arXiv subjects

Bolun Xu

Publications and source records attributed to Bolun Xu.

At least 19 recordsLinked to original sources

arXiv2026

Fairness as an Investment: Dynamic Participation and Long-Run Profit in Virtual Power Plants

We show that incorporating fairness constraints into virtual power plant (VPP) operations can incentivize consumer participation and thus improve the aggregator's long-run profitability. VPPs rely on sustained participation from heterogeneous consumers to provide a variety of grid services whose timing and frequency are often uncertain. As a result, consumers' willingness and ability to provide flexibility evolve over time, creating a dynamic link between past participation and future resource availability. We develop a dynamic aggregation framework to study how fairness in service allocation affects future participation and long-run profitability. By linking current dispatch decisions to future resource availability, we show that fairer allocations can strengthen consumer engagement, expand aggregate availability, and create additional value during high-price and high-demand events. To balance fairness and operational efficiency, we introduce a slack-augmented allocation mechanism that preserves most of the participation benefits from fairness while avoiding unnecessary reductions in service procurement. We derive conditions under which the resulting availability gains outweigh the short-run cost of redistribution and validate the approach using real-world consumer behavior and electricity market data from Norway.

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arXiv2026

Fair Aggregation in Virtual Power Plants

A virtual power plant (VPP) is operated by an aggregator that acts as a market intermediary, aggregating consumers to participate in wholesale power markets. By setting incentive prices, the aggregator induces consumers to sell energy and profits by providing this aggregated energy to the market. This supply is enabled by consumers' flexibility to adjust electricity consumption in response to market conditions. However, heterogeneity in flexibility means that profit-maximizing VPP pricing can create inequalities in participation and benefit allocation across consumers. In this paper, we develop a fairness-aware pricing framework to analyze how different fairness notions reshape system performance, measured by consumer Nash welfare, total consumer utility, and social welfare. We consider three fairness criteria: energy fairness, which ensures equitable energy provision; price fairness, which ensures similar incentive prices; and utility fairness, which ensures comparable levels of consumer utility. We model the aggregator-consumer interaction as a Stackelberg game and derive consumers' optimal responses to incentive prices. Using a stylized model, we show that profit-only pricing systematically disadvantages less flexible consumers. We further show that energy fairness can either improve or worsen all performance measures, and gains across most measures arise only at moderate fairness levels. Surprisingly, price fairness never benefits less flexible consumers, even when it reduces price disparities. By contrast, utility fairness protects less flexible consumers without benefiting more flexible ones. We validate our findings using data from an experiment in Norway under a tiered pricing scheme. Our results provide regulators and VPP operators with a systematic map linking fairness definitions and enforcement levels to operational and welfare outcomes.

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arXiv2026

Real-time Coordination of Cascaded Hydropower under Decision-Dependent Uncertainty

This study proposes a real-time control framework for cascaded hydropower systems that incorporates decision-dependent uncertainty (DDU) to capture the coupling of streamflow uncertainties across the reservoirs. The framework jointly models exogenous forecast errors and endogenous uncertainty propagation, explicitly characterizing the dependence between upstream releases and downstream inflow variability through a heteroskedastic variance model conditioned on past errors, variance, and control actions. We formulate a joint chance-constrained optimization problem to ensure reliable system operation under uncertainty and develop a tractable supporting hyperplane algorithm that enables explicit and adaptive risk allocation under DDU. We establish the convergence of the proposed method and show its risk allocation behavior under steady-state conditions. A randomized case study based on Columbia River data demonstrates that incorporating DDU reduces the constraint violations by up to 7.0\% and increases total generation by up to 0.5\% relative to decision-independent uncertainty (DIU). Sensitivity analyses of the dry-season streamflow conditions further highlight the value of adaptive risk allocation for resilient and risk-aware hydropower operations.

