Applications of interval matrices in power system stabilizer design

Pai, M.A.; Vournas, Costas; Michel, Anthony N.; Ye, H.

doi:10.1016/s0142-0615(96)00041-5

Cited by 13 publications

(4 citation statements)

References 5 publications

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“…A method to construct robust stability region in parameter space for PSS has been presented recently in [11]. The work uses the bialternate sum matrix approach and shown to be efficient over the branch and bound approach used in [12] for similar purpose. This approach works only if the reduced system matrix is affine and hence works for parameters variations of the system but not with the state variations.…”

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)

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“…A method to construct robust stability region in parameter space for power system stabilizer has been presented in [237]. The work uses the 'bialternate' sum matrix approach and shown to be e cient over the branch and bound approach used in [238] for similar purpose. This approach works only if the reduced system matrix is a ne and hence works for parameters variations of the system but not with the state variations.…”

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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“…Recently, a number of studies in the literature have investigated the application of robust control techniques to power systems. Among them Kharitonov's theorem, interval analysis, Irj, Hoo-, and structured singular value (SSV or ji) techniques have been used [22,23,24,25,26,27,28,29,30,31,32,36,37,38]. The robust stability of power systems using Kharitonov's theorem was studied in [22].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The robust stability of power systems using Kharitonov's theorem was studied in [22]. In [23], the interval matrix analysis was used for the design of the PSS.…”

Section: Literature Reviewmentioning

confidence: 99%

Robustness analysis and controller design for static var compensators in power systems

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Peak of RS fz-plot with SVC at different locations One parametric uncertainty-RS assessment of "Station A" power generation Two parametric uncertainties-RS assessment of "Station A" and "Station B" power generation Linear search for a in [1, 10] Linear search for a in [0.1, 2.0] Comparison of state space test and frequency sweep Linear search for o. in [0.5, 2.0], 4-machine system with two para metric uncertainties Comparison of state space test and frequency sweep-4-machine system with two parametric uncertainties Linear search for a in [0.1, 2.0]-50-generator system one para metric uncertainty Comparison of state space test and frequency sweep-50-generator system with one parametric uncertainty. xii ACKNOWLEDGMENTS I would like to thank my co-major advisors, Dr. Mustafa Khammash and Dr. Vijay Vittal, for their invaluable guidance and continual support throughout this research project. They have shown me what true professorship is all about. I would also like to express my gratitude to graduate committee members, Drs. V. Ajjarapu, Wolfgang Kliemann, and James McCalley for their generous contributions of time and effort in the process of this research project. My thanks also go to Dr. M. Djukanovic for his helpful suggestions to my research. In addition, I am grateful to all the professors and graduate students in the electric power program at Iowa State University. They have made my stay here both productive and enjoyable. Finally, I wish to thank my wife, Mei, for her understanding, encouragement, and support, especially during times of difficulty.

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Applications of interval matrices in power system stabilizer design

Cited by 13 publications

References 5 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

Robustness analysis and controller design for static var compensators in power systems

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