Exact convex relaxation for optimal power flow in distribution networks

Gan, Lingwen; Topcu, Ufuk; Li, Na; Low, Steven H.

doi:10.1145/2494232.2465535

Cited by 6 publications

(6 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interestingly, this is the case if SOCP-m is exact, as stated in the following theorem, which is proved in the extended version of this paper [16].…”

Section: Uniqueness Of Solutionsmentioning

confidence: 68%

“…for tree networks according to Theorem 1, which is proved in the extended version of this paper [16]. Theorem 1 establishes a bijective map between the feasible sets of OPF and OPF', that preserves the objective value.…”

Section: B Controllable Devices and Control Objectivementioning

confidence: 97%

“…In fact, the SOCP relaxation is in general not exact, and a 2-bus example is provided in the extended version of this paper [16].…”

Section: Proposition 1 ( [9])mentioning

confidence: 99%

“…Hence, we adjust the network to demonstrate our arguments. The adjustment is detailed in the extended version of this paper [16]. We also consider two practical networks of SCE, a 47-bus network [9] and a 56-bus network [24].…”

Section: A Test Distribution Networkmentioning

confidence: 99%

See 3 more Smart Citations

Exact convex relaxation for optimal power flow in distribution networks

Gan

Low

et al. 2013

Proceedings of the ACM SIGMETRICS/international Conference on Measurement and Modeling of Computer Systems

Self Cite

View full text Add to dashboard Cite

Abstract-The optimal power flow (OPF) problem seeks to control the generation/consumption of generators/loads to optimize certain objectives such as to minimize the generation cost or power loss in the network. It is becoming increasingly important for distribution networks due to the emerging distributed generation and controllable loads. In this paper, we study the OPF problem in distribution networks. In particular, OPF is nonconvex and we study solving it through convex relaxations. We prove that after a "small" modification to the OPF problem, the solution to its second-order-cone programming (SOCP) relaxation is the global optimum of OPF, under a "mild" condition that can be checked prior to solving the relaxation. Empirical studies justify that the modification to OPF is "small" and that the "mild" condition holds for all test distribution networks, including the IEEE 13-bus test distribution network and practical distribution networks with high penetration of distributed generation.

show abstract

“…Interestingly, this is the case if SOCP-m is exact, as stated in the following theorem, which is proved in the extended version of this paper [16].…”

Section: Uniqueness Of Solutionsmentioning

confidence: 68%

Section: B Controllable Devices and Control Objectivementioning

confidence: 97%

“…In fact, the SOCP relaxation is in general not exact, and a 2-bus example is provided in the extended version of this paper [16].…”

Section: Proposition 1 ( [9])mentioning

confidence: 99%

Section: A Test Distribution Networkmentioning

confidence: 99%

See 2 more Smart Citations

Exact convex relaxation for optimal power flow in distribution networks

Gan

Low

et al. 2013

Proceedings of the ACM SIGMETRICS/international Conference on Measurement and Modeling of Computer Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [6], [7], sufficient conditions are derived that guarantee the exactness of the SOCP relaxation under mild conditions for radial network. These convex relaxation based approaches attain much of research interest, see [8], [9] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A non-convex alternating direction method of multipliers heuristic for optimal power flow

You

Peng

2014

2014 IEEE International Conference on Smart Grid Communications (SmartGridComm)

View full text Add to dashboard Cite

Abstract-The optimal power flow (OPF) problem is fundamental to power system planing and operation. It is a nonconvex optimization problem and the semidefinite programing (SDP) relaxation has been proposed recently. However, the SDP relaxation may give an infeasible solution to the original OPF problem. In this paper, we apply the alternating direction method of multiplier method to recover a feasible solution when the solution of the SDP relaxation is infeasible to the OPF problem. Specifically, the proposed procedure iterates between a convex optimization problem, and a non-convex optimization with the rank constraint. By exploiting the special structure of the rank constraint, we obtain a closed form solution of the non-convex optimization based on the singular value decomposition. As a result, we obtain a computationally tractable heuristic for the OPF problem. Although the convergence of the algorithm is not theoretically guaranteed, our simulations show that a feasible solution can be recovered using our method. NOTATIONi is the imaginary unit. W * is the Hermitian of W , Tr (W ) is a trace of W , and W F = Tr (W W * ) is the Frobenius norm of W . The generalized inequality, W 0, means W is a positive semidefinite matrix.The projection operator Π S (W ) = argmin Z∈S W − Z 2 F , is the projection of W onto the set S.

show abstract