Session - Contributed talks
Contributed Talks Wednesday Session
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Towards a unified model for future powergrids. by Raphael Kogler at 14.00 - 14.30 (CET)
Abstract: The more and more pressing environmental concerns of recent years have propelled many advances concerning the stable operation of power grids with high penetration of renewable energy sources. Specifically, the idea of grid-forming inverters has gained great interest. While for the traditional synchronous machines there is a well established hierarchy of dynamical models with increasing degree of detail, the case of grid-forming inverters hosts yet a wide variety of different control concepts. This poses a significant challenge for modeling future power grids which we seek to address with this talk. By explicitly considering the rotational symmetry of a general AC power grid, we cast the system into a form that is suitable for a nonlinear approximation. This procedure reduces the description of the dynamics to a set of parameters that may be studied independently of concrete models, and provides a systematic way of adjusting model accuracy as well as complexity.
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The Key Player Problem in High-Voltage Power Networks. by Melvyn Tyloo at 14.30 - 15.00 (CET)
Abstract: Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power networks and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure and global network indices defined from effective resistance distances. The resistance distances can then be used to establish rankings of the nodes according to their impact on the overall synchronous state when they are perturbed.
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Spatio-temporal correlations in power-grid frequency recordings by Leonardo Rydin at 15.00 - 15.30 (CET)
Abstract: In this talk I will present a recent work focused on spatio-temporal correlations in power-grid frequency recordings (see Rydin Gorjão et al. [1]). In it, we have analysed an open database of measurements of electric power-grid frequencies across 17 locations in 12 synchronous areas on three continents (see Jumar et al. [2]). We show that the scaling law of fluctuations in power grids proposed in Schäfer et al. [3] is verified, with a small caveat particular to each power-grid control system and constraints. We study the dephasing of incremental correlations of power-grid frequency recordings, the puzzling decay of leptokurtic distribution of increments of power-grid frequency, and have a first look at long-distance synchronisation across the Continental European grid. In this talk I will bring forth the proposal to examine power-grid frequency recordings in the ambit of stochastic process, to make use of the more common stochastic analysis and estimators available, the parallel to other dynamical systems, and open question in this ambit.
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Predictability of Power Grid Frequency by Johannes Kruse at 15.30 - 16.00 (CET)
Abstract: The power grid frequency is the central observable in power system control, as it measures the balance of electrical supply and demand. A reliable frequency forecast can facilitate rapid control actions and may thus greatly improve power system stability. Here, we present a weighted-nearest-neighbour (WNN) predictor to investigate how predictable the frequency trajectories are. Our forecasts for up to one hour are more precise than averaged daily profiles and could increase the efficiency of frequency control actions. Furthermore, we gain an increased understanding of the specific properties of different synchronous areas by interpreting the optimal prediction parameters (number of nearest neighbours, the prediction horizon, etc.) in terms of the physical system. Finally, prediction errors indicate the occurrence of exceptional external perturbations. Overall, we provide a diagnostics tool and an accurate predictor of the power grid frequency time series, allowing better understanding of the underlying dynamics.
Contributed Talks Thursday Session
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Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid by Bálint Hartmann at 11.30 - 12.00 (CET)
Abstract: Since the introduction of small-world and scale-free properties, there is ongoing discussion on how certain real-world networks fit into these network science concepts. While the electrical power grid was among the most discussed example of these real-word networks, published results are controversial and usually missed to take the aspects of network evolution into consideration. As a result of this, there is a broad agreement that power grids are small-world networks and might show scale-free behaviour, although very little attempts were made to find how these characteristics of the network are related to grid infrastructure development or other underlying phenomena. In this paper the authors use the 70-year historical dataset of the Hungarian power grid to perform network analysis, which is the first attempt to evaluate small-world and scale-free properties on long-term real-world data. Results of the analysis suggest that power grids show small-world behaviour only after the introduction of multiple voltage levels. It is also demonstrated that the node distribution of the examined power grid does not show scale-free behaviour and that the scaling is stabilised around certain values after the initial phase of grid evolution.
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Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models by Géza Ódor at 12.00 - 12.30 (CET)
Abstract: Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous two-dimensional (2D) square lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D square lattice), is not sufficient for finding power-law distributed cascades. On the other hand, too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution, both for the US and Hungarian systems, remained insensitive and have kept the universal tails, being characterized by the exponent \tau~1.8 . We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid.
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Frequency fluctuations and stability of power grids with a large renewables penetration ratio by María Martínez Barbeito at 12.30 - 13.00 (CET)
Abstract: The integration of a high ratio of renewable energy sources in the power system is not a trivial task. In particular, their intermittent and unpredictable nature may lead to unwanted frequency fluctuations. We propose a model that includes both renewable and conventional generation and demand variations, which allows for the study of many different energy transition scenarios. We model the power grid as a network of substations and power plants (nodes) interconnected via power transmission lines (links). We focus our analysis on islands, which typically have on one side a high dependence on fossil fuels, and on the other a high renewable energy potential. More precisely, we analyze the cases of Gran Canaria and the Balearic Islands (Spain).
