arXiv subjects

Johanna L. Mathieu

Publications and source records attributed to Johanna L. Mathieu.

At least 19 recordsLinked to original sources

arXiv2026

A Model Predictive Control Approach to Dual-Axis Agrivoltaic Panel Tracking

Agrivoltaic systems--photovoltaic (PV) panels installed above agricultural land--have emerged as a promising dual-use solution to address competing land demands for food and energy production. In this paper, we propose a model predictive control (MPC) approach to dual-axis agrivoltaic panel tracking control that dynamically adjusts panel positions in real time to maximize power production and crop yield given solar irradiance and ambient temperature measurements. We apply convex relaxations and shading factor approximations to reformulate the MPC optimization problem as a convex second-order cone program that determines the PV panel position adjustments away from the sun-tracking trajectory. Through case studies, we demonstrate our approach, exploring the Pareto front between i) an approach that maximizes power production without considering crop needs and ii) crop yield with no agrivoltaics. We also conduct a case study exploring the impact of forecast error on MPC performance. We find that dynamically adjusting agrivoltaic panel position helps us actively manage the trade-offs between power production and crop yield, and that active panel control enables the agrivoltaic system to achieve land equivalent ratio values of up to 1.897.

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arXiv2026

Online Feedback Optimization of Energy Storage to Smooth Data Center Grid Impacts

The growing electricity demand of AI data centers introduces significant voltage variability in power networks, affecting not only their own operation but also the experience of all users sharing the network. To smooth data center impacts on power networks, we develop an online feedback optimization approach that controls distributed battery energy storage systems to mitigate voltage issues induced by data center operations. The controller adjusts the active and reactive power setpoints of distributed battery systems in response to voltage measurements, with a two-fold objective: managing voltage to minimize the magnitude of constraint violations and smoothing voltage profiles. Control performance is evaluated in a high-fidelity simulation environment that integrates a three-phase distribution feeder and a detailed battery system model, and benchmarked against a local control approach with similar objectives but without optimality guarantees and constraint enforcement. We show that the proposed controller delivers consistent voltage regulation in the long term, while the local control approach pursues the objectives more aggressively but quickly hits the storage limits.

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arXiv2025

Reconfiguration and Real-Time Operation of Networked Microgrids Under Load Uncertainty

Distribution networks are increasingly exposed to threats such as extreme weather, aging infrastructure, and cyber risks--resulting in more frequent contingencies and outages, a trend likely to persist. Microgrids, particularly dynamic networked microgrids (DNMGs), offer a promising solution to mitigate the impacts of such contingencies and enhance resiliency. However, distribution networks present unique challenges due to their unbalanced nature and the inherent uncertainty in both loads and generation. This paper builds upon our prior work on the two-stage mixed-integer robust optimization problem for configuring DNMGs, improving the solve time and scalability. Furthermore, we present a model-free, real-time optimal power flow algorithm to manage DNMG operations in the time between reconfigurations. A case study on a realistic network based on part of the San Francisco Bay Area demonstrates the scalability of both approaches. The case study also illustrates the ability to maintain power flow feasibility as loads vary and operating conditions change when the methods are used in tandem.

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arXiv2025

Incomplete Air Mixing Reduces the Efficiency of Commercial Buildings Behaving as Virtual Batteries

Commercial building Heating, Ventilation, and Air Conditioning (HVAC) systems can provide flexibility to the electricity grid. Some researchers have found it convenient to model HVAC systems as virtual batteries. These models also better align with models used by grid planners and operators. However, experiments have shown that HVAC load shifting can be inefficient, and virtual battery models do not capture this inefficiency well. While the models typically use the average room temperature as the system's ``state of charge," they do not capture other factors that affect HVAC power/energy such as airflow and mixing. Here, we develop a new analytical building model to explore how incomplete mixing of supply air into a conditioned space leads to inefficiency in a virtual battery capturing the dynamics of HVAC fan power load shifting. The model qualitatively matches experimental results better than previous models, and shows that, as mixing becomes worse, the virtual battery becomes less efficient. Unfortunately, air mixing is unmeasured/unmeasurable. However, we show that, by closing the loop around measurements of fan power, we can improve the virtual battery's performance without the need for air mixing measurements. For example, in one case, we show a roundtrip efficiency improvement from 0.75 to 0.99.

