Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia

Paganini, Fernando; Mallada, Enrique

doi:10.1109/allerton.2017.8262755

Cited by 35 publications

(78 citation statements)

References 24 publications

(44 reference statements)

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“…The RoCoF is often measured for the frequency averaged over the whole network. 10 As pointed out at the end of Sec. I, the global RoCoF is of no use in the case of a line contingency, because the total power exchanged always vanishes.…”

Section: The Rocofmentioning

confidence: 80%

“…8,9 Standard measures of the impact of a disturbance commonly used by electrical engineers as decision variables can be formulated in terms of L ∞ -norms. 10 The maximal frequency deviation (Nadir) and the maximal RoCoF are respectively the L ∞ -norm of the frequency deviation and of the time derivative of the frequency.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we evaluate the impact of a disturbance by the RoCoF following it. Instead of measuring the global RoCoF, i.e., the maximal derivative of the mean frequency of the network, 10 we are interested in the local RoCoF, which we define as the maximal derivative of the frequency at any bus. This choice is motivated by two reasons.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

Delabays

Tyloo

Jacquod

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In modern electric power networks with fast evolving operational conditions, assessing the impact of contingencies is becoming more and more crucial. Contingencies of interest can be roughly classified into nodal power disturbances and line faults. Despite their higher relevance, line contingencies have been significantly less investigated analytically than nodal disturbances. The main reason for this is that nodal power disturbances are additive perturbations, while line contingencies are multiplicative perturbations, which modify the interaction graph of the network. They are therefore significantly more challenging to tackle analytically. Here, we assess the direct impact of a line loss by means of the maximal Rate of Change of Frequency (RoCoF) incurred by the system. We show that the RoCoF depends on the initial power flow on the removed line and on the inertia of the bus where it is measured. We further derive analytical expressions for the expectation and variance of the maximal RoCoF, in terms of the expectations and variances of the power profile in the case of power systems with power uncertainties. This gives analytical tools to identify the most critical lines in an electric power grid.Electrical networks can be subjected to many types of disturbances, such as small to medium fluctuations of the power injections and consumptions due to intermittent energy sources, larger power disturbances such as power plant outages, or the breakdown of an electrical line. There are various measures of the impact of such disturbances. For instance, one may consider the time the system requires to settle back to a synchronous state, or the magnitude of the excursion of some quantities, such as voltage angles or frequency, away from their desired values. In this work, we investigate the effect of a line loss on the Rate of Change of Frequency (RoCoF), which is the largest time derivative of the voltage frequencies. It is a measure of the severity of a perturbation that is standardly used in the operation of electric power grids. In practice, the current operating state of the system is not known. We therefore derive statistical properties of the Ro-CoF after a line loss for cases when the exact operating state of the system is uncertain.

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Section: The Rocofmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

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Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

Delabays

Tyloo

Jacquod

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…When the damping ratio is constant, d i /m i = γ i = γ, ∀i, (2) can be integrated exactly [7], [12]. To see this we first transform angle coordinates as δθ = M −1/2 δθ M to obtaiṅ…”

Section: A Exact Solution For Homogeneous Damping Ratiomentioning

confidence: 99%

“…In this section we lift that constraint and write γ i = γ + δγ a i . With inhomogeneous damping ratios, (7) becomes…”

Section: B Inhomogeneity In Damping Ratiosmentioning

confidence: 99%

Optimal Placement of Inertia and Primary Control: A Matrix Perturbation Theory Approach

Pagnier

Jacquod

2019

IEEE Access

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The increasing penetration of inertialess new renewable energy sources reduces the overall mechanical inertia available in power grids and accordingly raises a number of issues of grid stability over short to medium time scales. It has been suggested that this reduction of overall inertia can be compensated to some extent by the deployment of substitution inertia -synthetic inertia, flywheels or synchronous condensers. Of particular importance is to optimize the placement of the limited available substitution inertia, to mitigate voltage angle and frequency disturbances following a fault such as an abrupt power loss. Performance measures in the form of H2−norms have been recently introduced to evaluate the overall magnitude of such disturbances on an electric power grid. However, despite the mathematical conveniance of these measures, analytical results can be obtained only under rather restrictive assumptions of uniform damping ratio, or homogeneous distribution of inertia and/or primary control in the system. Here, we introduce matrix perturbation theory to obtain analytical results for optimal inertia and primary control placement where both are heterogeneous. Armed with that efficient tool, we construct two simple algorithms that independently determine the optimal geographical distribution of inertia and primary control. These algorithms are then implemented on a model of the synchronous transmission grid of continental Europe. We find that the optimal distribution of inertia is geographically homogeneous but that primary control should be mainly located on the slow modes of the network, where the intrinsic grid dynamics takes more time to damp frequency disturbances.

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Explicit formulas for the asymptotic variance of a linearized model of a Gaussian disturbance driven power system with a uniform damping-inertia ratio

Wu,

Xi,

Cheng

et al. 2024

Chaos, Solitons & Fractals

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Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia

Cited by 35 publications

References 24 publications

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

Optimal Placement of Inertia and Primary Control: A Matrix Perturbation Theory Approach

Explicit formulas for the asymptotic variance of a linearized model of a Gaussian disturbance driven power system with a uniform damping-inertia ratio

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