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arXiv2026

Voluntary Renewable Programs: Optimal Pricing and Revenue Allocation

This paper develops a multi-period optimization framework to design a voluntary renewable program (VRP) for an electric utility company, aiming to maximize total renewable energy deployments. In the business model of VRP, the utility must ensure it generates renewable energy up to the total amount of contract during each market episode (i.e., a year), while all the revenue collected from the VRP must either be used to invest in procuring renewable capacities or to maintain the current renewable fleet and infrastructure. We thus formulate the problem as an optimal pricing problem coupled with revenue allocation and renewable deployment decisions. We model the demand function of voluntary renewable contracts as an exponential decay function based on survey data. We analytically derive the optimal pricing policy of the VRP as a function of the current grid carbon intensity. We prove that a myopic policy is conditionally optimal, which maximizes renewable capacity in each period, attains the long-run optimum due to the utility's revenue-neutral constraint. We show different binding conditions and marginal values of decision variables correspond to different phases of the energy transition, and that the utility should strategically design its revenue-sharing decisions, balancing investments in renewable expansion and subsidizing existing renewable fleets. Finally, we show that voluntary renewable programs can only extend renewable penetration but cannot achieve net-zero emissions or a fully renewable grid. This pricing-allocation-expansion framework highlights both the potential and limitations of voluntary renewable demand, providing analytical insight into optimal policy design and the qualitative shifts occurring during the energy transition process.

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arXiv2026

Nonparametric Kernel Regression for Coordinated Energy Storage Peak Shaving with Stacked Services

Developing effective control strategies for behind-the-meter energy storage to coordinate peak shaving and stacked services is essential for reducing electricity costs and extending battery lifetime in commercial buildings. This work proposes an end-to-end, two-stage framework for coordinating peak shaving and energy arbitrage with a theoretical decomposition guarantee. In the first stage, a non-parametric kernel regression model constructs state-of-charge trajectory bounds from historical data that satisfy peak-shaving requirements. The second stage utilizes the remaining capacity for energy arbitrage via a transfer learning method. Case studies using New York City commercial building demand data show that our method achieves a 1.3 times improvement in performance over the state-of-the-art forecast-based method, achieving cost savings and effective peak management without relying on predictions.

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arXiv2026

A Few-Shot LLM Framework for Extreme Day Classification in Electricity Markets

This paper proposes a few-shot classification framework based on Large Language Models (LLMs) to predict whether the next day will have spikes in real-time electricity prices. The approach aggregates system state information, including electricity demand, renewable generation, weather forecasts, and recent electricity prices, into a set of statistical features that are formatted as natural-language prompts and fed to an LLM along with general instructions. The model then determines the likelihood that the next day would be a spike day and reports a confidence score. Using historical data from the Texas electricity market, we demonstrate that this few-shot approach achieves performance comparable to supervised machine learning models, such as Support Vector Machines and XGBoost, and outperforms the latter two when limited historical data are available. These findings highlight the potential of LLMs as a data-efficient tool for classifying electricity price spikes in settings with scarce data.

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arXiv2025

Electric Arc Furnaces Scheduling under Electricity Price Volatility with Reinforcement Learning

This paper proposes a reinforcement learning-based framework for optimizing the operation of electric arc furnaces (EAFs) under volatile electricity prices. We formulate the deterministic version of the EAF scheduling problem into a mixed-integer linear programming (MILP) formulation, and then develop a Q-learning algorithm to perform real-time control of multiple EAF units under real-time price volatility and shared feeding capacity constraints. We design a custom reward function for the Q-learning algorithm to smooth the start-up penalties of the EAFs. Using real data from EAF designs and electricity prices in New York State, we benchmark our algorithm against a baseline rule-based controller and a MILP benchmark, assuming perfect price forecasts. The results show that our reinforcement learning algorithm achieves around 90% of the profit compared to the perfect MILP benchmark in various single-unit and multi-unit cases under a non-anticipatory control setting.

