arXiv subjects

Noah Rhodes

Publications and source records attributed to Noah Rhodes.

17 recordsLinked to original sources

arXiv2026

Simulating Arbitrage Optimization for Market Monitoring in Gas and Electricity Transmission Networks

We examine market outcomes in energy transport networks with a focus on gas-fired generators, which are producers in a wholesale electricity market and consumers in the natural gas market. Market administrators monitor bids to determine whether a participant wields market power to manipulate the price of energy, reserves, or financial transmission rights. If economic or physical withholding of generation from the market is detected, mitigation is imposed by replacing excessive bids with reference level bids to prevent artificial supply shortages. We review market monitoring processes in the power grid, and present scenarios in small interpretable test networks to show how gas-fired generators can bid in the gas market to alter outcomes in a power market. We develop a framework based on DC optimal power flow (OPF) and steady-state optimal gas flow (OGF) formulations to represent two interacting markets with structured exchange of price and quantity bids. We formulate optimization-based methods to identify market power in a power grid, as well as to identify market conditions that indicate market power being exerted by a generator using gas market bids.

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arXiv2025

Maximal Load Shedding Verification for Neural Network Models of AC Line Switching

Solving for globally optimal line switching decisions in AC transmission grids can be intractability slow. Machine learning (ML) models, meanwhile, can be trained to predict near-optimal decisions at a fraction of the speed. Verifying the performance and impact of these ML models on network operation, however, is a critically important step prior to their actual deployment. In this paper, we train a Neural Network (NN) to solve the optimal power shutoff line switching problem. To assess the worst-case load shedding induced by this model, we propose a bilevel attacker-defender verification approach that finds the NN line switching decisions that cause the highest quantity of network load shedding. Solving this problem to global optimality is challenging (due to AC power flow and NN nonconvexities), so our approach exploits a convex relaxation of the AC physics, combined with a local NN search, to find a guaranteed lower bound on worst--case load shedding. These under-approximation bounds are solved via MathOptAI.jl. We benchmark against a random sampling approach, and we find that our optimization-based approach always finds larger load shedding. Test results are collected on multiple PGLib test cases and on trained NN models which contain more than 10 million model parameters.

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arXiv2025

PowerPlots.jl: An Open Source Power Grid Visualization and Data Analysis Framework for Academic Research

Data visualization is essential for developing an understanding of a complex system. The power grid is one of the most complex systems in the world and effective power grid research visualization software must 1) be easy to use, 2) support unique data that may arise in research, and 3) be capable of creating custom figures for publication and presentation. However, no current software addresses all three of these needs. PowerPlots is an open-source data visualization tool for power grids that does address these needs. In addition, several tools created to support this software facilitate the analysis of power grid data by transforming the data into graph topology or data-frame data formats that are more compatible for some analyses. In this work, we use PowerPlots to investigate several case studies that involve exploring power grid data. These case studies demonstrate the valuable insights that are possible when using network visualization and how it can be applied to research applications.

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arXiv2025

Second-Order-Cone Formulations of Power Flow for Topology Optimization

Optimization problems that involve topology optimization in scenarios with large scale outages, such as post-disaster restoration or public safety power shutoff planning, are very challenging to solve. Using simple power flow representations such as DC power flow or network flow models results in low quality solutions which requires significantly higher-than-predicted load shed to become AC feasible. Recent work has shown that formulations based on the Second Order Cone (SOC) power flow formulation find very high quality solutions with low load shed, but the computational burden of these formulations remains a significant challenge. With the aim of reducing computational time while maintaining high solution quality, this work explores formulations which replace the conic constraints with a small number of linear cuts. The goal of this approach is not to find an exact power flow solution, but rather to identify good binary decisions, where the power flow can be resolved after the binary variables are fixed. We find that a simple reformulation of the Second Order Cone Optimal Power Shutoff problem can greatly improve the solution speed, but that a full linearization of the SOC voltage cone equation results in an overestimation of the amount of power that can be delivered to loads.

