I gave a talk on “Dynamic Droop Control for Low Inertia Power Systems” in the Panel session at IEEE ISGT 2019. Related publications include [1, 2, 3, 4]
![[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]
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}
}[Bibtex] [Abstract] [Download PDF]
Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters. Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.
@inproceedings{jpm2017cdc,
abstract = {Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters.
Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.},
author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
booktitle = {56th IEEE Conference on Decision and Control (CDC)},
doi = {10.1109/CDC.2017.8264414},
grants = {1544771, 1711188, W911NF-17-1-0092},
keywords = {Power Networks},
month = {12},
pages = {5098-5105},
title = {Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems},
url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-JPM.pdf},
year = {2017}
}[Bibtex] [Abstract] [Download PDF]
This paper presents a novel Dynam-i-c Droop (iDroop) control mechanism to perform primary frequency control with gird-connected inverters that improves the network dynamic performance while maintaining the same steady-state characteristics of droop control. The work is motivated by the increasing dynamic degradation experienced by the power grid due to the increment on asynchronous inverted-based generation. We show that the widely suggested virtual inertia solution suffers from unbounded noise amplification (infinite H2 norm) and therefore could potentially degrade further the grid performance once widely deployed. This motivates the proposed solution on this paper that over- comes the limitations of virtual inertia controllers while sharing the same advantages of traditional droop control. In particular, our iDroop controllers are decentralized, rebalance supply and demand, and provide power sharing. Furthermore, our solution improves the dynamic performance without affecting the steady state solution. Our algorithm can be incrementally deployed and can be guaranteed to be stable using a decentralized sufficient stability condition on the parameter values. We illustrate several features of our solution using numerical simulations.
@inproceedings{m2016cdc,
abstract = {This paper presents a novel Dynam-i-c Droop (iDroop) control mechanism to perform primary frequency control with gird-connected inverters that improves the network dynamic performance while maintaining the same steady-state characteristics of droop control. The work is motivated by the increasing dynamic degradation experienced by the power grid due to the increment on asynchronous inverted-based generation. We show that the widely suggested virtual inertia solution suffers from unbounded noise amplification (infinite H2 norm) and therefore could potentially degrade further the grid performance once widely deployed.
This motivates the proposed solution on this paper that over- comes the limitations of virtual inertia controllers while sharing the same advantages of traditional droop control. In particular, our iDroop controllers are decentralized, rebalance supply and demand, and provide power sharing. Furthermore, our solution improves the dynamic performance without affecting the steady state solution. Our algorithm can be incrementally deployed and can be guaranteed to be stable using a decentralized sufficient stability condition on the parameter values. We illustrate several features of our solution using numerical simulations.},
author = {Mallada, Enrique},
booktitle = {55th IEEE Conference on Decision and Control (CDC)},
doi = {10.1109/CDC.2016.7799027},
grants = {1544771},
keywords = {Power Networks},
month = {12},
pages = {4957-4964},
title = {iDroop: A dynamic droop controller to decouple power grid's steady-state and dynamic performance},
url = {https://mallada.ece.jhu.edu/pubs/2016-CDC-M.pdf},
year = {2016}
}