DREAM/CPAR Seminar @ Berkeley

I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Frequency Shaping Approach” at the DREAMS/CPAR Seminar, Berkeley (Hosts: Emily Jensen, Murat Arcak). Related publications include [1, 2, 3, 4]

[1] [doi] 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}
}
[2] [doi] Y. Jiang, R. Pates, and E. Mallada, “Dynamic Droop Control in Low Inertia Power Systems,” IEEE Transactions on Automatic Control, vol. 66, iss. 8, pp. 3518-3533, 2021.
[Bibtex] [Abstract] [Download PDF]

A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid’s stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies –droop control (DC) and virtual inertia (VI)– on several performance metrics induced by L2 and L∞ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

@article{jpm2021tac,
  abstract = {A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore
the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative
and quantitative study comparing the effect of conventional
control strategies --droop control (DC) and virtual inertia (VI)--
on several performance metrics induced by L2 and L∞ signal
norms. By extending a recently proposed modal decomposition
method, we capture the effect of step and stochastic power
disturbances, and frequency measurement noise, on the overall
transient and steady-state behavior of the system. Our analysis
unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without
increasing steady-state control effort, or the large frequency
variance that VI introduces in the presence of measurement
noise. We further propose a novel dynam-i-c Droop controller
(iDroop) that overcomes the limitations of DC and VI. More
precisely, we show that iDroop can be tuned to achieve high
noise rejection, fast system-wide synchronization, or frequency
overshoot (Nadir) elimination without affecting the steady-state
control effort share, and propose a tuning recommendation that
strikes a balance among these objectives. Extensive numerical
experimentation shows that the proposed tuning is effective even
when our proportionality assumptions are not valid, and that
the particular tuning used for Nadir elimination strikes a good
trade-off among various performance metrics.},
  author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
  doi = {10.1109/TAC.2020.3034198},
  grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092},
  journal = {IEEE Transactions on Automatic Control},
  month = {8},
  number = {8},
  pages = {3518-3533},
  record = {available online Nov. 2020, accepted Aug. 2020, revised Mar. 2020, submitted Aug. 2019},
  title = {Dynamic Droop Control in Low Inertia Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2021-TAC-JPM.pdf},
  volume = {66},
  year = {2021}
}
[3] [doi] Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, vol. 36, iss. 6, pp. 5006-5019, 2021.
[Bibtex] [Abstract] [Download PDF]

With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage — frequency shaping control — that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.

@article{jcvm2021tps,
  abstract = {With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage -- frequency shaping control -- that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.},
  author = {Jiang, Yan and Cohn, Eliza and Vorobev, Petr and Mallada, Enrique},
  doi = {10.1109/TPWRS.2021.3072833},
  grants = {CAREER-1752362;CPS-2136324},
  journal = {IEEE Transactions on Power Systems},
  month = {11},
  number = {6},
  pages = {5006-5019},
  record = {early access Apr 2021, accepted Mar 2021, revised Oct 2020, submitted May 2020},
  title = {Storage-Based Frequency Shaping Control},
  url = {https://mallada.ece.jhu.edu/pubs/2021-TPS-JCVM.pdf},
  volume = {36},
  year = {2021}
}
[4] [doi] H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 5, pp. 1741-1746, 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{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}
}

ECE Seminar @ UMich

I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Frequency Shaping Approach” at the ECE Seminar, UMich (Host: Johanna Mathieu). Related publications include [1, 2, 3, 4]

[1] [doi] 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}
}
[2] [doi] Y. Jiang, R. Pates, and E. Mallada, “Dynamic Droop Control in Low Inertia Power Systems,” IEEE Transactions on Automatic Control, vol. 66, iss. 8, pp. 3518-3533, 2021.
[Bibtex] [Abstract] [Download PDF]

A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid’s stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies –droop control (DC) and virtual inertia (VI)– on several performance metrics induced by L2 and L∞ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

