I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Dynamic Droop Approach” at The Mathematics of Energy Systems Workshop in Issac Newton Institute for Mathematical Sciences. Related publications include [1, 2, 3]

[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{pm2019tac,
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 = {9},
pubstate = {accepted, revised May 2019, submitted Oct. 2018},
title = {Global analysis of synchronization performance for power systems: bridging the theory-practice gap},
url = {https://mallada.ece.jhu.edu/pubs/2019-TAC-PM.pdf},
year = {2019}
}
```

[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.

```
@unpublished{jpm2019a-preprint,
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 = {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 = {01},
title = {Dynamic Droop Control in Low Inertia Power Systems},
url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-JPM.pdf},
year = {2020, under revision, submitted Aug. 2019}
}
```

[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}
}
```