2018, 12, (18), pp. 42254232.
    22. 22)
      • 22. Bao, H., Wei, H., Guo, X.: ‘Stochastic response surface method addressing correlated wind power for probabilistic evaluation of voltage stability’. IEEE PES Asia-Pacific Power and Energy Engineering Conf. (APPEEC), Xi'an, China2016, pp. 16601664.
    23. 23)
      • 23. Xu, X., Yan, Z., Shahidehpour, M., et al: ‘Power system voltage stability evaluation considering renewable energy with correlated variabilities’, IEEE Trans. Power Syst., 2018, 33, (3), pp. 32363245.
    24. 24)
      • 24. Chiang, H.D., Flueck, A.J., Shah, K.S., et al: ‘CPFLOW: a practical tool for tracing power system steady-state stationary behavior due to load and generation variations’, IEEE Trans. Power Syst., 1995, 10, (2), pp. 623634.
    25. 25)
      • 25. Figueiredo, L.H.D., Stolfi, J.: ‘Affine arithmetic: concepts and applications’, Numer. Algorithms, 2004, 37, pp. 147158.
    26. 26)
      • 26. Vaccaro, A., Cañizares, C.A., Villacci, D.: ‘An affine arithmetic-based methodology for reliable power flow analysis in the presence of data uncertainty’, IEEE Trans. Power Syst., 2010, 25, (2), pp. 624632.
    27. 27)
      • 27. Dobson, I., Lu, L.: ‘Voltage collapse precipitated by the immediate change in stability when generator reactive power limits are encountered’, IEEE Trans. Circuits Syst., 1992, 39, (9), pp. 762766.
    28. 28)
      • 28. Greene, S., Dobson, I., Alvarado, F.L.: ‘Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters’, IEEE Trans. Power Syst., 1997, 12, (1), pp. 262272.
    29. 29)
      • 29. Jiang, C., Zhang, Q.F., Han, X., et al: ‘A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model’, Acta Mech., 2014, 225, (2), pp. 383395.
    30. 30)
      • 30. Ayres, F.: ‘Schaum's outline of theory and problems of projective geometry’ (McGraw-Hill Book Company, New York, 1968), p. 648.
    31. 31)
      • 31. Hiskens, I.: ‘IEEE PES task force on benchmark systems for stability controls’, Technical Report, 2013.
    32. 32)
      • 32. Matevosyan, J., Soder, L.: ‘Minimization of imbalance cost trading wind power on the short-term power market’, IEEE Trans. Power Syst., 2006, 21, (3), pp. 13961404.
    33. 33)
      • 33. Siahkali, H., Vakilian, M.: ‘Stochastic unit commitment of wind farms integrated in power system’, Electr. Power Syst. Res., 2010, 80, (9), pp. 10061017.

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