Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses, and voltage dynamics

Böttcher, Philipp; Witthaut, Dirk; Gorjão, Leonardo Rydin

doi:10.1063/5.0082712

Cited by 5 publications

(3 citation statements)

References 57 publications

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“…In particular, the recent linear stability analysis of the extended swing equations proposed in ref. 60 . show that the conditions for the local stability of a synchronous state in lossy systems are very similar to those for lossless systems.…”

Section: Resultsmentioning

confidence: 99%

Multistability and anomalies in oscillator models of lossy power grids

2022

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The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the winding partition of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system’s transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows.

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Section: Resultsmentioning

confidence: 99%

Multistability and anomalies in oscillator models of lossy power grids

2022

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“…A synchronous machine j, a generator or a load, is described by its rotor-angle θ j (t) and its angular frequency ω j (t) = θi (t). It obeys the equations of motion [17,[38][39][40]]…”

Section: The Swing Equationmentioning

confidence: 99%

The stochastic nature of power-grid frequency in South Africa

Gorjão

Maritz²

2023

J. Phys. Complex.

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In this work, we explore two mechanisms that explain non-Gaussian behaviour of power-grid frequency recordings in the South African grid. We make use of a Fokker–Planck approach to power-grid frequency that yields a direct relation between common model parameters such as inertia, damping, and noise amplitude and non-parametric estimations of the same directly from power-grid frequency recordings. We propose two explanations for the non-Gaussian leptokurtic distributions in South Africa: The first based on multiplicative noise in power-grid frequency recordings, which we observe in South Africa; The second based on the well-known scheduled and unscheduled load shedding and rolling blackouts that beset South Africa. For the first we derive an analytic expression of the effects of multiplicative noise that permits the estimation of all statistical moments – and discuss drawbacks in comparison with the data; For the second we employ a simple numerical analysis with a modular power grid of South Africa. Both options help understand the statistics of power-grid frequency in South Africa – particularly the presence of heavy tails.

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“…[20], [21], and Ref. [22] dealing with synchronous machines, by providing a discussion of the interplay of frequency, voltage dynamics, the power-grid topology, and their impact on the stability of the full system. Additionally, we make use of these criteria to derive a set of necessary and sufficient conditions for the linear stability of power grids with an arbitrary topology.…”

Section: Introductionmentioning

confidence: 99%

Stability Bounds of Droop-Controlled Inverters in Power Grid Networks

Böttcher,

Gorjão,

Witthaut

2023

IEEE Access

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The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state of the electric power system, inverters are power electronic hardware and need to be programmed to react to the state of the system. Choosing an appropriate control scheme and the corresponding parameters is necessary to guarantee that the system operates safely. A prominent control scheme for inverters is droop control, which mimics the response of conventional generation. In this work, we investigate the stability of coupled systems of droop-controlled inverters in arbitrary network topologies. Employing linear stability analysis, we derive effective local stability criteria that consider both the overall network topology as well as its interplay with the inverters' intrinsic parameters. First, we explore the stability of an inverter coupled to an infinite grid in an analytic fashion and uncover stability and instability regions. Secondly, we extend the analysis to a generic topology of inverters and provide mathematical criteria for stability and instability of the system. Last, we showcase the usefulness of the criteria by examining two model systems using numerical simulations. The developed criteria show which parameters might lead to an unstable operating state.

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Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses, and voltage dynamics

Cited by 5 publications

References 57 publications

Multistability and anomalies in oscillator models of lossy power grids

Multistability and anomalies in oscillator models of lossy power grids

The stochastic nature of power-grid frequency in South Africa

Stability Bounds of Droop-Controlled Inverters in Power Grid Networks

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