Year: 2016

1 paper accepted to Allerton

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Our paper [1] on understanding the role of local and strong convexity on the convergence and robustness of saddle-point dynamics has been accepted to the Allerton Conference on Communication, Control and Computing!

[1] [doi] A. Cherukuri, E. Mallada, S. H. Low, and J. Cortes, “The role of strong convexity-concavity in the convergence and robustness of the saddle-point dynamics,” in 54th Allerton Conference on Communication, Control, and Computing, 2016, pp. 504-510.
[Bibtex] [Abstract] [Download PDF]

This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these dynamics in terms of the diagonal Hessian blocks of the saddle function. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexityconcavity of the saddle function. If this property is global, and for the case when the saddle function takes the form of the Lagrangian of an equality constrained optimization problem, we establish the input-to-state stability of the saddlepoint dynamics by providing an ISS Lyapunov function. Various examples illustrate our results.

@inproceedings{cmlc2016allerton,
  abstract = {This paper studies the projected saddle-point dynamics for a twice differentiable convex-concave function, which we term saddle function. The dynamics consists of gradient
descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We provide a novel characterization of the omega-limit set of the trajectories of these dynamics in terms of the diagonal Hessian blocks of the saddle function. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexityconcavity of the saddle function. If this property is global, and for the case when the saddle function takes the form of the Lagrangian of an equality constrained optimization problem, we establish the input-to-state stability of the saddlepoint dynamics by providing an ISS Lyapunov function. Various examples illustrate our results.},
  author = {Ashish Cherukuri and Mallada, Enrique and Steven H. Low and Jorge Cortes},
  booktitle = {54th Allerton Conference on Communication, Control, and Computing},
  doi = {10.1109/ALLERTON.2016.7852273},
  grants = {1544771},
  keywords = {Saddle-Point Dynamics; Caratheodory solutions},
  month = {09},
  pages = {504-510},
  title = {The role of strong convexity-concavity in the convergence and robustness of the saddle-point dynamics},
  url = {https://mallada.ece.jhu.edu/pubs/2016-Allerton-CMLC.pdf},
  year = {2016}
}

1 paper accepted to CDC

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My paper [1] on decoupling power grid’s dynamic and steady-state performance has been accepted to the Conference on Decision and Control!

[1] [doi] E. Mallada, “iDroop: A dynamic droop controller to decouple power grid’s steady-state and dynamic performance,” in 55th IEEE Conference on Decision and Control (CDC), 2016, pp. 4957-4964.
[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}
}

Seed grant from E2SHI

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Our research project with René Vidal on  Leveraging Dynamics, Sparsity and Nonlinearities for Secure and Reliable Power Grid Operation has been selected by E2SHI’s Seed Grant Program for the 2016-2017 academic year.

1 paper accepted to IEEE TNSE

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Our paper [1] on synchronization of phase-coupled oscillators was accepted to appear in IEEE Transactions on Network Science and Engineering

[1] [doi] A. Gushchin, E. Mallada, and A. Tang, “Phase-coupled oscillators with plastic coupling: Synchronization and stability,” IEEE Transactions on Network Science and Engineering, vol. 3, iss. 4, pp. 240-256, 2016.
[Bibtex] [Abstract] [Download PDF]

In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system’s parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.

@article{gmt2016tnse,
  abstract = {In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system's parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.},
  author = {Gushchin, Andrey and Mallada, Enrique and Tang, Ao},
  doi = {10.1109/TNSE.2016.2605096},
  journal = {IEEE Transactions on Network Science and Engineering},
  keywords = {Synchronization},
  month = {09},
  number = {4},
  pages = {240-256},
  title = {Phase-coupled oscillators with plastic coupling: Synchronization and stability},
  url = {https://mallada.ece.jhu.edu/pubs/2016-TNSE-GMT.pdf},
  volume = {3},
  year = {2016}
}

1 paper accepted to PSCC

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Our paper [1] on unified frequency control and congestion management has been accepted to Power System Computation Conference!

[1] [doi] C. Zhao, E. Mallada, S. H. Low, and J. W. Bialek, “A Unified Framework for Frequency Control and Congestion Management,” in Power Systems Computation Conference, 2016, pp. 1-7.
[Bibtex] [Abstract] [Download PDF]

The existing frequency control framework in power systems is challenged by lower inertia and more volatile power injections. We propose a new framework for frequency control and congestion management. We formulate an optimization problem that rebalances power, restores the nominal frequency, restores inter-area flows and maintains line flows below their limits in a way that minimizes the control cost. The cost can be squared deviations from the reference generations, minimizing the disruption from the last optimal dispatch. Our control thus maintains system security without interfering with the market operation. By deriving a primal-dual algorithm to solve this optimization, we design a completely decentralized primary frequency control without the need for explicit communication among the participating agents, and a distributed unified control which integrates primary and secondary frequency control and congestion management. Simulations show that the unified control not only achieves all the desired control goals in system equilibrium, but also improves the transient compared to traditional control schemes.

@inproceedings{zmlb2016pscc,
  abstract = {The existing frequency control framework in power systems is challenged by lower inertia and more volatile power injections. We propose a new framework for frequency control and congestion management. We formulate an optimization problem that rebalances power, restores the nominal frequency, restores inter-area flows and maintains line flows below their limits in a way that minimizes the control cost. The cost can be squared deviations from the reference generations, minimizing the disruption from the last optimal dispatch. Our control thus maintains system security without interfering with the market operation. By deriving a primal-dual algorithm to solve this optimization, we design a completely decentralized primary frequency control without the need for explicit communication among the participating agents, and a distributed unified control which integrates primary and secondary frequency control and congestion management. Simulations show that the unified control not only achieves all the desired control goals in system equilibrium, but also improves the transient compared to traditional control schemes.},
  author = {Zhao, Changhong and Mallada, Enrique and Low, Steven H and Bialek, Janusz W},
  booktitle = {Power Systems Computation Conference},
  doi = {10.1109/PSCC.2016.7541028},
  keywords = {Power Networks; Frequency Control; Congestion Management},
  month = {06},
  pages = {1--7},
  title = {A Unified Framework for Frequency Control and Congestion Management},
  url = {https://mallada.ece.jhu.edu/pubs/2016-PSCC-ZMLB.pdf},
  year = {2016}
}