Three-phase power-flow solutions using decomposed quasi-Newton method for unbalanced radial distribution networks
- Author(s): Nien-Che Yang 1 and Hsing-Chih Chen 1, 2
-
-
View affiliations
-
Affiliations:
1:
Department of Electrical Engineering , Yuan Ze University , 135, Yuan-Tung Road, Chung-Li, Taoyuan 32003 , Taiwan ;
2: Industrial Technology Research Institute Green Energy and Environment Research Laboratories , 195, Sec. 4, Chung Hsing Rd., Chutung, Hsinchu, 31040 , Taiwan
-
Affiliations:
1:
Department of Electrical Engineering , Yuan Ze University , 135, Yuan-Tung Road, Chung-Li, Taoyuan 32003 , Taiwan ;
- Source:
Volume 11, Issue 14,
28
September
2017,
p.
3594 – 3600
DOI: 10.1049/iet-gtd.2017.0281 , Print ISSN 1751-8687, Online ISSN 1751-8695
In this study, a three-phase power-flow method based on graph theory, injection current, and matrix decomposition techniques is proposed for unbalanced radial distribution networks. A decomposed quasi-Newton–Raphson-based method is used to solve the set of non-linear power equations described in polar coordinates. By using the injection current technique, the coupling-free component models can be integrated into the proposed method. To validate the performance and effectiveness of the proposed method, four three-phase IEEE test systems and a practical Taiwan Power Company (Taipower) distribution system are used for comparison. The test results show that the proposed method exhibits robust convergence characteristics and high performance even for ill-conditioned distribution networks.
Inspec keywords: nonlinear equations; matrix decomposition; graph theory; load flow; distribution networks; Newton-Raphson method
Other keywords: polar coordinates; decomposed quasiNewton-Raphson-based method; three-phase IEEE test systems; graph theory; injection current technique; Taiwan Power Company distribution system; matrix decomposition techniques; unbalanced radial distribution networks; nonlinear power equations; three-phase power-flow solutions; coupling-free component models
Subjects: Nonlinear and functional equations (numerical analysis); Distribution networks; Combinatorial mathematics; Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis)
References
-
-
1)
-
14. Penido, D.R.R., De Araujo, L.R., Carneiro, S., et al: ‘Three-phase power flow based on four-conductor current injection method for unbalanced distribution networks’, IEEE Trans. Power Syst., 2008, 23, (2), pp. 494–503.
-
-
2)
-
8. Vieira, J.C.M.Jr., Freitas, W., Morelato, A.: ‘Phase-decoupled method for three-phase power-flow analysis of unbalanced distribution systems’, IEE Proc. Gener. Transm. Distrib., 2004, 151, (5), pp. 568–574.
-
-
3)
-
15. Abdel-Akher, M., Nor, K.M., Rashid, A.H.A.: ‘Improved three-phase power-flow methods using sequence components’, IEEE Trans. Power Syst., 2005, 20, (3), pp. 1389–1397.
-
-
4)
-
10. Kersting, W.H.: ‘Distribution system modeling and analysis’ (CRC Press, 2012).
-
-
5)
-
35. Hsieh, T.-Y., Chen, T.-H., Yang, N.-C.: ‘Matrix decompositions-based approach to Z-bus matrix building process for radial distribution systems’, Int. J. Electr. Power Energy Syst., 2017, 89, pp. 62–68.
-
-
6)
-
34. Yang, N.-C., Le, M.-D.: ‘Loop frame of reference based harmonic power flow for unbalanced radial distribution systems’, Int. J. Electr. Power Energy Syst., 2016, 77, pp. 128–135.
-
-
7)
-
36. Stagg, G.W., El-Abiad, A.H.: ‘Computer methods in power system analysis’ (McGraw-Hill Book Company, 1980, 2nd edn.).
-
-
8)
-
25. Dzafic, I., Pal, B.C., Gilles, M., et al: ‘Generalized Fortescue equivalent admittance matrix approach to power flow solution’, IEEE Trans. Power Syst., 2014, 29, (1), pp. 193–202.
-
-
9)
-
11. Cheng, C.S., Shirmohammadi, D.: ‘A three-phase power flow method for real-time distribution system analysis’, IEEE Trans. Power Syst., 1995, 10, (2), pp. 671–679.
-
-
10)
-
17. Zhang, Y.-S., Chiang, H.-D.: ‘Fast Newton-FGMRES solver for large-scale power flow study’, IEEE Trans. Power Syst., 2010, 25, (2), pp. 769–776.
-
-
11)
-
12. Chang, G., Chu, S., Wang, H.: ‘An improved backward/forward sweep load flow algorithm for radial distribution systems’, IEEE Trans. Power Syst., 2007, 22, (2), pp. 882–884.
-
-
12)
-
3. Yang, N.C., Chen, T.H.: ‘Dual genetic algorithm-based approach to fast screening process for distributed-generation interconnections’, IEEE Trans Power Deliv., 2011, 26, (2), pp. 850–858.
-
-
13)
-
30. Yang, N.-C.: ‘Three-phase power flow calculations by direct Z LOOP method for microgrids with electric vehicle charging demands’, IET Gener. Transm. Distrib., 2013, 7, (9), pp. 1002–1010.
-
-
14)
-
23. Kocar, I., Mahseredjian, J., Karaagac, U., et al: ‘Multiphase load-flow solution for large-scale distribution systems using MANA’, IEEE Trans. Power Deliv., 2014, 29, (2), pp. 908–915.
