arXiv subjects

Line Roald

Publications and source records attributed to Line Roald.

At least 19 recordsLinked to original sources

arXiv2026

Scenario Reduction for Two-Stage Stochastic Mixed-Integer Programs

Two-stage stochastic mixed-integer programs are important tools for decision-making under uncertainty. Representing the uncertainty with many scenarios, however, can make them challenging to solve. Scenario reduction addresses this by finding a distribution supported on fewer scenarios that still yields similar optimal first-stage decisions. In this paper, we revisit the classical scenario reduction theory based on distances between probability distributions and the optimal mass transportation problem. The transportation problem's cost function captures scenario similarity and is central to the effectiveness of scenario reduction. We then review and compare various transportation cost functions from the literature and propose a new one. Using the Forward Selection Algorithm, we prove that our proposed cost function selects the best possible scenario from a given sample on the first draw with respect to the relative approximation error. To reduce the computational cost of evaluating this cost function, we further propose a hybrid algorithm with a scenario pre-selection phase. We assess solution quality and computational complexity on the two-stage stochastic unit commitment problem for small 24-bus and large 300-bus case studies. With only around five scenarios, the proposed cost function approximates the full-distribution optimum to within roughly 2.1% and 0.4% error for the small and large cases, respectively. In contrast, prevalent cost functions often need 25 scenarios or more to achieve that solution quality. The hybrid algorithm achieves similar solution quality while reducing wall-clock time by a factor of 18 and work (per Gurobi solver) by a factor of 66 on the large case study.

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arXiv2026

Strategic Spatial Load Shifting and Market Efficiency

Large, spatially flexible electricity consumers such as data centers can reallocate demand across locations, influencing dispatch and prices in wholesale electricity markets. While flexible load is often assumed to improve system efficiency, this intuition typically relies on price-taking behavior. We study price-anticipatory spatial load shifting by modeling a large flexible consumer as a Stackelberg leader interacting with DC optimal power flow (DC-OPF) based market clearing. We show that decentralized, cost-minimizing load shifting need not align with system operating cost minimization, and that misalignment arises at boundaries between DC-OPF operating regimes, where small changes in load can induce discrete changes in marginal generators or congestion patterns. We evaluate strategic load shifting on the 73-bus RTS-GMLC test system, where findings indicate reductions in system operating cost in most hours, but misalignment in a subset of cases that are driven by redispatch at merit-order discontinuities. We find that these outcomes are primarily redistributive relative to a price-taking benchmark, reducing generator profits while lowering electricity procurement costs for both flexible and inflexible consumers, even in cases where total system operating costs increase.

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arXiv2025

Scenario Reduction for the Two-Stage Stochastic Unit Commitment Problem

The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but challenges the solution process. One way to overcome this is by using scenario reduction methods, which aim at finding a distribution supported on fewer scenarios, but leading to similar optimal first-stage decisions. In this paper, we recap the classical scenario reduction theory based on the distance of probability distributions and the optimal mass transportation problem. We then review and compare various formulations of the underlying cost function of the latter used in the literature. Using the Forward Selection Algorithm, we show that a specific formulation of the cost function can be proven to select the best possible scenario from a given sample on the first draw with respect to the Relative Approximation Error. We demonstrate this result and compare the quality of the approximation as well as the computational performance of the different cost functions using a modified version of the IEEE RTS 24-Bus System. In many cases, we find that the optimal solution of the two-stage stochastic unit commitment problem with 200 scenarios can be approximated with around 2% scenarios when using this cost function.

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arXiv2025

Strategic Data Center Load Shifting: Implications for Market Efficiency and Transmission Value

Data center electricity use may reach 12% of U.S. demand by 2030, alongside growing ability to shift workloads geographically in response to prices or carbon signals. We examine the system-level implications of such strategic flexibility using a bilevel two-zone model that couples economic dispatch with consumer cost minimization. Two market failures emerge. First, discontinuous price changes at generator capacity limits can induce flexible consumers to shift load in socially inefficient directions; for example, toward a higher-cost region to trigger a price drop elsewhere. Second, by positioning near capacity boundaries, consumers can counteract the marginal benefit of transmission expansion: although shadow prices suggest additional capacity is valuable, strategic consumers reoptimize to offset resulting flow changes, leaving dispatch and costs unchanged. We derive conditions under which these effects arise and show that conventional price signals can misrepresent system value in the presence of large spatially flexible loads.