@article{jpm2021tac,
  abstract = {A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore
the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative
and quantitative study comparing the effect of conventional
control strategies --droop control (DC) and virtual inertia (VI)--
on several performance metrics induced by L2 and L∞ signal
norms. By extending a recently proposed modal decomposition
method, we capture the effect of step and stochastic power
disturbances, and frequency measurement noise, on the overall
transient and steady-state behavior of the system. Our analysis
unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without
increasing steady-state control effort, or the large frequency
variance that VI introduces in the presence of measurement
noise. We further propose a novel dynam-i-c Droop controller
(iDroop) that overcomes the limitations of DC and VI. More
precisely, we show that iDroop can be tuned to achieve high
noise rejection, fast system-wide synchronization, or frequency
overshoot (Nadir) elimination without affecting the steady-state
control effort share, and propose a tuning recommendation that
strikes a balance among these objectives. Extensive numerical
experimentation shows that the proposed tuning is effective even
when our proportionality assumptions are not valid, and that
the particular tuning used for Nadir elimination strikes a good
trade-off among various performance metrics.},
  author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
  doi = {10.1109/TAC.2020.3034198},
  grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092},
  journal = {IEEE Transactions on Automatic Control},
  month = {8},
  number = {8},
  pages = {3518-3533},
  record = {available online Nov. 2020, accepted Aug. 2020, revised Mar. 2020, submitted Aug. 2019},
  title = {Dynamic Droop Control in Low Inertia Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2021-TAC-JPM.pdf},
  volume = {66},
  year = {2021}
}
[3] [doi] Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, vol. 36, iss. 6, pp. 5006-5019, 2021.
[Bibtex] [Abstract] [Download PDF]

With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage — frequency shaping control — that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.

@article{jcvm2021tps,
  abstract = {With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage -- frequency shaping control -- that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.},
  author = {Jiang, Yan and Cohn, Eliza and Vorobev, Petr and Mallada, Enrique},
  doi = {10.1109/TPWRS.2021.3072833},
  grants = {CAREER-1752362;CPS-2136324},
  journal = {IEEE Transactions on Power Systems},
  month = {11},
  number = {6},
  pages = {5006-5019},
  record = {early access Apr 2021, accepted Mar 2021, revised Oct 2020, submitted May 2020},
  title = {Storage-Based Frequency Shaping Control},
  url = {https://mallada.ece.jhu.edu/pubs/2021-TPS-JCVM.pdf},
  volume = {36},
  year = {2021}
}
[4] [doi] H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 5, pp. 1741-1746, 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{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}
}

ARO Workshop on Synchronization

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]

[1] [doi] 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}
}
[2] [doi] H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 5, pp. 1741-1746, 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{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}
}
[3] [doi] Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 6, pp. 1988-1993, 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},
  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}
}

1 paper accepted to L4DC

Our paper on Reinforcement Learning with almost sure constraints [1] has been accepted to the Learning for Dynamics and Control Conference!

[1] A. Castellano, H. Min, J. Bazerque, and E. Mallada, “Reinforcement Learning with Almost Sure Constraints,” in Learning for Dynamics and Control (L4DC), 2022, pp. 1-10.
[Bibtex] [Abstract] [Download PDF]

In this work we address the problem of finding feasible policies for Constrained Markov Decision Processes under probability one constraints. We argue that stationary policies are not sufficient for solving this problem, and that a rich class of policies can be found by endowing the controller with a scalar quantity, so called budget, that tracks how close the agent is to violating the constraint. We show that the minimal budget required to act safely can be obtained as the smallest fixed point of a Bellman-like operator, for which we analyze its convergence properties. We also show how to learn this quantity when the true kernel of the Markov decision process is not known, while providing sample-complexity bounds. The utility of knowing this minimal budget relies in that it can aid in the search of optimal or near-optimal policies by shrinking down the region of the state space the agent must navigate. Simulations illustrate the different nature of probability one constraints against the typically used constraints in expectation.

@inproceedings{cmbm2022l4dc,
  abstract = {In this work we address the problem of finding feasible policies for Constrained Markov Decision Processes under probability one constraints. We argue that stationary policies are not sufficient for solving this problem, and that a rich class of policies can be found by endowing the controller with a scalar quantity, so called budget, that tracks how close the agent is to violating the constraint. We show that the minimal budget required to act safely can be obtained as the smallest fixed point of a Bellman-like operator, for which we analyze its convergence properties. We also show how to learn this quantity when the true kernel of the Markov decision process is not known, while providing sample-complexity bounds. The utility of knowing this minimal budget relies in that it can aid in the search of optimal or near-optimal policies by shrinking down the region of the state space the agent must navigate. Simulations illustrate the different nature of probability one constraints against the typically used constraints in expectation.},
  author = {Castellano, Agustin and Min, Hancheng and Bazerque, Juan and Mallada, Enrique},
  booktitle = {Learning for Dynamics and Control (L4DC)},
  grants = {CAREER-1752362;TRIPODS-1934979;CPS-2136324},
  month = {2},
  pages = {1-10},
  pubstate = {accepted, submitted Dec 2021},
  title = {Reinforcement Learning with Almost Sure Constraints},
  url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-CMBMb.pdf},
  year = {2022}
}

1 paper accepted to ACC

Our paper on closed-form Minkowski sum approximations [1] has been accepted to the American Control Conference!

