Bolun Xu

Bolun Xu, Yury Dvorkin, Daniel S. Kirschen et al.

Because energy storage systems have better ramping characteristics than traditional generators, their participation in frequency regulation should facilitate the balancing of load and generation. However, they cannot sustain their output indefinitely. System operators have therefore implemented new frequency regulation policies to take advantage of the fast ramps that energy storage systems can deliver while alleviating the problems associated with their limited energy capacity. This paper contrasts several U.S. policies that directly affect the participation of energy storage systems in frequency regulation and compares the revenues that the owners of such systems might achieve under each policy.

Yuanyuan Shi, Bolun Xu, Yushi Tan et al.

A vital aspect in energy storage planning and operation is to accurately model its operational cost, which mainly comes from the battery cell degradation. Battery degradation can be viewed as a complex material fatigue process that based on stress cycles. Rainflow algorithm is a popular way for cycle identification in material fatigue process, and has been extensively used in battery degradation assessment. However, the rainflow algorithm does not have a closed form, which makes the major difficulty to include it in optimization. In this paper, we prove the rainflow cycle-based cost is convex. Convexity enables the proposed degradation model to be incorporated in different battery optimization problems and guarantees the solution quality. We provide a subgradient algorithm to solve the problem. A case study on PJM regulation market demonstrates the effectiveness of the proposed degradation model in maximizing the battery operating profits as well as extending its lifetime.

Liudong Chen, Bolun Xu

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.

Yuanyuan Shi, Bolun Xu, Baosen Zhang et al.

Energy storage in data centers has mainly been used as devices to backup generators during power outages. Recently, there has been a growing interest in using energy storage devices to actively shape power consumption in data centers to reduce their skyrocketing electricity bills. In this paper, we consider using energy storage in data centers for two applications in a joint fashion: reducing peak demand charges and enabling data centers to participate in regulation markets. We develop an optimization framework that captures the cost of electricity, degradation of energy storage devices, as well as the benefit from regulation markets. Under this frame- work, using real data Microsoft data center traces and PJM regulation signals, we show the electricity bill of a data center can be reduced by up to 20%. Furthermore, we demonstrate that the saving from joint optimization can be even larger than the sum of individually optimizing each component. We quantify the particular aspects of data center load profiles that lead to this superlinear gain. Compared to prior works that consider using energy storage devices for each single application alone, our results suggest that energy storage in data centers can have much larger impacts than previously thought possible.

Bolun Xu, Andreas Ulbig, Goran Andersson

Dynamic line rating (DLR) models the transmission capacity of overhead lines as a function of ambient conditions. It takes advantage of the physical thermal property of overhead line conductors, thus making DLR less conservative compared to the traditional worst-case oriented nominal line rating (NLR). Employing DLR brings potential benefits for grid integration of variable Renewable Energy Sources (RES), such as wind and solar energy. In this paper, we reproduce weather conditions from renewable feed-ins and local temperature records, and calculate DLR in accordance with the RES feed-in and load demand data step. Simulations with high time resolution, using a predictive dispatch optimization and the Power Node modeling framework, of a six-node benchmark power system loosely based on the German power system are performed for the current situation, using actual wind and PV feed-in data. The integration capability of DLR under high RES production shares is inspected through simulations with scaled-up RES profiles and reduced dispatchable generation capacity. The simulation result demonstrates a comparison between DLR and NLR in terms of reductions in RES generation curtailments and load shedding, while discussions on the practicality of adopting DLR in the current power system is given in the end.

Yuanyuan Shi, Bolun Xu, Yushi Tan et al.

