http://iet.metastore.ingenta.com
1887

Combined cumulants and Laplace transform method for probabilistic load flow analysis

Combined cumulants and Laplace transform method for probabilistic load flow analysis

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Generation, Transmission & Distribution — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The simultaneity of power systems development and uncertainty of system elements has promoted the importance of probabilistic load flow (PLF) in the operating and planning studies of the system. This clarifies that the use of the fast and accurate approaches for PLF computation is necessary. To achieve this objective, this study presents an analytical technique, based on the properties of Laplace transform (LT). The suggested methodology is applicable for every continuous probability distribution function as the input random variable. The proposed procedure is applied to the MATPOWER 9- and 118-bus test systems. To validate the combined cumulants and LT (CCLT) technique, the results are compared with the Monte Carlo simulation and the cumulants method combined with the maximum entropy (CCME) principle. The test results show that the proposed approach gives accurate results, with the lower computational burden comparing CCME. Furthermore, the method formulation and case study results demonstrate that the CCLT method is mathematically straightforward and computationally efficient.

References

    1. 1)
      • 1. Seifi, H., Sepasian, M.S.: ‘Electric power system planning: issues, algorithms and solutions’ (Springer Science & Business Media, Berlin, 2011).
    2. 2)
      • 2. Borkowska, B.: ‘Probabilistic load flow’, IEEE Trans. Power Appar. Syst., 1974, PAS-93, (3), pp. 752759.
    3. 3)
      • 3. Gentle, J.E.: ‘Random number generation and Monte Carlo methods’ (Springer, New York, 2003).
    4. 4)
      • 4. Conti, S., Raiti, S.: ‘Probabilistic load flow using Monte Carlo techniques for distribution networks with photovoltaic generators’, Sol. Energy, 2007, 81, (12), pp. 14731481.
    5. 5)
      • 5. Villanueva, D., Feijóo, A., Pazos, J.L.: ‘Probabilistic load flow considering correlation between generation, loads and wind power’, Smart Grid Renew. Energy, 2011, 2, (1), pp. 1220.
    6. 6)
      • 6. Chen, P., Chen, Z., Bak-Jensen, B.: ‘Probabilistic load flow: a review’. Proc. Int. Conf. Electric Utility Deregulation and Restructuring and Power Technologies, April 2008, pp. 15861591.
    7. 7)
      • 7. Zhang, P., Lee, S.T.: ‘Probabilistic load flow computation using the method of combined cumulants and Gram–Charlier expansion’, IEEE Trans. Power Syst., 2004, 19, (1), pp. 676682.
    8. 8)
      • 8. Yu, H., Chung, C.Y., Wong, K.P., et al: ‘Probabilistic load flow evaluation with hybrid Latin hypercube sampling and Cholesky decomposition’, IEEE Trans. Power Syst., 2009, 24, (2), pp. 661667.
    9. 9)
      • 9. Cai, D., Shi, D., Chen, J.: ‘Probabilistic load flow computation with polynomial normal transformation and Latin hypercube sampling’, IET Gener. Transm. Distrib., 2013, 7, (5), pp. 474482.
    10. 10)
      • 10. Allan, R.N., Al-Shakarchi, M.R.G.: ‘Probabilistic ac load flow’, Proc. Inst. Electr. Eng., 1976, 123, (6), pp. 531536.
    11. 11)
      • 11. Allan, R.N., Al-Shakarchi, M.R.G.: ‘Probabilistic techniques in ac load-flow analysis’, Proc. Inst. Electr. Eng., 1977, 124, (2), pp. 154160.
    12. 12)
      • 12. Sanabria, L.A., Dillon, T.S.: ‘Stochastic power flow using cumulants and Von Mises functions’, Int. J. Electr. Power Energy Syst., 1986, 8, (1), pp. 4760.
    13. 13)
      • 13. Allan, R.N., Grigg, C.H., Al-Shakarchi, M.R.G.: ‘Numerical techniques in probabilistic load flow problems’, Int. J. Numer. Methods Eng., 1976, 10, (4), pp. 853860.