[1] J. Guthrie, M. Kobilarov, and E. Mallada, “Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance,” in American Control Conference (ACC), 2022, pp. 1-7.
[Bibtex] [Abstract] [Download PDF]

Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming solvers in the canonical setting of a circular robot navigating around $M$ convex polytopes over $N$ time steps. However, it requires introducing $(2+L)MN$ additional constraints and $LMN$ additional variables, with $L$ being the number of halfplanes per polytope, leading to larger nonlinear programs with slower and less reliable solving time. In this paper, we overcome this issue by building closed-form representations of the collision avoidance conditions by outer-approximating the Minkowski sum conditions for collision. Our solution requires only $MN$ constraints (and no additional variables), leading to a smaller nonlinear program. On motion planning problems for an autonomous car and quadcopter in cluttered environments, we achieve speedups of 4.0x and 10x respectively with significantly less variance in solve times and negligible impact on performance arising from the use of outer approximations.

@inproceedings{gkm2022acc,
  abstract = {Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming solvers in the canonical setting of a circular robot navigating around $M$ convex polytopes over $N$ time steps. However, it requires introducing $(2+L)MN$ additional constraints and $LMN$ additional variables, with $L$ being the number of halfplanes per polytope, leading to larger nonlinear programs with slower and less reliable solving time. In this paper, we overcome this issue by building closed-form representations of the collision avoidance conditions by outer-approximating the Minkowski sum conditions for collision. Our solution requires only $MN$ constraints (and no additional variables), leading to a smaller nonlinear program. On motion planning problems for an autonomous car and quadcopter in cluttered environments, we achieve speedups of 4.0x and 10x respectively with significantly less variance in solve times and negligible impact on performance arising from the use of outer approximations.},
  author = {Guthrie, James and Kobilarov, Marin and Mallada, Enrique},
  booktitle = {American Control Conference (ACC)},
  grants = {CAREER-1752362, CPS-2136324, TRIPODS-1934979},
  month = {2},
  pages = {1-7},
  pubstate = {accepted},
  record = {accepted, submitted Oct. 2021},
  title = {Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance},
  url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-GKM.pdf},
  year = {2022}
}

1 paper accepted to PSCC

Our paper on market mechanism for truthful bidding with energy storage [1] have been accepted to The Power Systems Computation Conference!

[1] R. K. Bansal, P. You, D. F. Gayme, and E. Mallada, “A Market Mechanism for Truthful Bidding with Energy Storage,” in Power Systems Computation Conference (PSCC), 2022, pp. 1-9.
[Bibtex] [Abstract] [Download PDF]

This paper proposes a market mechanism for multiinterval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energycycling functions that map prices to cycle depths. The resulting market-clearing process–implemented via convex programming–yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumerbased approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful cost, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.

@inproceedings{bygm2022pscc,
  abstract = {This paper proposes a market mechanism for multiinterval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energycycling functions that map prices to cycle depths. The resulting market-clearing process--implemented via convex programming--yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumerbased approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful cost, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.},
  author = {Bansal, Rajni Kant and You, Pengcheng and Gayme, Dennice F. and Mallada, Enrique},
  booktitle = {Power Systems Computation Conference (PSCC)},
  grants = {CAREER-1752362, TRIPODS-1934979, CPS-2136324},
  month = {7},
  pages = {1-9},
  record = {accepted Feb. 2022, submitted Oct. 2021},
  title = {A Market Mechanism for Truthful Bidding with Energy Storage},
  url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-BYGM.pdf},
  year = {2022}
}

1 paper accepted to SICON

Our paper on delays and saturation in contact tracing for disease control [1] have been accepted to SIAM Journal of Control and Optimization!

[1] Unknown bibtex entry with key [pfpypm2021sicon]
[Bibtex]

Rajni passes his GBO

Rajni Kant Bansal, ME Ph.D. student from our lab, passed his Graduate Board Oral Examination! Congratulations!