A Survey of Relaxations and Approximations of the Power Flow Equations

Molzahn, Daniel K.; Hiskens, Ian A.

doi:10.1561/3100000012

Cited by 197 publications

(219 citation statements)

References 41 publications

(44 reference statements)

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“…We are also looking at including more granular models of the net load variability in our model (such as power factor constraints on controllable loads and DER capability curves). Further, we are applying recent improvements to tighten the convex relaxation in order to reduce the conservativeness of our results [22,[29][30][31]35]. Finally, we are developing more systematic methods for locating where to impose appropriately restrictive voltage constraints (i.e., the choice of buses in V and limitsṼ i ,Ṽ i in (3d)) in order to securely apply grid-agnostic controllers without overly limiting DER capabilities.…”

Section: Discussionmentioning

confidence: 99%

“…Certifiably finding globally optimal solutions for optimization problems with AC power flow constraints is an active research topic [22], and is generally difficult [27,28]. Instead of directly searching for the globally optimal solution to (3), we leverage recently developed convex relaxation techniques that replace non-convex constraints with convex outer approximations to obtain a more tractable formulation.…”

Section: Obtaining Valid Bounds On the Maximum And Minimum Achievablementioning

confidence: 99%

“…2 2.4.1. Choice of Convex Relaxation There are many choices for convex relaxations of the AC power flow equations [22]. We use two main criteria to choose an appropriate relaxation: (i) tightness, which refers to how well the relaxation approximates the AC Figure 2.…”

Section: Obtaining Valid Bounds On the Maximum And Minimum Achievablementioning

confidence: 99%

“…This can be attributed to the fact that the convex relaxation exploits inaccuracies in the outer approximation of the AC power flow constraints (3e), (3f) to artificially achieve lower voltage magnitudes. Tightening the relaxation via improvements such as those in [22,[29][30][31]35] may lead to less conservative results. We leave implementations of such improvements to future work.…”

Section: Remark: Conservativeness Of the Convex Relaxationmentioning

confidence: 99%

“…We employ convex relaxations of the AC power flow constraints to obtain valid but conservative bounds for the extreme values obtained from these problems. We use the QC relaxation [19][20][21], but other relaxations are also applicable [22].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Grid-Aware versus Grid-Agnostic Distribution System Control: A Method for Certifying Engineering Constraint Satisfaction

Molzahn¹,

Roald²

2019

Proceedings of the Annual Hawaii International Conference on System Sciences

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Growing penetrations of distributed energy resources (DERs) in distribution systems have motivated the design of controllers that leverage DER capabilities to achieve system-wide objectives. These controllers may be either grid-agnostic or grid-aware, depending on whether distribution network constraints are considered. Grid-agnostic controllers have the benefit of not requiring network models or system measurements, but may cause dangerous constraint violations. Rather than develop a specific controller, this paper considers the potential impacts of DER controllers with respect to network constraint violations. Specifically, this paper develops an optimization-based method to rigorously certify when any grid-agnostic controller can be applied without concern regarding network constraint violations, or, conversely, when grid-aware control may be needed to maintain distribution grid security. The proposed method uses convex optimization techniques to bound the impacts of load variability, given a subset of buses with voltage measurements and control. The method either provides a certificate for secure operation or identifies potentially critical constraints and the need for additional controllability. Numerical tests illustrate the ability to certify secure operation for different ranges of variability.

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Section: Discussionmentioning

confidence: 99%

Section: Obtaining Valid Bounds On the Maximum And Minimum Achievablementioning

confidence: 99%

Section: Obtaining Valid Bounds On the Maximum And Minimum Achievablementioning

confidence: 99%

Section: Remark: Conservativeness Of the Convex Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Grid-Aware versus Grid-Agnostic Distribution System Control: A Method for Certifying Engineering Constraint Satisfaction

Molzahn¹,

Roald²

2019

Proceedings of the Annual Hawaii International Conference on System Sciences

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Applications of optimization models for electricity distribution networks

Claeys

Vanin

Geth

2021

WIREs Energy & Environment

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Increased penetration of low‐carbon technologies, such as residential photovoltaic systems, electric vehicles, and batteries, can potentially cause voltage quality issues in distribution networks. Active distribution networks adopt control schemes where these assets are actively managed to prevent potential issues, increasing the network utilization. Mathematical optimization is a key technology in enabling such applications, either directly as the underlying solution, or for benchmarking effectiveness. As networks are operated closer to their engineering limits, models representing distribution network physics become increasingly important. This article reviews how distribution networks are modeled with varying degrees of detail in the context of optimization problems. It goes on to catalog the applications that use such models, and ends with an overview of toolchains to implement them, to enable the transition from the passive to active management of the distribution system. This article is categorized under: Energy Systems Analysis > Systems and Infrastructure

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Power Network Design with Line Activity

Bienstock

Cerulli

Escobar

et al. 2022

AIRO Springer Series

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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A Survey of Relaxations and Approximations of the Power Flow Equations

Abstract: Also available as a combined paper and online subscription.

Cited by 197 publications

References 41 publications

Grid-Aware versus Grid-Agnostic Distribution System Control: A Method for Certifying Engineering Constraint Satisfaction

Grid-Aware versus Grid-Agnostic Distribution System Control: A Method for Certifying Engineering Constraint Satisfaction

Applications of optimization models for electricity distribution networks

Power Network Design with Line Activity

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