    14. 14)
      • 14. Allan, R.N., Da Silva, A.M.L., Abu-Nasser, A.A., et al: ‘Discrete convolution in power system reliability’, IEEE Trans. Reliab., 1981, R-30, (5), pp. 452456.
    15. 15)
      • 15. Usaola, J.: ‘Probabilistic load flow with wind production uncertainty using cumulants and Cornish–Fisher expansion’, Int. J. Electr. Power Energy Syst., 2009, 31, (9), pp. 474481.
    16. 16)
      • 16. Hu, Z., Wang, X.: ‘A probabilistic load flow method considering branch outages’, IEEE Trans. Power Syst., 2006, 21, (2), pp. 507514.
    17. 17)
      • 17. Tourandaz Kenari, M., Sepasian, M.S., Setayesh Nazar, M.: ‘Probabilistic load flow computation using saddle-point approximation’, COMPEL-Int. J. Comput. Math. Electr. Electron. Eng., 2017, 36, (1), pp. 4861.
    18. 18)
      • 18. Villanueva, D., Feijoo, A.E., Pazos, J.L.: ‘An analytical method to solve the probabilistic load flow considering load demand correlation using the DC load flow’, Electr. Power Syst. Res., 2014, 110, pp. 18.
    19. 19)
      • 19. Lei, D., Chuan-cheng, Z., Yi-han, Y., et al: ‘Improvement of probabilistic load flow to consider network configuration uncertainties’. Proc. Int. Conf. Asia-Pacific Power and Energy Engineering, March 2009, pp. 15.
    20. 20)
      • 20. Yuan, Y., Zhou, J., Ju, P., et al: ‘Probabilistic load flow computation of a power system containing wind farms using the method of combined cumulants and Gram–Charlier expansion’, IET Renew. Power Gener., 2011, 5, (6), pp. 448454.
    21. 21)
      • 21. Fan, M., Vittal, V., Heydt, G.T., et al: ‘Probabilistic power flow analysis with generation dispatch including photovoltaic resources’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 17971805.
    22. 22)
      • 22. Usaola, J.: ‘Probabilistic load flow in systems with wind generation’, IET. Gener. Transm. Distrib., 2009, 3, (12), pp. 10311041.
    23. 23)
      • 23. Fan, M., Vittal, V., Heydt, G.T., et al: ‘Probabilistic power flow studies for transmission systems with photovoltaic generation using cumulants’, IEEE Trans. Power Syst., 2012, 27, (4), pp. 22512261.
    24. 24)
      • 24. Morales, J.M., Perez-Ruiz, J.: ‘Point estimate schemes to solve the probabilistic power flow’, IEEE Trans. Power Syst., 2007, 22, (4), pp. 15941601.
    25. 25)
      • 25. Williams, T., Crawford, C.: ‘Probabilistic load flow modeling comparing maximum entropy and Gram–Charlier probability density function reconstructions’, IEEE Trans. Power Syst., 2013, 28, (1), pp. 272280.
    26. 26)
      • 26. Franceschini, S., Tsai, C., Marani, M.: ‘Point estimate methods based on Taylor series expansion – the perturbance moments method – a more coherent derivation of the second order statistical moment’, Appl. Math. Model., 2012, 36, (11), pp. 54455454.
    27. 27)
      • 27. Aien, M., Fotuhi-Firuzabad, M., Aminifar, F.: ‘Probabilistic load flow in correlated uncertain environment using unscented transformation’, IEEE Trans. Power Syst., 2012, 27, (4), pp. 22332241.
    28. 28)
      • 28. Da Silva, A.M.L., Arienti, V.L., Allan, R.N.: ‘Probabilistic load flow considering dependence between input nodal powers’, IEEE Trans. Power Appar. Syst., 1984, PAS-103, (6), pp. 15241530.
    29. 29)
      • 29. Villanueva, D., Pazos, J.L., Feijoo, A.: ‘Probabilistic load flow including wind power generation’, IEEE Trans. Power Syst., 2011, 26, (3), pp. 16591667.
    30. 30)
      • 30. Carpinelli, G., Di Vito, V., Varilone, P.: ‘Multi-linear Monte Carlo simulation for probabilistic three-phase load flow’, Int. Trans. Electr. Energy Syst., 2007, 17, (1), pp. 119.
    31. 31)
      • 31. Da Silva, A.M.L., Arienti, V.L.: ‘Probabilistic load flow by a multilinear simulation algorithm’, IET Gener. Transm. Distrib., 1990, 137, (4), pp. 276282.
