Power System Transient Stability: Regions Using Popov's Method

Pai, M.A.; Mohan, M. Ananda; Rao, J. Gopala

doi:10.1109/tpas.1970.292635

Cited by 68 publications

(5 citation statements)

References 16 publications

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“…Lure theory and Popov criteria ( [118] and [119]) can provide conditions for stability analysis. According to Kalman [120], the state-space model of the system can be transferred to a reduced-order model as follows:…”

Section: B Popov-lurementioning

confidence: 99%

Large-Signal Stability Analysis of Inverter-Based AC Microgrids: A Critical and Analytical Review

Hosseinpour,

MansourLakouraj,

Benidris

et al. 2023

IEEE Access

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With the ever-increasing development of microgrids to improve power supply reliability and resilience, large-signal stability analysis of microgrids is needed to provide accurate insights into system dynamics during significant disturbances and to offer a robust and comprehensive assessment of microgrids' ability to return to normal operation after contingencies. This paper presents a comprehensive analytical and critical review of large-signal stability analysis methods for inverter-based AC microgrids supported by both theoretical analyses and numerical case studies. These analyses and case studies are developed and implemented to analyze, compare, and identify the gaps in existing large-signal stability assessment methods, which have not been investigated in the literature. More specifically, the recent developments in large-signal stability analysis techniques for microgrids, including Lyapunov-based methods and energy function analysis, are reviewed and discussed. Also, as the accuracy of the dynamic models of inverterbased resources (IBRs) is a crucial factor for authentic and accurate stability assessment, the impacts of full-, reduced-, and second-order dynamic models of IBRs on the accuracy of large-signal stability assessment in microgrids are numerically scrutinized. The study concludes by identifying the applicability of existing stability analysis methods for microgrids (e.g., Krasovskii's, Popov-Lure, and sum of squares (SOS)-based methods) and presenting their challenges for further investigation in the field of large-signal stability of microgrids using numerical case studies. This comparative assessment of large-signal stability assessment provides an informative analysis of the system's capability to operate under contingencies and helps to set the protection system efficiently and prevent unnecessary outages and trips. The numerical assessment shows that SOS-based stability assessment can provide a more realistic and less conservative stability region. It is worth mentioning that other approaches are computationally more efficient and can be applied for online applications and control objectives.INDEX TERMS Large-signal stability, microgrids, inverter-based DER, Lyapunov function, the domain of attraction, nonlinear dynamic model, sum of squares method, Popov-Lure, Krasovskii's method. I. INTRODUCTIONM ICROGRIDS are more vulnerable to becoming unstable due to faults and large disturbances than larger and interconnected power grids because microgrids are smallscale and localized power systems with low or no inertia distributed energy resources (DERs). Evaluating the robustness of microgrids in the face of significant disturbances, the process referred to as large-signal stability assessment, helps to understand the dynamic behavior of DERs, ensures stable operation during islanded mode and generation shortages, addresses nonlinearities and control interactions, and ensures transient and steady-state stability.The importance and distinction of large-signal stability analysis for microgrids can be...

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Section: B Popov-lurementioning

confidence: 99%

Large-Signal Stability Analysis of Inverter-Based AC Microgrids: A Critical and Analytical Review

Hosseinpour,

MansourLakouraj,

Benidris

et al. 2023

IEEE Access

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“…The inequality holds when q ≥ 2H/k, and we choose q = 2H/k + k 2 /4H 2 as indicated in [23]. Then we can use the q as a parameter to construct a Lyapunov function.…”

Section: Popov Stability Criterionmentioning

confidence: 99%

“…( ) G jw satisfying the Popov condition on the complex plane.Apply the Popov condition to the system whose state equation is shown as (6): H as indicated in[23].…”

mentioning

confidence: 99%

Lyapunov-Based Large Signal Stability Assessment for VSG Controlled Inverter-Interfaced Distributed Generators

Huang

Tai

et al. 2018

Energies

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Inverter-interfaced distributed generators (IIDGs) have been widely applied due to their control flexibility. The stability problems of IIDGs under large signal disturbances, such as large load variations and feeder faults, will cause serious impacts on the system. The virtual synchronous generator (VSG) control is an effective scheme for IIDGs to increase transient stability. However, the existing linearized stability models of IIDGs are limited to small disturbances. Hence, this paper proposes a Lyapunov approach based on non-linearized models to assess the large signal stability of VSG-IIDG. The electrostatic machine model is introduced to establish the equivalent nonlinear model. On the basis of Popov’s theory, a Lyapunov function is derived to calculate the transient stability domain. The stability mechanism is revealed by depicting the stability domain using the locus of the angle and the angular frequency. Large signal stability of the VSG-IIDG is quantified according to the boundary of the stability domain. Effects and sensitivity analysis of the key parameters including the cable impedance, the load power, and the virtual inertia on the stability of the VSG-IIDG are also presented. The simulations are performed in PSCAD/EMTDC and the results demonstrate the proposed large signal stability assessment method.

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“…Several texts are now available in nonlinear control theory (37,41,46,69,71,80,102). As a result of these developments Lyapunov's methods, Popov's method and Zubov's method have been applied to power system stability studies (31,43,69,76,95,120,126,130,131,139,143).…”

Section: G Methods Of Analysismentioning

confidence: 99%

Effects of system nonlinearities on synchronous machine control

Oyetunji

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Power System Transient Stability: Regions Using Popov's Method

Cited by 68 publications

References 16 publications

Large-Signal Stability Analysis of Inverter-Based AC Microgrids: A Critical and Analytical Review

Large-Signal Stability Analysis of Inverter-Based AC Microgrids: A Critical and Analytical Review

Lyapunov-Based Large Signal Stability Assessment for VSG Controlled Inverter-Interfaced Distributed Generators

Effects of system nonlinearities on synchronous machine control

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