I gave a talk on “Inverter-based Control for Low Inertia Power Systems” in the Control Seminar at the University of Michigan. 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{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]

This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.

```
@article{pm2019tcns,
abstract = {This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.},
author = {Pates, Richard and Mallada, Enrique},
doi = {10.1109/TCNS.2019.2922503},
grants = {CPS:1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362},
journal = {IEEE Transactions on Control of Network Systems},
keywords = {Network Control; Power Networks},
month = {9},
number = {3},
pages = {1174-1184},
title = {Robust Scale Free Synthesis for Frequency Regulation in Power Systems},
url = {https://mallada.ece.jhu.edu/pubs/2019-TCNS-PM.pdf},
volume = {6},
year = {2019}
}
```

[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}
}
```