Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

被引：97

作者：

Hijazi H. ^{[1
]}

Coffrin C. ^{[2
]}

Hentenryck P.V. ^{[3
]}

机构：

[1] The Australian National University, NICTA / Data61-CSIRO, Decision Sciences, 7 London Circuit, Canberra, 2601, ACT

[2] Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, 87545, NM

[3] Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, 48109, MI

来源：

Mathematical Programming Computation | 2017年 / 9卷 / 3期

基金：

澳大利亚研究理事会;

关键词：

Capacitor placement; Convex relaxation; Global optimization; Mixed-integer nonlinear programming; Optimal power flow; Optimal transmission switching;

D O I：

10.1007/s12532-016-0112-z

中图分类号：

学科分类号：

摘要：

This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations. © 2016, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society.

引用

页码：321 / 367

页数：46

共 62 条

[1]

Borghetti A., Paolone M., C.A.N.: A mixed integer linear programming approach to the optimal configuration of electrical distribution networks with embedded generators, Proceedings of the 17th Power Systems Computation Conference (PSCC’11), (2011)

[2]

Achterberg T., SCIP: solving constraint integer programs, Math. Program. Comput., 1, 1, pp. 1-41, (2009)

[3]

Aguiar R., Cuervo P., Capacitor placement in radial distribution networks through a linear deterministic optimization model, Proceedings of the 15th Power Systems Computation Conference (PSCC’05), (2005)

[4]

Al-Khayyal F., Falk J., Jointly constrained biconvex programming, Math. Oper. Res., 8, 2, pp. 273-286, (1983)

[5]

Bai X., Wei H., Fujisawa K., Wang Y., Semidefinite programming for optimal power flow problems, Int. J. Electr. Power Energy Syst., 30, 6-7, pp. 383-392, (2008)

[6]

Baran M., Wu F., Optimal capacitor placement on radial distribution systems, IEEE Trans. Power Deliv., 4, 1, pp. 725-734, (1989)

[7]

Couenne: User manual. Published online at, (2009)

[8]

Bienstock D., Mattia S., Using mixed-integer programming to solve power grid blackout problems, Discret. Optim., 4, 1, pp. 115-141, (2007)

[9]

Bienstock D., Verma A., The n-k problem in power grids: new models, formulations, and numerical experiments, SIAM J. Optim., 20, 5, pp. 2352-2380, (2010)

[10]

Bonami P., Biegler L.T., Conn A.R., Cornuejols G., Grossmann I.E., Laird C.D., Lee J., Lodi A., Margot F., Sawaya N., Wachter A., An algorithmic framework for convex mixed integer nonlinear programs, Discret. Optim., 5, 2, pp. 186-204, (2008)

← 1 2 3 4 5 6 7 →