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

Development of combined Runge–Kutta Broyden's load flow approach for well- and ill-conditioned power systems

Development of combined Runge–Kutta Broyden's load flow approach for well- and ill-conditioned power systems

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.

Load flow (LF) is an extensively used tool in planning and operation of power systems. Formulation of LF problem can be assimilated as a set of autonomous ordinary differential equations, therefore, many numeric methods can be used to solve this problem. However, LF methods often need to compute one or more Jacobian matrix inversions in each iteration. Owing to this fact, these methods might not be computationally efficient. In this study, the authors propose combined Runge–Kutta Broyden's LF (RK4B) method in order to reduce the required Jacobian matrix inversion to only one in the first iteration. In this proposed method, Broyden's approach is employed in fourth-order Runge–Kutta method. In addition, two modifications of the proposed method are presented to reduce the number of iterations and improve the computational performance. The proposed method and the two modifications are validated using several well- and ill-conditioned cases. Results show that the combined approach has better computational performance than the classical multistage numeric methods, besides it preserves the robustness features of fourth-order Runge–Kutta method.

References

    1. 1)
      • 1. Kundur, P.: ‘Power system stability and control’ (McGraw-Hill, New York, 1994).
    2. 2)
      • 2. Grainger, J.J., Stevenson, W.D.: ‘Power system analysis’ (McGraw-Hill, New York, 1994).
    3. 3)
      • 3. Tinney, W.F., Hart, C.E.: ‘Power flow solution by Newton's method’, Trans. Power Appar. Syst., 1967, PAS-86, pp. 14491460.
    4. 4)
      • 4. Stott, B., Alsac, O.: ‘Fast decoupled load flow’, IEEE Trans. Power Appar. Syst., 1974, PAS-93, pp. 859869.
    5. 5)
      • 5. Powell, L.: ‘DC load flow’ (Mc Graw Hill, New York, 2004).
    6. 6)
      • 6. Fatemi, S.M., Abedi, S., Gharehpetian, G.B., et al: ‘Introducing a novel DC power flow method with reactive power considerations’, IEEE Trans. Power Syst., 2015, 30, (6), pp. 30123023.
    7. 7)
      • 7. Yang, J., Zhang, N., Kang, C., et al: ‘A state-independent linear power flow model with accurate estimation of voltage magnitude’, IEEE Trans. Power Syst., 2017, 32, (5), pp. 36073617.
    8. 8)
      • 8. Stott, B.: ‘Review of load-flow calculation methods’, Proc. IEEE, 1974, 62, (7), pp. 916929.
    9. 9)
      • 9. Yan, P., Sekar, A.: ‘Steady-state analysis of power system having multiple FACTS devices using line-flow-based equations’, IEEE Proc. Gener. Transm. Distrib., 2005, 152, (1), pp. 3139.
    10. 10)
      • 10. Mallick, S., Rajan, D.V., Thakur, S.S., et al: ‘Development of a new algorithm for power flow analysis’, Int. J. Electr. Power Energy Syst., 2011, 33, (8), pp. 14791488.
    11. 11)
      • 11. Kamel, S., Abdel-Akher, M., Jurado, F.: ‘Improved NR current injection load flow using power mismatch representation of PV bus’, Int. J. Electr. Power Energy Syst., 2013, 53, pp. 6468.
    12. 12)
      • 12. Derakhshandeh, S.Y., Pourbagher, R.: ‘Application of high-order Newton-like methods to solve power flow equations’, IET Gener. Transm. Distrib., 2016, 10, (8), pp. 18531859.
    13. 13)
      • 13. Saleh, S.A.: ‘The formulation of a power flow using d-q reference frame components - part I: balanced 3 ϕ systems’, IEEE Trans. Ind. Appl., 2016, 52, (5), pp. 36823693.
    14. 14)
      • 14. Tripathy, S.C., Durga Prasad, G., Malik, O.P., et al: ‘Load flow solutions for ill-conditioned power systems by a Newton-like method’, IEEE Trans. Power Appar. Syst., 1982, PAS-101, (10), pp. 36483657.
    15. 15)
      • 15. Shahriari, A., Mokhlis, H., Bakar, A.: ‘Critical reviews of load flow methods for well, ill and unsolvable condition’, J. Elect. Eng., 2012, 63, (3), pp. 144152.
    16. 16)
      • 16. Iwamoto, S., Tamura, Y.: ‘A load fow calculation method for ill-conditioned power systems’, IEEE Trans. Power Appar. Syst., 1981, PAS-100, pp. 17361743.
    17. 17)
      • 17. Milano, F.: ‘Continuous Newton's method for power flow analysis’, IEEE Trans. Power Syst., 2009, 24, (1), pp. 5057.
    18. 18)
      • 18. Schaffer, M.D., Tylavsky, D.J.: ‘A nondiverging polar-form Newton-based power flow’, IEEE Trans. Ind. Appl., 1988, 24, pp. 870877.
    19. 19)
      • 19. Tylavsky, D.J., Crouch, P., Jarriel, L.F., et al: ‘Improved power flow robustness for personal computers’, IEEE Trans. Ind. Appl., 1992, 28, pp. 11021108.
    20. 20)
      • 20. Braz, L.M.C., Castro, C.A., Murari, C.A.F.: ‘A critical evaluation of step size optimization based load flow methods’, IEEE Trans. Power Syst., 2000, 15, (1), pp. 202207.
    21. 21)
      • 21. Bijwe, P.R., Kelapure, S.M.: ‘Nondivergent fast power flow methods’, IEEE Trans. Power Syst., 2003, 18, (2), pp. 633638.
    22. 22)
      • 22. Tate, J.E., Overbye, T.J.: ‘A comparison of the optimal multiplier in polar and rectangular coordinates’, IEEE Trans. Power Syst., 2005, 20, (4), pp. 16671674.
    23. 23)
      • 23. Hetzler, S.M.: ‘A continuous version of Newton's method’, Coll. Math. J., 1997, 28, (5), pp. 348351.
    24. 24)
      • 24. Milano, F.: ‘Analogy and convergence of levenberg's and lyapunov-based methods for power flow analysis’, IEEE Trans. Power Syst., 2016, 31, (2), pp. 16631664.
    25. 25)
      • 25. Pourbagher, R., Derakhshandeh, S.Y.: ‘Application of high-order Levenberg–Marquardt method for solving the power flow problem in the ill-conditioned systems’, IET Gener. Transm. Distrib., 2016, 10, (12), pp. 30173022.
    26. 26)
      • 26. Saadat, H.: ‘Power system analysis’ (McGraw-Hill, New York, 2002).
    27. 27)
      • 27. Broyden, C.G.: ‘A class of methods for solving nonlinear simultaneous equations’, Math. Comput., 1965, 19, (92), pp. 577593.
    28. 28)
      • 28. 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.
    29. 29)
      • 29. Power systems test case archive. University of Washington, Seattle. Available at http://www.ee.washington.edu/research/pstca/.
    30. 30)
      • 30. Birchfield, A.B., Xu, T., Gegner, K.M., et al: ‘Grid structural characteristics as validation criteria for synthetic networks’, IEEE Trans. Power Syst., 2017, 32, (4), pp. 32583265.
    31. 31)
      • 31. Behnam-Guilani, K.: ‘Fast decoupled load flow: The hybrid model’, IEEE Trans. Power Syst., 1987, 3, (2), pp. 734742.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-gtd.2018.5633
Loading

Related content

content/journals/10.1049/iet-gtd.2018.5633
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address