Erhan Kutanoğlu

Large loads from industrial electrification and data centers are reshaping the planning and operation of the power grid. Identifying optimal large load siting decisions while accounting for transmission congestion is key to reducing expansion cost and operational risks. In this paper, we propose a leader-follower bilevel optimization framework to identify optimal large load allocation strategies. The leader determines the allocation of large loads, while the followers determine grid expansion cost and transmission utilization. This modeling approach explicitly integrates strategic planning with detailed short-term operational decisions. Moreover, we develop a Bayesian Optimization approach to efficiently solve the bilevel optimization problem by treating the followers as a black box. We use the framework to study large-scale load allocation from electrified oil refineries and data centers on a synthetic power grid that resembles key characteristics of the Texas (ERCOT) system. The results show that these large loads compete for electricity, and under high-load scenarios, data center demand is distributed across the entire grid, avoiding regions with high demand from industrial electrification.

Large loads from industrial electrification and data centers are reshaping the planning and operation of the power grid. Identifying optimal large load siting decisions while accounting for transmission congestion is key to reducing expansion cost and operational risks. In this paper, we propose a leader-follower bilevel optimization framework to identify optimal large load allocation strategies. The leader determines the allocation of large loads, while the followers determine grid expansion cost and transmission utilization. This modeling approach explicitly integrates strategic planning with detailed short-term operational decisions. Moreover, we develop a Bayesian Optimization approach to efficiently solve the bilevel optimization problem by treating the followers as a black box. We use the framework to study large-scale load allocation from electrified oil refineries and data centers on a synthetic power grid that resembles key characteristics of the Texas (ERCOT) system. The results show that these large loads compete for electricity, and under high-load scenarios, data center demand is distributed across the entire grid, avoiding regions with high demand from industrial electrification.

Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations or measurements. This work presents a framework that leverages the Normal-to-Anything (NORTA) generative model to enhance the reliability of two-stage stochastic programming solutions through comprehensive out-of-sample testing when scenario data is limited. The NORTA model efficiently generates synthetic scenarios that preserve both marginal distributions and correlation structures from limited available data, offering a computationally tractable alternative to expensive physics-based simulations. We demonstrate the approach through a case study on power grid resilience planning against flood events in Texas, where we use 16 high-fidelity flood scenarios to generate 800 additional synthetic scenarios for validation. The results show that NORTA-generated scenarios accurately capture essential statistical properties, with the out-of-sample performance of first-stage decisions closely matching expectations from the original stochastic programming model. This framework enables decision-makers to assess the robustness of their solutions when obtaining additional real-world data is prohibitively expensive. The approach bridges machine learning and operations research by providing a practical solution to scenario generation challenges in stochastic programming.

Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations or measurements. This work presents a framework that leverages the Normal-to-Anything (NORTA) generative model to enhance the reliability of two-stage stochastic programming solutions through comprehensive out-of-sample testing when scenario data is limited. The NORTA model efficiently generates synthetic scenarios that preserve both marginal distributions and correlation structures from limited available data, offering a computationally tractable alternative to expensive physics-based simulations. We demonstrate the approach through a case study on power grid resilience planning against flood events in Texas, where we use 16 high-fidelity flood scenarios to generate 800 additional synthetic scenarios for validation. The results show that NORTA-generated scenarios accurately capture essential statistical properties, with the out-of-sample performance of first-stage decisions closely matching expectations from the original stochastic programming model. This framework enables decision-makers to assess the robustness of their solutions when obtaining additional real-world data is prohibitively expensive. The approach bridges machine learning and operations research by providing a practical solution to scenario generation challenges in stochastic programming.