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arXiv2025

Online Energy Storage Arbitrage under Imperfect Predictions: A Conformal Risk-Aware Approach

This work proposes a conformal approach for energy storage arbitrage to control the downside risk arising from imperfect price forecasts. Energy storage arbitrage relies solely on predictions of future market prices, while inaccurate price predictions may lead to significant profit losses. Based on conformal decision theory, we describe a controller that dynamically adjusts decision conservativeness through prediction sets without distributional assumptions. To enable online calibration when online profit loss feedback is unobservable, we establish that a temporal difference error serves as a measurable proxy. Building on this insight, we develop two online calibration strategies: prediction error-based adaptation targeting forecast accuracy, and value error-based calibration focusing on decision quality. Analysis of the conformal controller proves bounded long-term risk with convergence guarantees in temporal difference error, which further effectively manages risk exposure in potential profit losses. Case studies demonstrate superior performance in balancing risk and opportunity compared to benchmarks under varying forecast conditions.

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arXiv2025

Design Optimization and Global Impact Assessment of Solar-Thermal Direct Air Carbon Capture

The dual challenge of decarbonizing the economy and meeting rising global energy demand underscores the need for scalable and cost-effective carbon dioxide removal technologies. Direct air capture (DAC) is among the most promising approaches, but its high energy intensity, particularly the thermal energy required for sorbent regeneration, remains a critical barrier to cost reduction and sustainable deployment. This study explores solar-thermal DAC systems that combine concentrated solar thermal technology with low-cost sand-based thermal energy storage to meet this demand. We analyze the techno-economic performance of such systems in both grid-connected and stand-alone configurations. Results show that solar-thermal DAC can achieve annual capacity factors exceeding 80% and CO2 removal costs as low as 160-200 USD per ton, making it competitive with leading DAC technologies. The proposed system operates most efficiently with short-cycle sorbents that align with solar availability. The stand-alone Solar-DAC systems, which rely solely on solar energy for both electricity and thermal energy, are particularly promising in regions with high solar capacity and sandy terrain, exhibiting minimal ambient sensitivity from temperature and humidity. An optimal 6000 ton/yr modular system design takes <1 km2 land-use requirement and potentially >26 Gt/year DAC capacity is identified for sandy terrain alone globally. In areas with sedimentary basins suitable for CO2 storage, solar-powered DAC offers a lower-cost alternative to geothermal heating, which often faces geological and economic constraints.

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arXiv2025

Enhancing Profit and CO2 Mitigation: Commercial Direct Air Capture Design and Operation with Power Market Volatility

Current decarbonization efforts are falling short of meeting the net-zero greenhouse gas (GHG) emission target, highlighting the need for substantial carbon dioxide removal methods such as direct air capture (DAC). However, integrating DACs poses challenges due to their enormous power consumption. This study assesses the commercial operation of various DAC technologies that earn revenue using monetized carbon incentives while purchasing electricity from wholesale power markets. We model four commercial DAC technologies and examine their operation in three representative locations including California, Texas, and New York. Our findings reveal that commercial DAC operations can take financial advantage of the volatile power market to operate only during low-price periods strategically, offering a pathway to facilitate a cost-efficient decarbonization transition. The ambient operational environment such as temperature and relative humidity has non-trivial impact on abatement capacity. Profit-driven decisions introduce climate-economic trade-offs that might decrease the capacity factor of DAC and reduce total CO2 removal. These implications extend throughout the entire lifecycle of DAC developments and influence power systems and policies related to full-scale DAC implementation. Our study shows that DAC technologies with shorter cycle spans and higher flexibility can better exploit the electricity price volatility, while power markets demonstrate persistent low-price windows that often synergize with low grid emission periods, like during the solar "duck curve" in California. An optimal incentive design exists for profit-driven operations while carbon-tax policy in electricity pricing is counterproductive for DAC systems.