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arXiv2025

Identifying Best Candidates for Busbar Splitting

Rising electricity demand and the growing integration of renewables are intensifying congestion in transmission grids. Grid topology optimization through busbar splitting (BuS) and optimal transmission switching can alleviate grid congestion and reduce the generation costs in a power system. However, BuS optimization requires a large number of binary variables, and analyzing all the substations for potential new topological actions is computationally intractable, particularly in large grids. To tackle this issue, we propose a set of metrics to identify and rank promising candidates for BuS, focusing on finding buses where topology optimization can reduce generation costs. To assess the effect of BuS on the identified buses, we use a combined mixed-integer convex-quadratic BuS model to compute the optimal topology and test it with the non-linear non-convex AC optimal power flow (OPF) simulation to show its AC feasibility. By testing and validating the proposed metrics on test cases of different sizes, we show that they are able to identify busbars that reduce the total generation costs when their topology is optimized. Thus, the metrics enable effective selection of busbars for BuS, with no need to test every busbar in the grid, one at a time.

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arXiv2025

Day-Ahead Transmission Grid Topology Optimization Considering Renewable Energy Sources' Uncertainty

The increasing renewable penetration introduces significant uncertainty in power system operations. At the same time, the existing transmission grid is often already congested, and urgently needed reinforcements are frequently delayed due to several constraints. To address these challenges, adjusting the grid topology based on congestion patterns is considered a non-costly remedy to guarantee efficient power transmission. Based on this idea, this paper proposes a grid topology optimization model combining optimal transmission switching and busbar splitting for AC and hybrid AC/DC grids. The methodology incorporates RES forecast uncertainty through a scenario-based stochastic optimization approach, using real offshore wind data and K-means clustering to generate representative forecast error scenarios. The proposed model includes several formulations to be compared with a plain optimal power flow (OPF) model: hourly optimizing the topology, one topology for 24 hours, or a limited number of switching actions over a day. The grid topology optimization model is formulated as a Mixed-Integer Quadratic Convex Problem, optimized based on the day-ahead (D-1) RES forecast and validated for AC-feasibility via an AC-OPF formulation. Based on the generation setpoints of the feasibility check, a redispatch simulation based on the measured (D) RES realization is then computed. The methodology is tested on an AC 30-bus test case and a hybrid AC/DC 50-bus test case, for a 24-hours (30-bus) and a 14-days (both test cases) time series. The results highlight the economic benefits brought by grid topology optimization for congested test cases with high penetration of RES. In addition, the results demonstrate that accounting for RES uncertainty with at least 6 to 8 scenarios leads to lower or comparable total costs to deterministic day-ahead forecasts, even when limiting the frequency of topological actions.

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arXiv2025

Error Bounds for Radial Network Topology Learning from Quantized Measurements

We probabilistically bound the error of a solution to a radial network topology learning problem where both connectivity and line parameters are estimated. In our model, data errors are introduced by the precision of the sensors, i.e., quantization. This produces a nonlinear measurement model that embeds the operation of the sensor communication network into the learning problem, expanding beyond the additive noise models typically seen in power system estimation algorithms. We show that the error of a learned radial network topology is proportional to the quantization bin width and grows sublinearly in the number of nodes, provided that the number of samples per node is logarithmic in the number of nodes.

