The influence of load characteristics on early warning signs in power systems
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1 The influence of load characteristics on early warning signs in power systems Submission no. 44 Steffen Blume Doctoral Researcher, Future Resilient Systems, Singapore-ETH Centre, Singapore Risk and Reliability Engineering Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, Switzerland Giovanni Sansavini Risk and Reliability Engineering Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, Switzerland CRITIS 2017, Lucca, Italy Oct Steffen Blume
2 Outline CIS and critical transitions: System stress. State of knowledge. Early warning signs: Open questions. Power system: Modelling approach. Early warning signs in power systems: Results. New findings: Some thoughts and conclusions. Steffen Blume
3 CIS and critical transitions: System stress. Increased stress pushes CIS towards critical conditions Critical loading conditions can cause system collapse Failures/contingencies can cause premature collapse [Figures: Noun Project] Steffen Blume
4 CIS and critical transitions: General state of knowledge. Complex dynamical systems: generic characteristics prior to critical transitions Transitions are related to bifurcations Some systems emit early warnings signs that the critical transition is imminent Steffen Blume
5 CIS and critical transitions: The theory. Bifurcation analysis α " α # α $ Saddle-node bifurcation Hopf bifurcation Steffen Blume
6 CIS and critical transitions: The theory. System behaviors: Critical slowing down Flickering Indicators: (Increase in) Autocorrelation (Increase in) Variance Skewness Kurtosis Spatial autocorrelation [Cotilla-Sanchez, et al., IEEE Trans. Smart Grid, 2012] [Scheffer, et al., Nature, 2009] [Ghanavati, et al., IEEE Trans. Power Sys., 2016] Steffen Blume
7 Early warning signs: Open questions. Effects of stressor characteristics on the behavior of networked systems and their early warning signs? Homogeneous vs. Non-homogeneous Lightly connected vs. Strongly connected Steffen Blume
8 Power system: Modelling approach. 10-machine, 39-bus New England test case Time-domain simulation in Power System Analysis Toolbox (PSAT) [M. Pai (1989), Kluwer] Steffen Blume
9 Power system: Modelling approach. Hopf bifurcation: Detectable from eigenvalue analysis A complex eigenvalue pair crosses the imaginary axis from the left to the right half plane B A HB A B Steffen Blume
10 Power system: Modelling approach. Monitor network-wide bus voltage magnitudes Determine autocorrelation coefficients Aggregate coefficients into median and measure of the spread Assess responses under different load scenarios given by load homogeneity and connectivity Steffen Blume
11 Power system: Load homogeneity and connectivity. Homogeneity: parameterizes spatial load distribution Connectivity: modulates the coupling between the stochastic load perturbations across network buses Homogeneous vs. Non-homogeneous Lightly connected vs. Strongly connected Steffen Blume
12 Early warning signs in power systems: Results. The effect of load homogeneity Shifts the bifurcation point Does not affect increase in autocorrelation Steffen Blume
13 Early warning signs in power systems: Results. The effect of load homogeneity Shifts the bifurcation point Does not affect increase in autocorrelation BUT: A given absolute value is not indicative of the proximity of the bifurcation Not a universal indicator applicable under unknown load conditions Steffen Blume
14 Early warning signs in power systems: Results. Changes in perturbation type: White noise perturbations Autocorrelated perturbations Steffen Blume
15 Early warning signs in power systems: Results. The effect of load connectivity Does not influence the degree to which individual loads may be correlated with past samples over time Ø Autocorrelation coefficients not sensitive to load connectivity. Steffen Blume
16 Conclusions: Final thoughts. Submission no. 44 Defined aggregate metrics to determine system-wide indicators of critical transitions Confirm previous findings of critical slowing down in power systems Load connectivity does not influence autocorrelation indicator Indicators may falsely alert about a critical condition in case of limited knowledge and misinformation about system stressors Predictability? Thank you! Acknowledgements: National Research Foundation Singapore, IT Services ETH Zürich Steffen Blume
17 References M. Scheffer, et al. (2009), Early-warning signals for critical transitions, Nature, vol. 461, no. 7260, pp E. Cotilla-Sanchez, P. Hines, C. Danforth (2012), Predicting Critical Transitions From Time Series Synchrophasor Data, IEEE Transactions on Smart Grid, vol. 3, no. 4, pp G. Ghanavati, P. D. Hines, and T. I. Lakoba (2016), Identifying useful statistical indicators of proximity to instability in stochastic power systems, IEEE Transactions on Power Systems, vol. 31, no. 2, pp Noun Project artists: Chameleon Design, Juan Pablo Bravo, Becris, Artem Kovyazin, Yorlmar Campos, iconsphere, Vectors Market, hash Steffen Blume
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