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arXiv2025

Online Convex Optimization for Coordinated Long-Term and Short-Term Isolated Microgrid Dispatch

This paper proposes a novel non-anticipatory long-short-term coordinated dispatch framework for isolated microgrid with hybrid short-long-duration energy storages (LDES). We introduce a convex hull approximation model for nonconvex LDES electrochemical dynamics, facilitating computational tractability and accuracy. To address temporal coupling in SoC dynamics and long-term contracts, we generate hindsight-optimal state-of-charge (SoC) trajectories of LDES and netloads for offline training. In the online stage, we employ kernel regression to dynamically update the SoC reference and propose an adaptive online convex optimization (OCO) algorithm with SoC reference tracking and expert tracking to mitigate myopia and enable adaptive step-size optimization. We rigorously prove that both long-term and short-term policies achieve sublinear regret bounds over time, which improves with more regression scenarios, stronger tracking penalties, and finer convex approximations. Simulation results show that the proposed method outperforms state-of-the-art methods, reducing costs by 73.4%, eliminating load loss via reference tracking, and achieving an additional 2.4% cost saving via the OCO algorithm. These benefits scale up with longer LDES durations, and the method demonstrates resilience to poor forecasts and unexpected system faults.

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arXiv2025

Economic Capacity Withholding Bounds of Competitive Energy Storage Bidders

Economic withholding in electricity markets refers to generators bidding higher than their true marginal fuel cost, and is a typical approach to exercising market power. However, existing market designs require storage to design bids strategically based on their own future price predictions, motivating storage to conduct economic withholding without assuming market power. As energy storage takes up more significant roles in wholesale electricity markets, understanding its motivations for economic withholding and the consequent effects on social welfare becomes increasingly vital. This paper derives a theoretical framework to study the economic capacity withholding behavior of storage participating in competitive electricity markets and validate our results in simulations based on the ISO New England system. We demonstrate that storage bids can reach unbounded high levels under conditions where future price predictions show bounded expectations but unbounded deviations. Conversely, in scenarios with peak price limitations, we show the upper bounds of storage bids are grounded in bounded price expectations. Most importantly, we show that storage capacity withholding can potentially lower the overall system cost when price models account for system uncertainties. Our paper reveals energy storage is not a market manipulator but an honest player contributing to the social welfare. It helps electricity market researchers and operators better understand the economic withholding behavior of storage and reform market policies to maximize storage contributing to a cost-efficient decolonization.

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arXiv2025

Gaming on Coincident Peak Shaving: Equilibrium and Strategic Behavior

Power system operators and electric utility companies often impose a coincident peak demand charge on customers when the aggregate system demand reaches its maximum. This charge incentivizes customers to strategically shift their peak usage away from the system's collective peak, which helps reduce stress on electricity infrastructure. In this paper, we develop a game-theoretic model to analyze how such strategic behavior affects overall system efficiency. We show that depending on the extent of customers' demand-shifting capabilities, the resulting coincident peak shaving game can exhibit concavity, quasi-concavity with discontinuities, or non-concavity with discontinuities. In a two-agent, two-period setting, we derive closed-form Nash equilibrium solutions for each scenario and generalize our findings to multi-agent contexts. We prove the stability of the equilibrium points and propose an algorithm for computing equilibrium outcomes under all game configurations. Our results indicate that the peak-shaving outcome at the equilibrium of the game model is comparable to the optimal outcome of the natural centralized model. However, there is a significant loss in efficiency. Under quasi-concave and non-concave conditions, this inefficiency grows with increased customer flexibility and larger disparities in marginal shifting costs; we also examine how the number of agents influences system performance. Finally, numerical simulations with real-world applications validate our theoretical insights.

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arXiv2025

A Decision-Focused Predict-then-Bid Framework for Strategic Energy Storage

This paper introduces a novel decision-focused framework for energy storage arbitrage bidding. Inspired by the bidding process for energy storage in electricity markets, we propose a predict-then-bid end-to-end method incorporating the storage arbitrage optimization and market clearing models. This is achieved through a tri-layer framework that combines a price prediction layer with a two-stage optimization problem: an energy storage optimization layer and a market-clearing optimization layer. We leverage the implicit function theorem for gradient computation in the first optimization layer and incorporate a perturbation-based approach into the decision-focused loss function to ensure differentiability in the market-clearing layer. Numerical experiments using electricity market data from New York demonstrate that our bidding design substantially outperforms existing methods, achieving the highest profits and showcasing the effectiveness of the proposed approach.

