Solvability and stability of a power system DAE model

Groß, Tjorben; Trenn, Stephan; Wirsen, Andreas

doi:10.1016/j.sysconle.2016.08.003

Cited by 23 publications

(15 citation statements)

References 9 publications

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“…Further applications, especially the ones in the context of Leontief input-output systems, are being considered to understand interdependencies and resiliency of critical infrastructures. Another interesting application arises in the context of power systems, as the DAEs are particularly suitable for modeling such systems [14]. It remains to be seen whether the particular structure of these systems bring computational tractability in implementing the solutions proposed in this paper.…”

Section: Discussionmentioning

confidence: 99%

“…The matrices S i , T i in Proposition 2 transform the system (14) in the so-called quasi-Weierstraß form [6], [43]. In the context of switched DAEs with deterministic transitions, the transformations introduced in Proposition 2 have been used for stability analysis [25], and solving observability related problems [39].…”

Section: B the Linear Regular Casementioning

confidence: 99%

“…In addition, we allow the differential and algebraic constraints to change randomly with time, and this switching in system dynamics is governed by a finite state Markov chain, giving rise to piecewisedeterministic Markov DAEs. The switching can represent the structural changes in the system dynamics and constraints for several applications of interest, such as power systems [14].…”

Section: Introductionmentioning

confidence: 99%

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Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Tanwani¹,

Zhu²

2020

IEEE Trans. Automat. Contr.

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As a subclass of stochastic differential games with algebraic constraints, this article studies dynamic noncooperative games where the dynamics are described by Markov jump differential-algebraic equations (DAEs). Theoretical tools, which require computing the extended generator and deriving Hamilton-Jacobi-Bellman (HJB) equation for Markov jump DAEs, are developed. These fundamental results lead to pure feedback optimal strategies to compute the Nash equilibrium in noncooperative setting. In case of quadratic cost and linear dynamics, these strategies are obtained by solving coupled Riccatilike differential equations. Under an appropriate stabilizability assumption on system dynamics, these differential equations reduce to coupled algebraic Riccati equations when the cost functionals are considered over infinite-horizon. As a first casestudy, the application of our results is studied in the context of an economic system where different suppliers aim to maximize their profits subject to the market demands and fluctuations in operating conditions. The second case-study refers to the conventional problem of robust control for randomly switching linear DAEs, which can be formulated as a two-player zero sum game and is solved using the results developed in this paper.Index Terms-Noncooperative games; differential-algebraic dynamical systems; piecewise deterministic Markov processes; infinitesimal generators; generalized HJB equation; coupled Riccati equations; minimax robust control; Leontief input-output models.

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Section: Discussionmentioning

confidence: 99%

Section: B the Linear Regular Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Tanwani¹,

Zhu²

2020

IEEE Trans. Automat. Contr.

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“…We use a power grid model described in (Groß et al, 2016), which consists of p generators and q load buses. The i-th generator is modeled aṡ …”

Section: Topological Changes In Power Gridsmentioning

confidence: 99%

“…In (Groß et al, 2016) it was shown that the overall DAE is regular if, and only if, each connected component of the network graph contains at least one generator bus, hence we can apply Theorem 5 to check whether there are possibly-indiscernible topological changes. Note that similar to the Wheatstone bridge example the DAEs corresponding the load buses are not regular.…”

Section: Topological Changes In Power Gridsmentioning

confidence: 99%

Indiscernible topological variations in DAE networks with applications to power grids

et al. 2017

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The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs.

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Nonlinear decentralized load frequency control of multi‐machine power systems with exponential stability and low L₂ gain against load disturbance

Wang

Liu

2020

Asian Journal of Control

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This paper proposes a novel nonlinear decentralized control method for a class of multi-machine power systems. The aim is to construct a suitable decentralized feedback control law so as to guarantee that the large-scale interconnected power system is exponentially stable and robust against load fluctuations. To this end, we propose a novel design algorithm based on the backstepping, which involves five steps and actively utilizes the locally measurable part of the tie-line power to improve the performance. The effectiveness of the proposed control scheme is demonstrated through extensive simulation studies.

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Solvability and stability of a power system DAE model

Cited by 23 publications

References 9 publications

Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Indiscernible topological variations in DAE networks with applications to power grids

Nonlinear decentralized load frequency control of multi‐machine power systems with exponential stability and low L₂ gain against load disturbance

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Solvability and stability of a power system DAE model

Cited by 23 publications

References 9 publications

Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Feedback Nash Equilibrium for Randomly Switching Differential–Algebraic Games

Indiscernible topological variations in DAE networks with applications to power grids

Nonlinear decentralized load frequency control of multi‐machine power systems with exponential stability and low L2 gain against load disturbance

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Nonlinear decentralized load frequency control of multi‐machine power systems with exponential stability and low L₂ gain against load disturbance