Overviews on the applications of the Kuramoto model in modern power system analysis

Guo, Yuhan; Zhang, Dongrui; Li, Zhuchun; Wang, Qi; Yu, Daren

doi:10.1016/j.ijepes.2021.106804

Cited by 40 publications

(19 citation statements)

References 119 publications

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“…Classical electrical grid dynamics are governed by large synchronous generators with large inertia. These electrical systems have been commonly modelled and represented, in a highlevel way, as a group of interacting oscillators which could be modelled for example as a Kuramoto-like model [3]. However, the future electrical grid with the introduction of novel highly non-linear elements and inertia reduction, is changing such behaviour and the stability concepts and definitions [4].…”

Section: Electrical Grid Modelling: New Dynamic Behaviourmentioning

confidence: 99%

Digital Grids beyond Smart Grids challenges to make future electric grids stable and resilient

Domínguez‐García

2021

Europhysics News

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Section: Electrical Grid Modelling: New Dynamic Behaviourmentioning

confidence: 99%

Digital Grids beyond Smart Grids challenges to make future electric grids stable and resilient

Domínguez‐García

2021

Europhysics News

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“…We apply the design framework to high voltage grids where each node i corresponds to a voltage phase angle θ i ∈ [−π, π), associated with a bus i, and evolves according to the coupled dynamics given in (1), [5]- [7]. Here, the voltage phaseoscillators' ability to maintain synchronized frequencies is essential to the functionality of the grid.…”

Section: Introductionmentioning

confidence: 99%

Designing for Robustness in Electric Grids via a General Effective Resistance Measure

Nagpal¹,

Nair²,

Parise³

et al. 2022

Preprint

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We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phaseoscillator's natural frequency impacts the system's global synchronized frequencies. Given a fixed complex network topology with specific governing dynamics, the proposed framework finds an optimal allocation of edge weights that minimizes such vulnerability measure(s) at the node(s) for which we expect perturbations to occur by solving a tractable semidefinite programming problem. We specify the mathematical model to high voltage electric grids where each node corresponds to a voltage phase angle associated with a bus and edges correspond to transmission lines. Edge weights are determined by the susceptance values along the transmission lines. In this application, frequency synchronization is increasingly challenged by the integration of renewable energy, yet is imperative to the grid's health and functionality. Our framework helps to alleviate this challenge by optimizing the placement of renewable generation and the susceptance values along the transmission lines.

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“…A Kuramoto model [15] consists of a network of interconnected oscillators, whose dynamics are described by coupled ordinary differential equations (ODEs). The Kuramoto oscillator model has been widely studied in various fields across engineering, physics, chemistry, and biology, due to its capability to model interesting collective behavior (e.g., global/partial synchronization) that emerge in complex networks [16]- [27]. For example, a microgrid system with droop-controlled inverters can be mathematically cast as a Kuramoto model, where the synchronization failure of the model corresponds to a power outage in the microgrid [22], [24], [27]- [31].…”

Section: Introductionmentioning

confidence: 99%

“…The Kuramoto oscillator model has been widely studied in various fields across engineering, physics, chemistry, and biology, due to its capability to model interesting collective behavior (e.g., global/partial synchronization) that emerge in complex networks [16]- [27]. For example, a microgrid system with droop-controlled inverters can be mathematically cast as a Kuramoto model, where the synchronization failure of the model corresponds to a power outage in the microgrid [22], [24], [27]- [31]. Another interesting example is the application of the Kuramoto model for studying brain dynamics [18], [19], [25], [26], where the synchronization phenomena may be associated with neurodegenerative diseases [25], [32].…”

Section: Introductionmentioning

confidence: 99%

Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning

Woo¹,

Hong²,

Kwon³

et al. 2021

IEEE Trans. Signal Process.

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Recent advances in objective-based uncertaintyquantification (objective-UQ) have shown that such a goal-driven approach for quantifying model uncertainty is extremely usefulin real-world problems that aim at achieving specific objectives based on complex uncertain systems. Central to this objective-UQ is the concept of mean objective cost of uncertainty (MOCU), which provides effective means of quantifying the impact of uncertainty on the operational goals at hand. MOCU is especially useful for optimal experimental design (OED) as the potential efficacy of an experimental (or data acquisition) campaign can be quantified by estimating the MOCU that is expected to remain after the campaign. However, MOCU-based OED tends to be computationally expensive, which limits its practical applicability. In this paper, we propose a novel machine learning (ML) scheme that can significantly accelerate MOCU computation and expedite MOCU-based experimental design. The main idea is to use an ML model to efficiently search for the optimal robust operator under model uncertainty, a necessary step for computing MOCU. We apply the proposed ML-based OED acceleration scheme to design experiments aimed at optimally enhancing the control performance of uncertain Kuramoto oscillator models. Our results show that the proposed scheme results in up to 154-fold speed improvement without any degradation of the OED performance.

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Overviews on the applications of the Kuramoto model in modern power system analysis

Cited by 40 publications

References 119 publications

Digital Grids beyond Smart Grids challenges to make future electric grids stable and resilient

Digital Grids beyond Smart Grids challenges to make future electric grids stable and resilient

Designing for Robustness in Electric Grids via a General Effective Resistance Measure

Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning

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