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DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗

DOE OSTI2024

A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

distributionally robust optimization↗

DOE OSTI2024

Improved microgrid resiliency through distributionally robust optimization under a policy-mode framework

Critical energy infrastructure are constantly under stress due to the ever increasing disruptions caused by wildfires, hurricanes, other weather related extreme events and cyber-attacks. Hence it becomes important to make critical infrastructure resilient to threats from such cyber-physical events. However, such events are hard to predict and numerous in nature and type and it becomes infeasible to make a system resilient to every possible such cyber-physical event. Such an approach can make the system operation overly conservative and impractical to operate. Furthermore, distributions of such events are hard to predict and historical data available on such events can be very sparse, making the problem even harder to solve. To deal with these issues, in this paper we present a policy-mode framework that enumerates and predicts the probability of various cyber-physical events and then a distributionally robust optimization (DRO) formulation that is robust to the sparsity of the available historical data. The proposed algorithm is illustrated on an islanded microgrid example: a modified IEEE 123-node feeder with distributed energy resources (DERs) and energy storage. Simulations are carried to validate the resiliency metrics under the sampled disruption events.

Nazir, Mohammad Nawaf↗

DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗

DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

distribution system operator↗

DOE OSTI2024

Distributionally Robust Bilevel Optimization Model for Distribution Network With Demand Response Under Uncertain Renewables Using Wasserstein Metrics

Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Dynamic Transmission Line Switching Amid Wildfire-Prone Weather Under Decision-Dependent Uncertainty

During dry and windy seasons, environmental conditions significantly increase the risk of wildfires, exposing power grids to disruptions caused by transmission line failures. Wildfire propagation exacerbates grid vulnerability, potentially leading to prolonged power outages. To address this challenge, we propose a multistage optimization model that dynamically adjusts transmission grid topology in response to wildfire propagation, aiming to develop an optimal response policy. By accounting for decision-dependent uncertainty, where line survival probabilities depend on usage, we employ distributionally robust optimization to model uncertainty in line survival distributions. We adapt the stochastic nested decomposition algorithm and derive a deterministic upper bound for its finite convergence. To enhance computational efficiency, we exploit the Lagrangian dual problem structure for a faster generation of Lagrangian cuts. Using realistic data from the California transmission grid, we demonstrate the superior performance of dynamic response policies against two-stage alternatives through a comprehensive case study. In addition, after solving the multistage formulation, we construct easy-to-implement policies that significantly reduce computational burden while maintaining good performance in real-time deployment. History: Accepted by Russell Bent, Area Editor for Network Optimization: Algorithms and Applications. Funding: This work was supported by the U.S. Department of Energy, Office of Electricity [Grant DE-AC02-05CH11231]. The work of R. Jiang was supported in part by the U.S. National Science Foundation, Division of Electrical, Communications and Cyber Systems [Grant ECCS-1845980] and the U.S. Air Force Office of Scientific Research [Grant FA9550-23-1-0323]. 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.2025.1210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Estrada-Garcia, Juan-Alberto↗

DOE OSTI2024

Robust Restoration From Cyber-Physical Attacks in Active Distribution Grids With Grid-Edge IBRs

The inverter-based resources (IBRs) have enabled the integration of renewable energy at the grid edge with enhanced control capabilities to support the reliable operation of power grids. Different control frameworks, such as hierarchical or distributed architecture, have been proposed with the expansion of cyber networks for real-time monitoring and control. This evolution of critical infrastructure into cyber-physical systems also brings more vulnerabilities for the broadened attack surfaces, and significantly increases the possibility of physical system failures or outages caused by cyberattacks. Among tremendous efforts in the defense-in-depth approach, it remains challenging to provide prompt detection and accurate location of attack entry points or paths. Therefore, the prevailing restoration framework may struggle to fully consider the cyber-physical interdependence, successfully isolate the compromised cyber and physical components, and safely recover the systems without the potential risks leading to secondary outages. This paper is motivated to develop a cyber-physical restoration framework for distribution grids to recover from cyber attacks by harnessing grid-edge IBRs. The framework is first built on the operational guidelines of IBRs considering the compromised cyber layer. Then, an ambiguity set is established to represent the uncertainty of attack scenarios and their possibility levels. Next, a distributionally robust optimization model is developed to provide the optimal load restoration strategy across all scenarios. The effectiveness of the proposed model is demonstrated through various use cases on the modified IEEE 13-node and 123-node test systems. Finally, simulation results demonstrate the effectiveness and advancement of developed post-attack restoration strategies.

