arXiv subjects

Bolun Xu

Publications and source records attributed to Bolun Xu.

At least 37 records · Page 2Linked to original sources

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.

eess.SY↗

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.

math.OC↗

arXiv2024

Conformal Uncertainty Quantification of Electricity Price Predictions for Risk-Averse Storage Arbitrage

This paper proposes a risk-averse approach to energy storage price arbitrage, leveraging conformal uncertainty quantification for electricity price predictions. The method addresses the significant challenges posed by the inherent volatility and uncertainty of real-time electricity prices, which create substantial risks of financial losses for energy storage participants relying on future price forecasts to plan their operations. The framework comprises a two-layer prediction model to quantify real-time price uncertainty confidence intervals with high coverage. The framework is distribution-free and can work with any underlying point prediction model. We evaluate the quantification effectiveness through storage price arbitrage application by managing the risk of participating in the real-time market. We design a risk-averse policy for profit-maximization of energy storage arbitrage to find the safest storage schedule with very minimal losses. Using historical data from New York State and synthetic price predictions, our evaluations demonstrate that this framework can achieve good profit margins with less than $35\%$ purchases.

math.OC↗

arXiv2024

Perturbed Decision-Focused Learning for Modeling Strategic Energy Storage

This paper presents a novel decision-focused framework integrating the physical energy storage model into machine learning pipelines. Motivated by the model predictive control for energy storage, our end-to-end method incorporates the prior knowledge of the storage model and infers the hidden reward that incentivizes energy storage decisions. This is achieved through a dual-layer framework, combining a prediction layer with an optimization layer. We introduce the perturbation idea into the designed decision-focused loss function to ensure the differentiability over linear storage models, supported by a theoretical analysis of the perturbed loss function. We also develop a hybrid loss function for effective model training. We provide two challenging applications for our proposed framework: energy storage arbitrage, and energy storage behavior prediction. The numerical experiments on real price data demonstrate that our arbitrage approach achieves the highest profit against existing methods. The numerical experiments on synthetic and real-world energy storage data show that our approach achieves the best behavior prediction performance against existing benchmark methods, which shows the effectiveness of our method.

eess.SY↗

arXiv2024

A WECC-based Model for Simulating Two-stage Market Clearing with High-temporal-resolution

This paper presents a new open-source model for simulating two-stage market clearing based on the Western Electricity Coordinating Council Anchor Data Set. We model accurate two-stage market clearing with day-ahead unit commitment at hourly resolution and real-time economic dispatch with five-minute resolution. Both day-ahead unit commitment and real-time economic dispatch can incorporate look-ahead rolling horizons. The model includes seven market regions and a full year of data, detailing 2,403 individual generation assets across diverse energy sources. The year-long simulation demonstrates the capability of our model to closely reflect the generation and price patterns of the California ISO. Our sensitivity analysis revealed that extending the ED look-ahead horizon reduces system costs by up to 0.12%. We expect this new system model to fulfill the needs of conducting electricity market analysis at finer time granularity for market designs and emerging technology integration. While we focus on the western interconnection, the model serves as a base to simulate other two-stage clearing market locations.

physics.soc-ph↗

arXiv2024

Long-Term Energy Management for Microgrid with Hybrid Hydrogen-Battery Energy Storage: A Prediction-Free Coordinated Optimization Framework

This paper studies the long-term energy management of a microgrid coordinating hybrid hydrogen-battery energy storage. We develop an approximate semi-empirical hydrogen storage model to accurately capture the power-dependent efficiency of hydrogen storage. We introduce a prediction-free two-stage coordinated optimization framework, which generates the annual state-of-charge (SoC) reference for hydrogen storage offline. During online operation, it updates the SoC reference online using kernel regression and makes operation decisions based on the proposed adaptive virtual-queue-based online convex optimization (OCO) algorithm. We innovatively incorporate penalty terms for long-term pattern tracking and expert-tracking for step size updates. We provide theoretical proof to show that the proposed OCO algorithm achieves a sublinear bound of dynamic regret without using prediction information. Numerical studies based on the Elia and North China datasets show that the proposed framework significantly outperforms the existing online optimization approaches by reducing the operational costs and loss of load by around 30% and 80%, respectively. These benefits can be further enhanced with optimized settings for the penalty coefficient and step size of OCO, as well as more historical references.