    32. 32)
      • 32. Cai, D., Shi, D., Chen, J.: ‘Probabilistic load flow with correlated input random variables using uniform design sampling’, Int. J. Electr. Power Energy Syst., 2014, 63, pp. 105112.
    33. 33)
      • 33. Papoulis, A., Pillai, S.U.: ‘Probability, random variables, and stochastic processes’ (Tata McGraw-Hill Education, New York, 2002).
    34. 34)
      • 34. Stuart, A., Ord, J.K.: ‘Kendall's advanced theory of statistics’ (Hodder Arnold, London, 1994, 6th edn.).
    35. 35)
      • 35. Grainger, J.J., Stevenson, W.D.: ‘Power system analysis’ (McGraw-Hill, New York, 1994).
    36. 36)
      • 36. Monticelli, A.J., Garcia, A., Saavedra, O.R.: ‘Fast decoupled load flow: hypothesis, derivations, and testing’, IEEE Trans. Power Syst., 1990, 5, (4), pp. 14251431.
    37. 37)
      • 37. Silver, R.N., Sivia, D.S., Gubernatis, J.E.: ‘Maximum-entropy method for analytic continuation of quantum Monte Carlo data’, Phys. Rev. B, 1990, 41, (4), pp. 23802389.
    38. 38)
      • 38. Harremoës, P.: ‘Maximum entropy and the Edgeworth expansion’. Information Theory Workshop, 2005, pp. 6871.
    39. 39)
      • 39. Rockinger, M., Jondeau, E.: ‘Entropy densities with an application to autoregressive conditional skewness and kurtosis’, J. Econ., 2002, 106, (1), pp. 119142.
    40. 40)
      • 40. Mohammad-Djafari, A.: ‘A MATLAB program to calculate the maximum entropy distributions’. Proc. 11th Int. Workshop on Maximum Entropy and Bayesian Methods, 1992, pp. 221233.
    41. 41)
      • 41. Van Erp, N., Van Gelder, P.: ‘Introducing entropy distributions’. Proc. Sixth Int. Probabilistic Workshop, November 2008, pp. 329340.
    42. 42)
      • 42. Berberan-Santos, M.N.: ‘Computation of one-sided probability density functions from their cumulants’, J. Math. Chem., 2007, 41, (1), pp. 7177.
    43. 43)
      • 43. Berberan-Santos, M.N.: ‘Expressing a probability density function in terms of another PDF: a generalized Gram–Charlier expansion’, J. Math. Chem., 2007, 42, (3), pp. 585594.
    44. 44)
      • 44. Berberan-Santos, M.N.: ‘Analytical inversion of the Laplace transform without contour integration: application to luminescence decay laws and other relaxation functions’, J. Math. Chem., 2005, 38, (2), pp. 165173.
    45. 45)
      • 45. Cohen, A.M.: ‘Numerical methods for Laplace transform inversion’ (Springer Science & Business Media, 2007), vol. 5.
    46. 46)
      • 46. Thukral, R.: ‘Solution of integral equations using Padé type approximants’, J. Integral Equ. Appl., 2001, 13, pp. 126.
    47. 47)
      • 47. Zimmerman, R.D., Murillo-Sánchez, C.E., Thomas, R.J.: ‘MATPOWER: steady-state operations, planning and analysis tools for power systems research and education’, IEEE Trans. Power Syst., 2011, 26, (1), pp. 1219.
    48. 48)
      • 48. Gupta, N.: ‘Probabilistic load flow with detailed wind generator models considering correlated wind generation and correlated loads’, Renew. Energy, 2016, 94, pp. 96105.
    49. 49)
      • 49. Decker, R., Fitzgibbon, D.: ‘The normal and Poisson approximations to the binomial: a closer look’. Technical Report, 82.3, Department of Mathematics, University of Hartford, Hartford, CT, 1991.
    50. 50)
      • 50. Aien, M., Rashidinejad, M., Fotuhi-Firuzabad, M.: ‘On possibilistic and probabilistic uncertainty assessment of power flow problem: a review and a new approach’, Renew. Sustain. Energy Rev., 2014, 37, pp. 883895.
    51. 51)
      • 51. , accessed April 2017.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-gtd.2017.0097
Loading

Related content

content/journals/10.1049/iet-gtd.2017.0097
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address