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arXiv2025

Consumer-based Carbon Costs: Integrating Consumer Carbon Preferences in Electricity Markets

An increasing share of consumers care about the carbon footprint of their electricity. This paper analyzes a method to integrate consumer carbon preferences in the electricity market-clearing by introducing consumer-based carbon costs and a carbon allocation mechanism. Specifically, consumers submit not only bids for power but also assign a cost to the carbon emissions incurred by their electricity use. The carbon allocation mechanism then assigns emissions from generation to consumers to minimize overall carbon costs. Our analysis starts from a previously proposed centralized market clearing formulation that maximizes social welfare under consideration of generation costs, consumer utility, and consumer carbon costs. We then derive an equivalent equilibrium formulation that incorporates a carbon allocation problem and gives rise to a set of carbon-adjusted electricity prices for both consumers and generators. We prove that the carbon-adjusted prices are higher for low-emitting generators and consumers with high carbon costs. Further, we prove that this new paradigm satisfies the same desirable market properties as standard electricity markets based on locational marginal prices, namely revenue adequacy and individual rationality, and demonstrate that a carbon tax on generators is equivalent to imposing a uniform carbon cost on consumers. Using a simplified three-bus system and the RTS-GMLC system, we illustrate that consumer-based carbon costs contribute to greener electricity market clearing both through generation redispatch and demand reductions.

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arXiv2025

Electrolyzers Bidding in Electricity Markets under Green Hydrogen Regulations and Uncertainty

Hydrogen produced through electrolysis offers a pathway to decarbonize hard-to-abate sectors by replacing gray hydrogen derived from natural gas reforming when produced using renewable power. However, grid-connected electrolyzers may inadvertently increase power-system emissions, resulting in hydrogen whose life-cycle intensity is similar to or higher than that of gray hydrogen. To address the high cost barrier of electrolytic hydrogen, both the E.U. and U.S. have introduced subsidy schemes conditional on low associated emissions. One key requirement is temporal matching, under which a subsidy applies only to the hydrogen volume that, ex-post, can be shown to match renewable generation over each one-hour interval. This requirement exposes the electrolyzer to uncertainty in the subsidy-eligible volume and thus the value of the produced hydrogen. This paper develops an uncertainty-aware day-ahead bid curve for a grid-connected electrolyzer. We formulate a linear program that maximizes expected profit across scenarios of renewable production and derive the bid curve from its Karush-Kuhn-Tucker conditions. A case study demonstrates that incorporating renewable uncertainty into the bid curve increases electrolyzer profit by approximately 4%, although it does not improve ex-post temporal matching. This finding highlights a potential distortion in the incentive effects of temporal-matching regulations when uncertainty is taken into account.

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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

Can Carbon-Aware Electric Load Shifting Reduce Emissions? An Equilibrium-Based Analysis

An increasing number of electric loads, such as hydrogen producers or data centers, can be characterized as carbon-sensitive, meaning that they are willing to adapt the timing and/or location of their electricity usage in order to minimize carbon footprints. However, the emission reduction efforts of these carbon-sensitive loads rely on carbon intensity information such as average carbon emissions, and it is unclear whether load shifting based on these signals effectively reduces carbon emissions. To address this open question, we design a carbon-aware equilibrium model, which expands the commonly used equilibrium model for standard (carbon-agnostic) electricity market clearing to include carbon-sensitive consumers that adapt their consumption based on average carbon emission signals and carbon costs. This analysis represents an idealized situation for carbon-sensitive consumers, where their carbon preferences are reflected directly in the market clearing, and contrasts with current practice, where carbon emission signals only become known to consumers a posteriori (i.e., after the market has already been cleared). Furthermore, we extend our model to consider temporal load shifting and time-varying maximum renewable generations. We employ illustrative three-bus examples and numerical simulations on the IEEE RTS-GMLC system to reveal the limitations of the widely adopted average carbon emission signal for guiding carbon emission reduction. Our model offers a novel perspective for evaluating the effectiveness of different carbon signals and contributes to new carbon signal design.

