TY - GEN
T1 - Polynomial SDP cuts for Optimal Power Flow
AU - Hijazi, Hassan
AU - Coffrin, Carleton
AU - Van Hentenryck, Pascal
N1 - Publisher Copyright:
© 2016 Power Systems Computation Conference.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) problem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability. In this work, we introduce an exact reformulation of the SDP relaxation, formed by a set of polynomial constraints defined in the space of real variables. The new constraints can be seen as "cuts", strengthening weaker second-order cone relaxations, and can be generated in a lazy iterative fashion. The new formulation can be handled by standard nonlinear programming solvers, enjoying better stability and computational efficiency. This new approach benefits from recent results on tree-decomposition methods, reducing the dimension of the underlying SDP matrices. As a side result, we present a formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional matrices. Preliminary results show a significant gain in computational efficiency compared to a standard SDP solver approach.
AB - The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) problem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability. In this work, we introduce an exact reformulation of the SDP relaxation, formed by a set of polynomial constraints defined in the space of real variables. The new constraints can be seen as "cuts", strengthening weaker second-order cone relaxations, and can be generated in a lazy iterative fashion. The new formulation can be handled by standard nonlinear programming solvers, enjoying better stability and computational efficiency. This new approach benefits from recent results on tree-decomposition methods, reducing the dimension of the underlying SDP matrices. As a side result, we present a formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional matrices. Preliminary results show a significant gain in computational efficiency compared to a standard SDP solver approach.
KW - Nonlinear Programming
KW - OPF
KW - Polynomial Constraints
KW - SDP relaxation
KW - SOCP relaxation
UR - http://www.scopus.com/inward/record.url?scp=84986607739&partnerID=8YFLogxK
U2 - 10.1109/PSCC.2016.7540908
DO - 10.1109/PSCC.2016.7540908
M3 - Conference contribution
T3 - 19th Power Systems Computation Conference, PSCC 2016
BT - 19th Power Systems Computation Conference, PSCC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 19th Power Systems Computation Conference, PSCC 2016
Y2 - 20 June 2016 through 24 June 2016
ER -