## EPCN grant award from NSF

I received a grant award from the Energy, Power, Control, and Networks (EPCN) program of the NSF!
The title is “An Optimization Decomposition Framework for Principled Multi-Timescale Market Design and Co-Optimization”

## 1 paper accepted to IEEE CSL

Our paper [1] on the existence and uniqueness of high-voltage solutions of power flow equations in tree networks has been IEEE Control System Letters!

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[1] K. Dvijotham, E. Mallada, and J. W. Simpson-Porco, “High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms,” IEEE Control Systems Letters, vol. 1, iss. 2, pp. 322-327, 2017.
[Bibtex] [Abstract] [Download PDF]

The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this paper, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: fixed point iterations, convex relaxations, and energy functions – we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that (i) voltage magnitudes are increasing functions of the reactive power injections, (ii) the solution is a continuous function of the injections, and (iii) the solution is the last one to vanish as the system is loaded past the feasibility boundary.

``````@article{dms2017ieee-csl,
abstract = {The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this paper, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: fixed point iterations, convex relaxations, and energy functions - we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that (i) voltage magnitudes are increasing functions of the reactive power injections, (ii) the solution is a continuous function of the injections, and (iii) the solution is the last one to vanish as the system is loaded past the feasibility boundary.},
author = {Dvijotham, Krishnamurthy and Mallada, Enrique and Simpson-Porco, John W.},
doi = {10.1109/LCSYS.2017.2717578},
grants = {1544771},
journal = {IEEE Control Systems Letters},
keywords = {Power Networks; Power Flow Solutions},
month = {10},
number = {2},
pages = {322-327},
title = {High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms},
url = {https://mallada.ece.jhu.edu/pubs/2017-IEEE-CSL-DMS.pdf},
volume = {1},
year = {2017}
}``````

## 1 paper accepted to IEEE TAC

Our paper [1] on load side frequency control and congestion management has been accepted to IEEE Transactions on Automatic Control!

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[1] E. Mallada, C. Zhao, and S. H. Low, “Optimal load-side control for frequency regulation in smart grids,” IEEE Transactions on Automatic Control, vol. 62, iss. 12, pp. 6294-6309, 2017.
[Bibtex] [Abstract] [Download PDF]

Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. Simulations are used to illustrate the properties of our solution.

``````@article{mzl2017tac,
abstract = {Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints.
In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. Simulations are used to illustrate the properties of our solution.},
author = {Mallada, Enrique and Zhao, Changhong and Low, Steven H},
doi = {10.1109/TAC.2017.2713529},
grants = {1544771},
journal = {IEEE Transactions on Automatic Control},
keywords = {Power Networks},
month = {12},
number = {12},
pages = {6294-6309},
title = {Optimal load-side control for frequency regulation in smart grids},
url = {https://mallada.ece.jhu.edu/pubs/2017-TAC-MZL.pdf},
volume = {62},
year = {2017}
}``````

## 1 paper accepted to IFAC World Congress

Our paper [1] on robust inverter-based control for low inertia power systems has been accepted to IFAC World Congress!

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[1] R. Pates and E. Mallada, “Decentralised Robust Inverter-based Control in Power Systems,” in IFAC World Congress, 2017, pp. 5548-5553.
[Bibtex] [Abstract] [Download PDF]

This paper develops a novel framework for power system stability analysis, that allows for the decentralised design of inverter based controllers. The method requires that each individual inverter satisfies a standard H1 design requirement. Critically each requirement depends only on the dynamics of the components and inverters at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The method is both robust to network and delay uncertainties, as well as heterogeneous network components, and when no network information is available it reduces to the standard decentralised passivity sufficient condition for stability. We illustrate the novelty and strength of our approach by studying the design of inverter-based control laws in the presence of delays.

``````@inproceedings{pm2017ifac-wc,
abstract = {This paper develops a novel framework for power system stability analysis, that allows for the decentralised design of inverter based controllers. The method requires that each individual inverter satisfies a standard H1 design requirement. Critically each requirement depends only on the dynamics of the components and inverters at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The method is both robust to network and delay uncertainties, as well as heterogeneous network components, and when no network information is available it reduces to the standard decentralised passivity sufficient condition for stability. We illustrate the novelty and strength of our approach by studying the design of inverter-based control laws in the presence of delays.},
author = {Pates, Richard and Mallada, Enrique},
booktitle = {IFAC World Congress},
doi = {https://doi.org/10.1016/j.ifacol.2017.08.1097},
grants = {1544771},
keywords = {Power Networks},
month = {7},
number = {1},
pages = {5548 - 5553},
title = {Decentralised Robust Inverter-based Control in Power Systems},
url = {https://mallada.ece.jhu.edu/pubs/2017-IFAC-WC-PM.pdf},
volume = {50},
year = {2017}
}``````

## 1 paper accepted to IEEE TPS

Our paper [1] on multi-timescale decomposition for joint economic dispatch and frequency regulation was accepted to appear in IEEE Transactions on Power Systems!

[1] D. Cai, E. Mallada, and A. Wierman, “Distributed optimization decomposition for joint economic dispatch and frequency regulation,” IEEE Transactions on Power Systems, vol. 32, iss. 6, pp. 4370-4385, 2017.
[Bibtex] [Abstract] [Download PDF]

Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

``````@article{cmw2017tps,
abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE
24-bus reliability test system.},
author = {Cai, Desmond and Mallada, Enrique and Wierman, Adam},
doi = {10.1109/TPWRS.2017.2682235},
grants = {1544771},
journal = {IEEE Transactions on Power Systems},
keywords = {Power Networks; Markets},
month = {11},
number = {6},
pages = {4370-4385},
title = {Distributed optimization decomposition for joint economic dispatch and frequency regulation},
url = {https://mallada.ece.jhu.edu/pubs/2017-TPS-CMW.pdf},
volume = {32},
year = {2017}
}``````

## ENERGISE grant award from DoE!

We just received an ENERGISE (Enabling Extreme Real-time Grid Integration of Solar Energy) award from the Department of Energy (DoE).

Project Description: The project seeks to overcome the challenges of managing an increasingly variable and uncontrollable power supply due to roof-top solar by adapting advanced real-time control and optimization concepts from high-voltage power systems to low-voltage three-phase distribution grid operations. This will allow us to develop state-of-the-science analytical and software tools necessary to ensure reliable and resilient distribution system operations under extreme penetration of solar PV generation. The team will also study the role and capability of novel energy market formulations and validate the resulting technology in multiple phases with industry partners.

## Grant award from Army Research Office

I received a grant award from the Army Research Office!
The title is “Beyond Consensus: A Distributed Optimization Approach for Complex Coordination in Large-scale Dynamic Networks”

## 1 paper accepted to Allerton

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] 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

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

[1] 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

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.