Our papers on evaluating the cost of security constrained OPF [1], evaluating the performance tradeoffs of designing inverter-based control for low inertia power systems [2], and characterizing performance of networked dynamical systems over directed graphs [3] have been accepted to IEEE Conference on Decision and Control. See you in Australia!

[Bibtex] [Abstract] [Download PDF]

The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks.

```
@inproceedings{hcm2017cdc,
abstract = {The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks.},
author = {Hajiesmaili, Mohammad H. and Cai, Desmond and Mallada, Enrique},
booktitle = {56th IEEE Conference on Decision and Control (CDC)},
doi = {10.1109/CDC.2017.8263947},
grants = {1544771, 1711188, 1736448},
keywords = {Power Networks},
month = {12},
pages = {2035-2040},
title = {Understanding the Inefficiency of Security-Constrained Economic Dispatch},
url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-HCM.pdf},
year = {2017}
}
```

[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]

In this paper we investigate the performance of linear networked dynamical systems over strongly connected digraphs. We consider first and second order systems subject to distributed disturbance inputs, and define an appropriate system output so that the performance measure is quantified through the input-output $\mathcal H_2$ norm of the system. We first develop a generalized framework for the computation of the $\mathcal H_2$ norm. We apply this framework to systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We consider two performance metrics and find closed form solutions for the first and bounds for the other; which both depend on the eigenvalues of these graph Laplacians. Numerical examples indicate that: (i) the tightness of the bounds are highly dependent on the graph structure, (ii) the $\mathcal H_2$ norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.

```
@inproceedings{omg2017cdc,
abstract = {In this paper we investigate the performance of linear networked dynamical systems over strongly connected digraphs. We consider first and second order systems subject to distributed disturbance inputs, and define an appropriate system output so that the performance measure is quantified through the input-output $\mathcal H_2$ norm of the system. We first develop a generalized framework for the computation of the $\mathcal H_2$ norm. We apply this framework to systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We consider two performance metrics and find closed form solutions for the first and bounds for the other; which both depend on the eigenvalues of these graph Laplacians.
Numerical examples indicate that: (i) the tightness of the bounds are highly dependent on the graph structure, (ii) the $\mathcal H_2$ norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.},
author = {Oral, H. Giray and Mallada, Enrique and Gayme, Dennice},
booktitle = {56th IEEE Conference on Decision and Control (CDC)},
doi = {10.1109/CDC.2017.8263893},
grants = {1544771, W911NF-17-1-0092},
keywords = {Power Networks},
month = {12},
pages = {1688-1694},
title = {Performance of first and second order linear networked systems over digraphs},
url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-OMG.pdf},
year = {2017}
}
```