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arXiv2025

ElectricityEmissions.jl: A Framework for the Comparison of Carbon Intensity Signals

An increasing number of individuals, companies and organizations are interested in computing and minimizing the carbon emissions associated with their real-time electricity consumption. To achieve this, they require a carbon signal, i.e. a metric that defines the real-time carbon intensity of their electricity supply. Unfortunately, in a grid with multiple generation sources and multiple consumers, the physics of the system do not provide an unambiguous way to trace electricity from source to sink. As a result, there are a multitude of proposed carbon signals, each of which has a distinct set of properties and method of calculation. It remains unclear which signal best quantifies the carbon footprint of electricity. This paper seeks to inform the discussion about which carbon signal is better or more suitable for two important use cases, namely carbon-informed load shifting and carbon accounting. We do this by developing a new software package ElectricityEmissions$.$jl, that computes several established and newly proposed carbon emission metrics for standard electric grid test cases. We also demonstrate how the package can be used to investigate the effects of using these metrics to guide load shifting. Our results affirm previous research, which showed that the choice of carbon emission metric has significant impact on shifting results and associated carbon emission reductions. In addition, we demonstrate the impact of load shifting on both the consumers that perform the shifting and consumers that do not. Disconcertingly, we observe that shifting according to common metrics such as average carbon emissions can reduce the amount of emissions allocated to the consumer doing the shifting, while increasing the total emissions of the power system.

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arXiv2025

Quantifying Metrics for Wildfire Ignition Risk from Geographic Data in Power Shutoff Decision-Making

Faults on power lines and other electric equipment are known to cause wildfire ignitions. To mitigate the threat of wildfire ignitions from electric power infrastructure, many utilities preemptively de-energize power lines, which may result in power shutoffs. Data regarding wildfire ignition risks are key inputs for effective planning of power line de-energizations. However, there are multiple ways to formulate risk metrics that spatially aggregate wildfire risk map data, and there are different ways of leveraging this data to make decisions. The key contribution of this paper is to define and compare the results of employing six metrics for quantifying the wildfire ignition risks of power lines from risk maps, considering both threshold- and optimization-based methods for planning power line de-energizations. The numeric results use the California Test System (CATS), a large-scale synthetic grid model with power line corridors accurately representing California infrastructure, in combination with real Wildland Fire Potential Index data for a full year. This is the first application of optimal power shutoff planning on such a large and realistic test case. Our results show that the choice of risk metric significantly impacts the lines that are de-energized and the resulting load shed. We find that the optimization-based method results in significantly less load shed than the threshold-based method while achieving the same risk reduction.

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arXiv2024

Advanced Scheduling of Electrolyzer Modules for Grid Flexibility

As the transition to sustainable power generation progresses, green hydrogen production via electrolysis is expected to gain importance as a means for energy storage and flexible load to complement variable renewable generation. With the increasing need for cost-effective and efficient hydrogen production, electrolyzer optimization is essential to improve both energy efficiency and profitability. This paper analyzes how the efficiency and modular setup of alkaline hydrogen electrolyzers can improve hydrogen output of systems linked to a fluctuating renewable power supply. To explore this, we propose a day-ahead optimal scheduling problem of a hybrid wind and electrolyzer system. The novelty of our approach lies in modeling the number and capacity of electrolyzer modules, and capturing the modules' impact on the hydrogen production and efficiency. We solve the resulting mixed-integer optimization problem with several different combinations of number of modules, efficiency and operating range parameters, using day-ahead market data from a wind farm generator in the ERCOT system as an input. Our results demonstrate that the proposed approach ensures that electrolyzer owners can better optimize the operation of their systems, achieving greater hydrogen production and higher revenue. Key findings include that as the number of modules in a system with the same overall capacity increases, hydrogen production and revenue increases.

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arXiv2024

Multistage Stochastic Program for Mitigating Power System Risks under Wildfire Disruptions

The frequency of wildfire disasters has surged five-fold in the past 50 years due to climate change. Preemptive de-energization is a potent strategy to mitigate wildfire risks but substantially impacts customers. We propose a multistage stochastic programming model for proactive de-energization planning, aiming to minimize economic loss while accomplishing a fair load delivery. We model wildfire disruptions as stochastic disruptions with varying timing and intensity, introduce a cutting-plane decomposition algorithm, and test our approach on the RTS-GLMC test case. Our model consistently offers a robust and fair de-energization plan that mitigates wildfire damage costs and minimizes load-shedding losses, particularly when pre-disruption restoration is considered.

