A Geršgorin theory for robust microgrid stability analysis

Li, Yan; Zhang, Peng; Ren, Lingyu; Orekan, Taofeek

doi:10.1109/pesgm.2016.7741211

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…On similar lines, a strategy for computing small-signal security margins has been presented recently, computing stability margin for load increase, in [8]. A method based on Gersgorin disks has also been used to identify the region of eigenvalue perturbation for disturbances in microgrid system [9]. An extension using reachable set computation (FAR) has also been presented in [10].…”

Section: Introductionmentioning

confidence: 99%

A Sufficient Condition for Small-Signal Stability and Construction of Robust Stability Region

Pareek

Turitsyn

Dvijotham

et al. 2019

2019 IEEE Power &Amp; Energy Society General Meeting (PESGM)

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The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the equilibrium point is varying rapidly. This paper focuses on the Differential Algebraic Equation (DAE) formulation of power systems and bridges the gap between the conventional reduced system and the original one using logarithmic norm. We propose a sufficient condition for stability using Bilinear Matrix Inequality and its inner approximation as Linear Matrix Inequality. Another contribution is the construction of robust stability regions in state-space in contrast to most existing approaches trying same in the parameter space. Performance evaluation of the sufficiency condition and its inner approximation has been given with the necessary and sufficient condition for a smallscale test case. The paper provides a necessary base to develop tractable construction techniques for the robust stability region of power systems.

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Section: Introductionmentioning

confidence: 99%

A Sufficient Condition for Small-Signal Stability and Construction of Robust Stability Region

Pareek

Turitsyn

Dvijotham

et al. 2019

2019 IEEE Power &Amp; Energy Society General Meeting (PESGM)

View full text Add to dashboard Cite

show abstract

“…On similar lines, a strategy for computing small-signal security margins has been presented for computing stability margin for load increase [234]. A method based on Gersgorin disks has also been used to identify the region of eigenvalue perturbation for disturbances in micro-grid system [235]. An extension using reachable set computation has also been presented in [236].…”

Section: Small-signal Stability: Concept and Methodsmentioning

confidence: 99%

Analytical approximations and decision-making techniques for power systems under uncertainty

Pareek¹

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The integration of distributed energy resources and increasing adoption of electric vehicles continue to drive uncertainty in power systems to an unprecedented level.In view of reduced applicability of traditional analysis and decision-making methods, this dissertation aims to address the need for new approaches, by attempting to solve three di↵erent sets of problems.This dissertation first proposes an analytical power flow approximation and develops a closed-form power flow framework. The thesis proposes a novel framework using Gaussian process regression to learn node voltage as a closed-form function of e↵ective bus load or injection vector. The proposed approximation is valid over a subspace of load, where the 'subspace' is used to describe a hypercube within which uncertain loads/injections lie. The approximation framework explains the system's behavior under uncertainty via Gaussian process hyper-parameter based interpretability. The proposed method achieves low mean absolute error of order 10 5 (per unit) in voltage magnitude and 10 4 (rad.) in angle when tested on 33-Bus and 56-Bus systems. Also, the proposed framework is used to develop an optimal steady-state voltage control framework using a linear voltage-power relationship. Simulation results on the 69-Bus system have shown the independence of approximation error with system loading and uncertainty levels. Therefore, control mechanisms developed based on the proposed analytical approximation are suitable under uncertainty. The framework also addresses the challenges posed by independent entity integration (e.g., peer-to-peer energy trading), as independent operational decisions of prosumers a↵ect the entire network. The proposed probabilistic feasibility set construction method-for privacy-preserving feasibility assessment-is tractable and handles non-parametric injection uncertainties by applying the worst-case performance analysis theorem over the proposed closed-form power flow approximation. The developed method's ability to capture the variations in probabilistic feasibility set for storage connected at a node in a 33-Bus network is shown via numerical simulations under di↵erent levels of total renewable penetration and uncertainty.xviiContents Statement of Originality iii

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Modeling and Stability Analysis of Microgrids

Li¹

2012

Cyber-Physical Microgrids

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A Geršgorin theory for robust microgrid stability analysis

Cited by 6 publications

References 7 publications

A Sufficient Condition for Small-Signal Stability and Construction of Robust Stability Region

A Sufficient Condition for Small-Signal Stability and Construction of Robust Stability Region

Analytical approximations and decision-making techniques for power systems under uncertainty

Modeling and Stability Analysis of Microgrids

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