Comprehensive Investigation of the Durability of Lithium-Ion Batteries Under Frequency Regulation Conditions

The large-scale investment in renewable energy makes the modern power system shift from the system based on rotary generators to the system based on inverters. Although this is very beneficial for the collection and utilization of renewable energy, because the power generation through the inverter does not provide enough mechanical inertia, it leads to insufficient inertia in the power system [1]. Because the moment of inertia has the ability to hinder the oscillation of the system and the frequency change speed is related to the moment of inertia, when the inertia of the system is insufficient, no matter what degree of power disturbance, it will lead to significant frequency fading and finally the frequency instability problem. At present, the main method to solve this problem is to add some virtual inertia into the system and deploy it appropriately to provide enough inertial response so as to enhance the stability of the system.

When the new energy power generation system is put into the industry on a large scale, considering the volatility characteristics of photovoltaic and wind power generation, the battery energy storage system will play a crucial role in the microgrid to maintain the continuous power supply for electric vehicle charging [2]. If the electric vehicle is charged without order in the power grid, it will cause the power grid load fluctuation to increase; that is, the peak value of the power grid fluctuation curve will increase. If the electric vehicle is charged orderly in the grid, that is, the V2G method, it will make the grid load “cut peak and fill valley”. This method is widely used to adjust the frequency stability of the power grid, that is, through the power grid to regulate the charging and discharging power of electric vehicles, to provide auxiliary services for the power grid such as peak regulation, frequency regulation, and promotion of new energy consumption.

Although the power battery is beneficial to the stability of the power grid in the process of frequency modulation, its own life will also be affected to a certain extent. In the large-scale application of V2G technology, the study of battery durability is the core scientific issue of system design and economic evaluation. Because the V2G bidirectional charge and discharge mode can significantly change the operating boundary conditions of the battery, the asymmetric cycle condition caused by it will cause the electrochemical system to be subjected to multi-dimensional stress coupling. The reciprocating insertion/withdrawal of lithium ions between positive and negative electrodes will aggravate the lattice distortion of electrode materials and the dynamic reconstruction of the solid electrolyte interface (SEI) film. Meanwhile, frequent shallow charging and discharge cycles may lead to continuous loss of active lithium in the local state of charge (SOC) region, accelerating capacity decay. The random power fluctuation introduced by the grid dispatching demand will deteriorate the thermodynamic state of the battery, resulting in the accumulation of mechanical stress induced by temperature gradient. These multi-physics coupling degradation mechanisms will not only shorten the battery service life but also directly affect the energy handling capacity of the V2G system and the reliability of grid auxiliary services. Therefore, to establish a battery durability prediction model based on a cyclic attenuation mechanism, it is necessary to focus on quantifying the nonlinear relationship between capacity fade rate and internal resistance rise under dynamic working conditions. By constructing a state of health (SOH) prediction framework considering the synergistic effect of calendar aging and cycle aging, the life optimization design of the V2G charging and discharging strategy is realized. These will provide theoretical support for V2G’s participation in the power market for battery residual value assessment, energy storage capacity allocation optimization, and life-cycle carbon footprint calculation, and ultimately achieve the dual goals of sustainable utilization of battery assets and improvement of grid elasticity in V2G technology. At present, determining the aging and degradation mechanism of the battery is the most important and most challenging goal, and the interaction of multiple factors in the use environment or use mode makes the battery produce different aging effects; that is, the capacity loss and the increase in internal resistance do not depend on the same variables, so these processes are not single but complex. This makes understanding battery aging a difficult task [3]. Over the years, many studies have attempted to explore the effects of battery aging more deeply.

Li Y. et al. [4] took electric vehicles as reactive power compensation devices to participate in voltage regulation of the power grid. The research results show that with the increase in the number of electric vehicles connected to the grid, electric vehicles can assist or even replace traditional reactive power compensation devices and obtain better voltage control performance. In order to alleviate the huge impact of disorderly charging of large-scale electric vehicles on the distribution network. Considering that the reduction in battery life will directly affect the economic benefits and sustainability of the V2G system, the battery capacity protection research usually quantifies the battery aging generated during the V2G process by different means and introduces the objective function. There are also some studies that limit battery aging to an acceptable range by adding constraints. Li S. et al. [5] pointed out that traditional methods for quantifying battery aging, such as electrochemical models and artificial intelligence algorithms, can only quantify battery degradation on a large time scale. Ebrahimi M. et al. [6] considered both cycle aging and calendar aging of batteries in the V2G process, but they believed that calendar aging only had a linear relationship with time.