math.OC↗

arXiv2024

Chance-Constrained Energy Storage Pricing for Social Welfare Maximization

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.

eess.SY↗

arXiv2024

Market Power and Withholding Behavior of Energy Storage Units

Electricity markets are experiencing a rapid increase in energy storage unit participation. Unlike conventional generation resources, quantifying the competitive operation and identifying if a storage unit is exercising market power is challenging, particularly in the context of multi-interval bidding strategies. We present a framework to differentiate strategic capacity withholding behaviors attributed to market power from inherent competitive bidding in storage unit strategies. Our framework evaluates the profitability of strategic storage unit participation, analyzing bidding behaviors as both price takers and price makers using a self-scheduling model, and investigates how they leverage market inefficiencies. Specifically, we propose a price sensitivity model derived from the linear supply function equilibrium model to examine the price-anticipating bidding strategy, effectively capturing the influence of market power. We introduce a sufficient ex-post analysis for market operators to identify potential exploitative behaviors by monitoring instances of withholding within the bidding profiles, ensuring market resilience and competitiveness. We discuss and verify applicability of the proposed framework to realistic settings. Our analysis substantiates commonly observed economic bidding behaviors of storage units. Furthermore, it demonstrates that significant price volatility offers considerable profit opportunities not only for participants possessing market power but also for typical strategic profit seekers.

eess.SY↗

arXiv2024

Energy Storage Arbitrage in Two-settlement Markets: A Transformer-Based Approach

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.

math.OC↗

arXiv2024

Operational Valuation for Energy Storage under Multi-stage Price Uncertainties

This paper presents an analytical method for calculating the operational value of an energy storage device under multi-stage price uncertainties. Our solution calculates the storage value function from price distribution functions directly instead of sampling discrete scenarios, offering improved modeling accuracy over tail distribution events such as price spikes and negative prices. The analytical algorithm offers very high computational efficiency in solving multi-stage stochastic programming for energy storage and can easily be implemented within any software and hardware platform, while numerical simulation results show the proposed method is up to 100,000 times faster than a benchmark stochastic-dual dynamic programming solver even in small test cases. Case studies are included to demonstrate the impact of price variability on the valuation results, and a battery charging example using historical prices for New York City.

math.OC↗

arXiv2024

Predicting Strategic Energy Storage Behaviors

Energy storage are strategic participants in electricity markets to arbitrage price differences. Future power system operators must understand and predict strategic storage arbitrage behaviors for market power monitoring and capacity adequacy planning. This paper proposes a novel data-driven approach that incorporates prior model knowledge for predicting the strategic behaviors of price-taker energy storage systems. We propose a gradient-descent method to find the storage model parameters given the historical price signals and observations. We prove that the identified model parameters will converge to the true user parameters under a class of quadratic objective and linear equality-constrained storage models. We demonstrate the effectiveness of our approach through numerical experiments with synthetic and real-world storage behavior data. The proposed approach significantly improves the accuracy of storage model identification and behavior forecasting compared to previous blackbox data-driven approaches.

eess.SY↗

arXiv2023

Equitable Time-Varying Pricing Tariff Design: A Joint Learning and Optimization Approach

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.

cs.LG↗

arXiv2023

Transferable Energy Storage Bidder

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.

cs.LG↗

arXiv2023

Vehicle-to-Grid Fleet Service Provision considering Nonlinear Battery Behaviors

The surging adoption of electric vehicles (EV) calls for accurate and efficient approaches to coordinate with the power grid operation. By being responsive to distribution grid limits and time-varying electricity prices, EV charging stations can minimize their charging costs while aiding grid operation simultaneously. In this study, we investigate the economic benefit of vehicle-to-grid (V2G) using real-time price data from New York State and a real-world charging network dataset. We incorporate nonlinear battery models and price uncertainty into the V2G management design to provide a realistic estimation of cost savings from different V2G options. The proposed control method is computationally tractable when scaling up to real-world applications. We show that our proposed algorithm leads to an average of 35% charging cost savings compared to uncontrolled charging when considering unidirectional charging, and bi-directional V2G enables additional 18% cost savings compared to unidirectional smart charging. Our result also shows the importance of using more accurate nonlinear battery models in V2G controllers and evaluating the cost of price uncertainties over V2G.