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arXiv2024

Long Solution Times or Low Solution Quality: On Trade-Offs in Choosing a Power Flow Formulation for the Optimal Power Shutoff Problem

The Optimal Power Shutoff (OPS) problem is an optimization problem that makes power line de-energization decisions in order to reduce the risk of igniting a wildfire, while minimizing the load shed of customers. This problem, with DC linear power flow equations, has been used in many studies in recent years. However, using linear approximations for power flow when making decisions on the network topology is known to cause challenges with AC feasibility of the resulting network, as studied in the related contexts of optimal transmission switching or grid restoration planning. This paper explores the accuracy of the DC OPS formulation and the ability to recover an AC-feasible power flow solution after de-energization decisions are made. We also extend the OPS problem to include variants with the AC, Second-Order-Cone, and Network-Flow power flow equations, and compare them to the DC approximation with respect to solution quality and time. The results highlight that the DC approximation overestimates the amount of load that can be served, leading to poor de-energization decisions. The AC and SOC-based formulations are better, but prohibitively slow to solve for even modestly sized networks thus demonstrating the need for new solution methods with better trade-offs between computational time and solution quality.

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arXiv2023

Multi-period Power System Risk Minimization under Wildfire Disruptions

Natural wildfire becomes increasingly frequent as climate change evolves, posing a growing threat to power systems, while grid failures simultaneously fuel the most destructive wildfires. Preemptive de-energization of grid equipment is effective in mitigating grid-induced wildfires but may cause significant power outages during natural wildfires. This paper proposes a novel two-stage stochastic program for planning preemptive de-energization and solves it via an enhanced Lagrangian cut decomposition algorithm. We model wildfire events as stochastic disruptions with random magnitude and timing. The stochastic program maximizes the electricity delivered while proactively de-energizing components over multiple time periods to reduce wildfire risks. We use a cellular automaton process to sample grid failure and wildfire scenarios driven by realistic risk and environmental factors. We test our method on an augmented version of the RTS-GLMC test case in Southern California and compare it with four benchmark cases, including deterministic, wait-and-see, and robust optimization formulations as well as a comparison with prior wildfire risk optimization. Our method reduces wildfire damage costs and load-shedding losses, and our nominal plan is robust against uncertainty perturbation.

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arXiv2023

California Test System (CATS): A Geographically Accurate Test System based on the California Grid

This paper presents the California Test System (CATS), a synthetic transmission grid in California that can be used by the public for power systems policy research without revealing any critical energy information. The proposed synthetic grid combines publicly available geographic data of California's electric infrastructure, such as the actual locations of transmission corridors, with invented topology and transmission line parameters that are ``realistic but not real". The result is a power grid test system that is suitable for power flow and policy analyses with geo-referenced applications, including studies related to weather, topography, and socio-economic considerations. The methods used to develop and evaluate the CATS grid are documented in detail in this report.

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arXiv2023

Security Constrained Optimal Power Shutoff

Electric grid faults are increasingly the source of ignition for major wildfires. To reduce the likelihood of such ignitions in high risk situations, utilities use pre-emptive deenergization of power lines, commonly referred to as Public Safety Power Shut-offs (PSPS). Besides raising challenging trade-offs between power outages and wildfire safety, PSPS removes redundancy from the network just at a time when component faults are likely to happen. This may leave the network particularly vulnerable to unexpected line faults that may occur while the PSPS is in place. Previous works have not explicitly considered the impacts of such outages. To address this gap, we propose the Security-Constrained Optimal Power Shutoff (SC-OPS) problem which uses post-contingency security constraints to model the impact of unexpected line faults when planning a PSPS. This SC-OPS model enables, for the first time, the exploration of a wide range of trade-offs between both wildfire risk and pre- and post-contingency load shedding while designing PSPS plans, providing useful insights for utilities and policy makers considering different approaches to PSPS.We demonstrate the efficacy of our model using the EPRI 39-bus test system as a case study. The results highlight the potential risks of not considering security constraints when planning PSPS and show that incorporating security constraints into the PSPS design process improves the resilience of current PSPS plans.

