Einfluss der Kurzzeitdynamik erneuerbarer Energiequellen auf die Stabilität von Stromnetzen
Zusammenfassung der Projektergebnisse
In this project the impact of fluctuations of wind speeds and solar irradiation on the short-term stability of power grids is studied. Beyond the scope of electrical engineering the intermittency character of the renewable energies, caused by turbulence, are considered by a new genetic model and it is shown that this intermittency is transferred to frequency and voltage fluctuations. The focus is on short time scales, where the dynamics of voltages and currents can be considered to be essentially autonomous. This holds true apart from primary control measures, which mainly comprise an automatic tuning of the power generated in fully controllable power plants for maintaining a stable state of synchronous operation. The methodology includes various mutually connected concepts. One approach is based on the assumption that the grid response to fluctuations of wind speed and solar irradiation is fast. The state of the power grid can then be regarded to adjust to the current level of renewable power feed-in. This corresponds to a quasi-stationary modelling. In an extended modelling, we included the dynamics of voltage phase angles and amplitudes at different nodes in the power grid. This approach has been further refined to include storage systems with control strategies. Knowing the voltage phase angles, one can evaluate power flows along transmission lines as well as local frequency deviations from the nominal value (50 Hz in Europe). The nonstationary dynamics is used to study the impact of sudden large changes of renewable power feed-in, as they originate from strong wind gusts, or sudden changes of the solar irradiance due to cloud effects. The stability against such perturbations is quantified by different measures, like the basin of stability, the return or escape times from the synchronous state. Continuously fluctuating input causes frequency deviations from the reference value, where large deviations can nucleate grid instabilities ranging from single-line overloads to malfunction of larger grid parts. Histograms of the local frequency fluctuations are determined, which shed light on the risk of such grid failures and which can also be used to quantify the effects of control strategies using storage systems. We find that probabilities of transmission line overloading vary strongly with the location of renewable power feed-in. They are much smaller for multiple-node than for single-node injection, when considering a given amount of total average feed-in. Feed-in locations and decentralisation should thus be involved in strategies of optimal renewables’ embedding into present grid structures. Spatial wind power correlations are a further relevant factor for optimal integration of renewables. Most strikingly, positive node couplings exist in the sense that an increase of injected power at one node can increase the threshold power for a line overload at another injection node. This surprising effect may be utilised to stabilise transmission lines by additional renewable energy feeding rather than by line strengthening. Suddenly perturbed nodes with highest probabilities of causing grid failure are identified as dead ends in the grid structure, or as only weakly connected to other nodes. Such grid structures should be avoided in grid extensions and eliminated in present ones. Return times to the stable state after perturbations are of about 10-20 seconds, which indicates that conclusions drawn from quasi-stationary modelings should be taken with care. Continuous stochastic power feed-in gives rise to exponentially decaying tails of local frequency distributions. This implies rare large frequency fluctuations to occur much more frequent than expected from assuming simple Gaussian statistics. In the studies both simplified grid models and realistic models with engineered parameters were used. The project has provided detailed insight into power grid stability and stability assessment under consideration of the non-Gaussian statistics of renewable energy feed-in, and it opens ways for an improved grid modelling bridging the more detailed engineering and the more generic physical approaches.
Projektbezogene Publikationen (Auswahl)
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“Normal behaviour models for wind turbine vibrations: comparison of neural networks and a stochastic approach”, Energies 10, 1944 (2017)
P. G. Lind, L. Vera-Tudela, M. Wächter, M. Kuhn, and J. Peinke
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“Resilience of electricity grids against transmission line overloads under wind power injection at different nodes”, Sci. Rep. 7, 11562 (2017)
C. Schiel, P. G. Lind, and P. Maass
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“The impact of turbulent renewable energy production on power grid stability and quality”, Eur. Phys. J. B 90 222 (2017)
K. Schmietendorf, J. Peinke, and O. Kamps
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“Power grid stability under perturbation of single nodes: Effects of heterogeneity and internal nodes”, Chaos 28, 103120 (2018)
M. F. Wolff, P. G. Lind, and P. Maass
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“Bridging between load-flow and Kuramoto-like power grid models: a flexible approach to integrating electrical storage units”, Chaos (2019)
K. Schmietendorf, O. Kamps, M. Wolff, P. G. Lind, P. Maass, and J. Peinke
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“Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input”
M. F. Wolff, K. Schmietendorf, O. Kamps, P. G. Lind, J. Peinke, and P. Maass
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“Propagation of wind-power-induced fluctuations in power grids”, Phys. Rev. E 99, 050301 (2019)
H. Hähne, K. Schmietendorf, S. Tamrakar, J. Peinke, and S. Kettemann
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“Wind speed modeling by nested ARIMA processes”, Energies 12, 69 (2019)
S.-K. Sim, P. Maass, and P. G. Lind
