DLR.de/ve • Slide 1 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Scaling and spatio-temporal properties of power-grid frequency: An open database
Special Track: Modelling Dynamics of Power Grids
DLR Institute of Networked Energy Systems Forschungszentrum Jülich - IEK-STE Institute of Energy and Climate Research Systems Analysis and Technology Evaluation Karlsruhe Institute of Technology Institute for Automation and Applied Informatics DLR.de/ve • Slide 2 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Power-grid frequency: The common indicator for stability
Power-grid frequency is the key indicator of stability in power-grid systems. It comprises the balance between generation and consumption, but much more is encoded in its physics. In this presentation we will investigate: ● The nature of power-grid fluctuation. ● A scaling law relating inertia/generation and fluctuation amplitude. ● The finer structure of power-grid frequency fluctuations in real-world recordings. DLR.de/ve • Slide 3 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Extant power-grid frequency recordings Excerpts February 2019
Three recordings from 11th of February 2019, from midnight.
60 Continental Europe 160 Great Britain 140 Nordic Grid 30 80 70 [mHz] 0 0 0 ref f
− 30 80 70 − −
f − 60 160 140 − − − 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 t [min] t [min] t [min]
Continental Europe Great Britain Nordic Grid DLR.de/ve • Slide 4 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Electrical Data Recorder (EDR) across the globe
There is a scarcity of power-grid frequency data freely available a b Reykjavik Vestmanna Salt Lake City Stockholm St. Petersburg College Station Tallinn Oldenburg Gran Canaria London Karlsruhe Gy˝or B´ek´escsaba
Istanbul Lisbon Palma de Mallorca
Cape Town
Work by: Richard Jumar, Heiko Maass, Benjamin Schäfer, LRG, Veit Hagenmeyer Location of data: https://power-grid-frequency.org/ DLR.de/ve • Slide 5 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Electrical Data Recorder (EDR) across the globe Excerpts of the power-grid frequency recordings
17 recordings, over 12 synchronous areas c Islands d Continents e Others 200 200 200 100 100 100 [mHz] 0 0 0 ref f 100 100 100
− − − −
f 200 200 200 − FO IS ES-GC ES-PM − SE GB DE EE − ZA RU US-TX US-UT 0 15 30 45 60 0 15 30 45 60 0 15 30 45 60 t [min] t [min] t [min]
FO: Faroe Islands SE: Sweden ZA: South Africa IS: Iceland GB: Great Britain RU: Russia ES-GC: Spain, Gran Canaria DE: Germany US-TX: USA, Texas ES-PM: Spain, Palma de Mallorca EE: Estonia US-UT: USA, Utah DLR.de/ve • Slide 6 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Electrical Data Recorder (EDR) across the globe Statistical properties of the recordings
a Islands b Continents c Others FO: Faroe Islands τ = 1 s IS τ = 1 s SE τ = 1 s RU 5 5 5 τ 10 τ = 10 s 10 τ = 10 s 10 τ = 10 s IS: Iceland f ES-GC: Spain, Gran Canaria 102 102 102 ES-PM: Spain, Palma de Mallorca PDF ∆
1 1 1 SE: Sweden 10− 10− 10− 10 5 0 5 10 10 5 0 5 10 10 5 0 5 10 GB: Great Britain − − − − − − ∆fτ /στ [mHz] ∆fτ /στ [mHz] ∆fτ /στ [mHz] DE: Germany 3 d e f
− 3 EE: Estonia 10 IS FO ES-PM ES-GC EE SE GB DE RU US-TX US-UT ZA κ 2 101 101 10 ZA: South Africa 101 RU: Russia 100 100 100 US-TX: USA, Texas US-UT: USA, Utah
Excess Kurtosis 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 τ [s] τ [s] τ [s] DLR.de/ve • Slide 7 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Power-grid frequency: A stochastic approach
We can precise an SDE for the “bulk” angle and “bulk” angular velocity
where is the primary control, is the secondary control, is the power mismatch, and dW is an uncorrelated Gaussian noise with amplitude . We can write a Fokker–Planck equation (for = 0) DLR.de/ve • Slide 8 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Power-grid frequency: A scaling law
Take that the stochastic noise present is a sum of i.i.d Gaussian distributed random variables
which results in a relation†
or strictly from the diffusion:
With the number of nodes and an estimator
†Schäfer, B., Beck, C., Aihara, K., Witthaut, D., Timme, M. Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics, Nature Energy 3(2):119–126, 2018, doi:10.1038/s41560-017-0058-z DLR.de/ve • Slide 9 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Power-grid frequency: A scaling law
FO: Faroe Islands This results in: IS: Iceland ES-GC: Spain, Gran Canaria ES-PM: Spain, Palma de Mallorca
SE: Sweden GB: Great Britain DE: Germany EE: Estonia
ZA: South Africa RU: Russia US-TX: USA, Texas US-UT: USA, Utah
or strictly from the diffusion: DLR.de/ve • Slide 10 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
The finer details in the same synchronous area Synchronised recordings in the Continental European grid
4 recordings with the EDR, +2 recording from the Hungarian TSO MAVIR. From 2019-07-09 to 2019-07-15, with a 1 second sampling.
