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Proceedings Article•DOI•

A study of the SMIB power system model with delayed feedback

Arindam B. Chowdhury1, Anil Kulhare1, Gaurav Raina1•
Indian Institute of Technology Madras1
01 Dec 2011-pp 1-6
TL;DR: In this article, the authors focus on the impact that time delayed feedback can have on the stability and performance of a traditional power system model and construct appropriate stability charts and bifurcation diagrams, which serve to exhibit the impact time delays may have on stability.
Abstract: Our focus is on the impact that time delayed feedback can have on the stability and performance of a traditional power system model. Stability analysis has played an important role in power system models, however most of the models assume that any feedback is instantaneous. For example, in wide area measurement systems (WAMS) it would be important and realistic to incorporate time delays. Our focus will be on the impact time delayed feedback may have on the stability and performance of the single machine infinite bus (SMIB) power system model. For this model, we construct appropriate stability charts and bifurcation diagrams, which serve to exhibit the impact time delays may have on stability and performance. Our work is step towards a more systematic understanding of delayed feedback in power system models.
Citations
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Journal Article•DOI•
Bifurcation behavior and coexisting motions in a time-delayed power system

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Mei-Ling Ma, Fu-Hong Min
01 Mar 2015-Chinese Physics B
TL;DR: In this article, the coexisting phenomenon in a fourth-order time-delayed power system was investigated for the first time with different initial conditions, including mechanical power, generator damping factor, exciter gain, and time delay varying.
Abstract: With the increase of system scale, time delays have become unavoidable in nonlinear power systems, which add the complexity of system dynamics and induce chaotic oscillation and even voltage collapse events. In this paper, coexisting phenomenon in a fourth-order time-delayed power system is investigated for the first time with different initial conditions. With the mechanical power, generator damping factor, exciter gain, and time delay varying, the specific characteristic of the time-delayed system, including a discontinuous "jump" bifurcation behavior is analyzed by bifurcation diagrams, phase portraits, Poincare maps, and power spectrums. Moreover, the coexistence of two different periodic orbits and chaotic attractors with periodic orbits are observed in the power system, respectively. The production condition and existent domain of the coexistence phenomenon are helpful to avoid undesirable behavior in time-delayed power systems.

17 citations

Journal Article•DOI•
Robust H∞ control of time delayed power systems

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Mohammed Jamal Alden1, Xin Wang1•
Southern Illinois University Edwardsville1
27 Jan 2015-Systems Science & Control Engineering
TL;DR: In this article, a stable, robust and efficient controller for a power-generation system with time delays, model uncertainties and disturbances based on the practical dynamics of generator, prime mover, exciter and automatic voltage regulator is proposed.
Abstract: Power system is the backbone of our society The purpose of this work is to design a stable, robust and efficient controller for a power-generation system with time delays, model uncertainties and disturbances Based on the practical dynamics of generator, prime mover, exciter and automatic voltage regulator, a mathematical power-generation system model is developed with state space dynamical equations involving time delays in the feedback A novel robust control framework based on linear matrix inequalities is proposed in the paper, which controls the energy system effectively Computer simulations are used to show the efficacy of the proposed control algorithm

13 citations

Cites background from "A study of the SMIB power system mo..."

  • ...Chowdhury, Kulhare, and Raina (2011) present the nonlinear limit cycle effect of time delays on local stability of the single machine infinite bus system....

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Proceedings Article•DOI•
Effect of delayed coupling in power system dynamics

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Sindhura Rose Thomas1, Usha Nair1, Bindu M. Krishna1•
Cochin University of Science and Technology1
01 Mar 2018
TL;DR: Numerical Simulations are used to investigate the effect of time delay and different coupling forms on the synchronisation dynamics of coupled SMIB systems.
Abstract: As the power systems exhibit chaotic behavior chaotic synchronisation and antisynchronisation between such systems can be made useful in achieving synchronisation and avoiding undesirable phenomenon like power blackout respectively. However significant transmission times and associated other inherent delays of individual systems have a significant effect on the dynamics of coupled power systems. It is necessary to analyse the effect of time delay in coupling on both synchronisation and anti synchronisation characteristics in power systems. Numerical Simulations are used to investigate the effect of time delay and different coupling forms on the synchronisation dynamics of coupled SMIB systems

Cites background from "A study of the SMIB power system mo..."

  • ...Also the impact of time delay on stability properties is studied [14]....