Cybersecurity↗

DOE OSTI2025

Enhancing the Survivability of Power Systems With Grid-Edge DERs Against DoS Attacks

Power system survivability, defined as the ability of a system to maintain steady-state functionality under varying operational conditions, reflects its resilience against disturbances. While existing research primarily focuses on physical-layer disturbances, the increasing prevalence of grid-edge DERs, which are primarily used for integrating renewable energy, has significantly expanded the cyber attack surface. As a result, operational disruptions caused by cyber threats are posing significant challenges to system survivability and cannot be overlooked. To fill this gap, we redefine system survivability to incorporate the cyber layer’s status and propose a Distributionally Robust Optimization (DRO) approach to enhance power system survivability against potential cyber-physical threats. In this paper, we first analyze the operational guidelines of systems with a high penetration of DERs under various cyber network conditions and redefine survivability in this context. Next, we focus on the most common cyber threat, Denial-of-Service (DoS) attacks, and develop a corresponding attack model. This model allows for the creation of a kernel-based ambiguity set that captures attack uncertainties using historical data. Finally, we transform the proposed DRO model as a tractable optimization problem, with its solution providing an optimal cyber redundancy plan to enhance system survivability in DoS attack scenarios. Simulation results on the IEEE 13-node and 123-node test feeders demonstrate the effectiveness of our proposed model in improving system survivability. This model can also be expanded to include other types of common attacks and serve as a comprehensive planning tool to improve overall cyber physical survival of the system.

cybersecurity↗

DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗

DOE OSTI2024

Multi-Timescale Optimal Operation Framework for Integrated Economic and Reliability Analysis of Hybrid Power Plants

This paper introduces a hierarchical modeling framework for hybrid power plants (HPP) to facilitate the operation of HPP in power systems similar to conventional generators (Congens) in the integrated multi-timescale optimal operation framework. To consider the uncertainties of HPP renewable power in the day-ahead scheduling, distributionally robust optimization (DRO) is used. To ensure that the state-of-charge (SOC) of energy storage systems in HPPs aligns closely with the planned value for long-term reliability, real-time SOC management is incorporated. In addition, an adjustable real-time control is designed for the robust delivery of HPP real-time services. Case studies performed on a revised IEEE 39-bus system demonstrate the effectiveness of the proposed framework for HPP operation. Simulation results highlight that the proposed framework not only can help operators schedule HPP similar to Congens in varying weather conditions but can also maintain the frequency reliability of the system.

frequency stability↗

DOE OSTI2024

Advanced Computational Techniques for Improving Resilience of Critical Energy Infrastructure under Cyber-Physical Attacks

In this chapter, we present recent advances in improving the resilience of cyber-physical systems, especially with regards to energy systems. We provide discussions around various types of cyber-physical events that can cause disruptions and new advances in optimization, control, and reinforcement learning (RL) to deal with the challenges posed by such cyber-physical events. The presented methods range from distributed robust optimization, autonomous and coordinated control, reinforcement learning based resilient control and topology reconfiguration in Inter-System resilient control.

Nazir, Mohammad Nawaf [BATTELLE (PACIFIC NW LAB)]↗

DOE OSTI2025

Decision-Dependent Uncertainty-Aware Distribution System Planning Under Wildfire Risk

The interaction between power systems and wildfires can be dangerous and costly. Distribution grids can be liable for the outbreak of wildfires during extreme weather. In wildfire-prone areas, investment planning should consider the impact of operational actions on wildfire-related uncertainties affecting line failure likelihood. Here, in this case, endogenous-based uncertainty modeling should comprise the backbone of the investment planning model viz-a-viz the inability of standard exogenous-based uncertainty modeling. Therefore, we propose a decision-dependent uncertainty (DDU) aware methodology to optimize investment portfolios for distribution systems, considering that high power-flow levels in high-threat areas can ignite wildfires and increase line failure probability. The methodology identifies the best combination of upgrades (new lines, hardening existing lines, and placing switching devices). Methodologically, we propose a two-stage distributionally robust planning optimization problem with DDU that considers the distribution system's multiperiod operation. The first stage determines optimal switching actions and line investments, and the second stage evaluates the worst-case expected operational cost under a DDU framework designed to account for the endogenous impact of power-flow levels and hardening investment decisions in the line failure probabilities. An iterative method is tailored to handle the problem and numerical experiments demonstrate a more prepared grid to deal with wildfire risk.

