10,440 research outputs found
A Framework for Robust Assessment of Power Grid Stability and Resiliency
Security assessment of large-scale, strongly nonlinear power grids containing
thousands to millions of interacting components is a computationally expensive
task. Targeting at reducing the computational cost, this paper introduces a
framework for constructing a robust assessment toolbox that can provide
mathematically rigorous certificates for the grids' stability in the presence
of variations in power injections, and for the grids' ability to withstand a
bunch sources of faults. By this toolbox we can "off-line" screen a wide range
of contingencies or power injection profiles, without reassessing the system
stability on a regular basis. In particular, we formulate and solve two novel
robust stability and resiliency assessment problems of power grids subject to
the uncertainty in equilibrium points and uncertainty in fault-on dynamics.
Furthermore, we bring in the quadratic Lyapunov functions approach to transient
stability assessment, offering real-time construction of stability/resiliency
certificates and real-time stability assessment. The effectiveness of the
proposed techniques is numerically illustrated on a number of IEEE test cases
Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 101102 (2018) and may be found at https://doi.org/10.1063/1.5054850.In view of highly decentralized and diversified power generation concepts, in particular with renewable energies, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model with inertia. The usual formulation in the form of a system of coupled ordinary differential equations is not always adequate. We present a new energy-based formulation of the Kuramoto model with inertia as a polynomial port-Hamiltonian system of differential-algebraic equations, with a quadratic Hamiltonian function including a generalized order parameter. This leads to a robust representation of the system with respect to disturbances: it encodes the underlying physics, such as the dissipation inequality or the deviation from synchronicity, directly in the structure of the equations, and it explicitly displays all possible constraints and allows for robust simulation methods. The model is immersed into a system of model hierarchies that will be helpful for applying adaptive simulations in future works. We illustrate the advantages of the modified modeling approach with analytics and numerical results.
To reach the goal of temperature reduction to limit the climate change, as stipulated at the Paris Conference in 2015, it is necessary to integrate renewable energy sources into the existing power networks. Wind and solar power are the most promising ones, but the integration into the electric power grid remains an enormous challenge due to their variability that requires storage facilities, back-up plants, and accurate control processing. The current approach to describe the dynamics of power grids in terms of simplified nonlinear models, like the Kuramoto model with inertia, may not be appropriate when different control and optimization tasks are needed to be addressed. Under this aspect, we present a new energy-based formulation of the Kuramoto model with inertia that allows for an easy extension if further effects have to be included and higher fidelity is required for qualitative analysis. We illustrate the new modeling approach with analytic results and numerical simulations carried out for a semi-realistic model of the Italian grid and indicate how this approach can be generalized to models of finer granularity.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Second-order mixed-moment model with differentiable ansatz function in slab geometry
We study differentiable mixed-moment models (full zeroth and first moment,
half higher moments) for a Fokker-Planck equation in one space dimension.
Mixed-moment minimum-entropy models are known to overcome the zero net-flux
problem of full-moment minimum entropy models. Realizability theory for
these modification of mixed moments is derived for second order. Numerical
tests are performed with a kinetic first-order finite volume scheme and
compared with , classical and a reference scheme.Comment: arXiv admin note: text overlap with arXiv:1611.01314,
arXiv:1511.0271
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