Three-phase probabilistic load flow in radial and meshed distribution networks

Alexander C. Melhorn; Aleksandar Dimitrovski

Three-phase probabilistic load flow in radial and meshed distribution networks

View Fulltext

Author(s): Alexander C. Melhorn ¹ and Aleksandar Dimitrovski ²
- Affiliations: 1: Electricity Research Centre, School of Electrical, Electronic and Communications Engineering, University College Dublin, Dublin, Ireland ;
  2: Electrical and Electronics Systems Research Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA
Source: Volume 9, Issue 16, 03 December 2015, p. 2743 – 2750
DOI: 10.1049/iet-gtd.2015.0521 , Print ISSN 1751-8687, Online ISSN 1751-8695

Received 22/04/2015, Accepted 12/08/2015, Revised 17/07/2015, Published 03/12/2015

With the introduction of higher levels of renewables and demand response programs, traditional deterministic power system tools fall short of expectations. Probabilistic load flow (PLF) takes into account the inconsistency or the unknown loads, and generation in the fundamental load flow analysis. This study proposes a PLF solution for both balanced and unbalanced, radial and weakly meshed networks without explicitly using the Y -bus matrix. It allows for discrete probability density functions as input variables without having to assume a predefined distribution. The nodal voltages and the power flows can be calculated independently from one another. The proposed method is applied to the IEEE 123 Node Test Feeder and the IEEE 13 Node Test Feeder in both its original radial configuration and a modified mesh configuration, including a load replaced with a wind turbine. The results are validated by comparison of the proposed method's solutions to those obtained using cumulants and Monte Carlo simulation. The proposed PLF method provides an accurate and practical way for finding the solution to stochastic problems occurring in power distribution systems allowing for real-system data to be analysed.