Abstract: The more and more pressing environmental concerns of recent years have propelled many advances concerning the stable operation of power grids with high penetration of renewable energy sources. Specifically, the idea of grid-forming inverters has gained great interest. While for the traditional synchronous machines there is a well established hierarchy of dynamical models with increasing degree of detail, the case of grid-forming inverters hosts yet a wide variety of different control concepts. This poses a significant challenge for modeling future power grids which we seek to address with this talk. By explicitly considering the rotational symmetry of a general AC power grid, we cast the system into a form that is suitable for a nonlinear approximation. This procedure reduces the description of the dynamics to a set of parameters that may be studied independently of concrete models, and provides a systematic way of adjusting model accuracy as well as complexity.
Abstract: Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power networks and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure and global network indices defined from effective resistance distances. The resistance distances can then be used to establish rankings of the nodes according to their impact on the overall synchronous state when they are perturbed.
Abstract: In this talk I will present a recent work focused on spatio-temporal correlations in power-grid frequency recordings (see Rydin Gorjão et al. [1]). In it, we have analysed an open database of measurements of electric power-grid frequencies across 17 locations in 12 synchronous areas on three continents (see Jumar et al. [2]). We show that the scaling law of fluctuations in power grids proposed in Schäfer et al. [3] is verified, with a small caveat particular to each power-grid control system and constraints. We study the dephasing of incremental correlations of power-grid frequency recordings, the puzzling decay of leptokurtic distribution of increments of power-grid frequency, and have a first look at long-distance synchronisation across the Continental European grid. In this talk I will bring forth the proposal to examine power-grid frequency recordings in the ambit of stochastic process, to make use of the more common stochastic analysis and estimators available, the parallel to other dynamical systems, and open question in this ambit.
Abstract: The power grid frequency is the central observable in power system control, as it measures the balance of electrical supply and demand. A reliable frequency forecast can facilitate rapid control actions and may thus greatly improve power system stability. Here, we present a weighted-nearest-neighbour (WNN) predictor to investigate how predictable the frequency trajectories are. Our forecasts for up to one hour are more precise than averaged daily profiles and could increase the efficiency of frequency control actions. Furthermore, we gain an increased understanding of the specific properties of different synchronous areas by interpreting the optimal prediction parameters (number of nearest neighbours, the prediction horizon, etc.) in terms of the physical system. Finally, prediction errors indicate the occurrence of exceptional external perturbations. Overall, we provide a diagnostics tool and an accurate predictor of the power grid frequency time series, allowing better understanding of the underlying dynamics.
-
Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid by Bálint Hartmann at 11.30 - 12.00 (CET)
Abstract: Since the introduction of small-world and scale-free properties, there is ongoing discussion on how certain real-world networks fit into these network science concepts. While the electrical power grid was among the most discussed example of these real-word networks, published results are controversial and usually missed to take the aspects of network evolution into consideration. As a result of this, there is a broad agreement that power grids are small-world networks and might show scale-free behaviour, although very little attempts were made to find how these characteristics of the network are related to grid infrastructure development or other underlying phenomena. In this paper the authors use the 70-year historical dataset of the Hungarian power grid to perform network analysis, which is the first attempt to evaluate small-world and scale-free properties on long-term real-world data. Results of the analysis suggest that power grids show small-world behaviour only after the introduction of multiple voltage levels. It is also demonstrated that the node distribution of the examined power grid does not show scale-free behaviour and that the scaling is stabilised around certain values after the initial phase of grid evolution. -
Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models by Géza Ódor at 12.00 - 12.30 (CET)
Abstract: Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous two-dimensional (2D) square lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D square lattice), is not sufficient for finding power-law distributed cascades. On the other hand, too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution, both for the US and Hungarian systems, remained insensitive and have kept the universal tails, being characterized by the exponent \tau~1.8 . We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid. -
Frequency fluctuations and stability of power grids with a large renewables penetration ratio by María Martínez Barbeito at 12.30 - 13.00 (CET)
Abstract: The integration of a high ratio of renewable energy sources in the power system is not a trivial task. In particular, their intermittent and unpredictable nature may lead to unwanted frequency fluctuations. We propose a model that includes both renewable and conventional generation and demand variations, which allows for the study of many different energy transition scenarios. We model the power grid as a network of substations and power plants (nodes) interconnected via power transmission lines (links). We focus our analysis on islands, which typically have on one side a high dependence on fossil fuels, and on the other a high renewable energy potential. More precisely, we analyze the cases of Gran Canaria and the Balearic Islands (Spain).