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arXiv2023

Co-optimization of power line shutoff and restoration under high wildfire ignition risk

Electric power infrastructure has ignited several of the most destructive wildfires in recent history. Preemptive power shutoffs are an effective tool to mitigate the risk of ignitions from power lines, but at the same time can cause widespread power outages. This work proposes a mathematical optimization problem to help utilities decide where and when to implement these shutoffs, as well as how to most efficiently restore power once the wildfire risk is lower. Specifically, our model co-optimizes the power shutoff (considering both wildfire risk reduction and power outages) as well as the post-event restoration efforts given constraints related to inspection and energization of lines, and is implemented as a rolling horizon optimization problem that is resolved whenever new forecasts of load and wildfire risk become available. We demonstrate our method on the IEEE RTS-GMLC test case using real wildfire risk data and forecasts from US Geological Survey, and investigate the sensitivity of the results to the forecast quality, decision horizon and system restoration budget. The software implementation is available in the open source software package PowerModelsWildfire.jl.

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arXiv2022

Recursive Restoration Refinement: A Fast Heuristic for Near-Optimal Restoration Prioritization in Power Systems

The prioritization of restoration actions after large power system outages plays a key role in how quickly power can be restored. It has been shown that fast and intuitive heuristics for restoration prioritization most often result in low-quality restoration plans. Meanwhile, mathematical optimization tools that find high-quality restoration plans are too slow to be applied to restoration planning problems of practical interest. This work makes a significant step in closing this quality vs compute time gap by proposing the Recursive Restoration Refinement heuristic for power system restoration. This heuristic is shown to produce near-optimal restoration plans up to 1,000 times faster than other state-of-the-art solution methods on a range of test cases with up to 500 buses and 700 damaged components. The potential impact of this new heuristic is demonstrated by a preliminary analysis of the key features of high-quality restoration plans. The recursive restoration refinement algorithm and other methods explored in this work have been made available as part of the open-source software package, PowerModelsRestoration, to support ongoing research in power restoration algorithms.

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arXiv2021

The Role of Distributed Energy Resources in Distribution System Restoration

With increasing levels of distributed energy resources (DERs) connected to the grid, it is important to understand the role that DERs can play in post-disaster restoration. In this paper, we propose a two-step optimization method to identify and implement an optimal restoration schedule under different DER operating scenarios. We investigate how the presence and geographical distribution of DERs change the optimal restoration order, and assess the impacts on customers with and without DERs. In our case study using the IEEE 123 single phase distribution system, we find that optimal restoration order changes significantly when DERs are concentrated in one part of the grid. We also observe that the presence of DERs generally reduces the energy not served across all customers and can help prioritize grid reconnection of customers without DERs.

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arXiv2020

Balancing Wildfire Risk and Power Outages through Optimized Power Shut-Offs

Electric grid faults can cause catastrophic wildfires, particularly in regions with high winds and low humidity. In real-time operations, electric utilities are often left with few options for wildfire risk mitigation, leading to use of disruptive measures such as proactive de-energization of equipment, frequently referred to as public safety power shut-offs. Such power shut-offs have significant impacts on customers, who experience power cuts in an attempt to protect them from fires. This work proposes the optimal power shut-off problem, an optimization model to support short-term operational decision making in the context of extreme wildfire risk. Specifically, the model optimizes grid operations to maximize the amount of power that can be delivered, while proactively minimizing the risk of wildfire ignitions by selectively de-energizing components in the grid. This is the first optimization model to consider how preventive wildfire risk measures impact both wildfire risk \emph{and} power systems reliability at a short-term, operational time-frame. The effectiveness of the method is demonstrated on an augmented version of the RTS-GMLC test case, located in Southern California, and compared against two approaches based on simple risk thresholds. The proposed optimization-based model reduces both wildfire risk and lost load shed relative to the benchmarks.

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arXiv2020

PowerModelsRestoration.jl: An Open-Source Framework for Exploring Power Network Restoration Algorithms

With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also give rise to challenging mixed-integer nonlinear optimization problems, where tractable solution methods are not yet available. To assist in research on such solution methods, this work proposes PowerModelsRestoration, a flexible, open-source software framework for rapidly designing and testing power restoration algorithms. PowerModelsRestoration constructs a mathematical modeling layer for formalizing core restoration tasks that can be combined to develop complex workflows and high performance heuristics. The efficacy of the proposed framework is demonstrated by proof-of-concept studies on three established cases from the literature, focusing on single-phase positive sequence network models. The results demonstrate that PowerModelsRestoration reproduces the established literature, and for the first time provide an analysis of restoration with nonlinear power flow models, which have not been previously considered.

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