I gave a talk on “Coherence and concentration on tightly connected networks” at the ARO Workshop on Synchronization in Natural and Engineering Systems. Hosts: Derya Cansever (ARO), Fabio Pasqualetti (UCR), Jorge Cortes (UCSD). Related publications include [1, 2, 3]
![[doi]](https://mallada.ece.jhu.edu/wp-content/plugins/papercite/img/external.png){kind=small}
F. Paganini and E. Mallada, “Global analysis of synchronization performance for power systems: bridging the theory-practice gap,” IEEE Transactions on Automatic Control, vol. 67, iss. 7, pp. 3007-3022, 2020. [Bibtex] [Abstract] [Download PDF]
The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define –and compute in closed form– several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.
@article{pm2020tac,
abstract = {The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.},
author = {Paganini, Fernando and Mallada, Enrique},
doi = {10.1109/TAC.2019.2942536},
grants = {CPS-1544771, AMPS-1736448, EPCN-1711188, CAREER-1752362, ENERGISE-DE-EE0008006},
journal = {IEEE Transactions on Automatic Control},
month = {7},
number = {7},
pages = {3007-3022},
title = {Global analysis of synchronization performance for power systems: bridging the theory-practice gap},
url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-PM.pdf},
volume = {67},
year = {2020}
}[Bibtex] [Abstract] [Download PDF]
We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.
@article{mpm2021lcss,
abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.},
author = {Min, Hancheng and Paganini, Fernando and Mallada, Enrique},
doi = {10.1109/LCSYS.2020.3043733},
grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
journal = {IEEE Control Systems Letters (L-CSS)},
month = {11},
note = {also in ACC 2021},
number = {5},
pages = {1741-1746},
record = {early accesss Nov 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020},
title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators},
url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-MPM.pdf},
volume = {5},
year = {2021}
}[Bibtex] [Abstract] [Download PDF]
We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.
@article{jbvm2021lcss,
abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.},
author = {Jiang, Yan and Bernstein, Andrey and Vorobev, Petr and Mallada, Enrique},
doi = {10.1109/LCSYS.2020.3044551},
grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, CPS-2136324},
journal = {IEEE Control Systems Letters (L-CSS)},
month = {12},
note = {also in ACC 2021},
number = {6},
pages = {1988-1993},
record = {early access Dec 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020},
title = {Grid-forming frequency shaping control in low inertia power systems},
url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-JBVM.pdf},
volume = {5},
year = {2021}
}