# Three-phase Optimal Power Flow for Smart Grids by Iterative Nonsmooth Optimization

### Y. Shi, H.D. Tuan, A. V. Savkin

#### Abstract

Optimal power flow is important for operation and planning of smart grids. The paper considers the so called unbalanced thee-phase optimal power flow problem (TOPF) for smart grids, which involves multiple quadratic equality and indefinite quadratic inequality constraints to model the bus interconnections, hardware capacity and balance between power demand and supply. The existing Newton search based or interior point algorithms are often trapped by a local optimum while semidefinite programming relaxation (SDR) even fails to locate a feasible point. Following our previously developed nonsmooth optimization approach, computational solution for TOPF is provided. Namely, an iterative procedure for generating a sequence of improved points that converges to an optimal solution, is developed. Simulations for TOPF in unbalanced distributed networks are provided to demonstrate the practicability and efficiency of our approach.

#### References

- Abdelaziz, M. M. A., Farag, H. E., El-Saadany, E. F., and Mohamed, Y. A. R. I. (2013). A novel and generalized 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 problem. 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 reactive 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 software 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 optimal power flow problem. IEEE Trans. Power Systems, 27(1):92-107.
- Madani, R., Sojoudi, S., and Lavaei, J. (2015). Convex relaxation for optimal power flow problem: Mesh networks. 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., Guerrero, J. M., and Li, C. (2015). Optimal power flow in three-phase islanded microgrids with inverter interfaced units. Electric Power Systems Research, 123:48- 56.
- Shi, Y., Tuan, H. D., and Su, S. (2015). Nonsmooth optimization 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 toolbox 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 feasibility problems. Inter. J. of Control, 73:89-104.
- Yang, F. and Li, Z. (2016). Effects of balanced and unbalanced distribution system modeling on power flow analysis. In Proc. of 2016 IEEE Power Energy Society 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 research and education. IEEE Trans. Power Systems,, 26(1):12-19.

#### Paper Citation

#### in Harvard Style

Shi Y., Tuan H. and V. Savkin A. (2017). **Three-phase Optimal Power Flow for Smart Grids by Iterative Nonsmooth Optimization** . In *Proceedings of the 6th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,* ISBN 978-989-758-241-7, pages 323-328. DOI: 10.5220/0006365803230328

#### in Bibtex Style

@conference{smartgreens17,

author={Y. Shi and H.D. Tuan and A. V. Savkin},

title={Three-phase Optimal Power Flow for Smart Grids by Iterative Nonsmooth Optimization},

booktitle={Proceedings of the 6th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,},

year={2017},

pages={323-328},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006365803230328},

isbn={978-989-758-241-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,

TI - Three-phase Optimal Power Flow for Smart Grids by Iterative Nonsmooth Optimization

SN - 978-989-758-241-7

AU - Shi Y.

AU - Tuan H.

AU - V. Savkin A.

PY - 2017

SP - 323

EP - 328

DO - 10.5220/0006365803230328