In the 1970s, M. Stanley Whittingham proposed an initial concept of lithium-ion batteries that use Li_xTiS₂ as cathode and lithium metal as anode materials, where intercalation effects were demonstrated with a small lattice expansion [1]. In 1979-1980, John B. Goodenough discovered that the transition metal Li_xCoO₂ at the cathode produces a potential as high as 4~5 V at room temperature [1]. In these systems, however, uncontrolled lithium dendrites were formed at the surface of lithium-metal anodes over charge-discharge cycles. The dendrite growth could trigger short circuits and a fire hazard by penetrating the separator and reaching the cathode [1]. In 1985, Akira Yoshino used graphite as anode material, minimizing the lithium dendrite growth that had previously caused safety concerns [1]. These ground-breaking advances have secured the 2019 Nobel Prize in Chemistry to the three aforementioned developers. After being commercialized by Sony in 1991, lithium-ion batteries have been widely used in many practical applications ranging from mobile phones and laptops to medical devices and electric vehicles [1].

Today, lithium-ion batteries are considered the best means to store energy to keep the balance between electricity generation and demand (see figure 1). Among different renewable energy applications, significant energy and cost savings can be achieved by optimal battery participation strategies enabling greater depth of discharge, smaller size, and longer life for renewable grid size from kilowatts (microgrid) to megawatts (power grid).

This article discusses the important role of modeling and control of lithium-ion batteries deployed in grid-storage applications as a means to develop robust, efficient, and long-lasting and widely spread integrated renewable energy resources into the power system to increase resilience in the context of grid modernization.

Background
Despite progress made in materials and manufacturing processes that contributed to significantly reducing the cost of batteries over the years, lithium-ion batteries still account for a significant portion of the entire grid component costs [2]. Ad-hoc application-driven sizing and chemistry-based optimization hold the potential to significantly improve cost, performance, and usability. This can be achieved through the development of adequate models for design and real-time operational optimization.

It’s common practice in battery modeling for renewable grid applications to use oversimplified models (e.g., either in the form of empirical/equivalent circuit-based or coulomb counting/cycle-based models), which do not contain any physical insight about the electrochemistry nor the aging degradation mechanisms the battery undergoes [2]. These simplistic models are calibrated upon laboratory-based experimental data (e.g., 1C-constant charging and discharging) and used to predict battery behavior under grid-specific operational conditions. Moreover, it’s sometimes the case that models used to predict grid-level battery dynamics are borrowed from automotive battery models, which on the other hand, are tuned specifically for electric vehicle batteries.

The lack of any available validation/verification of available grid-storage models poses questions on the predictability/accuracy of such models which could be either too conservative with a concern of underutilization of the battery system or over predicting with consequent over utilization prediction of the storage system, leading to system abuse and premature end of life estimate.

The current grid-level storage modeling practice motivates our research. Physics-based models can maximize the usability and performance of the individual electrochemical components. Two key benefits of adopting physics-based models are to: i) accurately predict utilization, and therefore performance, of battery systems, and ii) maximize the battery life by implanting proper aging mechanisms developing in grid-application usage patterns– such as frequency regulation and peak shaving.

Research trends
Simplistic battery models for renewable grid applications have been adopted since only the early 2000s (see figure 2), whereas research publications on the use of physics-based battery models for renewable grid-storage systems emerged only starting from 2016.

In physics-based battery models, single particle models (SPMs) and pseudo two-dimensional (P2D) models are the most popular system-level mathematical tools to interpret battery electrochemical dynamics. The SPM considers transport phenomena and intercalation effects within a particle but ignores the concentration gradients in electrolytes. Also, the SPM does not account for the potential effects of solution phases in microscopic and macroscopic scales. This simplification enables straightforward implementation and quick simulations of battery dynamics [3]. As a result, in 2016, Patsios et al. integrated SPMs with detailed power electronic models for the first time [4]. In 2018, Reniers et al. compared the performance between SPMs and empirical models, using duty cycles obtained from peak shaving data [5]. In the following year, Bonkile et al. proposed control strategies for SPMs in PV-battery microgrid systems when batteries exceed 4.2V or below 2.7 V [6]. However, the approximation of SPMs limits the validity of such models to low C-rates, highly conductive electrolytes, and thin electrodes [3]. For this reason, the operation of batteries remains conservative when adopting SPMs, and therefore, more advanced system-level battery models are required.

