1 paper accepted to TAC

Our paper [1] on the role of convexity on the convergence and robustness of saddle-point dynamics has been accepted to IEEE Transactions on Automatic Control!

[1] [doi] A. Cherukuri, E. Mallada, S. H. Low, and J. Cortes, “The role of convexity on saddle-point dynamics: Lyapunov function and robustness,” IEEE Transactions on Automatic Control, vol. 63, iss. 8, pp. 2449-2464, 2018.
[Bibtex] [Abstract] [Download PDF]

This paper studies the projected saddle-point dynamics associated to a 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 examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.

@article{cmlc2018tac,
  abstract = {This paper studies the projected saddle-point dynamics associated to a 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 examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit  set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.},
  author = {Cherukuri, Ashish and Mallada, Enrique and Steven H. Low and Jorge Cortes},
  doi = {10.1109/TAC.2017.2778689},
  grants = {W911NF-17-1-0092},
  journal = {IEEE Transactions on Automatic Control},
  keywords = {Saddle-Point Dynamics; Caratheodory solutions},
  month = {08},
  number = {8},
  pages = {2449-2464},
  title = {The role of convexity on saddle-point dynamics: Lyapunov function and robustness},
  url = {https://mallada.ece.jhu.edu/pubs/2018-TAC-CMLC.pdf},
  volume = {63},
  year = {2018}
}

1 invited paper in Allerton

I presented our work on characterizing the dynamic performance of power networks with heterogeneously rated machines [1] in an invited session in the 55th Annual Allerton Conference on Communication, Control, and Computing.

[1] [doi] F. Paganini and E. Mallada, “Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia,” in 55th Allerton Conference on Communication, Control, and Computing, 2017, pp. 324-331.
[Bibtex] [Abstract] [Download PDF]

A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations. We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine’s rating); we characterize Nadir and RoCoF by the Linf norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the L2 norm of the error of the vector of bus frequencies w.r.t. the system frequency. For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.

@inproceedings{pm2017allerton,
  abstract = {A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations.

We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine's rating); we characterize Nadir and RoCoF by the Linf norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the L2 norm of the error of the vector of bus frequencies w.r.t. the system frequency.

For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.},
  author = {Paganini, Fernando and Mallada, Enrique},
  booktitle = {55th Allerton Conference on Communication, Control, and Computing},
  doi = {10.1109/ALLERTON.2017.8262755},
  grants = {1544771, 1711188, 1736448},
  keywords = {Power Networks; Synchronization},
  month = {10},
  pages = {324-331},
  title = {Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia},
  url = {https://mallada.ece.jhu.edu/pubs/2017-Allerton-PM.pdf},
  year = {2017}
}

AMPS grant award from NSF

I received a grant award from the Algorithms for Modern Power Systems (AMPS) program of the NSF!
The title is “Dynamics-aware Algorithms for Real-time Structured Fault Detection in Power Systems”

3 papers accepted to CDC 17

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!

[1] [doi] M. H. Hajiesmaili, D. Cai, and E. Mallada, “Understanding the Inefficiency of Security-Constrained Economic Dispatch,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 2035-2040.
[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}
}
[2] [doi] Y. Jiang, R. Pates, and E. Mallada, “Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 5098-5105.
[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}
}
[3] [doi] G. H. Oral, E. Mallada, and D. Gayme, “Performance of first and second order linear networked systems over digraphs,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 1688-1694.
[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}
}

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!

Read more

[1] [doi] 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!

Read more

[1] [doi] 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!

Read more

[1] [doi] 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] [doi] 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.