Because lithium-ion batteries contain a variety of different chemical materials, the internal structure is very complex, and these materials will produce a variety of complex side reactions during the battery charging and discharging process, resulting in diversified aging mechanisms. Different aging modes will affect each other, and the same aging mechanism may lead to multiple aging modes. Battery temperature, SOC, charge/discharge ratio, depth of discharge, and cycle times are the main factors affecting battery aging [7]. Therefore, in order to study the durability of batteries, it is necessary to establish a perfect battery aging model. There are many kinds of battery aging models, and the accuracy, calculation amount, and application range of different models are different. At present, electrochemical models, empirical models, and semi-empirical models are commonly used in mainstream research. In the 1990s, Newman’s group tried to estimate battery performance based on the Butler–Volmer equation and the theory of porous electrodes. Darling and Newman [8] for the first time tried to simulate the aging process in an electrochemical model and realized a simple solvent oxidation reaction, obtained good results, and gave a good conclusion on the selection of solvents. Dalverny et al. [9] determined the morphology of the LiCoO₂ electrode by ab initio calculation. In addition, the phase transition process of lithium iron phosphate (LFP) active particles was also theoretically studied. Ab initio calculations can explain battery aging by estimating the energy associated with solvent decomposition or dissolution of lithium components. Tasaki et al. [10] have linked the dissolution of lithium salts near the negative solid electrolyte interface (SEI) to calendar aging. As for empirical models, the aging model based on Arrhenius is the most widely used. Based on the empirical formula of the relationship between chemical reaction rate constant and temperature, the model can model cyclic aging and calendar aging, respectively, when various stress factors are comprehensively considered [7]. In recent years, with the development of artificial intelligence technology, the battery aging model based on a neural network can accurately reflect the relationship between various factors and capacity decay without establishing complicated mathematical expressions and updating network parameters through training [11]. The semi-empirical aging model not only has the simplicity and ease of use of the empirical model but also makes full use of the basic knowledge of the physical and chemical characteristics of the battery, which is very suitable for offline analysis. The Arrhenius formula is used to correct the growth of the SEI film and electrolyte loss during the initial use of the battery in the electrochemical model, which improved the accuracy of the model under different environments [12]. Based on the hypothesis that SEI film growth leads to battery degradation, Ecker M. et al. [13] combined the electrothermal model with empirical mathematical expressions to establish a semi-empirical aging model that can analyze battery degradation under different electrothermal environments. The lithium evolution behavior of lithium-ion batteries is one of the key factors leading to battery life decay, and the lithium evolution situation of batteries is mainly reflected by the negative electrode position of the battery, so this study will mainly focus on the analysis of the negative electrode potential distribution of lithium-ion batteries under the frequency modulation condition.

Through the above findings, the existing models, mostly based on laboratory-accelerated aging data, fail to effectively reflect the irregular charge–discharge characteristics brought by the grid demand response in the actual V2G working conditions. Secondly, the current economic analysis generally adopts a linear attenuation model, ignoring key nonlinear factors such as temperature change, charge and discharge rate, SOC, discharge depth heterogeneity, and calendar aging coupling effect. Third, most studies focus on battery degradation but do not establish a dynamic optimization model between battery degradation and power grid frequency fluctuations.

The goal of this study is to minimize the attenuation of lithium-ion batteries and maximize the benefits of the grid while controlling the frequency stability of the grid. Firstly, the typical frequency regulation conditions are obtained in the American PJM market. Secondly, a P2D model related to lithium-ion batteries was built by studying the power performance and durability mechanism of lithium-ion batteries, and the above conditions were input into the model to investigate the distribution of the model’s negative potential under different SOC, temperature, and reported power, and the results were analyzed to find out the influence of different factors on the battery. The research route is shown in Figure 1. In the future, the frequency regulation model will be built according to the relevant knowledge of the power system, and the P2D model will be built according to the above results, and the two will be coupled. The coupling model is optimized to minimize the negative impact on the negative battery potential. At the same time, it is also necessary to consider that electric vehicles participate in the frequency regulation of the grid, and the grid gains the most benefits.

Based on the theory of porous electrodes, the battery P2D model describes the mass transfer, dynamics, thermodynamics, and other processes inside the battery through a set of partial differential equations. On the basis of the basic composition, the P2D model has the following three core assumptions: the electrode material is composed of spherical particles; the double-layer effect is not considered; and the positive and negative collector conductivities are very high, so the collector does not change significantly in the y- and z-axes; in other words, the electrochemical reaction dynamics only work in the x-axis. These three core assumptions simplify the battery model building process at three levels. The regular porous structure of spherical particles avoids the complex structure and particle distribution of active substances in practice, which is the most basic physical simplification method. Secondly, avoiding the double-layer effect can greatly simplify the distribution of ions on the electrolyte and electrode surface. Limiting the electrochemical dynamics to the x-axis further facilitates the mathematical processing. The internal structure of the battery is roughly shown in Figure 2. To study a battery from a mechanism point of view, it is necessary to investigate its internal material distribution and potential distribution, corresponding to the material transfer and charge transfer within the battery, respectively. Therefore, in order to quantitatively describe the P2D model, it is necessary to establish the solid–liquid phase potential distribution, solid–liquid-phase diffusion process, electrochemical reaction model of interfacial reaction, and charge conservation as constraints. The following process is shown.