The P2D model has been widely used for battery cell design. The P2D model is based on the concentrated solution theory, consisting of porous electrodes, separators, and current collectors. The P2D model is known to be suitable to predict battery systems over restricted and well-defined operational conditions [7]. In 2017, researchers at the University of Washington implemented a bottom-up approach to efficiently integrate and simulate P2D models for PV-battery microgrid applications [2]. The authors converted all relevant equations into a differential-algebraic equation (DAE) system and simultaneously solved the DAE framework to simulate and control all the grid components in real-time. However, even though the proposed approach is a good start showing how the incorporation of P2D battery model can lead to more realistic renewable grid systems simulations, the limitation is that other grid component models and electrical circuit structures were oversimplified.

Research tasks
The adoption of physics-based battery models for grid-storage design and optimization tasks is motivated by the following research questions:

• What is the impact of characteristic battery duty cycles – e.g. frequency regulation versus peak shaving – on battery performance and lifetime?
o What are the battery degradation trajectories under different usage patterns?
• Among today’s available lithium-ion chemistries, what is the more grid-prone for enhanced performance, durability, and safety?
• If physics-based models can identify grid-prone chemistries, can those models reversely provide guidelines on the optimal materials and design for each grid application?

The above questions are system-level grid storage challenges that can be tackled by adopting suitable electrochemical models. Calibration of such models over different chemistry and characteristic duty cycles would allow the creation of ad-hoc modeling tools to use in capacity-expansion planning models, for instance, to evaluate performance and durability of the integrated power system. Developing grid-batteries electrochemical-aging models will also enhance health-conscious real-time energy management strategies with the intent to prolong battery life when used within the power grid.

We believe that these questions are worth addressing to accelerate the penetration of renewable energy sources and optimize the design of storage systems with the main goal of minimizing overall costs and improving short and long-term performance.

A duty cycle is a charge/discharge profile representing the demands associated with a specific grid application. Physics-based battery models properly calibrated over grid-specific duty cycles are missing in today’s literature. This is imperative to understand and predict the performance and durability of large grid-level battery packs. Moreover, different chemistries of lithium-ion batteries, which produce different performance, are available today. For example, among the most prominent cathode materials, we find lithium-nickel-manganese-cobalt (NMC), lithium-iron- phosphate (LFP), and lithium-nickel-cobalt-aluminum (NCA). LFP is safer but provides low specific energy with longer life span; NMC keeps a good balance between specific energy, power, and life span; and NCA provides higher power and energy but can cause safety issues. Identifying suitable chemistries using (grid-derived) duty cycles will ultimately have a positive societal impact. Lastly, capacity/power fade is a critical consideration in renewable grid markets; however, today’s battery models do not account for physics-based degradation prediction. As a result, the current cycling-based prediction does not provide an accurate estimate for partial charging and discharging cycles in renewable grid applications. In contrast, electrochemical aging models can provide a means to account for degradation mechanisms. In lithium-ion battery systems, solid electrolyte interface (SEI) layer growth is assumed to be the primary cause of capacity fade in graphite-anode batteries, and adequate SEI layer effects can be identified and added to the physics-based model framework [8]. Understanding the grid-specific duty cycles (e.g., peak shaving and frequency regulation) and properly defining operating conditions these batteries undergo will help streamline main aging mechanisms.

Towards cost-effective and longer-lasting renewable grid systems
More efficient and robust physics-based models can contribute to the full utilization of battery systems in renewable grid-storage applications. The traditionally accepted P2D model is based on the assumption that electrodes can be idealized as spherical-shaped particles. Moreover, simplifications are made to derive the effective coefficients for ionic diffusion and conductivity based on not-validated empirical laws [1]. These assumptions can make the model ineffective–with lack of predictability leading to underutilization (or overutilization) of the battery system–and inaccuracy at the condition of operations in which renewable grid-level batteries would experience, e.g., low state of charge (SoC), medium-high temperature, and medium-high C-rate and aging.

