1 paper accepted to TAC

Our paper on Dynamic Droop Control in Low-inertia Power Systems [1] has been accepted to IEEE Transactions on Automatic Control!

[1] Y. Jiang, R. Pates, and E. Mallada, “Dynamic Droop Control in Low Inertia Power Systems,” IEEE Transactions on Automatic Control, pp. 1-16, 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},
  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 = {08},
  pages = {1-16},
  pubstate = {accepted, revised Mar. 2020, submitted Aug. 2019},
  title = {Dynamic Droop Control in Low Inertia Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-JPM.pdf},
  year = {2020}
}

1 paper accepted to TSUSC

Our paper on online EV scheduling for adaptive charging networks [1] has been accepted to IEEE Transactions on Sustainable Computing!

[1] [doi] A. Bahram, M. H. Hajiesmaili, Z. Lee, N. Crespi, and E. Mallada, “Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints,” IEEE Transactions on Sustainable Computing, 2020.
[Bibtex] [Abstract] [Download PDF]

Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.

@article{bhlcm2019tsusc,
  abstract = {Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.},
  author = {Bahram, Alina and Hajiesmaili, Mohammad H. and Lee, Zachary and Crespi, Noel and Mallada, Enrique},
  doi = {10.1109/TSUSC.2020.2979854},
  grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979,EPCN-1711188,},
  journal = {IEEE Transactions on Sustainable Computing},
  month = {1},
  title = {Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints},
  url = {https://mallada.ece.jhu.edu/pubs/2020-TSUSC-BHLCM.pdf},
  year = {2020}
}

2 papers accepted to ECC 20

Our papers on minimum-time charging of energy storage via approximate conic relaxation [1] and on generation cost reduction [2] have been accepted to European Control Conference 2020!

[1] J. Guthrie and E. Mallada, “Minimum-Time Charging of Energy Storage in Microgrids via Approximate Conic Relaxation,” in 19th IEEE European Control Conference (ECC), 2020, pp. 1713-1718.
[Bibtex] [Abstract] [Download PDF]

We study the problem of maximizing energy transfer to a load in a DC microgrid while respecting constraints on bus voltages and currents, and accounting for the impact of neighboring constant power loads. Both the objective and dynamics give rise to indefinite quadratic terms, resulting in a non-convex optimization problem. Through change of variables and relaxations we develop a closely related second-order cone program. The problem retains the same feasible set as the original problem but utilizes a linear approximation of the non-convex objective. We demonstrate how this can be used to design approximately optimal charging profiles for periodic pulsed loads in real time.

@inproceedings{gm2020ecc,
  abstract = {We study the problem of maximizing energy transfer to a load in a DC microgrid while respecting constraints on bus voltages and currents, and accounting for the impact of neighboring constant power loads.  Both the objective and dynamics give rise to indefinite quadratic terms, resulting in a non-convex optimization problem. Through change of variables and relaxations we develop a closely related second-order cone program. The problem retains the same feasible set as the original problem but utilizes a linear approximation of the non-convex objective. We demonstrate how this can be used to design approximately optimal charging profiles for periodic pulsed loads in real time.},
  author = {Guthrie, James and Mallada, Enrique},
  booktitle = {19th IEEE European Control Conference (ECC)},
  grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
  keywords = {Power Networks},
  month = {5},
  pages = {1713-1718},
  title = {Minimum-Time Charging of Energy Storage in Microgrids via Approximate Conic Relaxation},
  url = {https://mallada.ece.jhu.edu/pubs/2020-ECC-GM-b.pdf},
  year = {2020}
}
[2] Y. Shen, M. Bichuch, and E. Mallada, “On the Value of Energy Storage in Generation Cost Reduction,” in 19th IEEE European Control Conference (ECC), 2020, pp. 1526-1532.
[Bibtex] [Abstract] [Download PDF]

This work seeks to quantify the benefits of using energy storage toward the reduction of the energy generation cost of a power system. A two-fold optimization framework is provided where the first optimization problem seeks to find the optimal storage schedule that minimizes operational costs. Since the operational cost depends on the storage capacity, a second optimization problem is then formulated with the aim of finding the optimal storage capacity to be deployed. Although, in general, these problems are difficult to solve, we provide a lower bound on the cost savings for a parametrized family of demand profiles. The optimization framework is numerically illustrated using real-world demand data from ISO New England. Numerical results show that energy storage can reduce energy generation costs by at least 2.5 percent.

@inproceedings{sbm2020ecc,
  abstract = {This work seeks to quantify the benefits of using energy storage toward the reduction of the energy generation cost of a power system.  A two-fold optimization framework is provided where the first optimization problem seeks to find the optimal storage schedule that minimizes operational costs. Since the operational cost depends on the storage capacity, a second optimization problem is then formulated with the aim of finding the optimal storage capacity to be deployed. Although, in general, these problems are difficult to solve, we provide a lower bound on the cost savings for a  parametrized family of demand profiles.
The optimization framework is numerically illustrated using real-world demand data from ISO New England. Numerical results show that energy storage can reduce energy generation costs by at least 2.5 percent.},
  author = {Shen, Yue and Bichuch, Maxim and Mallada, Enrique},
  booktitle = {19th IEEE European Control Conference (ECC)},
  grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
  keywords = {Power Networks},
  month = {5},
  pages = {1526-1532},
  title = {On the Value of Energy Storage in Generation Cost Reduction},
  url = {https://mallada.ece.jhu.edu/pubs/2020-ECC-SBM.pdf},
  year = {2020}
}

1 paper accepted to ACC 20

Our paper on implicit trajectory planning for feedback linearizable systems [1] has been accepted to American Control Conference 2020!

[1] [doi] T. Zheng, J. W. Simpson-Porco, and E. Mallada, “Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach,” in American Control Conference, 2020, pp. 4677-4682.
[Bibtex] [Abstract] [Download PDF]

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.

@inproceedings{zsm2020acc,
  abstract = { We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.},
  author = {T. Zheng and J. W. Simpson-Porco and E. Mallada},
  booktitle = {American Control Conference},
  doi = {10.23919/ACC45564.2020.9147997},
  grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, ARO-W911NF-17-1-0092},
  month = {7},
  pages = {4677-4682},
  title = {Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach},
  url = {https://mallada.ece.jhu.edu/pubs/2020-ACC-ZSM.pdf},
  year = {2020}
}

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] Unknown bibtex entry with key [jpm2019a-preprint]
[Bibtex]
[3] Unknown bibtex entry with key [jcvm2019a-preprint]
[Bibtex]