Coherent Swing Instability of Power Grids

Susuki, Yoshihiko; Mezić, Igor; Hikihara, Takashi

doi:10.1007/s00332-010-9087-5

Cited by 88 publications

(87 citation statements)

References 44 publications

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“…Much of our current understanding about this process has been derived from quasi-steady-state cascade models [16][17][18][19][20][21], which use iterative procedures to model the successive inactivation of network components caused by power flow redistributions, while omitting the transient dynamics between steady states as well as the dynamics of the generators. Further understanding has resulted from stability studies focused on the synchronization dynamics of power generators in the absence of flow redistributions [22][23][24][25][26].…”

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confidence: 99%

Cascading Failures as Continuous Phase-Space Transitions

Yang¹,

Motter²

2017

Phys. Rev. Lett.

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In network systems, a local perturbation can amplify as it propagates, potentially leading to a largescale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steadystate cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.Cascading processes underlie a myriad of network phenomena [1], including blackouts in power systems [2,3], secondary extinctions in ecosystems [4,5], and complex contagion in financial networks [6,7]. In all such cases, an otherwise small perturbation may propagate and eventually cause a sizable portion of the system to fail. Various system-independent cascade models have been proposed [8][9][10][11][12][13] and used to draw general conclusions, such as on the impact of interdependencies [14] and countermeasures [15]. There are outstanding questions, however, for which it is necessary to model the cascade dynamics starting from the actual dynamical state of the system.In power-grid networks, the state of the system is determined by the power flow over transmission lines and the frequency of the power generators, which must be respectively below capacity and synchronized under normal steady-state conditions. Although a local perturbation has a limited impact on the connectivity of the network, it may trigger a cascade of failures and protective responses that switch off grid components and may also lead generators to lose synchrony. Much of our current understanding about this process has been derived from quasi-steady-state cascade models [16][17][18][19][20][21], which use iterative procedures to model the successive inactivation of network components caused by power flow redistributions, while omitting the transient dynamics between steady states as well as the dynamics of the generators. Further understanding has resulted from stability studies focused on the synchronization dynamics of power generators in the absence of flow redistributions [22][23][24][25][26].Yet, to date no theoretical approach has been developed to incorporate at the same time these two fundamental aspects of power-grid dynamics-frequency change and flow ...

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confidence: 99%

Cascading Failures as Continuous Phase-Space Transitions

Yang¹,

Motter²

2017

Phys. Rev. Lett.

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“…A mechanism of the swing instability was recently reported in [10] for multi-machine power grids. Traditionally, three oscillatory modes have been used to explain the instability: local plant mode oscillations, inter-area mode instabilities, and multi-swing instabilities [1,3,[11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 83%

“…3. It should be noted that the CSI involves the loss of stability of inter-area oscillations [10], and hence the two primary modes of the instabilities-interarea and local oscillations-in power grid studies are addressed in this paper. Other modes of the instabilities, e.g.…”

Section: Definitionmentioning

confidence: 99%

“…Traditionally, three oscillatory modes have been used to explain the instability: local plant mode oscillations, inter-area mode instabilities, and multi-swing instabilities [1,3,[11][12][13][14][15][16][17][18]. In [10] the authors revealed how the three different mode oscillations interacted to destabilize a power grid and showed that the so-called collective mode of the grid was destabilized due to a perturbation from oscillatory modes with finite amplitudes determined by the grid's topology. The instability mechanism is named as the coherent swing instability (CSI).…”

Section: Introductionmentioning

confidence: 99%

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Decomposition of energy function and hierarchical diagnosis of power grid swing instabilities

Kojima

Susuki

Tsumura

et al. 2016

NOLTA

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This paper considers an electric power grid with multiple synchronous machines exhibiting coupled swing dynamics and aims at developing a hierarchical diagnosis of loss of transient stability of the machines, which we term as swing instabilities. We introduce a standard energy function for the power grid and decompose it into individual energy functions of a collective system of the grid, of the motions relative to the collective system, and of the infinite bus. This decomposition enables us to extract distinctive behaviors embedded in the swing instabilities in terms of energy. We numerically apply the individual energy functions in the proposed decomposition to analysis of swing instabilities in the IEEE New England 39-bus test system. We then propose a hierarchical diagnosis of the swing instabilities based on the decomposition and discuss its validity by approximating the individual energy functions along solutions representing the grid's instabilities.

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“…The data used in the study is given in Table 1, all the values are given in per-unit system. The values used in the current study are adapted from the study of Susuki et al [33] with the addition of damping to ensure the steady state stability of the power grid. Also, the number of generators in the study of Susuki et al are only 20 and the focus of their study is to demonstrate the coherent swing instabilities.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Reduced order modeling for transient simulation of power systems using trajectory piece-wise linear approximation

Malik

Borzacchiello

Chinesta

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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This paper concerns the application of reduced order modeling techniques to power grid simulation. Swing dynamics is a complex non-linear phenomenon due to which model order reduction of these problems is intricate. A multi point linearization based model reduction technique trajectory piece-wise linearization (TPWL) method is adopted to address the problem of approximating the nonlinear term in swing models. The method combines proper orthogonal decomposition with TPWL in order to build a suitable reduced order model that can accurately predict the swing dynamics. The method consists of two stages, an offline stage where model reduction and selection of linearization points is performed and an online stage where the reduced order multi-point linear simulation is performed. An improvement of the strategy for point selection is also proposed. The TPWL method for a swing dynamics model shows that the method provides accurate reduced order models for non-linear transient problems.

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Coherent Swing Instability of Power Grids

Cited by 88 publications

References 44 publications

Cascading Failures as Continuous Phase-Space Transitions

Cascading Failures as Continuous Phase-Space Transitions

Decomposition of energy function and hierarchical diagnosis of power grid swing instabilities

Reduced order modeling for transient simulation of power systems using trajectory piece-wise linear approximation

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