Exact Convex Relaxation of Optimal Power Flow in Radial Networks

By Lingwen Gan, Na Li, Ufuk Topcu, Steven H. Low. IEEE Transactions on Automatic Control, 2013

533 citations recorded by the source corpus.

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/bfb14cc406b0f10d1c4a70031b8906f80f578e33

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In Electrical and Electronic Engineering

Citations in the corpus

Feeder Reconfiguration in Distribution Networks Based on Convex Relaxation of OPF (2015, methodology): “For a network with a tree topology, SOCP relaxation is exact under somemild conditions[18], [19].”
A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, background): “and (2), and [14], [15], [26], [48]–[50] for the DistFlow model (3); see [18] for other references.”
Convex Relaxation of Optimal Power Flow—Part II: Exactness (2014, methodology): “This seems to hold with a signiﬁcant margin in practice; see [35] for examples from real systems.”
Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence (2014, methodology): “These bounds are used in [56] to prove a sufficient condition for exact relaxation.”
Convex Optimization Based Distributed Optimal Gas-Power Flow Calculation (2018, methodology): “Under the radial topology assumption of the power distribution network, the original nonlinear and nonconvex OPF problem is converted into an SOCP by convexification techniques in [28], [29], which is readily to be solved by the commercial solvers such as Cplex and Gurobi.”
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks (2017, background): “For radial networks, [11]–[13] have proposed several sufficient conditions for the convex relaxation to be exact.”
Network Equilibrium of Coupled Transportation and Power Distribution Systems (2018, background): “A more thorough discussion on system parameters that will lead to an exact convex relaxation model is provided in [67].”
Real-Time Energy Management in Microgrids (2017, methodology): “Sufficient conditions for the exactness of the relaxation have been derived in [29]–[31], which hold for a variety of IEEE test systems and real-world distribution systems.”