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= [index.html Keith Moffat]

= Research

*For people in the power systems field*, my research is best described as ``data-driven distribution network optimization. The tools I have developed include parameter, topology, and state estimation techniques, as well as feedback optimization and distributed phasor feedback control, which adjust power output/load in real time in response to distribution network conditions. In addition to distribution network automation, I am also interested in electricity markets, transmission network applications, and inverter control for low inertia grids.''

# ``new tools that automate distributed energy resource dispatch, tune inverter control loops and power system stabilizers on low inertia grids, and provide situational awareness to grid operators such as state estimation, online topology identification, and online network admittance estimation.'' 
# , orchestrate power systems markets, 
# provide stability guarantees for low-inertia systems, 

*For people in the learning, control, and optimization fields*, my research is best described as ``online, data-driven control and optimization methods for stochastic network systems with a focus on power system applications, with additional interests in hybrid systems, market design, unsupervised learning, reinforcement learning, and graph theory.''

*For general audiences*, my research is best described as ``developing mathematical techniques which use new technologies such as satellite-synchronized grid sensors to help with our transition from fossil fuels to intermittent renewable energy resources by keeping track of what's happening on the grid and coordinating grid-connected batteries, electric vehicle charging, and electric home heaters\/AC units.'' #With modification, the math can also be used in other areas such as biological\/epidemic networks, transportation networks, and computer networks.'' 
# social

# ``developing mathematical techniques to help with our transition from fossil fuels to intermittent renewable energy resources by keeping track of what's happening on the grid and coordinating grid-connected batteries, electric vehicle charging, and electric home heaters/AC units. I also use satellite-synchronized grid sensors to detect when something weird, such as a tree falling on a power line, has occurred on the grid.'' 


# *Below* is a list of some of the projects that I have worked on over the course of my Ph.D. and the relevant publications.

*Below* is a list of some of the projects that I have worked on over the course of my Ph.D. and a short statement on my long term research interests.


== Voltage Phasor Control

~~~
{}{img_left}{figures/VPC13node.png}{alt text}{261}{213}{}
# Voltage Phasor Control (VPC), introduced by our team at Berkeley \[[https://www.mdpi.com/1996-1073/13/1/190/htm PBC paper]\] 
Voltage Phasor Control (VPC), introduced by our team at Berkeley and made possible by high-precision Phasor Measurement Units (PMU), is a new way of controlling distributed energy resources in which the power flow optimization broadcasts voltage phasor targets to distributed feedback controllers, rather than open-loop power setpoints. 
We demonstrated PBC on unbalanced, three-phase distribution networks in Hardware-In-the-Loop simulations at Lawrence Berkeley Lab ([https://www.lbl.gov LBL])'s [https://flexlab.lbl.gov FLEXLAB] test site using the Distributed Extensible Grid Control (DEGC) software platform \[[https://ieeexplore.ieee.org/document/9372161 DEGC paper]\] developed by our lab \[[https://ieeexplore.ieee.org/abstract/document/9303006 VPC with DEGC paper]\] and adaptive MIMO feedback control \[[https://drive.google.com/file/d/1EbxyzJttJS4RzteYMSn6hbg7ngvoYNUA/view?usp=sharing P-V Sensitivity presentation], [https://drive.google.com/file/d/1u0oX5BjLyWSDIbnrRIJ-9QyqzoRkEjfH/view?usp=sharing MIMO Phasor Control presentation]\].
We have also proved that VPC is more effective than both open-loop power commands and voltage magnitude control in avoiding upstream line flow constraint violations, providing a clear use case for VPC and guidelines for how it should be applied. 
~~~

# [[https://drive.google.com/file/d/1EbxyzJttJS4RzteYMSn6hbg7ngvoYNUA/view?usp=sharing P-V Sensitivity presentation] and [https://ieeexplore.ieee.org/document/9494799 paper], [https://drive.google.com/file/d/1u0oX5BjLyWSDIbnrRIJ-9QyqzoRkEjfH/view?usp=sharing MIMO Phasor Control presentation] and [https://ieeexplore.ieee.org/document/9494835 paper]\].