a b Oldenburg Karlsruhe Istanbul Lisbon Oldenburg Karlsruhe Istanbul Lisbon 90 20 60 10 . [mHz] 30 0 ref
f ∆fτ=4s RoCoF . l 0 − 10 ↔
f − 30 − 20 60 − − 19:45 20:00 20:15 20:30 20:45 0 10 20 30 40 50 60 time [min] t [s]
Increment statistics: DLR.de/ve • Slide 11 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
The finer details in the same synchronous area Synchronised recordings in the Continental European grid
] 2
20 a b 1 e f − 10 1
[mHz] 0 0 τ f 2 2 R2 = 1.000 R2 = 0.955 ∆ 10 R = 0.720 R = 0.011 1 − − Oldenburg vs. Karlsruhe Istanbul vs. Karlsruhe Oldenburg vs. Karlsruhe Istanbul vs. Karlsruhe 20 RoCoF [mHz s 2 − −
] 2
20 c d 1 g h − 10 1
[mHz] 0 0 τ f 2 2 R2 = 0.985 R2 = 0.933 ∆ 10 R = 0.178 R = 0.003 1 − − Lisbon vs. Karlsruhe Lisbon vs. Istanbul Lisbon vs. Karlsruhe Lisbon vs. Istanbul 20 RoCoF [mHz s − 2 20 10 0 10 20 20 10 0 10 20 − 2 1 0 1 2 2 1 0 1 2 − − − − − − 1 − − 1 ∆fτ [mHz] ∆fτ [mHz] RoCoF [mHz s− ] RoCoF [mHz s− ]
Is there more to the nature of stochastic fluctuation? DLR.de/ve • Slide 12 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Quantifying fluctuations
a b c
uncorrelated correlated correlated different amplitudes different amplitudes identical amplitudes
Applying Detrended Fluctuation Analysis (DFA): we can obtain a fluctuation function for a segment with length :
comprises solely the variance of the increments DLR.de/ve • Slide 13 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Quantifying fluctuations Regime of amplitude synchronisation
104 Oldenburg Lisbon Karlsruhe B´ek´escsaba 103 Istanbul Gy˝or ) `
( 2
2 10 F 101
100
101 102 103 104 ` [s] For a detailed analysis of DFA, see: Meyer, P. G., Anvari, M., Kantz, H. Identifying characteristic time scales in power grid frequency fluctuations with DFA, Chaos: An Interdisciplinary Journal of Nonlinear Science 30:013130, 2020, doi:10.1063/1.5123778 DLR.de/ve • Slide 14 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Quantifying fluctuations Regime of amplitude synchronisation: “time-to-bulk” behaviour a b Oldenburg Lisbon fit a Distance Istanbul 1.00 × Karlsruhe B´ek´escsaba 12 fit a Distance2 × Lisbon Istanbul Gy˝or 0.75 9 ) ` (
η 0.50 6
3 Karlsruhe 0.25 Time to bulk [s] B´ek´escsaba 0 Gy˝or 0.00 Oldenburg 3 6 9 12 15 18 0 500 1000 1500 2000 ` [s] Distance [km] DLR.de/ve • Slide 15 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Envoi: Space and time correlations
We have: ● Gathered a large dataset of power-grid frequency which is still growing. ● Identified characteristic scaling of the diffusion with the number of consumers. ● Devised a method to uncover a global synchronisation of fluctuations across a synchronous area.
doi:10.1038/s41467-020-19732-7 Future work: ● Is the physics fluctuation amplitude universal? – What is the impact of the topology of power grids? ● What are the consequences for smaller (island) grids? DLR.de/ve • Slide 16 > Scaling and spatio-temporal properties of power-grid frequency > Leonardo Rydin Gorjão
Funding and support
Thank you for your attention
Funding: the German Federal Ministry of Education and Research (grant no. 03EK3055B) and the Helmholtz Association (via the joint initiative “Energy System 2050 – A Contribution of the Research Field Energy”, the grant “Uncertainty Quantification – From Data to Reliable Knowledge (UQ)” with grant no. ZT-I-0029 and the grant no. VH-NG-1025). This work was performed as part of the Helmholtz School for Data Science in Life, Earth and Energy (HDS-LEE). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 840825.