Three-phase AC/DC power-flow for balanced/unbalanced microgrids including wind/solar, droop-controlled and electronically-coupled distributed energy resources using radial basis function neural networks

Three-phase AC/DC power-flow for balanced/unbalanced microgrids including wind/solar, droop-controlled and electronically-coupled distributed energy resources using radial basis function neural networks

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

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(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
Your details
Why are you recommending this title?
Select reason:
IET Power Electronics — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study presents a novel approach for robust, balanced and unbalanced power-flow analysis of microgrids including wind/solar, droop-controlled and electronically-coupled distributed energy resources. This method is based on using radial basis function neural networks that can be applied to a wide range of non-linear equation sets. Unlike conventional Newton–Raphson, the presented method does not need to calculate partial derivatives and inverse Jacobian matrix and so, has less computation time, can solve all the equation sets for the power grid and distributed energy resources exactly and simultaneously, and has enough robustness with respect to the R/X ratio and load changes. Also, because the power electronic interface provides some degrees of freedom in the steady-state and dynamic models, a new approach is required to solve the non-linear set of the power grid and distributed energy resource equations even with unequal number of equations and variables. The proposed method is a general method applicable to all types of power networks, including radial, meshed, and open-loop, and includes all types of buses, i.e. PQ, photovoltaic and slack buses. This method is tested on different microgrid test systems, and the comparative results validate its efficiency and accuracy.


    1. 1)
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
    21. 21)
    22. 22)
      • 22. Krause, P.C.: ‘Analysis of electric machinery and drive systems’ (Wiley-IEEE Press, 1986, 3rd edn.2013).
    23. 23)
      • 23. Payasi, R., Singh, A., Singh, D.: ‘Effect of voltage step constraint and load models in optimal location and size of distributed generation’. Proc. Int. Conf. Power Energy Control (ICPEC), Dindigul, Tamil Nadu, India, February 2013, pp. 710716.
    24. 24)
      • 24. Price, W.W.: ‘Load representation for dynamic performance analysis’, 1993, IEEE Trans. Power Syst., 8, (2), pp. 472482.
    25. 25)
      • 25. Kundur, P., Balu, N., Lauby, M.: ‘Power system stability and control’ (McGraw-Hill, New York, NY, USA, 1994).
    26. 26)
    27. 27)
      • 27. IEEE Standard 1547: ‘IEEE standard for interconnecting distributed resources with electric power systems’, 2003.
    28. 28)
    29. 29)
    30. 30)
      • 30. Dadhania, A.: ‘Modeling of doubly fed induction generators for distribution system power-flow analysis’. M.A.S. thesis, Dept. Elect. Comput. Eng., Univ. Ryerson, Toronto, ON, Canada, 2010.
    31. 31)
      • 31. Alam, M.J.E., Muttaqi, K.M., Sutanto, D.: ‘A three-phase power-flow approach for integrated 3-wire MV and 4-wire multigrounded LV networks with ooftop solar PV’, IEEE Trans. Power Electr., 2013, 28, (2), pp. 17281737.
    32. 32)
      • 32. Alquthami, T., Ravindra, H., Faruque, M.O., et al: ‘Study of photovoltaic integration impact on system stability using custom model of PV arrays integrated with PSS/E’. Proc. 2010 North American Power Symp. (NAPS), Arlington, TX, USA, 2010, pp. 18.
    33. 33)
    34. 34)
      • 34. Masters, G.M.: ‘Renewable and efficient electric power systems’ (Wiley-IEEE Press, New York, NY, USA, 2004, 2nd edn.2013).
    35. 35)
    36. 36)
      • 36. Wood, A.J., Wollenberg, B.F., Sheblé, G.B.: ‘Power generation, operation and control’ (Wiley-Interscience, NY, USA, 1984, 3rd edn.2013).
    37. 37)
      • 37. Opathella, C., Venkatesh, B.: ‘Three-phase unbalanced power-flow using π-model of controllable AC–DC converters’, IEEE Trans. Power Syst., 2016, PP, (99), pp. 111.
    38. 38)
      • 38. Demuth, H., Beale, M.: ‘Neural network toolbox for use with MATLAB’ (The MathWorks Massachuset, MA, USA, 1993, 4th edn.2015).
    39. 39)
    40. 40)
    41. 41)
    42. 42)
      • 42. Baghaee, H.R., Kaviani, A.K., Mirsalim, M., et al: ‘Harmonic optimization in single DC source multi-level inverters using RBF neural networks’. Proc. Third Power Electronics and Drive Systems Technology (PEDSTC), Tehran, Iran, 2012, pp. 403409.
    43. 43)
    44. 44)
    45. 45)
    46. 46)
      • 46. Baghaee, H.R., Mirsalim, M., Gharehpetian, G.B., Talebi, H.A.: ‘Reliability/Cost based Multi-Objective Pareto Optimal Design of Stand-Alone Wind/PV/FC generation Microgrid System’, Energy, 115, (1), pp. 10221041, DOI: 10.1016/
    47. 47)
      • 47. IEEE Power Engineering Society: ‘Distribution test feeders – 13 bus feeder’, Available at
    48. 48)

Related content

This is a required field
Please enter a valid email address