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.

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.

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, 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.

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.

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.