Advertisement

The Role of Affine Arithmetic in Robust Optimal Power Flow Analysis

  • Alfredo VaccaroEmail author
Chapter
  • 7 Downloads
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 276)

Abstract

Optimal Power Flow (OPF) analysis represents the mathematical foundation of many power engineering applications. For the most common formalization of the OPF problem, all input data are specified using deterministic variables, and the corresponding solutions are deemed representative of the limited set of system conditions. Hence, reliable algorithms aimed at representing the effect of data uncertainties in OPF analyses are required in order to allow analysts to estimate both the data and solution tolerance, providing, therefore, insight into the level of confidence of OPF solutions. To address this issue, this Chapter outline the role of novel solution methodologies based on the use of Affine Arithmetic.

References

  1. 1.
    Verbic, G., Cañizares, C.A.: Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Trans. Power Syst. 21(4), 1883–1893 (2006)CrossRefGoogle Scholar
  2. 2.
    Wan, Y.H., Parsons, B.K.: Factors Relevant to Utility Integration of Intermittent Renewable Technologies. National Renewable Energy Laboratory (1993)Google Scholar
  3. 3.
    Chen, P., Chen, Z., Bak-Jensen, B.: Probabilistic load flow: a review. In: Proceedings of the 3rd International Conference on Deregulation and Restructuring and Power Technologies, DRPT 2008, pp. 1586–1591 (2008)Google Scholar
  4. 4.
    Zou, B., Xiao, Q.: Solving probabilistic optimal power flow problem using quasi Monte Carlo method and ninth-order polynomial normal transformation. IEEE Trans. Power Syst. 29(1), 300–306 (2014)CrossRefGoogle Scholar
  5. 5.
    Hajian, M., Rosehart, W.D., Zareipour, H.: Probabilistic power flow by monte carlo simulation with latin supercube sampling. IEEE Trans. Power Syst. 28(2), 1550–1559 (2013)CrossRefGoogle Scholar
  6. 6.
    Zhang, H., Li, P.: Probabilistic analysis for optimal power flow under uncertainty. IET Gener. Transm. Distrib. 4(5), 553–561 (2010)Google Scholar
  7. 7.
    Yu, H., Chung, C.Y., Wong, K.P., Lee, H.W., Zhang, J.H.: Probabilistic load flow evaluation with hybrid latin hypercube sampling and cholesky decomposition. IEEE Trans. Power Syst. 24(2), 661–667 (2009)CrossRefGoogle Scholar
  8. 8.
    Mori, H., Jiang, W.: A new probabilistic load flow method using mcmc in consideration of nodal load correlation. In: Proceedings of the 15th International Conference on Intelligent System Applications to Power Systems, pp. 1–6 (2009)Google Scholar
  9. 9.
    Yu, H., Rosehart, B.: Probabilistic power flow considering wind speed correlation of wind farms. In: Proceedings of the 17th Power Systems Computation Conference, pp. 1–7 (2011)Google Scholar
  10. 10.
    Zhang, H., Li, P.: Probabilistic power flow by monte carlo simulation with latin supercube sampling. IET Gener., Transm. Distrib. 4(5), 553–561 (2010)CrossRefGoogle Scholar
  11. 11.
    Schellenberg, A., Rosehart, W., Aguado, J.: Cumulant-based probabilistic optimal power flow (p-opf) with gaussian and gamma distributions. IEEE Trans. Power Syst. 20(2), 773–781 (2005)CrossRefGoogle Scholar
  12. 12.
    Meliopoulos, A.P.S., Cokkinides, G.J., Chao, X.Y.: A new probabilistic power flow analysis method. IEEE Trans. Power Syst. 5(1), 182–190 (1990)Google Scholar
  13. 13.
    Allan, R.N., da Silva, A.M.L., Burchett, R.C.: Evaluation methods and accuracy in probabilistic load flow solutions. IEEE Trans. Power Appar. Syst., PAS 100(5), 2539–2546 (1981)Google Scholar
  14. 14.
    Zhang, P., Lee, S.T.: Probabilistic load flow computation using the method of combined cumulants and gram-charlier expansion. IEEE Trans. Power Syst. 19(1), 676–682 (2004)Google Scholar
  15. 15.
    Sanabria, L.A., Dillon, T.S.: Stochastic power flow using cumulants and von mises functions. Int. J. Electr. Power Energy Syst. 8(1), 47–60 (1986)CrossRefGoogle Scholar
  16. 16.
    Dimitrovski, A., Tomsovic, K.: Boundary load flow solutions. IEEE Trans. Power Syst. 19(1), 348–355 (2004)CrossRefGoogle Scholar
  17. 17.
    Alvarado, F., Hu, Y., Adapa, R.: Uncertainty in power system modeling and computation. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp. 754–760 (1992)Google Scholar
  18. 18.
    Vaccaro, A., Villacci, D.: Radial power flow tolerance analysis by interval constraint propagation. IEEE Trans. Power Syst. 24(1), 28–39 (2009)CrossRefGoogle Scholar
  19. 19.