We study the optimal control of battery energy storage under a general "pay-for-performance" setup such as providing frequency regulation and renewable integration. In these settings, batteries need to carefully balance the trade-off between following the instruction signals and their degradation costs in real-time. Existing battery control strategies either do not consider the uncertainty of future signals, or cannot accurately account for battery cycle aging mechanism during operation. In this work, we take a different approach to the optimal battery control problem. Instead of attacking the complexity of battery degradation function or the lack of future information one at a time, we address these two challenges together in a joint fashion. In particular, we present an electrochemically accurate and trackable battery degradation model called the rainflow cycle-based model. We prove the degradation cost is convex. Then we propose an online control policy with a simple threshold structure and show it achieve near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize the optimality gap and show it is independent to the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

Yousuf Baker, Ningkun Zheng, Bolun Xu

Energy storage resources must consider both price uncertainties and their physical operating characteristics when participating in wholesale electricity markets. This is a challenging problem as electricity prices are highly volatile, and energy storage has efficiency losses, power, and energy constraints. This paper presents a novel, versatile, and transferable approach combining model-based optimization with a convolutional long short-term memory network for energy storage to respond to or bid into wholesale electricity markets. We test our proposed approach using historical prices from New York State, showing it achieves state-of-the-art results, achieving between 70% to near 90% profit ratio compared to perfect foresight cases, in both price response and wholesale market bidding setting with various energy storage durations. We also test a transfer learning approach by pre-training the bidding model using New York data and applying it to arbitrage in Queensland, Australia. The result shows transfer learning achieves exceptional arbitrage profitability with as little as three days of local training data, demonstrating its significant advantage over training from scratch in scenarios with very limited data availability.

Ningkun Zheng, Xiaoxiang Liu, Bolun Xu et al.

This paper proposes a novel energy storage price arbitrage algorithm combining supervised learning with dynamic programming. The proposed approach uses a neural network to directly predicts the opportunity cost at different energy storage state-of-charge levels, and then input the predicted opportunity cost into a model-based arbitrage control algorithm for optimal decisions. We generate the historical optimal opportunity value function using price data and a dynamic programming algorithm, then use it as the ground truth and historical price as predictors to train the opportunity value function prediction model. Our method achieves 65% to 90% profit compared to perfect foresight in case studies using different energy storage models and price data from New York State, which significantly outperforms existing model-based and learning-based methods. While guaranteeing high profitability, the algorithm is also light-weighted and can be trained and implemented with minimal computational cost. Our results also show that the learned prediction model has excellent transferability. The prediction model trained using price data from one region also provides good arbitrage results when tested over other regions.

Liudong Chen, Hyemi Kim, Adam N. Elmachtoub et al.

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.

Liudong Chen, Bolun Xu

Time-varying pricing tariffs incentivize consumers to shift their electricity demand and reduce costs, but may increase the energy burden for consumers with limited response capability. The utility must thus balance affordability and response incentives when designing these tariffs by considering consumers' response expectations. This paper proposes a joint learning-based identification and optimization method to design equitable time-varying tariffs. Our proposed method encodes historical prices and demand response data into a recurrent neural network (RNN) to capture high-dimensional and non-linear consumer price response behaviors. We then embed the RNN into the tariff design optimization, formulating a non-linear optimization problem with a quadratic objective. We propose a gradient-based solution method that achieves fast and scalable computation. Simulation using real-world consumer data shows that our equitable tariffs protect low-income consumers from price surges while effectively motivating consumers to reduce peak demand. The method also ensures revenue recovery for the utility company and achieves robust performance against demand response uncertainties and prediction errors.

Zhiyuan Fan, Elizabeth Dentzer, James Glynn et al.

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.

Ning Qi, Ningkun Zheng, Bolun Xu

This paper proposes a novel framework to price energy storage in economic dispatch with a social welfare maximization objective. This framework can be utilized by power system operators to generate default bids for storage or to benchmark market power in bids submitted by storage participants. We derive a theoretical framework based on a two-stage chance-constrained formulation which systematically incorporates system balance constraints and uncertainty considerations. We present tractable reformulations for the joint chance constraints. Analytical results show that the storage opportunity cost is convex and increases with greater net load uncertainty. We also show that the storage opportunity prices are bounded and are linearly coupled with future energy and reserve prices. We demonstrate the effectiveness of the proposed approach on an ISO-NE test system and compare it with a price-taker storage profit-maximizing bidding model. Simulation results show that the proposed market design reduces electricity payments by an average of 17.4% and system costs by 3.9% while reducing storage's profit margins, and these reductions scale up with the renewable and storage capacity.

