There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Rechargeable lithium-ion batteries are promising candidates for building grid-level storage systems because of their high energy and power density, low discharge rate, and decreasing cost. A vital aspect in energy storage planning and operations is to accurately model the aging cost of battery cells, especially in irregular cycling operations. This paper proposes a semi-empirical lithium-ion battery degradation model that assesses battery cell life loss from operating profiles. We formulate the model by combining fundamental theories of battery degradation and our observations in battery aging test results. The model is adaptable to different types of lithium-ion batteries, and methods for tuning the model coefficients based on manufacturer’s data are presented. A cycle-counting method is incorporated to identify stress cycles from irregular operations, allowing the degradation model to be applied to any battery energy storage (BES) applications. The usefulness of this model is demonstrated through an assessment of the degradation that a BES would incur by providing frequency control in the PJM regulation market.

Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment

The integration of renewable energy source (RES) and energy storage systems (ESS) in microgrids has provided potential benefit to end users and system operators. However, intermittent issues of RES and high cost of ESS need to be placed under scrutiny for economic operation of microgrids. This paper presents a two-layer predictive energy management system (EMS) for microgrids with hybrid ESS consisting of batteries and supercapacitors. Incorporating degradation costs of the hybrid ESS with respect to the depth of charge and lifetime, long-term costs of batteries and supercapacitors are modeled and transformed to short-term costs related to real-time operation. In order to maintain high system robustness at minimum operational cost, a hierarchical dispatch model is proposed to determine the scheduling of utilities in microgrids within a finite time horizon, in which the upper layer EMS minimizes the total operational cost and the lower layer EMS eliminates fluctuations induced by forecast errors. Simulation studies demonstrate that different types of energy storages can be utilized at two control layers for multiple decision-making objectives. Scenarios incorporating different pricing schemes, prediction horizon lengths, and forecast accuracies also verify the effectiveness of the proposed EMS structure.

A Two-Layer Energy Management System for Microgrids With Hybrid Energy Storage Considering Degradation Costs

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.

Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

Batteries are prevalent energy providers for modern systems. They can also be regarded as storage units for renewable and sustainable energy. Failures of batteries can bring huge losses in terms of personnel, facility, environment, and reputation aspects. Therefore the accurate health estimation and high availability of batteries is urgently required by corresponding users, distributors, and manufactures. Fortunately, prognostics and health management (PHM) technique has been demonstrated the capability of supporting the improvement of the availability and reliability of batteries. In this paper, we gave a review on the state-of-the-art of the PHM study on batteries. We observed the increase of publication related to battery PHM in the past decade (2009–2018), especially in the past five years. Approaches related to battery performance prognostics are categorized into physics-based, data-driven and hybrid classes. Selection of the battery PHM approach requires to take the user requirement, data availability and degradation mechanisms attainability into consideration. Based on the survey, we also proposed research and development perspectives to conduct further studies on the battery PHM, including the approach selection, health management, performance evaluation, uncertainty treatment, application economics, as well as environmental issues. We focused on PHM of lithium-ion batteries, given the fact that several publications discussed other types of batteries (e.g., lead-acid batteries).

A review on prognostics and health management (PHM) methods of lithium-ion batteries

Transmission expansion and energy storage increase the flexibility of power systems and, hence, their ability to deal with uncertainty. Transmission lines have a longer lifetime and a more predictable performance than energy storage, but they require a very large initial investment. While battery energy storage systems (BESS) can be built faster and their capacity can be increased gradually, their useful life is shorter because their energy capacity degrades with time and each charge and discharge cycle. Additional factors, such as the expected profiles of load and renewable generation significantly affect planning decisions. This paper proposes a stochastic, multistage, coplanning model of transmission expansion, and BESS that considers both the delays in transmission expansion and the degradation in storage capacity under different renewable generation and load increase scenarios. The proposed model is tested using a modified version of the IEEE-RTS. Sensitivity analyses are performed to assess how factors such as the planning method, the storage chemistry characteristics, the current transmission capacity, and the uncertainty on future renewable generation and load profiles affect the investment decisions.

Stochastic Multistage Coplanning of Transmission Expansion and Energy Storage

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 12%. 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 superlinear 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.

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

The large-scale integration of a grid-scale energy storage and the increasing penetration of renewable resources motivate the development of techniques for determining the optimal ratings and locations of storage devices. This paper proposes a method for identifying the sites where energy storage systems should be located to perform spatio-temporal energy arbitrage most effectively and the optimal size of these systems. This method takes a centralized perspective where the objective is to minimize the sum of the expected operating cost and the investment cost of energy storage. It has been tested on a realistic 240-bus 448-line model of the Western Electricity Coordinating Council (WECC) interconnection. The influence on the results of the following parameters is analyzed: Maximum number of storage locations, maximum size of storage systems, capital cost of deploying storage, value assigned to spillage of renewable energy, marginal cost of conventional generation, and renewable generation capacity. These numerical results are used to characterize the benefits that energy storage can provide in prospective large-scale power systems with renewable generation.

Bolun Xu

Papers

Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment

Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

Stochastic Multistage Coplanning of Transmission Expansion and Energy Storage

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

Optimal Energy Storage Siting and Sizing: A WECC Case Study