Abstract
This paper addresses a nonconvex optimal power flow problem (OPF). Specifically, a new B-spline approach in the context of OPF problem is introduced. The applicability of this new approach is shown on a real-world 3-bus power system. The numerical results obtained with this new approach for this problem a 3-bus system reveal a satisfactory improvement in terms of optimality when compared against traditional interior-point method based MATPOWER toolbox. Similarly, the results are also found to be satisfactory with respect to the global optimization solvers like BARON and GloptiPoly.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Capitanescu, F.: Critical review of recent advances and further developments needed in AC optimal power flow. Electr. Power Syst. Res. 136, 57–68 (2016)
Huneault, M., Galiana, F.: A survey of the optimal power flow literature. IEEE Trans. Power Syst. 6(2), 762–770 (1991)
Torres, G., Quintana, V.: Optimal power flow by a nonlinear complementarity method. In: Proceedings of the 21st IEEE International Conference Power Industry Computer Applications (PICA’99), 211–216 (1999)
Wang, H., Murillo-Sanchez, C., Zimmerman, R., Thomas, R.: On computational issues of market-based optimal power flow. IEEE Trans. Power Syst. 22(3), 1185–1193 (2007)
Momoh, J.: Electric Power System Applications of Optimization. Markel Dekker, New York (2001)
Momoh, J., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part I. Nonlinear and quadratic programming approaches. IEEE Trans. Power Syst. 14(1), 96–104 (1999)
Momoh, J., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part II. Newton, linear programming and interior point methods. IEEE Trans. Power Syst. 14(1), 105–111 (1999)
Gawali, D., Zidna, A., Nataraj, P.: Algorithms for unconstrained global optimization of nonlinear (polynomial) programming problems: the single and multi-segment polynomial B-spline approach. Comput. Oper. Res. Elsevier 87, 201–220 (2017)
Gawali, D., Zidna, A., Nataraj, P.: Solving nonconvex optimization problems in systems and control: a polynomial B-spline approach. In: Modelling, Computation and Optimization in Information Systems and Management Sciences, Springer, 467–478 (2015)
Bukhsh, W., Grothey, A., McKinnon, K., Trodden, P.: Local solutions of the optimal power flow problem. IEEE Trans. Power Syst. 28(4), 4780–4788 (2013)
Zimmerman, R., Murillo-Sanchez, C., Thomas, R.: MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26(1), 12–19 (2011)
Tawarmalani, M., Sahinidis, N.: GloptiPoly: a polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2), 225–249 (2005)
Henrion, D., Lasserre, J.: GloptiPoly: global optimization over polynomials with Matlab and SeDuMi. ACM Trans. Math. Softw. (TOMS) 29(2), 165–194 (2003)
Lin, Q., Rokne, J.: Methods for bounding the range of a polynomial. J. Comput. Appl. Math. 58(2), 193–199 (1995)
Lin, Q., Rokne, J.: Interval approximation of higher order to the ranges of functions. Comput. Math. Appl. 31(7), 101–109 (1996)
NEOS Server for optimization. http://www.neos-server.org/neos/solvers/
De Boor, C.: A Practical Guide to Splines. Applied Mathematical Sciences. Springer, Berlin (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gawali, D.D., Patil, B.V., Zidna, A., Nataraj, P.S.V. (2020). A B-Spline Global Optimization Algorithm for Optimal Power Flow Problem. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)