-
-
15)
-
32. Yang, N.-C.: ‘Three-phase power flow calculations using direct Z BUS method for large-scale unbalanced distribution networks’, IET Gener. Transm. Distrib., 2016, 10, (4), pp. 1048–1055.
-
-
16)
-
19. Kamh, M.Z., Iravani, R.: ‘Steady-state model and power-flow analysis of single-phase electronically coupled distributed energy resources’, IEEE Trans. Power Deliv., 2012, 27, (1), pp. 131–139.
-
-
17)
-
9. Tinney, W.F., Hart, C.E.: ‘Power flow solution by Newton's method’, IEEE Trans. Power Appar. Syst., 1967, PAS-86, (11), pp. 1449–1460.
-
-
18)
-
5. Yang, N.-C., Tseng, W.-C.: ‘Impact assessment of a hybrid energy-generation system on a residential distribution system in Taiwan’, Energy Build., 2015, 91, pp. 170–179.
-
-
19)
-
16. Marinho, J.T., Taranto, G.: ‘A hybrid three-phase single-phase power flow formulation’, IEEE Trans. Power Syst., 2008, 23, (3), pp. 1063–1070.
-
-
20)
-
24. Ramos, E.R., Exposito, A.G., Cordero, G.A.: ‘Quasi-coupled three-phase radial load flow’, IEEE Trans. Power Syst., 2004, 19, (2), pp. 776–781.
-
-
21)
-
22. Li, H.W., Zhang, A.A., Shen, X., et al: ‘A load flow method for weakly meshed distribution networks using powers as flow variables’, Int. J. Electr. Power Energy Syst., 2014, 58, pp. 291–299.
-
-
22)
-
1. Chen, T.H., Yang, N.C.: ‘Simplified annual energy loss evaluation method for branch circuits of a home or building’, Energy Build., 2010, 42, (12), pp. 2281–2288.
-
-
23)
-
27. Sunderland, K., Coppo, M., Conlon, M., et al: ‘A correction current injection method for power flow analysis of unbalanced multiple-grounded 4-wire distribution networks’, Electr. Power Syst. Res., 2016, 132, pp. 30–38.
-
-
24)
-
38. 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.
-
-
25)
-
6. Chen, T.-H., Chiang, L.-S., Yang, N.-C.: ‘Examination of major factors affecting voltage variation on distribution feeders’, Energy Build., 2012, 55, pp. 494–499.
-
-
26)
-
37. Kersting, W.H.: ‘Radial distribution test feeders’, IEEE Trans. Power Syst., 1991, 6, (3), pp. 975–985.
-
-
27)
-
20. de Moura, A.P., de Moura, A.A.F.: ‘Newton–Raphson power flow with constant matrices: a comparison with decoupled power flow methods’, Int. J. Electr. Power Energy Syst., 2013, 46, pp. 108–114.
-
-
28)
-
13. Garcia, P.A.N., Pereira, J.L.R., Carneiro, S., et al: ‘Three-phase power flow calculations using the current injection method’, IEEE Trans. Power Syst., 2000, 15, (2), pp. 508–514.
-
-
29)
-
2. Yang, N.-C., Chen, T.-H.: ‘Assessment of loss factor approach to energy loss evaluation for branch circuits or feeders of a dwelling unit or building’, Energy Build., 2012, 48, pp. 91–96.
-
-
30)
-
28. Chen, T.H., Yang, N.C.: ‘Loop frame of reference based three-phase power flow for unbalanced radial distribution systems’, Electr. Power Syst. Res., 2010, 80, (7), pp. 799–806.
-
-
31)
-
33. Yang, N.-C., Le, M.-D.: ‘Three-phase harmonic power flow by direct Z BUS method for unbalanced radial distribution systems with passive power filters’, IET Gener. Transm. Distrib., 2016, 10, (13), pp. 3211–3219.
-
-
32)
-
31. Yang, N.-C., Tseng, W.-C.: ‘Adaptive three-phase power-flow solutions for smart grids with plug-in hybrid electric vehicles’, Int. J. Electr. Power Energy Syst., 2015, 64, pp. 1166–1175.
-
-
33)
-
4. Yang, N.C., Chen, T.H.: ‘Evaluation of maximum allowable capacity of distributed generations connected to a distribution grid by dual genetic algorithm’, Energy Build., 2011, 43, (11), pp. 3044–3052.
-
-
34)
-
21. Alam, M.J., Muttaqi, K.M., Sutanto, D.: ‘A three-phase power flow approach for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop solar PV’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 1728–1737.
-
-
35)
-
26. Arboleya, P., González-Morán, C., Coto, M.: ‘Unbalanced power flow in distribution systems with embedded transformers using the complex theory in stationary reference frame’, IEEE Trans. Power Syst., 2014, 29, (3), pp. 1012–1022.
-
-
36)
-
29. Chen, T.-H., Yang, N.-C.: ‘Three-phase power-flow by direct Z BR method for unbalanced radial distribution systems’, IET Gener. Transm. Distrib., 2009, 3, (10), pp. 903–910.
-
-
37)
-
18. Kamh, M.Z., Iravani, R.: ‘Unbalanced model and power-flow analysis of microgrids and active distribution systems’, IEEE Trans. Power Deliv., 2010, 25, (4), pp. 2851–2858.
-
-
38)
-
7. Chen, T.H., Chen, M.S., Hwang, K.J., et al: ‘Distribution system power flow analysis – a rigid approach’, IEEE Trans. Power Deliv., 1991, 6, (3), pp. 1146–1152.
-
-
1)