Power systems investment planning↗

DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

A Scalable and Robust Multi-Agent Approach to Distributed Optimization

Modularizing a large optimization problem so that the solutions to the subproblems provide a good overall solution is a challenging problem. In this paper we present a multi-agent approach to this problem based on aligning the agent objectives with the system objectives, obviating the need to impose external mechanisms to achieve collaboration among the agents. This approach naturally addresses scaling and robustness issues by ensuring that the agents do not rely on the reliable operation of other agents We test this approach in the difficult distributed optimization problem of imperfect device subset selection [Challet and Johnson, 2002]. In this problem, there are n devices, each of which has a "distortion", and the task is to find the subset of those n devices that minimizes the average distortion. Our results show that in large systems (1000 agents) the proposed approach provides improvements of over an order of magnitude over both traditional optimization methods and traditional multi-agent methods. Furthermore, the results show that even in extreme cases of agent failures (i.e., half the agents fail midway through the simulation) the system remains coordinated and still outperforms a failure-free and centralized optimization algorithm.

Tumer, Kagan↗

NASA NTRS2019

Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty

The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process.

Stanford, Bret K.↗

NASA NTRS2006

Efficient and Robust Data Collection Using Compact Micro Hardware, Distributed Bus Architectures and Optimizing Software

Future In-Space propulsion systems for exploration programs will invariably require data collection from a large number of sensors. Consider the sensors needed for monitoring several vehicle systems states of health, including the collection of structural health data, over a large area. This would include the fuel tanks, habitat structure, and science containment of systems required for Lunar, Mars, or deep space exploration. Such a system would consist of several hundred or even thousands of sensors. Conventional avionics system design will require these sensors to be connected to a few Remote Health Units (RHU), which are connected to robust, micro flight computers through a serial bus. This results in a large mass of cabling and unacceptable weight. This paper first gives a survey of several techniques that may reduce the cabling mass for sensors. These techniques can be categorized into four classes: power line communication, serial sensor buses, compound serial buses, and wireless network. The power line communication approach uses the power line to carry both power and data, so that the conventional data lines can be eliminated. The serial sensor bus approach reduces most of the cabling by connecting all the sensors with a single (or redundant) serial bus. Many standard buses for industrial control and sensor buses can support several hundreds of nodes, however, have not been space qualified. Conventional avionics serial buses such as the Mil-Std-1553B bus and IEEE 1394a are space qualified but can support only a limited number of nodes. The third approach is to combine avionics buses to increase their addressability. The reliability, EMI/EMC, and flight qualification issues of wireless networks have to be addressed. Several wireless networks such as the IEEE 802.11 and Ultra Wide Band are surveyed in this paper. The placement of sensors can also affect cable mass. Excessive sensors increase the number of cables unnecessarily. Insufficient number of sensors may not provide adequate coverage of the system. This paper also discusses an optimal technique to place and validate sensors.

micro hardware↗

NASA NTRS2003

Providing Effective Access to Shared Resources: A COIN Approach

Managers of systems of shared resources typically have many separate goals. Examples are efficient utilization of the resources among its users and ensuring no user's satisfaction in the system falls below a preset minimal level. Since such goals will usually conflict with one another, either implicitly or explicitly the manager must determine the relative importance of the goals, encapsulating that into an overall utility function rating the possible behaviors of the entire system. Here we demonstrate a distributed, robust, and adaptive way to optimize that overall function. Our approach is to interpose adaptive agents between each user and the system, where each such agent is working to maximize its own private utility function. In turn, each such agent's function should be both relatively easy for the agent to learn to optimize, and 'aligned' with the overall utility function of the system manager - an overall function that is based on but in general different from the satisfaction functions of the individual users. To ensure this we enhance the COllective INtelligence (COIN) framework to incorporate user satisfaction functions in the overall utility function of the system manager and accordingly in the associated private utility functions assigned to the users agents. We present experimental evaluations of different COIN-based private utility functions and demonstrate that those COIN-based functions outperform some natural alternatives.

Airiau, Stephane↗