Seminar @ KTH

I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Dynamic Droop Approach” at KTH, Sweden. 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] Y. Jiang, R. Pates, and E. Mallada, Dynamic Droop Control in Low Inertia Power Systems, 2020, revised, submitted Aug. 2019.
[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.

@unpublished{jpm2019a-preprint,
  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},
  grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092},
  month = {03},
  title = {Dynamic Droop Control in Low Inertia Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-JPM.pdf},
  year = {2020, revised, submitted Aug. 2019}
}
[3] Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, Dynamic Droop Approach for Storage-based Frequency Control, 2019, submitted.
[Bibtex] [Abstract] [Download PDF]

Transient frequency dips that follow sudden power imbalances –frequency Nadir– represent a big challenge for frequency stability of low-inertia power systems. Since low inertia is identified as one of the causes for deep frequency Nadir, virtual inertia, which is provided by energy storage units, is said to be one of the solutions to the problem. In the present paper, we propose a new method for frequency control with energy storage systems (ESS), called dynamic droop control (iDroop), that can completely eliminate frequency Nadir during transients. Nadir elimination allows us to perform frequency stability assessment without the need for direct numerical simulations of system dynamics. We make a direct comparison of our developed strategy with the usual control approaches –virtual inertia (VI) and droop control (DC)– and show that iDroop is more effective than both in eliminating the Nadir. More precisely, iDroop achieves the Nadir elimination under significantly lower gains than virtual inertia and requires almost 40 percent less storage power capacity to implement the control. Moreover, we show that rather unrealistic control gains are required for virtual inertia in order to achieve Nadir elimination.

@unpublished{jcvm2019a-preprint,
  abstract = {Transient frequency dips that follow sudden power imbalances --frequency Nadir-- represent a big challenge for frequency stability of low-inertia power systems. Since low inertia is identified as one of the causes for deep frequency Nadir, virtual inertia, which is provided by energy storage units, is said to be one of the solutions to the problem. In the present paper, we propose a new method for frequency control with energy storage systems (ESS),  called dynamic droop control (iDroop), that can completely eliminate frequency Nadir during transients. Nadir elimination allows us to perform frequency stability assessment without the need for direct numerical simulations of system dynamics. We make a direct comparison of our developed strategy with the usual control approaches --virtual inertia (VI) and droop control (DC)-- and show that iDroop is more effective than both in eliminating the Nadir. 
More precisely, iDroop achieves the Nadir elimination under significantly lower gains than virtual inertia and requires almost 40 percent less storage power capacity to implement the control. Moreover, we show that rather unrealistic control gains are required for virtual inertia in order to achieve Nadir elimination. },
  author = {Jiang, Yan and Cohn, Eliza and Vorobev, Petr and Mallada, Enrique},
  grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
  month = {10},
  title = {Dynamic Droop Approach for Storage-based Frequency Control},
  url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-JCVM.pdf},
  year = {2019, submitted}
}