==== Relevant publications:

*K. Moffat* and A. Von Meier. Using voltage phasor control to avoid distribution network constraint violations. In 2022 IEEE Power Systems Computation Conference (PSCC), Submitted, pages 1–6. IEEE, 2022. [https://arxiv.org/abs/2201.05919 Pre-print Link].

*K. Moffat* and A. von Meier. Linear quadratic phasor control of unbalanced distribution networks. In 2021 IEEE Madrid PowerTech, pages 1–6. IEEE, 2021. [https://ieeexplore.ieee.org/document/9494835 Paper link], [https://drive.google.com/file/d/1u0oX5BjLyWSDIbnrRIJ-9QyqzoRkEjfH/view?usp=sharing PowerTech 2021 presentation].

*K. Moffat* Local power-voltage sensitivity and thevenin impedance estimation from phasor measurements. In 2021 IEEE Madrid PowerTech, pages 1–6. IEEE, 2021. [https://ieeexplore.ieee.org/document/9494799 Paper link], [https://drive.google.com/file/d/1EbxyzJttJS4RzteYMSn6hbg7ngvoYNUA/view?usp=sharing PowerTech2021 presentation].

*K. Moffat*, J. Pakshong, L. Chu, G. Fierro, Baudette J. Gehbauer C. Swartz, J., and A. von Meier. Phasor based control with the  distributed, extensible grid control platform. In 2021 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), pages 1–5. IEEE, 2021. [https://ieeexplore.ieee.org/document/9372161 Paper link].

G. Fierro, *K. Moffat*, J. Pakshong, and A. von Meier. An extensible software and communication platform for distributed energy resource management. In 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), pages 1–6. IEEE, 2020. [https://ieeexplore.ieee.org/abstract/document/9303006 Paper link].

M. Baudette, J. Swartz, *K. Moffat*, J. Pakshong, C. Gehbauer, and A. von Meier. Hardware-in-the-loop benchmarking setup for phasor based control validation. 2021. [https://eta-publications.lbl.gov/publications/hardware-loop-benchmarking-setup Paper link].

# von Meier, A., E. L. Ratnam, K. Brady, K. Moffat, and J. Swartz. Phasor-based control for scalable integration of variable energy resources. Energies 13, no. 1 (2020): 190. [https://www.mdpi.com/1996-1073/13/1/190/htm Paper link].



== Grid Parameter Estimation

~~~
{}{img_left}{figures/eiv.png}{alt text}{215}{180}{}
The lack of accurate distribution network models and knowledge of the operating state prevent most DER dispatch methods from being deployed in real life.
We have proved that, while it is impossible to estimate the full network admittance matrix from voltage and current phasor measurements, it is always possible to estimate the admittance matrix for the Kron-reduced network \[[https://ieeexplore.ieee.org/document/8918302 Limitations and Tools paper]\].
We also demonstrated that estimating the ``subKron'' impedance matrix, motivated by Laplacian graph theory, is more robust to measurement noise because the data is better conditioned. 
We have also implemented the least squares complex data regression recursively, eliminating the need for storing and processing large batches of PMU data \[[https://ieeexplore.ieee.org/abstract/document/9087766 Real Time paper]\].

Subsequent work, in collaboration with researchers at EPFL/ETHZ, has leveraged a Bayesian Error-In-Variables formulation to produce the first accurate, reproducible 3-phase distribution grid estimation from PMU measurements with realistic signal-to-noise ratios without active perturbation \[[https://arxiv.org/abs/2107.04480 Bayesian Error-In-Variables preprint]\].
~~~

==== Relevant publications:

*K.  Moffat*, M. Bariya, and A. Von Meier. Unsupervised impedance and topology estimation of distribution networks—limitations and tools. IEEE Transactions on Smart Grid, 11(1):846–856, 2019. [https://ieeexplore.ieee.org/document/8918302 Paper link].

*K. Moffat*, M. Bariya, and A. von Meier, Network Impedance Estimation For Microgrid Control Using Noisy Synchrophasor Measurements, 2018 IEEE 19th Workshop on Control and Modeling for Power Electronics (COMPEL), 2018, pp. 1-6 [https://ieeexplore.ieee.org/document/8458497 Paper link].