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arXiv2025

Dimension-reduced Optimization of Multi-zone Thermostatically Controlled Loads

This study proposes a computationally efficient method for optimizing multi-zone thermostatically controlled loads (TCLs) by leveraging dimensionality reduction through an auto-encoder. We develop a multi-task learning framework to jointly represent latent variables and formulate a state-space model based on observed TCL operation data. This significantly reduces the dimensionality of TCL variables and states while preserving critical nonlinear interdependencies in TCL control. To address various application scenarios, we introduce optimization algorithms based on system identification (OptIden) and system simulation (OptSim) tailored to the latent variable representation. These approaches employ automatic differentiation and zeroth-order techniques, respectively, for efficient implementation. We evaluate the proposed method using a 90-zone apartment prototype, comparing its performance to traditional high-dimensional optimization. Results demonstrate that our approach effectively reduces control costs while achieving significantly higher computational efficiency.

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arXiv2025

A Lagrangian-Informed Long-Term Dispatch Policy for Coupled Hydropower and Photovoltaic Systems

This paper presents a long-term dispatch framework for coupled hydropower and floating photovoltaic systems. We introduce a temporal decomposition algorithm based on partial Lagrangian relaxation to address long-term water contract constraints. We derive a real-time, non-anticipatory dispatch policy based on water contract pricing. Our framework is evaluated with a case study using real-world hydrology and power system data from Lake Mead and Lake Powell, on the Colorado River, demonstrating competitive performance against commercial solvers for both linearized and nonlinear reservoir models. We conduct a sensitivity analysis on transmission capacity, electricity price and uncertainty scenarios, showing that the operational performance is significantly impacted by the transmission capacity and electricity prices while remaining relatively robust under uncertainty scenarios.

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arXiv2025

Comparative Withholding Behavior Analysis of Historical Energy Storage Bids in California

The rapid growth of battery energy storage in wholesale electricity markets calls for a deeper understanding of storage operators' bidding strategies and their market impacts. This study examines energy storage bidding data from the California Independent System Operator (CAISO) between July 1, 2023, and October 1, 2024, with a primary focus on economic withholding strategies. Our analysis reveals that storage bids are closely aligned with day-ahead and real-time market clearing prices, with notable bid inflation during price spikes. Statistical tests demonstrate a strong correlation between price spikes and capacity withholding, indicating that operators can anticipate price surges and use market volatility to increase profitability. Comparisons with optimal hindsight bids further reveal a clear daily periodic bidding pattern, highlighting extensive economic withholding. These results underscore potential market inefficiencies and highlight the need for refined regulatory measures to address economic withholding as storage capacity in the market continues to grow.

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arXiv2025

Energy Storage Arbitrage Under Price Uncertainty: Market Risks and Opportunities

We investigate the profitability and risk of energy storage arbitrage in electricity markets under price uncertainty, exploring both robust and chance-constrained optimization approaches. We analyze various uncertainty representations, including polyhedral, ellipsoidal uncertainty sets and probabilistic approximations, to model price fluctuations and construct efficient frontiers that highlight the tradeoff between risk and profit. Using historical electricity price data, we quantify the impact of uncertainty on arbitrage strategies and compare their performance under distinct market conditions. The results reveal that arbitrage strategies under uncertainties can effectively secure expected profits, and robust strategies perform better in risk management across varying levels of conservativeness, especially under highly volatile market conditions. This work provides insights into storage arbitrage strategy selection for market participants with differing risk preferences, emphasizing the adaptability of efficient frontiers to the electricity market.

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