Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization

Cherukuri, Ashish; Mallada, Enrique; Cortés, Jorge

doi:10.1137/1.9781611974072.40

“…We refer the reader to [41] for a detailed treatment that formalizes its application for primal-dual systems. The former issue is solved in Theorem 10 which makes use of the following additional lemma whose proof can be found in the Appendix.…”

Section: Optimality and Convergencementioning

confidence: 99%

Optimal Load-Side Control for Frequency Regulation in Smart Grids

Mallada

¹

,

Zhao

²

,

Low

³

2017

IEEE Trans. Automat. Contr.

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Frequency control rebalances supply and demand while maintaining the network state within operational margins.It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints.In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. In particular, our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike the currently implemented frequency control), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. We illustrate its effectiveness through simulations.

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“…We solve the latter issue using an invariance principle for Caratheodory systems [40]. We refer the reader to [41] for a detailed treatment that formalizes its application for primal-dual systems. The former issue is solved in Theorem 10 which makes use of the following additional lemma whose proof can be found in the Appendix.…”

Section: Optimality and Convergencementioning

confidence: 99%

Optimal load-side control for frequency regulation in smart grids

Mallada

¹

,

Zhao

²

,

Low

³

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

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Frequency control rebalances supply and demand while maintaining the network state within operational margins.It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints.In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. In particular, our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike the currently implemented frequency control), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. We illustrate its effectiveness through simulations.

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“…The underlying premise of such autonomous (or feedback-based) optimization schemes as illustrated in Fig. 1 is that a nonlinear feedback controller induces closed-loop dynamics, usually in the form of simple gradient-or saddle-point flows [11], that steer a steady-state physical system to an optimal state.…”

Section: Introductionmentioning

confidence: 99%

Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems

Hauswirth

¹

,

Subotić

²

,

Bolognani

³

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion of projected dynamical systems to time-varying, possibly non-regular, domains and derive conditions for the existence of so-called Krasovskii solutions. The key insight is that for trajectories to exist, informally, the time-varying domain can only contract at a bounded rate whereas it may expand discontinuously. This condition is met, in particular, by feasible sets delimited via piecewise differentiable functions under appropriate constraint qualifications. To illustrate the necessity and usefulness of such a general framework, we consider a simple yet insightful power system example, and we discuss the implications of the proposed conditions for the design of feedback optimization schemes.Index Terms-Non-smooth analysis, nonlinear dynamical systems, power systems. arXiv:1809.07288v2 [math.OC]

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Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization

Cited by 7 publications

References 20 publications

Optimal Load-Side Control for Frequency Regulation in Smart Grids

Optimal Load-Side Control for Frequency Regulation in Smart Grids

Optimal load-side control for frequency regulation in smart grids

Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems

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