*K. Moffat*, M. Bariya, and A. Von Meier. Real time effective impedance estimation for power system state estimation. In 2020 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), pages 1–5. IEEE, 2020. [https://ieeexplore.ieee.org/abstract/document/9087766 Paper link].

J.-S. Brouillon, E. Fabbiani, P. Nahata, *K. Moffat*, F. Dorfler, and G. Ferrari-Trecate. Bayesian error-in-variables models for the identification of distribution grids. IEEE Transactions on Power Systems, In Revision, 2022. [https://arxiv.org/abs/2107.04480 Preprint link].






== State and Topology Estimation

~~~
{}{img_left}{figures/MAPSE.png}{alt text}{200}{141}{}
Electric grids have switches which reconfigure the network topology. Considering an alternative grid operation scenario in which a network model /is/ available but the switch statuses are unknown, we introduced the Multiple model Adaptive Power system State Estimator (MAPSE) \[[https://drive.google.com/file/d/1ytW8harTNkcxA2W60b0yPVT2Pd0jP7Jo/view?usp=sharing MAPSE presentation]\], which models the distribution network as a dynamic hybrid system---the voltage phasors are the continuous state variables, while each discrete ``mode'' corresponds to a different network configuration. The MAPSE estimates the hybrid state by 1) maintaining a continuous state estimate for each discrete mode using a bank of Unscented Kalman Filters (UKFs), and 2) estimating the topology/discrete mode by applying Bayesian recursion on the UKF residuals.
We demonstrated that the MAPSE can accurately detect network topology changes using PMU with noise levels consistent with real PMU data \[[https://ieeexplore.ieee.org/document/8784639 Empirical paper]\].
~~~
# \cite{moffat2021MMAE}

# Considering an alternative grid operation scenario in which a network model /is/ available but the network switch configurations are unknown, we introduced the Multiple model Adaptive Power system State Estimator (MAPSE) \[[https://drive.google.com/file/d/1ytW8harTNkcxA2W60b0yPVT2Pd0jP7Jo/view?usp=sharing MAPSE presentation]\]. The MAPSE models a power system as a dynamic hybrid system, 1) maintaining multiple state estimates using a bank of Unscented Kalman Filters (UKF), and 2) estimating the network topology from the set of candidate topologies by applying Bayesian recursion to the UKF residuals. We demonstrated that the MAPSE can accurately detect network topology changes using PMU with noise levels consistent with real PMU data \[[https://ieeexplore.ieee.org/document/8784639 Empirical Noise paper]\].


==== Relevant publications:

*K. Moffat* and C. Tomlin. The multiple model adaptive power system state estimator. In 2021 IEEE Conference on Decision and Control (CDC), pages 1–6. IEEE, 2021. [https://drive.google.com/file/d/1ytW8harTNkcxA2W60b0yPVT2Pd0jP7Jo/view?usp=sharing CDC 2021 presentation].

M. Bariya, *K. Moffat*, and A. Von Meier. Empirical noise estimation in distribution synchrophasor measurements. In 2019 International Conference on Smart Grid Synchronized Measurements and Analytics, pages 1–7. IEEE, 2019. [https://ieeexplore.ieee.org/document/8784639 Paper link].



== Feedback Optimization for EV Charging Control

~~~
{}{img_left}{figures/GEMINI.png}{alt text}{314}{186}{}
I have been working with teams at the National Renewable Energy Lab ([https://www.nrel.gov NREL]) and ([https://www.lbl.gov LBL]) on the Department of Energy's [https://www.nrel.gov/docs/fy20osti/76718.pdf GEMINI-XFC project] to coordinate EV charging on oversubscribed distribution networks.
The demonstration is a full-detail transportation network-and-distribution grid co-simulation of the Bay Area. Thus, the control algorithm must work at scale. 
I am implementing Feedback Optimization algorithm, which runs the optimization algorithm in closed loop with the physical system. Computational effort is saved because the Feedback Optimization uses the physical grid to ``solve'' power flow.
~~~