We present and analyze a three-stage stochastic optimization model that integrates output from a geoscience-based flood model with a power flow model for transmission grid resilience planning against flooding. The proposed model coordinates the decisions made across multiple stages of resilience planning and recommends an optimal allocation of the overall resilience investment budget across short- and long-term measures. While doing so, the model balances the cost of investment in both short- and long-term measures against the cost of load shed that results from unmitigated flooding forcing grid components go out-of-service. We also present a case study for the Texas Gulf Coast region to demonstrate how the proposed model can provide insights into various grid resilience questions. Specifically, we demonstrate that for a comprehensive yet reasonable range of economic values assigned to load loss, we should make significant investments in the permanent hardening of substations such that we achieve near-zero load shed. We also show that not accounting for short-term measures while making decisions about long-term measures can lead to significant overspending. Furthermore, we demonstrate that a technological development enabling to protect substations on short notice before imminent hurricanes could vastly influence and reduce the total investment budget that would otherwise be allocated for more expensive substation hardening. Lastly, we also show that for a wide range of values associated with the cost of mitigative long-term measures, the proportion allocated to such measures dominates the overall resilience spending.

Abstract Hydrogen trucks (HTs) offer promising potential for decarbonizing the transportation sector. Based on current technologies, they have significant advantages over electric trucks (ETs) in terms of range, refueling time, and performance in cold conditions. However, HTs are costly, and there are insufficient hydrogen refueling stations (HRSs). Gradually integrating HTs into the existing diesel truck (DT) fleet is a practical approach for many freight logistics companies. In this article, we formulate a mathematical model to route a mixed fleet of HTs and DTs, and we propose an algorithm called the curve descent search (CDS) to generate the Pareto set based on cost and carbon emissions. We find that CDS can generate better Pareto sets compared to existing algorithms in the literature. We use CDS to comprehensively explore the cost–carbon trade‐off in using a mixed fleet. This question differentiates our study from previous research and is motivated by discussions with one of the largest third‐party logistics companies in North America. Detailed experiments reveal important managerial insights, such as: (1) Achieving a significant reduction in carbon emissions (e.g., a 30% reduction compared to the current diesel fleet) does not need a very dense refueling infrastructure; (2) The cost–carbon trade‐off for mixed fleets is relatively insensitive to variations in customer density and demand, suggesting that HTs can be applicable across a wide range of scenarios (including different sectors or regions); and (3) Although ETs are cheaper to use compared to HTs, their shorter range limits their competitiveness in terms of decarbonization efficiency and customer service.

Several stochastic programming models have been developed for critical infrastructure's resilience decision-making to extreme flood events. Generating flood scenarios for such models requires running advanced flood models on a sophisticated computing infrastructure for different parameterizations (for example, different hurricane intensity levels, tracks, etc.), which may not always be practical. To address this issue, in this study, we propose a Normal-to-Anything (NORTA) model-based flood scenario generation scheme, which requires significantly fewer computing resources. The scenarios we generate using the proposed approach preserve correlation in flood height at locations of interest, in our case, the power transmission grid's substation locations. We demonstrate our approach's efficacy with a case study using a synthetic power grid with statistical similarities with the actual Texas grid and the flood maps developed by the National Atmospheric and Oceanic Administration that represent the storm-surge risk in Texas.

We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electric substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.

We compare stochastic programming and robust optimization decision models for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce adaptations of the direct current (DC) and linear programming alternating current (LPAC) power flow approximation models that feature relatively complete recourse by way of an indicator variable. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful, whereas choosing between the DC and LPAC power flow models is of little to no consequence. To validate our models, we assess the performance of the mitigation solutions they prescribe in an alternating current (AC) power flow model. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Energy Institute, The University of Texas at Austin. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0125 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0125 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We present an optimization model defined on the manifold of the set of stochastic matrices. Geometrically, the model is akin to identifying a maximum-volume $n$-dimensional simplex that has a given barycenter and is enclosed by the $n$-dimensional standard simplex. Maximizing the volume of a simplex is equivalent to maximizing the determinant of its corresponding matrix. In our model, we employ trace maximization as a linear alternative to determinant maximization. We identify the analytical form of a solution to this model. We prove the solution is optimal and present necessary and sufficient conditions for it to be the unique optimal solution. Additionally, we show the identified optimal solution is an inverse $M$-matrix, and that its eigenvalues are the same as its diagonal entries. We demonstrate how the model and its solutions apply to the task of synthesizing conditional cumulative distribution functions (CDFs) that, in tandem with a given discrete marginal distribution, coherently preserve a given CDF.