References

1. 1)
  - 21. Papoulis, A.: ‘Probability, random variables and stochastic processes’ (McGraw-Hill Inc., New York, 1965).
2. 2)
  - 9. Allan, R., Borkowska, B., Grigg, C.: ‘Probabilistic analysis of power flows’, Proc. Inst. Electric. Eng., 1974, 121, (12), pp. 1551–1556 (doi: 10.1049/piee.1974.0320).
3. 3)
  - 22. Allan, R., Leite da Silva, A.: ‘Probabilistic load flow using multilinearisations’, IEE Proc. C, Gener. Transm. Distrib., 1981, 128, (5), pp. 280–287 (doi: 10.1049/ip-c.1981.0047).
4. 4)
  - 17. Dimitrovski, A., Ačkovski, R.: ‘Probabilistic load flow in radial distribution networks’. Proc. 1996 IEEE Transmission and Distribution Conf., 1996, September 1996, pp. 102–107.
5. 5)
  - 19. Melhorn, A.C., Dimitrovski, A., Tomsovic, K.: ‘Three phase probabilistic load flow in radial distribution networks’. Proc. of the 12th Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS), June 2012.
6. 6)
  - 14. Schellenberg, A., Rosehart, W., Aguado, J.: ‘Cumulant-based probabilistic optimal power flow (p-opf) with gaussian and gamma distributions’, IEEE Trans. Power Syst., 2005, 20, (2), pp. 773–781 (doi: 10.1109/TPWRS.2005.846184).
7. 7)
  - 21. Papoulis, A.: ‘Probability, random variables and stochastic processes’ (McGraw-Hill Inc., New York, 1965).
8. 8)
  - 7. Allan, R.N., Al-Shakarchi, M.R.G.: ‘Probabilistic techniques in ac load flow analysis’, Proc. Inst. Electr. Eng., 1977, 124, (2), pp. 154–160 (doi: 10.1049/piee.1977.0027).
9. 9)
  - 11. Allan, R., Grigg, C., Newey, D., et al: ‘Probabilistic power-flow techniques extended and applied to operational decision making’, Proc. Inst. Electric. Eng., 1976, 123, (12), pp. 1317–1324 (doi: 10.1049/piee.1976.0264).
10. 10)
  - 20. Melhorn, A.C., Dimitrovski, A.: ‘A method for modeling voltage regulators in probabilistic load flow for radial systems’. Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS), 2014, July 2014, pp. 1–6.
11. 11)
  - 2. Mohanpurkar, M., Ramakumar, R.: ‘Probability density functions for power output of wind electric conversion systems’. IEEE Power and Energy Society General Meeting, 2010, July 2010, pp. 1–7.
12. 12)
  - 24. Kersting, W.: ‘Distribution system modeling and analysis’ (CRC Press, 2007, 2nd edn.).
13. 13)
  - 15. Caramia, P., Varilone, P.: ‘Probabilistic ac/dc 3-phase load flow’. Proc. 8th Int. Conf. on Harmonics and Quality of Power Proc., 1998, October 1998, vol. 2, pp. 1018–1028.
14. 14)
  - 10. Allan, R., Al-Shakarchi, M.: ‘Probabilistic a.c. load flow’, Proc. Inst. Electric. Eng., 1976, 123, (6), pp. 531–536 (doi: 10.1049/piee.1976.0120).
15. 15)
  - 1. Louie, H.: ‘Evaluation of probabilistic models of wind plant power output characteristics’. IEEE 11th Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS), 2010, June 2010, pp. 442–447.
16. 16)
  - 21. Caramia, P., Carpinelli, G., Pagano, M., Varilone, P.: ‘Probabilistic three-phase load flow for unbalanced electrical distribution systems with wind farms’, IET Renew. Power Gener., 2007, 1, (2), pp. 115–122 (doi: 10.1049/iet-rpg:20060013).
17. 17)
  - 18. Dimitrovski, A.: ‘Probabilistic load flow in weakly meshed distribution networks’. Proc. of the 5th Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS), September 1997.
18. 18)
  - 23. Kersting, W.: ‘Radial distribution test feeders’. IEEE Power Engineering Society Winter Meeting, 2001, 2001, vol. 2, pp. 908–912.
19. 19)
  - 5. Dong, L., Cheng, W., Bao, H., et al: ‘Probabilistic load flow analysis for power system containing wind farms’. Asia-Pacific Power and Energy Engineering Conf. (APPEEC), 2010, March 2010.
20. 20)
  - 14. Shirmohammadi, D., Hong, H.W., Semlyen, A., et al: ‘A compensation-based power flow method for weakly meshed distribution and transmission networks’, IEEE Trans. Power Syst., 1988, 3, (2), pp. 753–762 (doi: 10.1109/59.192932).
21. 21)
  - 3. Li, X., Pei, J., Zhang, S.: ‘A probabilistic wind farm model for probabilistic load flow calculation’. Asia-Pacific Power and Energy Engineering Conf. (APPEEC), 2010, March 2010, pp. 1–4.
22. 22)
  - 4. Richardson, P., Flynn, D., Keane, A.: ‘Impact assessment of varying penetrations of electric vehicles on low voltage distribution systems’. IEEE Power and Energy Society General Meeting, 2010, 2010, pp. 1–6.
23. 23)
  - 17. Caramia, P., Carpinelli, G., Varilone, P., Verde, P.: ‘Probabilistic three-phase load flow’, Int. J. Electr. Power Energy Syst., 1996, 21, pp. 55–69 (doi: 10.1016/S0142-0615(98)00030-1).
24. 24)
  - 6. 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. 676–682 (doi: 10.1109/TPWRS.2003.818743).
25. 25)
  - 6. Rui-xiang, F., Su-nong, W., Yan, W., et al: ‘The analysis of distribution system with photovoltaic system generation based on probabilistic power flow’. Asia-Pacific Power and Energy Engineering Conf. (APPEEC), 2011, March 2011, pp. 1–5.
26. 26)
  - 1. Borkowska, B.: ‘Probabilistic load flow’, IEEE Trans. Power Appar. Syst., 1974, PAS-93, (3), pp. 752–759 (doi: 10.1109/TPAS.1974.293973).

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Three-phase probabilistic load flow in radial and meshed distribution networks

References

Related content