    Madrigal, M., Ponnambalam, K., Quintana, V.H.: Probabilistic optimal power flow. In: Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 385–388 (1998)Google Scholar
  20. 20.
    Li, X., Li, Y., Zhang, S.: Analysis of probabilistic optimal power flow taking account of the variation of load power. IEEE Trans. Power Syst. 23(3), 992–999 (2008)CrossRefGoogle Scholar
  21. 21.
    Mohammadi, M., Shayegani, A., Adaminejad, H.: A new approach of point estimate method for probabilistic load flow. Int. J. Electr. Power Energy Syst. 51, 54–60 (2013)CrossRefGoogle Scholar
  22. 22.
    Stolfi, J., De Figueiredo, L.H.: Self-validated numerical methods and applications. In: Proceedings of the Monograph for 21st Brazilian Mathematics Colloquium. Citeseer (1997)Google Scholar
  23. 23.
    Moore, R.: Methods and Applications of Interval Analysis, vol. 2. SIAM (1979)Google Scholar
  24. 24.
    Wang, S., Xu, Q., Zhang, G., Yu, L.: Modeling of wind speed uncertainty and interval power flow analysis for wind farms. Autom. Electr. Power Syst. 33(1), 82–86 (2009)Google Scholar
  25. 25.
    Pereira, L.E.S., Da Costa, V.M., Rosa, A.L.S.: Interval arithmetic in current injection power flow analysis. Int. J. Electr. Power Energy Syst. 43(1), 1106–1113 (2012)CrossRefGoogle Scholar
  26. 26.
    Neher, M.: From interval analysis to Taylor models-an overview. In: Proceedings of the International Association for Mathematics and Computers in Simulation (2005)Google Scholar
  27. 27.
    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. 25(2), 624–632 (2010)Google Scholar
  28. 28.
    Armengol, J., Travé-Massuyès, L., Vehi, J., de la Rosa, J.L.: A survey on interval model simulators and their properties related to fault detection. Annu. Rev. Control. 24, 31–39 (2000)Google Scholar
  29. 29.
    Bontempi, G., Vaccaro, A., Villacci, D.: Power cables’ thermal protection by interval simulation of imprecise dynamical systems. IEE Proc.-Gener., Transm. Distrib. 151(6), 673–680 (2004)CrossRefGoogle Scholar
  30. 30.
    Barboza, L.V., Dimuro, G.P., Reiser, R.H.S.: Towards interval analysis of the load uncertainty in power electric systems. In: Proceedings of the International Conference on Probabilistic Methods Applied to Power Systems, pp. 538–544 (2004)Google Scholar
  31. 31.
    Alvarado, F., Wang, Z.: Direct Sparse Interval Hull Computations for Thin Non-M Matrices (1993)Google Scholar
  32. 32.
    Vaccaro, A., Cañizares, C.A., Bhattacharya, K.: A range arithmetic-based optimization model for power flow analysis under interval uncertainty. IEEE Trans. Power Syst. 28(2), 1179–1186 (2013)Google Scholar
  33. 33.
    Pirnia, M., Cañizares, C.A., Bhattacharya, K., Vaccaro, A.: An affine arithmetic method to solve the stochastic power flow problem based on a mixed complementarity formulation. Electr. Power Compon. Syst. 29(6), 2775–2783 (2014)Google Scholar
  34. 34.
    Hao, L., Tamang, A.K., Weihua, Z., Shen, X.S.: Stochastic information management in smart grid. IEEE Commun. Surv. Tutor. 16(3), 1746–1770 (2014)Google Scholar
  35. 35.
    Rakpenthai, C., Uatrongjit, S., Premrudeepreechacharn, S.: State estimation of power system considering network parameter uncertainty based on parametric interval linear systems. IEEE Trans. Power Syst. 27(1), 305–313 (2012)CrossRefGoogle Scholar
  36. 36.
    Pirnia, M., Cañizares, C.A., Bhattacharya, K., Vaccaro, A.: A novel affine arithmetic method to solve optimal power flow problems with uncertainties. In: Proceedings of the IEEE Power and Energy Society General Meeting, pp. 1–7 (2012)Google Scholar
  37. 37.
    Bo, R., Guo, Q., Sun, H., Wenchuan, W., Zhang, B.: A non-iterative affine arithmetic methodology for interval power flow analysis of transmission network. Proc. Chin. Soc. Electr. Eng. 33(19), 76–83 (2013)Google Scholar
  38. 38.
    Wang, S., Han, L., Zhang, P.: Affine arithmetic-based dc power flow for automatic contingency selection with consideration of load and generation uncertainties. Electr. Power Compon. Syst. 42(8), 852–860 (2014)CrossRefGoogle Scholar
  39. 39.
    Wei, G., Lizi, L., Tao, D., Xiaoli, M., Wanxing, S.: An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties. Int. J. Electr. Power Energy Syst. 58, 242–245 (2014)CrossRefGoogle Scholar
  40. 40.
    Ding, T., Cui, H.Z., Gu, W., Wan, Q.L.: An uncertainty power flow algorithm based on interval and affine arithmetic. Autom. Electr. Power Syst. 36(13), 51–55 (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of SannioBeneventoItaly

Personalised recommendations