Generation Expansion Planning is used to obtain future planning decisions that ensure the system reliability while minimizing cost. However, the past decade has seen an increase in weather-dependent faults in the electric grid, higher shares of weather-dependent renewable generation, and increased reliance on weather-dependent dynamic line ratings. To account for those dependencies, we propose a two-stage stochastic generation expansion planning model integrates leverages a spatial weather model to assess the generation and transmission line availability. This includes both variations of renewable generation capacity factors and dynamic line rating, and weather-dependent outage rates. The proposed framework is tested using a synthetic network, demonstrating that dynamic line rating outperforms static line ratings by reducing total operational costs and load shedding.

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 and generation cost reduction compared to the AC-OPF simulations. 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.

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.

Two-stage stochastic mixed-integer programs (MIPs) are important tools for decision-making under uncertainty, but representing uncertainty with a large number of scenarios – while ensuring accurate results – 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. 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 that includes 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

The increasing penetration of renewable energy sources (RES) introduces significant uncertainty in power system operations. At the same time, the existing transmission grid is often congested, and grid reinforcements are frequently delayed. To address these challenges, the transmission grid topology can be optimized as a non-costly remedy to enable a more efficient power transmission. Therefore, this paper proposes a multistep stochastic grid topology optimization model with busbar splitting for both AC and hybrid AC/DC grids. RES forecast uncertainty is represented via a scenario-based approach, using real offshore wind data and K-means clustering to generate representative forecast error scenarios. We then compare a plain optimal power flow (OPF) model with the proposed models which either optimizes the topology hourly, creates one optimal topology for a given time horizon (24 h), or allows a limited number of switching actions over a given time horizon. The 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 a full nonlinear non-convex OPF formulation. Based on the generation setpoints of the feasibility check, a redispatch simulation based on the measured (D) RES realization is computed. The methodology is tested on a AC 30-bus test case and a hybrid AC/DC 50-bus test case, for a 24-hours (30-bus test case) and a 14-days (both test cases) time series. The results highlight the economic benefits brought by accounting for RES uncertainty by including 6 to 8 scenarios in day-ahead grid topology optimization models, compared to only a single deterministic one. We show how the proposed approach leads to lower (up to 1.55%) or comparable total (generation and redispatch) costs with respect to deterministic day-ahead forecasts, even when limiting the frequency of topological actions.

Ensuring the security of the power system against potentially catastrophic cascading failures involves the screening of an enormous space of potential initiating failures across various load and renewable generation profiles. As traditional engineering simulations are often too slow to efficiently cover this large space, a variety of machine-learning-based approaches have been proposed to quickly screen contingencies and identify risky conditions, showing promising initial results. However, the practical usefulness of these methods is strongly dependent on their inference speed and ability to generalize to unseen “out of distribution” load profiles and initiating contingencies. In this work, we conduct such testing on a previously-trained GNN-based blackout model, finding positive results in inference speed and generalization to unseen outages but surprisingly poor generalization to unseen load and generation profiles.

Investment in technologies that allow for dynamic formation of microgrids, such as distributed energy resources to provide power and switches to adapt network topology, can improve the reliability of distribution networks. However, deciding what resources and devices to install and their locations is challenging. We propose a two-stage stochastic programming model to choose distribution-level investments in switches, batteries, generators, solar arrays, and network upgrades to allow for microgrid formation and serving more load when outages occur. Our model maximizes the average (across failure scenarios) power served in the feeder when an outage occurs, which distinguishes it from existing models that include fixed feasibility thresholds. We propose and compare several variants of our model with respect to whether customer load is dispatchable, the number of time periods in a failure scenario, and the relaxation obtained by ignoring binary restriction on the recourse variables. We conduct a study of the computational challenge of the model variants and the quality of solutions they provide. Our model uses a simple network flow approximation of power flow in the recourse model that evaluates the amount of load that is served. We investigate the impact of this approximation by introducing a two-phase method in which candidate solutions generated via the network flow model are evaluated in a more accurate power flow model for selection. We find that the network flow model is sufficient to guide the investment model to solutions that are high-quality in the more accurate model, especially under more flexible dispatch policies. We also observe that allowing customer loads to be dispatchable during an outage leads to an investment model that is easier to solve and has less error in the network flow approximation.