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arXiv2024

A Hardware-in-the-Loop Experimental Testbed using Air Conditioners for Grid Balancing

Driven by the need to offset the variability of renewable generation on the grid, development of load control is a highly active field of research. However, practical use of residential loads for grid balancing remains rare, in part due to the cost of communicating with large numbers of small loads and also the limited experimentation done so far to demonstrate reliable operation. To establish a basis for the safe and reliable use of fleets of compressor loads as distributed energy resources, we constructed an experimental testbed in a laboratory, so that load coordination schemes could be tested at extreme conditions. This experimental testbed was used to tune a simulation testbed to which it was then linked, thereby augmenting the effective size of the fleet. Modeling of the system was done both to demonstrate the experimental testbed's behavior and also to understand how to tune the behavior of each load. Implementing this testbed has enabled rapid turnaround of experiments on various load control algorithms, and year-round testing without the constraints and limitations arising in seasonal field tests with real houses. Experimental results show the practical feasibility of an ensemble of small loads contributing to grid balancing.

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arXiv2024

A New Definition of Demand Response in the Distributed Energy Resource Era

Demand response is a concept that has been around since the very first electric power systems. However, we have seen an explosion of research on demand response and demand-side technologies in the past 30 years, coinciding with the shift towards liberalized/deregulated electricity markets and efforts to decarbonize the power sector. Now we are also seeing a shift towards more distributed/decentralized electric systems; we have entered the era of "distributed energy resources," which require new grid management, operational, and control strategies. Given this paradigm shift, we argue that the concept of demand response needs to be revisited, and more carefully/consistently defined to enable us to better utilize this massive resource for economic, technical, environmental, and societal aims. In this paper, we survey existing demand response definitions, highlight their shortcomings, propose a new definition, and describe how this new definition enables us to more effectively harness the value of demand response in modern power systems. We conclude with a demand response research agenda informed by a discussion of demand response barriers and enablers.

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arXiv2024

Robust Partitioning and Operation for Maximal Uncertain-Load Delivery in Distribution Grids

To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids could improve resiliency and maximize load delivery, though the modeling of three-phase unbalanced network physics and computational complexity pose challenges. These challenges are further exacerbated by an increased penetration of uncertain loads. In this paper, we present a two-stage mixed-integer robust optimization problem that configures and operates networked microgrids, and is guaranteed to be robust and feasible to all realizations of loads within a specified uncertainty set, while maximizing load delivery. To solve this problem, we propose a cutting-plane algorithm, with convergence guarantees, which approximates a convex recourse function with sub-gradient cuts. Finally, we provide a detailed case study on the IEEE 37-bus test system to demonstrate the economic benefits of networking microgrids to maximize uncertain-load delivery.

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arXiv2023

Tunable Experimental Testbed for Evaluating Load Coordination Methods

Driven by the need to offset the variability of wind and solar generation on the electrical grid, development of load controls is a highly active field in the engineering literature. However, practical use of residential loads for grid balancing and ancillary services remains rare, in part due to the relative cost of communicating with hordes of small loads and also due to the limited experimentation done so far to demonstrate reliable operation. To establish a basis for the safe and reliable use of fleets of small compressor loads as distributed energy resources (DERs), we have constructed an experimental testbed in a laboratory, so that load coordination schemes can be tested at extreme conditions within a laboratory environment. This experiment can be used to tune a simulation testbed to which it can then be linked, thereby augmenting the effective size of the ensemble of loads. Control algorithms can simply be plugged in for testing. Modeling of the system was done both to demonstrate the experimental testbed's behavior and also to understand how to tune the behavior of each participating model house in the system. Implementing this testbed has been useful for the rapid turnaround of experiments on various control types, and it enables testing year-round without the constraints and limitations arising in seasonal field tests with real human participants.

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arXiv2023

Using Demand Response to Improve Power System Small-Signal Stability

With the increase of uncertain and intermittent renewable energy supply on the grid, the power system has become more vulnerable to instability. In this paper, we develop a demand response strategy to improve power system small-signal stability. We pose the problem as an optimization problem wherein the total demand-responsive load is held constant at each time instance but shifted between different buses to improve small-signal stability, which is measured by small-signal stability metrics that are functions of subsets of the system's eigenvalues, such as the smallest damping ratio. To solve the problem, we use iterative linear programming and generalized eigenvalue sensitivities. We demonstrate the approach via a case study that uses the IEEE 14-bus system. Our results show that shifting the load between buses, can improve a small-signal stability margin. We explore the use of models of different fidelity and find that it is important to include models of the automatic voltage regulators and power system stabilizers. In addition, we show that load shifting can achieve similar improvements to generation shifting and better improvement than simply tuning power system stabilizers.