Homogenization methods to upscale pore-scale battery dynamics were successfully used in [9] to design a full homogenized macroscale (FHM) model for Li-ion batteries [10]. The FHM model can be regarded as a good candidate to overcome the limitations of current P2D models, describing lithium-ion batteries in a one-dimensional setting. The FHM model is formulated under the assumption that the electrodes are composed of spatial unit cells, causing micro-scale continuity in the cell system. In addition, the FHM model’s effective ionic properties are determined by resolving the closure problem in the unit cell of the electrode microstructure. Compared to the DFN model, the FHM model provides more accurate predictions over the low state of charge and medium-high temperature, as well as high C-rate. These are conditions the battery system will be most likely to work on due to the dynamic duty cycles from renewable grid applications. In [10], the implemented 1-D FHM modeling framework exhibits a decreased root mean square (RMS) error up to 75% when compared to the error generated from the P2D model under medium-high temperature conditions.

We envision that the creation of such physics-based aging models could accelerate the spread of advanced and modernized power system platforms. For example, with the advent of new technologies (e.g. 5G networks), cloud services can connect current independent energy applications, such as power, transportation, and communication systems [11]. Cloud computing-based services collect a variety of data related to energy management and recommend optimal power strategies [11] and can be used as the platform where such models can be executed to maximize and improve energy efficiency, sustainability, and reliability of electrical services.

Advances on electrochemical battery modeling hold the potential to optimize battery system design and enhance its utilization for cost and resource reduction. This will set a new framework to evaluate future integrated renewable energy and storage systems models, which, at the same time, can evolve to capture and explore emerging trends in grid storage technologies and systems.

References
[1] O. Ramström, “Scientific Background on the Nobel Prize in Chemistry 2019: Lithium-ion Batteries”. The Royal Swedish Academy of Science (2019)
[2] S. B. Lee, C. Pathak, V. Ramadesigan, W. Gao, & V. R. Subramanian, “Direct, Efficient, and Real-time Simulation of Physics-based Battery Models for Stand-alone PV-Battery Microgrids”, Journal of The Electrochemical Society 164, E3026-E3034 (2017)
[3] S. Santhanagopalan, Q. Guo, & R. E. White, “Parameter Estimation and Model Discrimination for a Lithium-ion Cell”, Journal of the Electrochemical Society 154, A198-A206 (2007)
[4] C. Patsios, B. Wu, E. Chatzinikolaou, D. J. Rogers, N. Wade, N. P.Brandon, & P. Taylor, “An Integrated Approach for the Analysis and Control of Grid Connected Energy Storage Systems, 5, 48-6 (2016)
[5] J. M.Renier, G. Mulder, S. Ober-Blöbauma, & D. A. Howey, “Improving Optimal Control of Grid-connected Lithium-ion Batteries through More Accurate Battery and Degradation Modelling”, 379, 91-102 (2018)
[6] M. P. Bonkile & V. Ramadesigan, “Power Management Control Strategy using Physics-based Battery Models in Standalone PV-battery Hybrid Systems”, Journal of Energy Storage 23, 258-268 (2019)
[7] M. Doyle, T. F. Fuller, & J. Newman, “Modeling of Galvanostatic Charge and Discharge of the Lithium/polymer/insertion Cell”, Journal of the Electrochemical society 140, 1526-1533 (1993)
[8] P. Ramadass, B. Haran, P. M. Gomadam, R. E. White, & B. N. Popov, “Development of First Principles Capacity Fade Model for Li-ion cells”, Journal of the Electrochemical Society 151, A196-A203 (2004)
[9] H. Arunachalam, S. Onori, & I. Battiato, “On Veracity of Macroscopic Lithium-Ion Battery Models”, J. Electrochem. Soc., 162 (10), A1940-A1951 (2015)
[10] H. Arunachalam, & S. Onori, “Full Homogenized Macroscale Model and Pseudo-2-Dimensional Model for Lithium-Ion Battery Dynamics: Comparative Analysis, Experimental Verification and Sensitivity Analysis”, Journal of The Electrochemical Society 166, A1380-A1392 (2019)
[11] D. S. Markovic, D. Zivkovic, I. Branovic, R. Popovic, and D. Cvetkovic, “Smart Power Grid and Cloud Computing”, Renewable and Sustainable Energy Reviews 24, 566-577 (2013)