![](bg6.png)
Figure 3: Topology of the 10-node three-phase network.
6 CONCLUSIONS
TOPF is a very computationally difficult problem as
it involves multiple quadratic equality and indefinite
quadratic inequality constraints of the bus intercon-
nections, hardware operating capacity and balance be-
tween power demand and supply. We have proposed
an iterative nonsmooth algorithm for its computatio-
nal solution. The provided simulations demonstrate
its merit. Its applications to larger scale TOPFs are
currently under consideration.
REFERENCES
Abdelaziz, M. M. A., Farag, H. E., El-Saadany, E. F., and
Mohamed, Y. A. R. I. (2013). A novel and genera-
lized three-phase power flow algorithm for islanded
microgrids using a Newton trust region method. IEEE
Trans. Power Systems, 28(1):190–201.
Bukhsh, W., Grothey, A., McKinnon, K., and Trodden, P.
(2013). Local solutions of the optimal power flow pro-
blem. IEEE Trans. Power Systems, 28(4):4780–4788.
Dall’Anese, E., Zhu, H., and Giannakis, G. B. (2013).
Distributed optimal power flow for smart microgrids.
IEEE Trans. Smart Grid, 4(3):1464–1475.
Deshmukh, S., Natarajan, B., and Pahwa, A. (2012).
Voltage/var control in distribution networks via re-
active power injection through distributed generators.
IEEE Trans. Smart Grid, 3(3):1226–1234.
Farhangi, H. (2010). The path of the smart grid. IEEE
Power and Energy Magazine, 8:18–28.
Grant, M. and Boyd, S. (2014). CVX: Matlab soft-
ware for disciplined convex programming, version
2.1. http://cvxr.com/cvx.
Kersting, W. H. (2007). Distribution System Modeling and
Analysis. Boca Raton, FL, USA: CRC, 2rd edition.
Lavaei, J. and Low, S. H. (2012). Zero duality gap in opti-
mal power flow problem. IEEE Trans. Power Systems,
27(1):92–107.
Madani, R., Sojoudi, S., and Lavaei, J. (2015). Convex re-
laxation for optimal power flow problem: Mesh net-
works. IEEE Trans. Power Systems, 30:199–211.
Phan, H. A., Tuan, H. D., Kha, H. H., and Ngo, D. T. (2012).
Nonsmooth optimization for efficient beamforming in
cognitive radio multicast transmission. IEEE Trans.
Signal Processing, 60(6):2941–2951.
Sanseverino, E. R., Quang, N. N., Di Silvestre, M. L., Guer-
rero, J. M., and Li, C. (2015). Optimal power flow in
three-phase islanded microgrids with inverter interfa-
ced units. Electric Power Systems Research, 123:48–
56.
Shi, Y., Tuan, H. D., and Su, S. (2015). Nonsmooth opti-
mization for optimal power flow. In Proc. of the 3rd
IEEE Global Conference on Signal and Information
Processing, pages 1–4.
Sturm, J. F. (1999). Using SeDuMi 1.02: A Matlab tool-
box for optimization over symmetric cones. Optim.
Methods Software, 11-12:625–653.
Tuan, H. D., Apkarian, P., Hosoe, S., and Tuy, H. (2000).
D.c. optimization approach to robust controls: the fe-
asibility problems. Inter. J. of Control, 73:89–104.
Yang, F. and Li, Z. (2016). Effects of balanced and un-
balanced distribution system modeling on power flow
analysis. In Proc. of 2016 IEEE Power Energy So-
ciety Innovative Smart Grid Technologies Conference
(ISGT), pages 1–5.
Zimmerman, R. D., Murillo-Sanchez, C. E., and Thomas,
R. J. (2011). Matpower: Steady-state operations,
planning, and analysis tools for power systems re-
search and education. IEEE Trans. Power Systems,,
26(1):12–19.
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