Characterization of power systems near their stability boundary using the sub-Gramian method

Yadykin, Igor B.; Kataev, Dmitry E.; Iskakov, Alexey B.; Shipilov, V.

doi:10.1016/j.conengprac.2015.09.014

Cited by 19 publications

(6 citation statements)

References 17 publications

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“…At the same time, it does not allow the detection of specific nonlinear effects that lead to a loss of stability. Although there were proposed some more developed theories to describe the effects of resonances in power systems (Yadykin et al, 2016;Vassilyev et al, 2017;Du et al, 2019), there is no generally accepted theory so far. Therefore, a novel theory and methods are urgently required to describe and estimate resonance effects observed in modern power systems.…”

Section: Resultsmentioning

confidence: 99%

Estimation of the resonance between forcing and weakly stable oscillations in power systems

Iskakov

Panasetsky

2019

EPJ Web Conf.

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Using a simple test example, this paper demonstrates that a weakly damped eigen-oscillation of an electric power system can lead to a loss of stability in the presence of its resonance with forcing oscillation. Such resonant interactions can risk the power system security, as confirmed by recent events in the Western American and Nordic power systems. Conventional eigenvalue analysis cannot detect the observed instability due to its non-linear nature. We show that the critical condition for the appearance of this type of instability can be the value of the perturbation energy accumulated in the system over time. To quantify the risk of stability loss, we examine the model of forcing oscillations and the resonance response of power system in a linear approximation and compare it with the simulation results for the two-area Kundur test system.

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Section: Resultsmentioning

confidence: 99%

Estimation of the resonance between forcing and weakly stable oscillations in power systems

Iskakov

Panasetsky

2019

EPJ Web Conf.

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“…Each eigen-part was denoted a sub-Gramian. These allow estimations of the interactions between eigenmodes and were applied to the stability analysis of power system in (Yadykin et al, 2016).…”

Section: Literature Reviewmentioning

confidence: 99%

“…It allows the identification of low-frequency oscillations dangerous for small-signal stability and the detection of the effect of energy accumulation in these oscillations. Unlike works on spectral decompositions of Lyapunov functions (Yadykin et al, 2014(Yadykin et al, , 2016Zubov et al, 2017), the proposed method allows the association of these decompositions with specific state variables and their application to problems of modal analysis. The idea of combining selective modal analysis and Lyapunov spectral expansions has been already mentioned in (Vassilyev et al, 2017).…”

Section: Main Contributionmentioning

confidence: 99%

Lyapunov modal analysis and participation factors with applications to small-signal stability of power systems

Iskakov¹,

Yadykin²

2019

Preprint

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When random disturbances are regularly introduced into a dynamical system over time, its small-signal stability is determined by the energy of perturbations accumulated in the system. To analyze this perturbation energy, this paper proposes a novel physically motivated Lyapunov modal analysis (LMA) framework, which combines selective modal analysis with the spectral decompositions of specially chosen Lyapunov functions. This approach allows the modal interactions in dynamical systems to be characterized and estimated in connection with specific state variables. Conventional participation factors characterize the relative contribution of the system modes and state variables to the evolution of states and modes, respectively. In contrast, the proposed Lyapunov participation factors characterize similar contributions to corresponding Lyapunov functions, which determine the integral energy associated with the states and modes on an infinite or finite time interval. This allows the estimation of modal interactions in terms of total energy produced by their mutual actions over time. Using a two-area four-machines power system, we demonstrate that LMA reliably identifies resonant modal interactions, merging of modes, and loss of stability, even for a linear model, and associates them with certain state variables. The Lyapunov participation factors corresponding to the selected part of the system spectrum can be calculated independently and serve as a basis for rapid real-time calculations of critical mode behaviors in large-scale dynamical systems.

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“…Recently, a faulttolerant emergency control was proposed to maintain power system stability (Pedersen et al, 2016). Moreover, Yadykin et al (2016) adopted a sub-Gramian method to analyse the stability of a power system stability near its stability boundaries. In addition, a wide-area damping controller was designed (Shen et al, 2017;Yao et al, 2014bYao et al, , 2015 for inter-area oscillation suppression.…”

Section: Introductionmentioning

confidence: 99%

Sliding-mode perturbation observer-based sliding-mode control design for stability enhancement of multi-machine power systems

Yang

Shu

et al. 2018

Transactions of the Institute of Measurement and Control

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This paper presents the design of a sliding-mode perturbation observer-based sliding-mode control for stability enhancement of multi-machine power systems. The combinatorial effect of nonlinearities, parameter uncertainties, unmodelled dynamics and time-varying external disturbances is aggregated into a perturbation, which is rapidly estimated by a sliding-mode state and perturbation observer and then fully compensated by a sliding-mode controller in real time. The attractiveness of the sliding surface is analysed theoretically in the context of the Lyapunov criterion. The proposed control does not require an accurate system model and only one state measurement is needed. In addition, an over-conservative control effort can be effectively avoided via perturbation compensation. Simulation results for a three-machine power system and the New England power system verify the effectiveness of the proposed approach.

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Characterization of power systems near their stability boundary using the sub-Gramian method

Cited by 19 publications

References 17 publications

Estimation of the resonance between forcing and weakly stable oscillations in power systems

Estimation of the resonance between forcing and weakly stable oscillations in power systems

Lyapunov modal analysis and participation factors with applications to small-signal stability of power systems

Sliding-mode perturbation observer-based sliding-mode control design for stability enhancement of multi-machine power systems

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