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References
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Book•
Nonlinear dynamics and Chaos

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Steven H. Strogatz
01 Jan 1994
TL;DR: The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.
Abstract: We explore several basic aspects of chaos, chaotic systems, and non-linear dynamics through three different setups. The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter. We consider maps of its phase space, and the progression through period-doubling bifurcations to the onset of chaos. The Feigenbaum ratio of successive bifurcation periods is estimated at 4.674, in good agreement with the accepted value. The Liapunov exponent, governing the exponential growth of small perturbations in chaotic systems, is calculated and its fractal structure compared to the corresponding bifurcation diagram for the logistic map. Using a non-linear p-n junction circuit we analyze the return maps and power spectrums of the resulting time series at various types of system behavior. Similarly, an electronic analog to a ball bouncing on a vertically driven table provides insight into real-world applications of chaotic motion. For both systems we calculate the fractal information dimension and compare with theoretical behavior for dissipative versus Hamiltonian systems. Subject headings: non-linear dynamics; non-linear dynamical systems; fractal dimension; chaos; strange attractors; logistic map

5,372 citations

"A study of the SMIB power system mo..." refers background in this paper

  • ...The loss of stability is often characterized by bifurcation phenomena which may lead to the existence of limit cycles or other sophisticated nonlinear dynamics [7]....

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Book•
Power System Engineering

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I.J. Nagrath
01 Jan 2007

181 citations

Additional excerpts

  • ...THE SMIB POWER SYSTEM MODEL WITH DELAY The equations of the SMIB power system model, as obtained from [1], [5] and [6], are described as follows: Σ : δ̇ = ωBω, Mω̇ = −Dω + (PM − PG), Td0Ė = −E − (xd − xd1)Id + Efdx, TA ̇ Efd = −KA(V − Vref )− (Efd − Efd0)....

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Journal Article•DOI•
A new nonlinear voltage controller for power systems

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Chunlei Zhu1, Rujing Zhou1, Youyi Wang1•
Nanyang Technological University1
01 Jan 1997-International Journal of Electrical Power & Energy Systems
TL;DR: In this paper, a new nonlinear voltage controller is proposed, which involves the direct feedback linearization (DFL) technique and robust control theory, and the performance of the proposed nonlinear controller in a single machine-infinite bus power system is simulated.

89 citations

Additional excerpts

  • ...THE SMIB POWER SYSTEM MODEL WITH DELAY The equations of the SMIB power system model, as obtained from [1], [5] and [6], are described as follows: Σ : δ̇ = ωBω, Mω̇ = −Dω + (PM − PG), Td0Ė = −E − (xd − xd1)Id + Efdx, TA ̇ Efd = −KA(V − Vref )− (Efd − Efd0)....

    [...]

Journal Article•DOI•
Power system small signal stability region with time delay

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Hongjie Jia1, Xiaodan Yu1, Yixin Yu1, Chengshan Wang1•
Tianjin University1
01 Jan 2008-International Journal of Electrical Power & Energy Systems
TL;DR: In this paper, the influence of time delay on power system small signal stability region is deeply investigated and an optimal-based algorithm is given to trace boundaries of the stability region with considering the time delay.

72 citations

"A study of the SMIB power system mo..." refers background in this paper

  • ...(9) Putting the value of the constants and then simplifying the set of equations (6)-(9) following the steps given in [5], lead us to a new set of equations that gives the value of the states at fixed points ω = 0, (10) E fd = 5 3 E − 2 3 cos(δ), (11) E sin(δ) = 0....

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  • ...THE SMIB POWER SYSTEM MODEL WITH DELAY The equations of the SMIB power system model, as obtained from [1], [5] and [6], are described as follows: Σ : δ̇ = ωBω, Mω̇ = −Dω + (PM − PG), Td0Ė = −E − (xd − xd1)Id + Efdx, TA ̇ Efd = −KA(V − Vref )− (Efd − Efd0)....

    [...]

  • ...The effect of time delays has only recently started to get attention; for example, see [5] which motivates the introduction of time delays in the SMIB and some other power system models....

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Journal Article•DOI•
Hard-limit induced chaos in a fundamental power system model

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W. Ji1, Vaithianathan Venkatasubramanian1•
Washington State University1
01 Jun 1996-International Journal of Electrical Power & Energy Systems
TL;DR: In this paper, the authors investigated complex nonlinear phenomena in a fundamental power system model represented in a single-machine infinite-bus formulation, where the generator electro-magnetics, electromechanics and its excitation control are modelled together by fourth-order differential equations.

70 citations

"A study of the SMIB power system mo..." refers background in this paper

  • ...The effect of excitation limits on the model has been studied in [2]....

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  • ...In previous papers, stability and bifurcation properties of the SMIB model without time delays have been conducted [2]....

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