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.

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 usage. 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.

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 piecewise 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 a short-term electricity market 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.

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.

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.

With the growing integration of stochastic renewable generation and adaptable resources in electrical distribution systems, distribution utilities are increasingly eager to improve the visibility of their networks using distribution system state estimation (DSSE). However, scarcity of measurements and limited communication bandwidth challenge the ability of the distribution utilities to estimate distribution system states. This paper presents a forecast-aided real-time state estimation method for distribution networks, using forecasts for nodes lacking direct measurements. While other recent studies have also used forecast-aided state estimation methods, existing approaches require large amounts of historical data to train the forecasting model or depend on phasor measurements, both of which are not easily accessible to distribution utilities. In contrast, we introduce a joint forecasting and state estimation methodology. Our forecasts are generated by a Vector-Autoregressive (VAR) model, which is recursively trained as new measurements are acquired, and thus does not rely on a full set of historical data or phasor measurements. These forecasts, together with the available measurements, are subsequently used for DSSE. We validate the effectiveness of our approach on the IEEE 123-bus benchmark network, taking into account various correlation assumptions and differing quantities of accessible measurements.

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.

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.

This paper discusses results of an informal survey intended to identify the most impactful electric power system papers from 1975 to 2024 written in English. The survey was shared primarily over email to a large number of electric power engineers asking them to identify up to three papers that they consider among the most impactful papers of the last 50 years. A total of 144 valid responses were received, identifying 101 unique publications. Of those publications, 18 received multiple votes. The paper receiving the most votes are in the areas of electricity markets, optimal power flow, synthetic electric grids, voltage phasor measurements, electric grid stability, and associated with the open-source power system analysis program. This paper is a follow-up to a 2000 paper identifying the top papers of the 20th century.

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.

Data center electricity use may reach 12

Uncertainty in renewable energy generation has the potential to adversely impact the operation of electric networks. Numerous approaches to manage this impact have been proposed, ranging from stochastic and chance-constrained programming to robust optimization. However, these approaches either tend to be conservative or leave the system vulnerable to low probability, high impact uncertainty realizations. To address this issue, we propose a new formulation for stochastic optimal power flow that explicitly distinguishes between “normal operation”, in which automatic generation control (AGC) is sufficient to guarantee system security, and “adverse operation”, in which the system operator is required to take additional actions, e.g., manual reserve deployment. The new formulation has been compared with the classical ones in a case study on the IEEE-118 and IEEE-300 bus systems. We observe that our consideration of extreme scenarios enables solutions that are more secure than typical chance-constrained formulations, yet less costly than solutions that guarantee robust feasibility with only AGC.

Modern society is at a critical inflection point with rapidly accelerating demand for energy due to growth in domestic manufacturing, datacenters, artificial intelligence (AI), electric vehicles, and electric heat pumps. Sustaining this growth while also reducing society's carbon emissions will necessitate a shift beyond our long-standing focus on improving energy efficiency to optimizing carbon efficiency. This paper lays out a vision for a new field of computational decarbonization, which focuses on optimizing and reducing the lifecycle carbon emissions of complex computing and societal infrastructure systems. We identify an important class of decarbonization problems that arise from interdependencies across multiple infrastructure domains, including computing, transportation, the built environment, and the electric power grid. As we discuss, solving these problems will require developing novel computational techniques, algorithms, systems, and AI methods that sense, optimize, and reduce the operational, embodied, and lifecycle greenhouse gas emissions of societal infrastructure over long temporal and spatial scales.