arXiv subjects

Laurent Pagnier

Publications and source records attributed to Laurent Pagnier.

22 records · Page 2Linked to original sources

arXiv2018

The Key Player Problem in Complex Oscillator Networks and Electric Power Grids: Resistance Centralities Identify Local Vulnerabilities

Identifying key players in a set of coupled individual systems is a fundamental problem in network theory. Its origin can be traced back to social sciences and led to ranking algorithms based on graph theoretic centralities. Coupled dynamical systems differ from social networks in that, they are characterized by degrees of freedom with a deterministic dynamics and the coupling between individual units is a well-defined function of those degrees of freedom. One therefore expects the resulting coupled dynamics, and not only the network topology, to also determine the key players. Here, we investigate synchronizable network-coupled dynamical systems such as high voltage electric power grids and coupled oscillators. We search for nodes which, once perturbed by a local noisy disturbance, generate the largest overall transient excursion away from synchrony. A spectral decomposition of the coupling matrix leads to an elegant, concise, yet accurate solution to this identification problem. We show that, when the internodal coupling matrix is Laplacian, these key players are peripheral in the sense of a centrality measure defined from effective resistance distances. For linearly coupled dynamical systems such as weakly loaded power grids or consensus algorithms, the nodal ranking is efficiently obtained through a single Laplacian matrix inversion, regardless of the operational synchronous state. We call the resulting ranking index LRank. For heavily loaded power grids or coupled oscillators systems closer to the transition to synchrony, nonlinearities render the nodal ranking dependent on the synchronous state. In this case a weighted Laplacian matrix inversion gives another ranking index, which we call WLRank. Quite surprisingly, we find that LRank provides a faithful ranking even for well developed coupling nonlinearities, corresponding to oscillator angle differences up to $40^o$ approximately.

nlin.AO↗

arXiv2018

Disturbance propagation, inertia location and slow modes in large-scale high voltage power grids

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. We have constructed a model of the synchronous grid of continental Europe with which 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 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. These results for our model of the European transmission grid are corroborated by numerical investigations on the ERCOT transmission grid.

eess.SY↗

arXiv2018

How fast can one overcome the paradox of the energy transition? A physico-economic model for the European power grid

The paradox of the energy transition is that the low marginal costs of new renewable energy sources (RES) drag electricity prices down and discourage investments in flexible productions that are needed to compensate for the lack of dispatchability of the new RES. The energy transition thus discourages the investments that are required for its own harmonious expansion. To investigate how this paradox can be overcome, we argue that, under certain assumptions, future electricity prices are rather accurately modeled from the residual load obtained by subtracting non-flexible productions from the load. Armed with the resulting economic indicator, we investigate future revenues for European power plants with various degree of flexibility. We find that, if neither carbon taxes nor fuel prices change, flexible productions would be financially rewarded better and sooner if the energy transition proceeds faster but at more or less constant total production, i.e. by reducing the production of thermal power plants at the same rate as the RES production increases. Less flexible productions, on the other hand, would see their revenue grow more moderately. Our results indicate that a faster energy transition with a quicker withdrawal of thermal power plants would reward flexible productions faster.

physics.soc-ph↗

arXiv2017

A predictive pan-European economic and production dispatch model for the energy transition in the electricity sector

The energy transition is well underway in most European countries. It has a growing impact on electric power systems as it dramatically modifies the way electricity is produced. To ensure a safe and smooth transition towards a pan-European electricity production dominated by renewable sources, it is of paramount importance to anticipate how production dispatches will evolve, to understand how increased fluctuations in power generations can be absorbed at the pan-European level and to evaluate where the resulting changes in power flows will require significant grid upgrades. To address these issues, we construct an aggregated model of the pan-European transmission network which we couple to an optimized, few-parameter dispatch algorithm to obtain time- and geographically-resolved production profiles. We demonstrate the validity of our dispatch algorithm by reproducing historical production time series for all power productions in fifteen different European countries. Having calibrated our model in this way, we investigate future production profiles at later stages of the energy transition - determined by planned future production capacities - and the resulting interregional power flows. We find that large power fluctuations from increasing penetrations of renewable sources can be absorbed at the pan-European level via significantly increased electricity exchanges between different countries. We identify where these increased exchanges will require additional power transfer capacities. We finally introduce a physically-based economic indicator which allows to predict future financial conditions in the electricity market. We anticipate new economic opportunities for dam hydroelectricity and pumped-storage plants.

physics.soc-ph↗