Exact convex relaxation for optimal power flow in distribution networks

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

doi:10.1145/2465529.2465535

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…have a unique solution as long as the underlying network is radial, where s ij , c ij are obtained from solving (2). An alternative proof can be seen in [7]. For meshed networks, however, the reformulation (2) is exact only if we include (3)-(4) in the constraints.…”

Section: Optimal Power Flowmentioning

confidence: 99%

Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

Kocuk

Dey

Sun

2016

IEEE Trans. Power Syst.

121

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It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present.We show that even for a two-bus one-generator system, the SDP relaxation can have all possible approximation outcomes, that is (1) SDP relaxation may be exact or (2) SDP relaxation may be inexact or (3) SDP relaxation may be feasible while the OPF instance may be infeasible. We provide a complete characterization of when these three approximation outcomes occur and an analytical expression of the resulting optimality gap for this two-bus system. In order to facilitate further research, we design a library of instances over radial networks in which the SDP relaxation has positive optimality gap.Finally, we propose valid inequalities and variable bound tightening techniques that significantly improve the computational performance of a global optimization solver.Our work demonstrates the need of developing efficient global optimization methods for the solution of OPF even in the simple but fundamental case of radial networks.

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Section: Optimal Power Flowmentioning

confidence: 99%

Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

Kocuk

Dey

Sun

2016

IEEE Trans. Power Syst.

121

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show abstract

“…A universal linearisation technique is using an inscribed equilateral polygon, for example, an octagon, to approximate the circle, as illustrated in Figure 2. Hence, the quadratic constraint could be substituted by several linear inequalities as represented in Equations (27)(28)(29)(30).…”

Section: Linearisation Of Quadratic Inequality Constraintmentioning

confidence: 99%

“…Nevertheless, non-linear programing algorithms are subject to low computational efficiency and local optima. In the third group, the three-phase OPF model is first convexified into semi-definite constraints [27][28][29] and then solved by semi-definite programing (SDP). Still, solving SDP is computationally intensive.…”

Section: Introductionmentioning

confidence: 99%

Linearised three‐phase optimal power flow for coordinated optimisation of residential solid‐state power substations

Liu

Moorthy

Choi

et al. 2021

IET Energy Syst Integration

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With the increasing integration of single-phase resources, for example, PV, batteries and solid-state power substations (SSPSs), in residential distribution networks, voltage regulation and phase balancing of distribution feeders are facing growing challenges. To solve these challenges, a linearised three-phase optimal power flow (OPF) model is proposed to coordinate the operation of residential solid-state power substations for voltage regulation and phase balancing of distribution feeders. The proposed three-phase OPF model schedules both real and reactive power of each components in the SSPSs with the purpose of minimising the total operating cost as well as improving the grid performance, for example, voltage regulation and phase balancing. Results of case studies validate the accuracy of the proposed three-phase OPF model. In addition, the effectiveness of coordinating multiple SSPSs for voltage regulation and phase balancing has been demonstrated. article for publication, acknowledges that the US government retains a non-exclusive, paid-up, irrevocable, worldwide licence to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).How to cite this article: Liu G., et al.: Linearised threephase optimal power flow for coordinated optimisation of residential solid-state power substations. IET Energy Syst. Integr. 1-11 (2021).

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“…The branch flow model especially for radial networks has a convenient recursive structure that not only allows a more efficient computation of power flows e.g. [46]- [48], but also plays a crucial role in proving the sufficient conditions for exact relaxation in [49], [50]. Since the variables in the branch flow model correspond directly to physical quantities such as branch power flows and injections it is sometimes more convenient in applications.…”

Section: B Summarymentioning

confidence: 99%

Equivalent Relaxations of Optimal Power Flow

Bose

Low

Teeraratkul

et al. 2015

IEEE Trans. Automat. Contr.

135

105

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Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results imply that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.

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Exact convex relaxation for optimal power flow in distribution networks

Cited by 11 publications

References 12 publications

Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

Linearised three‐phase optimal power flow for coordinated optimisation of residential solid‐state power substations

Equivalent Relaxations of Optimal Power Flow

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