Markov jump linear system analysis of microgrid stability

Rasheduzzaman, Md.; Paul, Tamal; Kimball, Jonathan W.

doi:10.1109/acc.2014.6859040

Cited by 12 publications

(6 citation statements)

References 15 publications

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“…The corresponding stationary distribution are [1] = [3∕7 4∕7], [2] ] . Figure 4 shows the switching laws of deterministic switching and stochastic switching, the control law is based on Theorem 2, and the dwell time of deterministic switching satisfies 6 ≥ k p + 1 − k p ≥ 4.…”

Section: Numerical Examplementioning

confidence: 99%

“…Markov jump linear system (MJLS) is a class of stochastic switched systems with wide applications. They are often used to model the dynamics of systems with random faults, unpredictable events, structural changes, networked control systems, etc . In recent decades, a great deal of attention has been devoted toward the stability of stochastic systems, particular in the case that transition probabilities is unknown or uncertain .…”

Section: Introductionmentioning

confidence: 99%

“…They are often used to model the dynamics of systems with random faults, unpredictable events, structural changes, networked control systems, etc. [1][2][3][4][5][6][7] In recent decades, a great deal of attention has been devoted toward the stability of stochastic systems, particular in the case that transition probabilities is unknown or uncertain. 8,9 Several different notions of stability are defined, respectively, for stochastic systems, which are also applicable to MJLSs.…”

Section: Introductionmentioning

confidence: 99%

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Mean square stabilization of discrete‐time switching Markov jump linear systems

Song

et al. 2018

Optim Control Appl Methods

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Summary This paper considers a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper, the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions, ie, having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results.

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Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean square stabilization of discrete‐time switching Markov jump linear systems

Song

et al. 2018

Optim Control Appl Methods

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“…To be precise, in an AFTCS based on a MJLS, the normal and fault dynamic behaviors of the system are described by a set of differential (or difference) equations with a transition between them that is governed by a finite-state Markov chain which represents the random nature of faults [14,18,19,21]. Although MJLSs have been extensively studied from the theoretical [24][25][26][27][28][29][30][31][32][33][34][35][36] and practical [26,28] point of views, AFTCSs by MJLSs still need further investigations.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

2016

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This article investigates the stabilization and control problems for a general active fault-tolerant control system (AFTCS) in a stochastic framework. The novelty of the research lies in utilizing uncertain nonhomogeneous Markovian structures to take account for the imperfect fault detection and diagnosis (FDD) algorithms of the AFTCS. The underlying AFTCS is supposed to be modeled by two random processes of Markov type; one characterizing the system fault process and the other describing the FDD process. It is assumed that the FDD algorithm is imperfect and provides inaccurate Markovian parameters for the FDD process. Specifically, it provides uncertain transition rates (TRs); the TRs that lie in an interval without any particular structures. This framework is more consistent with realworld applications to accommodate different types of faults. It is more general than the previously developed AFTCSs because of eliminating the need for an accurate estimation of the fault process. To solve the stabilizability and the controller design problems of this AFTCS, the whole system is viewed as an uncertain nonhomogeneous Markovian jump linear system (NHMJLS) with time-varying and uncertain specifications. Based on the multiple and stochastic Lyapunov function for the NHMJLS, first a sufficient condition is obtained to analyze the system stabilizability and then, the controller gains are synthesized. Unlike the previous fault-tolerant controllers, the proposed robust controller only needs to access the FDD process, besides it is easily obtainable through the existing optimization techniques. It is successfully tested on a practical inverted pendulum controlled by a fault-prone DC motor.

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“…The reduced-order model would be useful to assess the system's stability [31]- [33]. The reduced-order models are also important for evaluating the feasible bounds on state jumps when the microgrid switches from grid-tied to islanded mode, the load perturbation events in an islanded system [34], or to study the Markov chain models [35].…”

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confidence: 99%

Reduced-Order Small-Signal Model of Microgrid Systems

Rasheduzzaman

Mueller

Kimball

2015

IEEE Trans. Sustain. Energy

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194

108

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The objective of this study was to develop a reducedorder small-signal model of a microgrid system capable of operating in both the grid-tied and the islanded conditions. The nonlinear equations of the proposed system were derived in the dq reference frame and then linearized around stable operating points to construct a small-signal model. The high-order state matrix was then reduced using the singular perturbation technique. The dynamic equations were divided into two groups based on the small-signal model parameters ε. The "slow" states, which dominated the system's dynamics, were preserved, whereas the "fast" states were eliminated.Step responses of the model were compared to the experimental results from a hardware test to assess their accuracy and similarity to the full-order system. The proposed reduced-order model was applied to a modified IEEE-37 bus gridtied microgrid system to evaluate system's dynamic response in grid-tied mode, islanded mode, and transition from grid-tied to islanded mode.

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Markov jump linear system analysis of microgrid stability

Cited by 12 publications

References 15 publications

Mean square stabilization of discrete‐time switching Markov jump linear systems

Mean square stabilization of discrete‐time switching Markov jump linear systems

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

Reduced-Order Small-Signal Model of Microgrid Systems

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