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arXiv2022

Uncertainty-Aware Methods for Leveraging Water Pumping Flexibility for Power Networks

Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding and/or overly conservative. In this paper, we develop a computationally tractable probabilistic approach to schedule and control water pumping to provide voltage support to the power distribution network subject to power and water distribution network constraints under power demand uncertainty. Building upon robust and chance-constrained reformulation approaches, we analytically reformulate the probabilistic problem into a deterministic one and solve for the scheduled pump operation and the control policy parameters that adjust the pumps based on the power demand forecast error realizations. In a case study, we compare our proposed approach to an adjustable robust method and investigate the performance in terms of computation time, cost, and empirical violation probabilities. We find that our proposed approach is computationally tractable and is less conservative than the robust approach, indicating that our formulation would be scalable to larger networks.

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arXiv2022

An Invariant Set Construction Method, Applied to Safe Coordination of Thermostatic Loads

We consider the problem of coordinating a collection of switched subsystems under both local and global constraints for safe operation of the system. Although an invariant set can be leveraged to construct a safety-guaranteed controller for this kind of problem, computing an invariant set is not scalable to high-dimensional systems. In this paper, we introduce a strategy to obtain an implicit representation of a controlled invariant set for a collection of switched subsystems, and construct a safety-guaranteed controller to coordinate the subsystems using the representation. Specifically, we incorporate the invariant set into a model predictive controller to guarantee safety and recursive feasibility. Since the amount of computations is independent of the number of subsystems, this approach scales to large collections of switched subsystems. We use our approach to safely control a collection of thermostatically controlled loads to provide grid balancing services. The problem includes constraints on each load's temperature and duration it must remain in a mode after a switch, and also on aggregate power consumption to ensure network safety. Numerical simulations show that the proposed approach outperforms benchmark strategies in terms of safety and recursive feasibility.

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arXiv2020

Strategies for Network-Safe Load Control with a Third-Party Aggregator and a Distribution Operator

When providing bulk power system services, a third-party aggregator could inadvertently cause operational issues at the distribution level. We propose a coordination architecture in which an aggregator and distribution operator coordinate to avoid distribution network constraint violations, while preserving private information. The aggregator controls thermostatic loads to provide frequency regulation, while the distribution operator overrides the aggregator's control actions when necessary to ensure safe network operation. Using this architecture, we propose two control strategies, which differ in terms of measurement and communication requirements, as well as model complexity and scalability. The first uses an aggregate model and blocking controller, while the second uses individual load models and a mode-count controller. Both outperform a benchmark strategy in terms of tracking accuracy. Furthermore, the second strategy performs better than the first, with only 0.10% average RMS error (compared to 0.70%). The second is also able to maintain safe operation of the distribution network while overriding less than 1% of the aggregator's control actions (compared to approximately 15% by the first strategy). However, the second strategy has significantly more measurement, communication, and computational requirements, and therefore would be more complex and expensive to implement than the first strategy.

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arXiv2020

Baseline Estimation of Commercial Building HVAC Fan Power Using Tensor Completion

Commercial building heating, ventilation, and air conditioning (HVAC) systems have been studied for providing ancillary services to power grids via demand response (DR). One critical issue is to estimate the counterfactual baseline power consumption that would have prevailed without DR. Baseline methods have been developed based on whole building electric load profiles. New methods are necessary to estimate the baseline power consumption of HVAC sub-components (e.g., supply and return fans), which have different characteristics compared to that of the whole building. Tensor completion can estimate the unobserved entries of multi-dimensional tensors describing complex data sets. It exploits high-dimensional data to capture granular insights into the problem. This paper proposes to use it for baselining HVAC fan power, by utilizing its capability of capturing dominant fan power patterns. The tensor completion method is evaluated using HVAC fan power data from several buildings at the University of Michigan, and compared with several existing methods. The tensor completion method generally outperforms the benchmarks.