Zhiyuan Fan, Tianyi Lin, Bolun Xu

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.

Eliza Cohn, Ning Qi, Upmanu Lall et al.

This paper proposes a real-time control policy for cascaded hydropower systems that incorporates decision-dependent uncertainty (DDU) to capture the coupling of streamflow uncertainties across the network. 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 convergence of the proposed method and show that it recovers the Bonferroni approximation under steady-state conditions. A randomized case study based on Columbia River data demonstrates that the proposed framework improves both energy generation and reservoir reliability by accounting for DDU. Sensitivity analyses on drought severity and model parameters further highlight the value of adaptive risk allocation for resilient hydropower operations.

Ning Qi, Yousuf Baker, Bolun Xu

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.

Saud Alghumayjan, Jiajun Han, Ningkun Zheng et al.

This paper presents an integrated model for bidding energy storage in day-ahead and real-time markets to maximize profits. We show that in integrated two-stage bidding, the real-time bids are independent of day-ahead settlements, while the day-ahead bids should be based on predicted real-time prices. We utilize a transformer-based model for real-time price prediction, which captures complex dynamical patterns of real-time prices, and use the result for day-ahead bidding design. For real-time bidding, we utilize a long short-term memory-dynamic programming hybrid real-time bidding model. We train and test our model with historical data from New York State, and our results showed that the integrated system achieved promising results of almost a 20\% increase in profit compared to only bidding in real-time markets, and at the same time reducing the risk in terms of the number of days with negative profits.

Saud Alghumayjan, Ming Yi, Bolun Xu

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.

Yuanyuan Shi, Bolun Xu

This paper proposes a novel end-to-end deep learning framework that simultaneously identifies demand baselines and the incentive-based agent demand response model, from the net demand measurements and incentive signals. This learning framework is modularized as two modules: 1) the decision making process of a demand response participant is represented as a differentiable optimization layer, which takes the incentive signal as input and predicts user's response; 2) the baseline demand forecast is represented as a standard neural network model, which takes relevant features and predicts user's baseline demand. These two intermediate predictions are integrated, to form the net demand forecast. We then propose a gradient-descent approach that backpropagates the net demand forecast errors to update the weights of the agent model and the weights of baseline demand forecast, jointly. We demonstrate the effectiveness of our approach through computation experiments with synthetic demand response traces and a large-scale real world demand response dataset. Our results show that the approach accurately identifies the demand response model, even without any prior knowledge about the baseline demand.

Yuxiao Liu, Bolun Xu, Audun Botterud et al.

Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models under all possible training and testing scenarios, and proposes an evaluation implementation based on Rademacher complexity theory. We answer key questions for data-driven models: how much training data is required to guarantee a certain error bound, and how partial physical knowledge can be utilized to reduce the required amount of data. Our results are crucial for the evaluation and application of data-driven models in power grid analysis. We demonstrate the proposed method by finding generalization error bounds for two applications, i.e. branch flow linearization and external network equivalent under different degrees of physical knowledge. Results identify how the bounds decrease with additional power grid physical knowledge or more training data.

Yuanyuan Shi, Bolun Xu, Di Wang et al.

We consider using a battery storage system simultaneously for peak shaving and frequency regulation through a joint optimization framework which captures battery degradation, operational constraints and uncertainties in customer load and regulation signals. Under this framework, using real data we show the electricity bill of users can be reduced by up to 15\%. Furthermore, we demonstrate that the saving from joint optimization is often larger than the sum of the optimal savings when the battery is used for the two individual applications. A simple threshold real-time algorithm is proposed and achieves this super-linear gain. Compared to prior works that focused on using battery storage systems for single applications, our results suggest that batteries can achieve much larger economic benefits than previously thought if they jointly provide multiple services.