We propose a three-stage stochastic programming model to inform risk-averse investment in power system resilience to winter storms. The first stage pertains to long-term investment in generator winterization and mobile battery energy storage system (MBESS) resources, the second stage to MBESS deployment prior to an imminent storm, and the third stage to operational response. Serving as a forecast update, an imminent winter storm’s severity is assumed to be known at the time the deployment decisions are made. We incorporate conditional value-at-risk (CVaR) as the risk measure in the objective function to target loss, represented in our model by unserved energy, experienced during high-impact, low-frequency events. We apply the model to a Texas-focused case study based on the ACTIVS 2000-bus synthetic grid with winter storm scenarios generated using historical Winter Storm Uri data. Results demonstrate how the optimal investments are affected by parameters like cost and risk aversion, and also how effectively using CVaR as a risk measure mitigates the outcomes in the tail of the loss distribution over the winter storm impact uncertainty.

This article studies the Transmission Restoration Problem with Mobile Substation Resources, a novel mixed-integer linear programming model that prescribes the most effective usage of mobile-substation resources to enhance the resilience of a power transmission system against a particular, widespread flood event. The model is a two-stage stochastic program in which each scenario captures a different potential progression of flood heights at substations over the event horizon. The first stage concerns the pre-event selection and positioning of mobile-substation resources. The second stage concerns the coordination of mobile-substation resource deployment and permanent-substation restoration to maintain and recover service within the horizon. Experiments in the IEEE 24-Bus System and a synthetic Houston grid confirm the efficacy of the model. Even when isolated from effects related to restoration of permanent substations, the effect of four mobile transformers and eight mobile breakers for a realistic set of flood scenarios in the synthetic Houston grid was found to be an average total-cost reduction of approximately $35MM (i.e., approximately 8% of a default optimal objective value). Additionally, a novel, parallel heuristic is designed that can efficiently solve the problem as well as, with minor modifications, similar stochastic problems on pre-selection of mobile resources or placement of static ones. For a 40-scenario model instance in the IEEE 24-Bus System, the extensive form was not able to find an integer-feasible solution in six hours, yet the heuristic achieved an optimality gap no worse than 4.5% in two hours.

We compare stochastic programming and robust optimization decision models for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of an indicator variable. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas choosing between the DC and LPAC power flow models is of little to no consequence. To validate our models, we assess the performance of the mitigation solutions they prescribe in an AC power flow model.

We propose two scenario-based optimization models for power grid resilience decision making that integrate output from a hydrology model with a power flow model. The models are used to identify an optimal substation hardening strategy against potential flooding from storms for a given investment budget, which if implemented enhances the resilience of the power grid, minimizing the power demand that is shed. The same models can alternatively be used to determine the optimal budget that should be allocated for substation hardening when long-term forecasts of storm frequency and impact (specifically restoration times) are available. The two optimization models differ in terms of capturing risk attitude: one minimizes the average load shed for given scenario probabilities and the other minimizes the worst-case load shed without needing scenario probabilities. To demonstrate the efficacy of the proposed models, we further develop a case study for the Texas Gulf Coast using storm surge maps developed by the National Oceanic and Atmospheric Administration and a synthetic power grid for the state of Texas developed as part of an ARPA-E project. For a reasonable choice of parameters, we show that a scenario-based representation of uncertainty can offer a significant improvement in minimizing load shed as compared to using point estimates or average flood values. We further show that when the available investment budget is relatively high, solutions that minimize the worst-case load shed can offer several advantages as compared to solutions obtained from minimizing the average load shed. Lastly, we show that even for relatively low values of load loss and short post-hurricane power restoration times, it is optimal to make significant investments in substation hardening to deal with the storm surge considered in the NOAA flood scenarios.

We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.