Stability of power grids: An overview

Gajduk, Andrej; Todorovski, Mirko; Kocarev, Ljupčo

doi:10.1140/epjst/e2014-02212-1

Cited by 53 publications

(28 citation statements)

References 44 publications

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“…If the relevant admittance matrix has zero real components, the problem can be tackled by energy function-based approaches [24], which can also be used in combination with bi-stable representation of transmission lines for the modeling of the dynamics of cascading failure propagation in power grids [39]. Other approaches include estimating the region of attraction of a synchronous state [40], quantifying the size of the region using a recently proposed measure called the basin stability [41], and analyzing nonlinear modes using Koopman operators [42,43]. Such analyses of synchronization stability against small and large perturbations may help develop strategies for improving the existing power grids by elucidating the relation between network structure and stability, which we have recently demonstrated to be highly non-intuitive in general models of coupled oscillator networks [44].…”

Section: Discussionmentioning

confidence: 99%

Comparative analysis of existing models for power-grid synchronization

2015

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The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks-a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations (available at https://sourceforge.net/projects/pg-sync-models).

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Section: Discussionmentioning

confidence: 99%

Comparative analysis of existing models for power-grid synchronization

2015

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“…from radial basis functions [7] or sum of squares decomposition (see e.g. [6] for a comparison of different methods). From an analytic perspective, the method of nonequlibrium potentials [9,10] determines a special case of Lyapunov functions, namely potentials.…”

Section: Introductionmentioning

confidence: 99%

Potentials and limits to basin stability estimation

Schultz¹,

Menck²,

Heitzig³

et al. 2017

New J. Phys.

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Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. Their application requires numerical estimation via Monte Carlo sampling and integration of differential equations. Here, we analyse the applicability of basin stability to systems with basin geometries that are challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.

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“…See, e.g., several recent papers [7, 8]. (5) Last but not least, for more complicated cases, such as more detailed models for synchronous generator considering damping windings, the interaction of multiple synchronous generators [42–48], different types of stability in power systems including rotor angle stability [49] and voltage stability [50–51], and interplay with delayed power price [52] so on, further theoretic analysis methods have to be developed. It is of interest to study these problems from nonlinear dynamics point of view in the future.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect

Sun

Yuan

et al. 2016

PLoS ONE

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Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

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Stability of power grids: An overview

Cited by 53 publications

References 44 publications

Comparative analysis of existing models for power-grid synchronization

Comparative analysis of existing models for power-grid synchronization

Potentials and limits to basin stability estimation

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect

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