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arXiv2019

The Value of Including Unimodality Information in Distributionally Robust Optimal Power Flow

To manage renewable generation and load consumption uncertainty, chance-constrained optimal power flow (OPF) formulations and various solution methodologies have been proposed. However, conventional solution approaches often rely on accurate estimates of uncertainty distributions, which may not exist. When the distributions are not known but can be limited to a set of plausible distributions, termed an ambiguity set, distributionally robust (DR) optimization can be used to ensure that chance constraints hold for all distributions in that set. However, DR OPF yields conservative solutions if the ambiguity set is too large. In this paper, we assess the value of using both moment and unimodality information, which shrinks the ambiguity set and reduces conservatism, in DR OPF problems. Most practical uncertainty distributions in power systems are unimodal. Exact reformulations, approximations, and efficient solving techniques were developed in a previous paper. This paper develops an optimal parameter selection approach that searches for an optimal approximation, significantly improving the computational efficiency and solution quality. We evaluate the performance of the approach against existing chance-constrained OPF approaches using modified IEEE 118-bus and 300-bus systems with high penetrations of renewable generation. Results show that including unimodality information reduces solution conservatism and cost without significantly degrading reliability.

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arXiv2018

Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes

Chance constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of distributions called the ambiguity set. Commonly, ambiguity sets are only based on moment information (e.g., mean and covariance) of the random variables; however, specifying additional characteristics of the random variables reduces conservatism and cost. Here, we consider ambiguity sets that additionally incorporate unimodality information. In practice, it is difficult to estimate the mode location from the data and so we allow it to be potentially misspecified. We formulate the problem and derive a separation-based algorithm to efficiently solve it. Finally, we evaluate the performance of the proposed approach on a modified IEEE-30 bus network with wind uncertainty and compare with other distributionally robust approaches. We find that a misspecified mode significantly affects the reliability of the solution and the proposed model demonstrates a good trade-off between cost and reliability.

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arXiv2018

Effects of Load-Based Frequency Regulation on Distribution Network Operation

This paper examines the operation of distribution networks that have large aggregations of thermostatically controlled loads (TCLs) providing secondary frequency regulation to the bulk power system. Specifically, we assess the prevalence of distribution network constraint violations, such as over- or under-voltages and overloading of transformers. Our goal is to determine the set of constraints that are at increased risk of being violated when TCLs provide regulation. We compare network operation in two cases: first with TCLs operating freely, and second with TCLs controlled to track a regulation signal. Using GridLAB-D, we run power flow simulations of five real distribution networks. Our results indicate that voltage limits are at increased risk of violation when TCLs provide regulation because of increased voltage variation. Effects on transformer aging are more nuanced and depend on the method used for dispatching TCLs. We find that in many distribution networks it may only be necessary to consider voltage constraints when designing a TCL control strategy that protects the distribution network.

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arXiv2018

Real-Time Energy Disaggregation of a Distribution Feeder's Demand Using Online Learning

Though distribution system operators have been adding more sensors to their networks, they still often lack an accurate real-time picture of the behavior of distributed energy resources such as demand responsive electric loads and residential solar generation. Such information could improve system reliability, economic efficiency, and environmental impact. Rather than installing additional, costly sensing and communication infrastructure to obtain additional real-time information, it may be possible to use existing sensing capabilities and leverage knowledge about the system to reduce the need for new infrastructure. In this paper, we disaggregate a distribution feeder's demand measurements into: 1) the demand of a population of air conditioners, and 2) the demand of the remaining loads connected to the feeder. We use an online learning algorithm, Dynamic Fixed Share (DFS), that uses the real-time distribution feeder measurements as well as models generated from historical building- and device-level data. We develop two implementations of the algorithm and conduct case studies using real demand data from households and commercial buildings to investigate the effectiveness of the algorithm. The case studies demonstrate that DFS can effectively perform online disaggregation and the choice and construction of models included in the algorithm affects its accuracy, which is comparable to that of a set of Kalman filters.

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arXiv2017

Modeling and Optimal Operation of Distributed Battery Storage in Low Voltage Grids

Due to high power in-feed from photovoltaics, it can be expected that more battery systems will be installed in the distribution grid in near future to mitigate voltage violations and thermal line and transformer overloading. In this paper, we present a two-stage centralized model predictive control scheme for distributed battery storage that consists of a scheduling entity and a real-time control entity. To guarantee secure grid operation, we solve a robust multi-period optimal power flow (OPF) for the scheduling stage that minimizes battery degradation and maximizes photovoltaic utilization subject to grid constraints. The real-time controller solves a real-time OPF taking into account storage allocation profiles from the scheduler, a detailed battery model, and real-time measurements. To reduce the computational complexity of the controllers, we present a linearized OPF that approximates the nonlinear AC-OPF into a linear programming problem. Through a case study, we show, for two different battery technologies, that we can substantially reduce battery degradation when we incorporate a battery degradation model. A further finding is that we can reduce battery losses by 30% by using the detailed battery model in the real-time control stage.

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