arXiv subjects

Bolun Xu

Publications and source records attributed to Bolun Xu.

54 records · Page 3Linked to original sources

arXiv2022

Arbitraging Variable Efficiency Energy Storage using Analytical Stochastic Dynamic Programming

This paper presents a computation-efficient stochastic dynamic programming algorithm for solving energy storage price arbitrage considering variable charge and discharge efficiencies. We formulate the price arbitrage problem using stochastic dynamic programming and model real-time prices as a Markov process. Then we propose an analytical solution algorithm using a piecewise linear approximation of the value-to-go function. Our solution algorithm achieves extreme computation performance and solves the proposed arbitrage problem for one operating day in less than one second on a personal computer. We demonstrate our approach using historical price data from four price zones in New York Independent System Operator, with case studies comparing the performance of different stochastic models and storage settings. Our results show that the proposed method captures 50% to 90% of arbitrage profit compared to perfect price forecasts. In particular, our method captures more than 80% of arbitrage profit in three out of the four price zones when considering batteries with more than two-hour duration and realistic degradation cost.

math.OC↗

arXiv2021

Dynamic Valuation of Battery Lifetime

This paper proposes a dynamic valuation framework to determine the opportunity value of battery capacity degradation in grid applications based on the internal degradation mechanism and utilization scenarios. The proposed framework follows a dynamic programming approach and includes a piecewise linear value function approximation solution that solves the optimization problem over a long planning horizon. The paper provides two case studies on price arbitrage and frequency regulation using real market and system data to demonstrate the broad applicability of the proposed framework. Results show that the battery lifetime value is critically dependent on both the external market environment and its internal state of health. On the grid service side, results show that second-life batteries can provide more than 50% of the value compared to new batteries, and frequency regulation provides two times more revenue than price arbitrage throughout the battery lifetime.

math.OC↗

arXiv2021

End-to-End Demand Response Model Identification and Baseline Estimation with Deep Learning

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.

eess.SY↗

arXiv2021

A Data-driven Nonlinear Recharge Controller for Energy Storage in Frequency Regulation

Battery energy storage boosts up the response speed of power system frequency regulation, but must be recharged carefully to minimize the distortion to the frequency regulation response. This paper proposes a nonlinear feedback controller to optimize the recharge for storage resources in frequency regulation. This controller is designed using a data-driven best-hindsight optimization framework, the resulting nonlinear recharge controller's gain depends on the storage state of charge as well as its power and energy rating. The developed controller is compared with two benchmark automatic generation control designs, one is a proportional-integral-based control from PJM Interconnection, the other one is based on linear-quadratic regulator. Simulation results using real area control error data from PJM Interconnection show the proposed controller achieves smaller deviations in both the area control error and the storage state of charge compared to the two benchmark controllers under various storage configurations.

eess.SY↗

arXiv2020

Bounding Regression Errors in Data-driven Power Grid Steady-state Models

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.

cs.LG↗

arXiv2020

Techno-economic model of a second-life energy storage system for utility-scale solar power considering li-ion calendar and cycle aging

While the use of energy storage combined with grid-scale photovoltaic power plants continues to grow, given current lithium-ion battery prices, there remains uncertainty about the profitability of these solar-plus-storage projects. At the same time, the rapid proliferation of electric vehicles is creating a fleet of millions of lithium-ion batteries that will be deemed unsuitable for the transportation industry once they reach 80 percent of their original capacity. The repurposing and deployment of these batteries as stationary energy storage provides an opportunity to reduce the cost of solar-plus-storage systems, if the economics can be proven. We present a techno-economic model of a solar-plus-second-life energy storage project in California, including a data-based model of lithium nickel manganese cobalt oxide battery degradation, to predict its capacity fade over time, and compare it to a project that uses a new lithium-ion battery. By setting certain control policy limits, to minimize cycle aging, we show that a system with SOC limits in a 65 to 15 percent range, extends the project life to over 16 years, assuming a battery reaches its end-of-life at 60 percent of its original capacity. Under these conditions, a second-life project is more economically favorable than a project that uses a new battery and 85 to 20 percent SOC limits, for second-life battery costs that are less than 80 percent of the new battery. The same system reaches break-even and profitability for second-life battery costs that are less than 60 percent of the new battery. Our model shows that using current benchmarked data for the capital and O&M costs of solar-plus-storage systems, and a semi-empirical data-based degradation model, it is possible for EV manufacturers to sell second-life batteries for less than 60 percent of their original price to developers of profitable solar-plus-storage projects.

physics.soc-ph↗

arXiv2019

A Lagrangian Policy for Optimal Energy Storage Control

This paper presents a millisecond-level look-ahead control algorithm for energy storage with constant space complexity and worst-case linear run-time complexity. The algorithm connects the optimal control with the Lagrangian multiplier associated with the state-of-charge constraint. It is compared to solving look-ahead control using a state-of-the-art convex optimization solver. Simulation results show that both methods obtain the same control result, while the proposed algorithm runs up to 100,000 times faster and solves most problems within one millisecond. The theoretical results from developing this algorithm also provide key insights into designing optimal energy storage control schemes at the centralized system level as well as under distributed settings.

