Inertie

Résumé

En physique, l'inertie d'un corps, dans un référentiel galiléen (dit inertiel), est sa tendance à conserver sa vitesse : en l'absence d'influence extérieure, tout corps ponctuel perdure dans un mouvement rectiligne uniforme. L'inertie est aussi appelée principe d'inertie, ou loi d'inertie, et, depuis Newton, première loi de Newton. La loi d'inertie exprime le fait que si la vitesse \vec{v} du corps ponctuel par rapport au repère galiléen est constante, « la somme des forces \vec{F} s'exerçant sur le corps est nulle ». :\vec{v} = \vec{cte} \Leftrightarrow \sum\vec{F}=\vec{0} La notion d'inertie est encore considérée comme la norme en physique classique. La formulation de l'inertie est faite par la deuxième loi de Newton, ou principe fondamental de la dynamique : l'inertie étant fonction de la masse inerte du corps, plus celle-ci est grande, plus la force requise pour modifier son mouvement sera importante. Si le corps est observé à partir d'un

Source officielle

https://fr.wikipedia.org/wiki/Inertie

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Most European countries are committed to an energy transition which consists in the substitution of conventional CO2 emitting energy sources by new renewable energy sources (RES), in particular wind and solar power. As opposed to conventional energy sources, new RES are distributed, non-dispatchable, fluctuating and inertialess and have negligible marginal costs. In this thesis, we investigate the impact of the energy transition on the electricity sector in Europe. In the first part of this thesis, we investigate the future electricity production and prices in Europe. We develop a dispatch algorithm on an aggregated model of the pan-European power grid with which we study the future European productions. We show that, as the penetration of new RES increases, the transmission grids are more strongly used and that more flexibility is required from conventional generators. The existing infrastructures seem to able to absorb, through increased international power exchanges and usage of the existing pumped-storage hydroelectricity, the variations of new RES productions even for high penetrations. Then we investigate the effects of new RES on electricity prices. We explain why, due to their negligible marginal cost and their lack of dispatchability, they tend to drag electricity prices down and can be considered as a reduction of the load in the electricity pricing. In particular, photovoltaics decreases the volatility of electricity prices. We show that, in most European countries, the day-ahead electricity price is strongly correlated with the residual load, which is obtained by subtracting the non-dispatchable productions, in particular those of the new RES, from the load. From this observation, we build an effective price model based solely on the residual load with which the revenues of different electricity producers are evaluated. The second part of this thesis deals with disturbances in large transmission grids. The substitution of conventional generators by inertialess RES reduces the amount of inertia connected to power systems which might affect their reliability. To examine the propagation of disturbances in large transmission grids, we develop a dynamical model of the continental European transmission grid. We observe that the magnitude of the disturbance following a power loss depends on the fault location. We show that when inertia and primary control are uniformly distributed, the faults exciting the slowest eigenmodes of the network Laplacian are followed by the strongest disturbances. Reducing inertia on those eigenmodes, which are mostly located in the periphery of the grid, affects more its resilience than when the reduction occurs in its center. Finally, we use perturbation theory to derive algorithms for optimal placement of inertia and primary control when some mild inhomogeneities are present in their distributions. We show that,when the vulnerability of the whole grid is taken into account, a uniform distribution of inertia is optimal and the primary control is best placed in the periphery of the grid.

EPFL2019

Chargement

A New Approach to the On-line Estimation of the Loss of Generation Size in Power Systems

Rasoul Azizipanah-Abarghooee, Mario Paolone

Following an unintended disconnection of a synchronous generator (SG) from the power system, what is also known as a loss of generation (LoG), it is not trivial to precisely estimate the post-event power system's inertia and the LoG size. One of reasons for that is that both of them are a function of the unknown inertia reduction. To solve this challenging problem, this paper presents an analytical method based on the rate-of-change-of-frequency (RoCoF). The method relies on a modified swing equation, allowing a simultaneous estimation of both unknowns. To this end, the values of mechanical starting time, apparent power and loading of lost generator are formulated for the power system under study. In a practical application, the method can use RoCoF measured by phasor measurement units (PMUs). The paper discusses the impact of various frequency estimation approaches to the proposed LoG estimation. Furthermore, a new method for LoG size estimation, based on the interpolated estimated inertial response, is proposed. The efficiency of the proposed approach is validated through extensive simulations with Matlab/Simulink using a simple power system and the IEEE 39-bus test network.

2018

Chargement

Inertia location and slow network modes determine disturbance propagation in large-scale power grids

Philippe Jacquod

Conventional generators in power grids are steadily substituted with new renewable sources of electric power. The latter are connected to the grid via inverters and as such have little, if any rotational inertia. The resulting reduction of total inertia raises important issues of power grid stability, especially over short-time scales. With the motivation in mind to investigate how inertia reduction influences the transient dynamics following a fault in a large-scale electric power grid, we have constructed a model of the high voltage synchronous grid of continental Europe. To assess grid stability and resilience against disturbance, we numerically investigate frequency deviations as well as rates of change of frequency (RoCoF) following abrupt power losses. The magnitude of RoCoF's and frequency deviations strongly depend on the fault location, and we find the largest effects for faults located on the support of the slowest mode-the Fiedler mode-of the network Laplacian matrix. This mode essentially vanishes over Belgium, Eastern France, Western Germany, northern Italy and Switzerland. Buses inside these regions are only weakly affected by faults occuring outside. Conversely, faults inside these regions have only a local effect and disturb only weakly outside buses. Following this observation, we reduce rotational inertia through three different procedures by either (i) reducing inertia on the Fiedler mode, (ii) reducing inertia homogeneously and (iii) reducing inertia outside the Fiedler mode. We find that procedure (iii) has little effect on disturbance propagation, while procedure (i) leads to the strongest increase of RoCoF and frequency deviations. This shows that, beyond absorbing frequency disturbances following nearby faults, inertia also mitigates frequency disturbances from distant power losses, provided both the fault and the inertia are located on the support of the slowest modes of the grid Laplacian. These results for our model of the European transmission grid are corroborated by numerical investigations on the ERCOT transmission grid.

2019

Chargement

Inertia location and slow network modes determine disturbance propagation in large-scale power grids

Philippe Jacquod

2019

EPFL2019