Performance Limitations of Distributed Integral Control in Power Networks Under Noisy Measurements

Flamme, Hendrik; Tegling, Emma

doi:10.23919/acc.2018.8431122

Cited by 7 publications

(8 citation statements)

References 24 publications

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“…See e.g. [26], [27] for details. We note that our theory allows for q neighbor connections in each lattice direction, making such embedding arguments less restrictive than they may seem.…”

Section: A Non-regular Networkmentioning

confidence: 99%

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

Tegling

Mitra

Bamieh

2019

IEEE Trans. Automat. Contr.

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We study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a 1-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20-200 vehicles we show that the performance limitations we derive manifest as unwanted accordion-like motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.

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“…See e.g. [26], [27] for details. We note that our theory allows for q neighbor connections in each lattice direction, making such embedding arguments less restrictive than they may seem.…”

Section: A Non-regular Networkmentioning

confidence: 99%

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

Tegling

Mitra

Bamieh

2019

IEEE Trans. Automat. Contr.

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“…Stability analyses for nonlinear dynamic models can be found in [100]- [103], with communication network design and delay issues treated in [104], [105], and higher-order dynamic models in [106], [107]; see [108], [109] for further microgrid applications. Tuning and fundamental performance limitations have been examined in [110]- [113]. Stability proofs for distributed controller have been restricted to the case of quadratic cost functions J i ; a more general stability proof, e.g., for strictly convex J i , remains an open problem.…”

Section: Distributed Averaging Integral Controlmentioning

confidence: 99%

Distributed Control and Optimization for Autonomous Power Grids

Dörfler

Bolognani

Simpson-Porco

et al. 2019

2019 18th European Control Conference (ECC)

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“…The systems considered in this paper all have H 2 norm densities that can be written as in (16) with r ∈ {0, 2, 4}. To show this, the following Lemma is needed: Lemma 4.…”

Section: Bounds On Asymptotic Scalingsmentioning

confidence: 99%

Noise-induced limitations to the scalability of distributed integral control

Tegling

2019

Systems & Control Letters

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We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H 2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise's impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this may in practice imply that very large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.

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Performance Limitations of Distributed Integral Control in Power Networks Under Noisy Measurements

Cited by 7 publications

References 24 publications

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

Distributed Control and Optimization for Autonomous Power Grids

Noise-induced limitations to the scalability of distributed integral control

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