math.OC↗

arXiv2018

Optimal Battery Control Under Cycle Aging Mechanisms in Pay for Performance Settings

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.

math.OC↗

arXiv2018

Optimal Battery Participation in Frequency Regulation Markets

Battery participants in performance-based frequency regulation markets must consider the cost of battery aging in their operating strategies to maximize market profits. In this paper we solve this problem by proposing an optimal control policy and an optimal bidding policy based on realistic market settings and an accurate battery aging model. The proposed control policy has a threshold structure and achieves near-optimal performance with respect to an offline controller that has complete future information. The proposed bidding policy considers the optimal control policy to maximize market profits while satisfying the market performance requirement through a chance-constraint. It factors the value of performance and supports a trade-off between higher profits and a lower risk of violating performance requirements. We demonstrate the optimality of both policies using simulations. A case study based on the PJM regulation market shows that our approach is effective at maximizing operating profits.

math.OC↗

arXiv2017

Using Battery Storage for Peak Shaving and Frequency Regulation: Joint Optimization for Superlinear Gains

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.

eess.SY↗

arXiv2017

Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial part of this operating cost, the cost of battery degradation must be factored in these bids. However, existing models of battery degradation either do not fit market clearing software or do not reflect the actual battery aging mechanism. In this paper we model battery cycle aging using a piecewise linear cost function, an approach that provides a close approximation of the cycle aging mechanism of electrochemical batteries and can be incorporated easily into existing market dispatch programs. By defining the marginal aging cost of each battery cycle, we can assess the actual operating profitability of batteries. A case study demonstrates the effectiveness of the proposed model in maximizing the operating profit of a battery energy storage system taking part in the ISO New England energy and reserve markets.

math.OC↗

arXiv2017

A Convex Cycle-based Degradation Model for Battery Energy Storage Planning and Operation

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.

math.OC↗

arXiv2017

Scalable Planning for Energy Storage in Energy and Reserve Markets

Energy storage can facilitate the integration of renewable energy resources by providing arbitrage and ancillary services. Jointly optimizing energy and ancillary services in a centralized electricity market reduces the system's operating cost and enhances the profitability of energy storage systems. However, achieving these objectives requires that storage be located and sized properly. We use a bi-level formulation to optimize the location and size of energy storage systems which perform energy arbitrage and provide regulation services. Our model also ensures the profitability of investments in energy storage by enforcing a rate of return constraint. Computational tractability is achieved through the implementation of a primal decomposition and a subgradient-based cutting-plane method. We test the proposed approach on a 240-bus model of the Western Electricity Coordinating Council (WECC) system and analyze the effects of different storage technologies, rate of return requirements, and regulation market policies on ES participation on the optimal storage investment decisions. We also demonstrate that the proposed approach outperforms exact methods in terms of solution quality and computational performance.

math.OC↗

arXiv2017

Optimal Regulation Response of Batteries Under Cycle Aging Mechanisms

When providing frequency regulation in a pay-for-performance market, batteries need to carefully balance the trade-off between following regulation signals and their degradation costs in real-time. Existing battery control strategies either do not consider mismatch penalties in pay-for-performance markets, or cannot accurately account for battery cycle aging mechanism during operation. This paper derives an online control policy that minimizes a battery owner's operating cost for providing frequency regulation in a pay-for-performance market. The proposed policy considers an accurate electrochemical battery cycle aging model, and is applicable to most types of battery cells. It has a threshold structure, and achieves near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize this gap and show it is independent of the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

math.OC↗

arXiv2017

Impact of Local Transmission Congestion on Energy Storage Arbitrage Opportunities

Reduced installation and operating costs give energy storage systems an opportunity to participate actively and profitably in electricity markets. In addition to providing ancillary services, energy storage systems can also arbitrage temporal price differences. Congestion in the transmission network often accentuates these price differences and will under certain circumstances enhance the profitability of arbitrage. On the other hand, congestion may also limit the ability of a given storage device to take advantage of arbitrage opportunities. This paper analyzes how transmission congestion affects the profitability of arbitrage by storage devices in markets with perfect and imperfect competition. Imperfect competition is modeled using a bilevel optimization where the offers and bids submitted by the storage devices can alter the market outcome. Price-taker and price-maker assumptions are also investigated through market price duration curves. This analysis is based on simulating an entire year of market operation on the IEEE Reliability Test system.

math.OC↗

arXiv2016

Impact of Dynamic Line Rating on Dispatch Decisions and Integration of Variable RES Energy

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.

math.OC↗

arXiv2016

Leveraging energy storage to optimize data center electricity cost in emerging power markets

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.

cs.DC↗

arXiv2016

A Comparison of Policies on the Participation of Storage in U.S. Frequency Regulation Markets

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.

math.OC↗