# === Adaptive Power Systems Stabilization
# ~~~
# {}{img_left}{figures/WestMurrayAusOscillations.png}{alt text}{318}{136}{}
# Traditionally, the rotating inertia of large generators has stabilized power systems.
# Replacing large generators with DER/Inverter-Based Resources (IBR) removes inertia from the system and introduces new dynamics, determined by proprietary and heterogeneous IBR control laws, which can produce oscillations/system instability.
# The power systems operating community refers to this as the ``low inertia problem.'' 
# From a controls perspective, however, the problem is not the lack of inertia; \textbf{the problem is the instabilities}.
#~~~
#\footnotetext{Ahvand Jalali, Babak Badrzadeh, “System strength challenges and solutions developed for a remote area of  australian power system with high penetration of inverter-based  resources,” in 2021/2 CIGRE Science Engineering Journal. CIGRE, 2021/2.}



== Longer Term Perspective

Engineers, computer scientists, and mathematicians are grappling with how to use massive data, computing power, and communication to improve automated decisions for network systems such as electric grids. 
Data-driven control methods such as (deep) reinforcement learning have demonstrated impressive results in simulation, but *applying data-driven control to safety-critical systems* remains an open problem.
For safety-critical systems, the guarantees that come with principled mathematical approaches are paramount.
# My lab will produce theory and tools that provide guarantees and theoretical foundations for electric grids and other network systems, allowing the tools to be applied on real network systems.

I am interested in developing theory and tools that bridge the gap between simulation and real-world implementation.
# I am interested in developing data processing and control methods for power systems operation and other safety-critical network systems.
# I am interested in developing data processing and control methods.
In particular, I am interested in:
. combining online optimization with distributed feedback control,   
. incorporating a priori model knowledge and intuition into unsupervised learning methods, and
. integrating unsupervised learning with online control\/optimization.

# I will continue to work on power systems, as evolving power system use has introduced a number of important and interesting engineering challenges. In addition to power systems, I am also interested in collaborating on other network systems such as biological\/epidemic, transportation, and computation networks.


# Engineers, computer scientists, and mathematicians are grappling with how to use massive data, computing power, and communication to improve automated decisions for network systems such as power grids. 
# Data-driven control methods such as deep reinforcement learning have demonstrated impressive results for a priori unknown systems in simulation, but *applying data-driven control to a priori unknown, stochastic, and/or safety-critical systems* remains an open problem.
# For a priori unknown systems, the characteristics of the system must be learned from experience;
# for stochastic systems, the decision process must incorporate online feedback;
# and for safety-critical systems, the guarantees that come with principled mathematical approaches are paramount.
# # My lab will produce theory and tools that provide guarantees and theoretical foundations for electric grids and other network systems, allowing the tools to be applied on real network systems.
# I am interested in developing *theory and tools that can be used on real network systems*, bridging the gap between simulation and implementation.
# In particular, I am interested in:
# . combining online optimization with distributed feedback control for stochastic network systems,   
# . incorporating a priori model knowledge and intuition into unsupervised learning methods, and
# . integrating unsupervised learning with online control\/optimization of high dimensional network systems.

# I will continue to work on power systems, as there are a number of important and interesting problems that have not yet been resolved. In addition to power systems, I am also interested in collaborating on other network systems such as biological\/epidemic, transportation, and computation networks.



# Engineers, computer scientists, and mathematicians are grappling with how to use massive data, computing power, and communication to improve automated decisions for network systems such as power grids. 
# Data-driven control methods such as deep reinforcement learning have demonstrated impressive results in simulations, but *applying data-driven control to stochastic and/or safety-critical systems* remains an open problem.
#For stochastic systems, the decision process must incorporate online feedback.
#For safety-critical systems, the guarantees that come with principled mathematical approaches are paramount.
# #My lab will produce theory and tools that provide guarantees and theoretical foundations for electric grids and other network systems, allowing the tools to be applied on real network systems.
#I am interested in working on *theory and tools for electric grids and other network systems that can be applied on real systems*.
#In particular, I am interested in:
#. combining online optimization with distributed feedback control for stochastic network systems,   
#. incorporating a priori model knowledge and intuition into unsupervised learning methods, and
#. integrating unsupervised learning with online control/optimization of stochastic network systems. #high dimensional systems.



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[https://scholar.google.com/citations?user=dkWaKkvUJBQC&hl=en Google Scholar], [https://ieeexplore.ieee.org/author/37085628855 IEEE Profile]


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