eess.SY↗

arXiv2023

Energy Storage State-of-Charge Market Model

This paper introduces and rationalizes a new model for bidding and clearing energy storage resources in wholesale energy markets. Charge and discharge bids in this model depend on the storage state-of-charge (SoC). In this setting, storage participants submit different bids for each SoC segment. The system operator monitors the storage SoC and updates their bids accordingly in market clearings. Combined with an optimal bidding design algorithm using dynamic programming, our paper shows that the SoC segment market model provides more accurate representations of the opportunity costs of energy storage compared to existing power-based bidding models. The new model also captures the inherent SoC-dependent operational characteristics of energy storage. We benchmark the SoC segment market model against an existing single-segment model in price-taker and price-influencer simulations. The simulation results show that compared to the existing power-based bidding model, the proposed model improves profits by 10-56% in the price-taker case study; the model also improves total system cost reduction from storage by around 5%, and helps reduce price volatilities in the price-influencer case study.

eess.SY↗

arXiv2022

Energy Storage Price Arbitrage via Opportunity Value Function Prediction

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.

eess.SY↗

arXiv2022

A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features

By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known alternating direction method of multipliers (ADMM) has turned out to be one of the most popular tools for distributed optimization due to many advantages, such as modular structure, superior convergence, easy implementation and high flexibility. In the past decade, ADMM has experienced widespread developments. The developments manifest in both handling more general problems and enabling more effective implementation. Specifically, the method has been generalized to broad classes of problems (i.e.,multi-block, coupled objective, nonconvex, etc.). Besides, it has been extensively reinforced for more effective implementation, such as improved convergence rate, easier subproblems, higher computation efficiency, flexible communication, compatible with inaccurate information, robust to communication delays, etc. These developments lead to a plentiful of ADMM variants to be celebrated by broad areas ranging from smart grids, smart buildings, wireless communications, machine learning and beyond. However, there lacks a survey to document those developments and discern the results. To achieve such a goal, this paper provides a comprehensive survey on ADMM variants. Particularly, we discern the five major classes of problems that have been mostly concerned and discuss the related ADMM variants in terms of main ideas, main assumptions, convergence behaviors and main features. In addition, we figure out several important future research directions to be addressed. This survey is expected to work as a tutorial for both developing distributed optimization in broad areas and identifying existing theoretical research gaps.

cs.DC↗

arXiv2022

Impact of Bidding and Dispatch Models over Energy Storage Utilization in Bulk Power Systems

Energy storage is a key enabler towards a low-emission electricity system, but requires appropriate dispatch models to be economically coordinated with other generation resources in bulk power systems. This paper analyzes how different dispatch models and bidding strategies would affect the utilization of storage with various durations in deregulated power systems. We use a dynamic programming model to calculate the operation opportunity value of storage from price predictions, and use the opportunity value result as a base for designing market bids. We compare two market bidding and dispatch models in single-period economic dispatch: one without state of charge (SoC) constraints and one with SoC constraints. We test the two storage dispatch models, combined with different price predictions and storage durations, using historical real-time price data from New York Independent System Operator. We compare the utilization rate with respect to results from perfect price forecast cases. Our result shows that while price prediction accuracy is critical for short duration storage with a less than four hours capacity, storage with a duration longer than twelve hours can easily achieve a utilization rate higher than 80\% even with naive day-ahead price predictions. Modeling storage bids as dependent of SoC in single-period real-time dispatch will provide around 5% of improvement in storage utilization over all duration cases and bidding strategies, and higher renewable share will likely improve storage utilization rate due to higher occurrence of negative prices.

math.OC↗