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DDC: 510 × Type: article × Subject: Stability ×

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Now showing 1 - 3 of 3
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    How Price-Based Frequency Regulation Impacts Stability in Power Grids: A Complex Network Perspective
    (London : Hindawi, 2020) Ji, Peng; Zhu, Lipeng; Lu, Chao; Lin, Wei; Kurths, Jürgen
    With the deregulation of modern power grids, electricity markets are playing a more and more important role in power grid operation and control. However, it is still questionable how the real-time electricity price-based operation affects power grid stability. From a complex network perspective, here we investigate the dynamical interactions between price-based frequency regulations and physical networks, which results in an interesting finding that a local minimum of network stability occurs when the response strength of generators/consumers to the varying price increases. A case study of the real world-based China Southern Power Grid demonstrates the finding and exhibits a feasible approach to network stability enhancement in smart grids. This also provides guidance for potential upgrade and expansion of the current power grids in a cleaner and safer way. © 2020 Peng Ji et al.
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    The invariant distribution of wealth and employment status in a small open economy with precautionary savings
    (Amsterdam : North-Holland, 2019) Bayer, Christian; Rendall, Alan D.; Wälde, Klaus
    We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c). © 2019 The Author(s)
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    Stability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion
    (Basel : MDPI, 2021) Erhardt, André H.
    We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values.