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arXiv2025

Electricity Market Bidding for Renewable Electrolyzer Plants: An Opportunity Cost Approach

Hydrogen produced through electrolysis with renewable power is considered key to decarbonize several hard-to-electrify sectors. This work proposes a novel approach to model the active electricity market participation of co-located renewable energy and electrolyzer plants, based on opportunity-cost bidding. While a renewable energy plant typically has zero marginal cost, selling power to the grid carries a potential opportunity-cost of not producing hydrogen when it is co-located with a hydrogen electrolyzer. We first consider only the electrolyzer, and derive its revenue of consuming electricity based on the non-convex hydrogen production curve. We then consider the available renewable energy production and form a piece-wise linear cost curve representing the opportunity cost of selling (or revenue from consuming) various levels of electricity. This cost curve can be used to model a stand-alone electrolyzer or a co-located hydrogen and renewable energy plant participating in an electricity market. Our case study analyzes the effects of market-bidding electrolyzers on electricity markets and grid operations. We compare two strategies for a co-located electrolyzer-wind plant; one based on the proposed bid curve and one with a more conventional fixed electrolyzer consumption. The results show that electrolyzers that actively participate in the electricity market lower the average cost of electricity and the amount of curtailed renewable energy in the system compared with a fixed consumption case. However, the difference in total system emissions between the two strategies is insignificant. The specific impacts vary based on electrolyzer capacity and hydrogen price, which determines the location of the co-located plant in the electricity market merit order.

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arXiv2025

Greening the Grid: Electricity Market Clearing with Consumer-Based Carbon Cost

To enhance decarbonization efforts in electric power systems, we propose a novel electricity market clearing model that internalizes the allocation of emissions from generations to loads and allows for consideration of consumer-side carbon costs. Specifically, consumers can not only bid for power but also assign a cost to the carbon emissions incurred by their electricity use. These carbon costs provide consumers, ranging from carbon-agnostic to carbon-sensitive, with a tool to actively manage their roles in carbon emission mitigation. By incorporating carbon allocation and consumer-side carbon costs, the market clearing is influenced not solely by production and demand dynamics but also by the allocation of carbon emission responsibilities. To demonstrate the effect of our proposed model, we conduct a case study comparing market clearing outcomes across various percentages of carbon-sensitive consumers with differing carbon costs.

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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

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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arXiv2024

A Framework for Balancing Power Grid Efficiency and Risk with Bi-objective Stochastic Integer Optimization

Power grid expansion planning requires making large investment decisions in the present that will impact the future cost and reliability of a system exposed to wide-ranging uncertainties. Extreme temperatures can pose significant challenges to providing power by increasing demand and decreasing supply and have contributed to recent major power outages. We propose to address a modeling challenge of such high-impact, low-frequency events with a bi-objective stochastic integer optimization model that finds solutions with different trade-offs between efficiency in normal conditions and risk to extreme events. We propose a conditional sampling approach paired with a risk measure to address the inherent challenge in approximating the risk of low-frequency events within a sampling based approach. We present a model for spatially correlated, county-specific temperatures and a method to generate both unconditional and conditionally extreme temperature samples from this model efficiently. These models are investigated within an extensive case study with realistic data that demonstrates the effectiveness of the bi-objective approach and the conditional sampling technique. We find that spatial correlations in the temperature samples are essential to finding good solutions and that modeling generator temperature dependence is an important consideration for finding efficient, low-risk solutions.

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arXiv2024

Cascading Blackout Severity Prediction with Statistically-Augmented Graph Neural Networks

Higher variability in grid conditions, resulting from growing renewable penetration and increased incidence of extreme weather events, has increased the difficulty of screening for scenarios that may lead to catastrophic cascading failures. Traditional power-flow-based tools for assessing cascading blackout risk are too slow to properly explore the space of possible failures and load/generation patterns. We add to the growing literature of faster graph-neural-network (GNN)-based techniques, developing two novel techniques for the estimation of blackout magnitude from initial grid conditions. First we propose several methods for employing an initial classification step to filter out safe "non blackout" scenarios prior to magnitude estimation. Second, using insights from the statistical properties of cascading blackouts, we propose a method for facilitating non-local message passing in our GNN models. We validate these two approaches on a large simulated dataset, and show the potential of both to increase blackout size estimation performance.

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arXiv2023

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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