Solid-phase potential distribution: According to the conductivity of the electrode material, the relationship between current and potential gradient can be expressed (Equation (1)) as follows: where ${\sigma }_s^{eff}$ is a solid-phase effective conductivity; ${\phi }_s$ is the potential for solid phase; and $i_s$ is the current density. The minus sign in the formula is because the x direction takes the negative extreme as the origin during modeling, and the field strength and current direction are opposite; that is, the current inside the battery flows from the negative electrode to the positive electrode, while the field strength points from the positive electrode to the negative electrode. The boundary conditions for this equation are expressed as Equations (2) and (3).

Liquid-phase potential distribution: According to the liquid-phase conductivity and particle-specific surface area, the relationship between the potential gradient and lithium-ion concentration, reaction rate, temperature, and current can be expressed through Equation (4). where ${\sigma }_e^{eff}$ is the liquid effective conductivity; ${\phi }_e$ is the potential for the liquid phase; $j_n$ is the solid–liquid junction chemical reaction rate per unit area; $a$ is the particle-specific surface area; $F$ is the Faraday constant; $t_{+}^0$ is the lithium-ion transference number; $R$ is the state of the ideal gas constant; $T$ is the battery temperature; and $c_e$ is the liquid lithium-ion concentration. Integrating x on both sides of this equation yields the following equation (Equation (6)), where the boundary condition is shown.

Solid-phase ion diffusion: According to the solid-phase diffusion coefficient, the distribution of lithium-ion concentration over time in the polar diameter direction can be obtained via the following equation: where $c_s$ is the solid lithium-ion concentration; $D_s$ is the solid-phase diffusion coefficient; $t$ is time; and $r$ is the pole size. This equation is a polar form of Fick’s second law and represents the diffusion process of matter driven only by concentration. In the P2D model, the lithium ions of the porous electrode are removed or generated from the surface of active particles, so the lithium ions inside active particles will appear as a concentration gradient and will only be driven by it; therefore, the diffusion process of lithium ions in the solid particles can be described by this model. The boundary conditions are shown as Equations (8) and (9). where $R_s$ is the grain boundary radius, and $j_n$ is the molar flow rate for ions.

Liquid-phase ion diffusion: Based on the diffusion coefficient and porosity of the liquid phase, and combined with the reaction process, the distribution of lithium-ion concentration in the liquid phase with time can be obtained via the following expression: where $c_e$ is the liquid lithium-ion concentration; $D_e^{eff}$ is the liquid-phase diffusion coefficient; ${\epsilon }_e$ is the electrode porosity; $t$ is time; $t_{+}^0$ is the lithium-ion transference number; $j_n$ is the solid–liquid junction chemical reaction rate per unit area; and $a$ is the particle-specific surface area. This is a revision of Fick’s second law, where lithium ions migrate from the negative active particles into the electrolyte diffusion, and eventually become embedded in the positive active particles. There is a lithium-ion concentration gradient in the battery internal electrolyte; this concentration gradient is driven by lithium-ion diffusion, and, at the same time, by the internal electric field and migration. The boundary conditions are shown in Equation (11).

Solid-charge conservation: As a constraint to the P2D model, it describes that the number of disembedded or generated lithium ions during the reaction is equal to the number of charge transfer, as shown in Equation (12). where $j_n$ is the solid–liquid junction chemical reaction rate per unit area; $a$ is the particle-specific surface area; $F$ is the Faraday constant; ${\sigma }_s^{eff}$ is the solid-phase effective conductivity; ${\phi }_s$ is the potential for solid phase; and $i_s$ is the current density. Boundary conditions are expressed via Equation (13).

Solid–liquid interface reaction: According to the Bulter–Volmer equation of the electrochemical reaction of lithium ions during deintercalation and formation at the solid–liquid interface, changes in the current of the electrode and changes in the electrode potential can be described through Equation (14). where $j_n$ is the current density; $i_0$ is the exchange-current density; ${\alpha }_{an}$ and ${\alpha }_{ca}$ are migration coefficients of anions and cations, respectively; ${\eta }_{act}$ is the electrode potential; $R$ is the state of the ideal gas constant; and $T$ is the battery temperature.

After the mathematical foundation of the P2D model is completed, parameter identification of the research object is needed to further calibrate the parameters required by the P2D model. Finally, a model was built in the COMSOL Multiphysics^® ver5.6 simulation software. The model is shown in Figure 3. To achieve subsequent measurements, 20 probes were selected at an interval of 1 × 10⁻⁵ m and numbered 120 from left to right.

In this paper, a large number of research studies on power grid frequency regulation, virtual inertia, and battery durability are investigated. The virtual inertia system and battery life estimation models are introduced, and the advantages and disadvantages of each model are given. Based on the above-mentioned problems, the effects of temperature, SOC, half-pulse period, and reported power on battery capacity loss were investigated experimentally. The range analysis method is used to compare the difference in the influence of four factors on capacity loss; the internal influence of each factor is compared. In addition, in order to simplify the number of experimental groups, the orthogonal test method was also introduced.

Since the lithium evolution phenomenon of the battery will lead to the capacity loss of the battery, and the criterion that directly leads to the lithium evolution phenomenon states that the negative potential is less than zero, this study explored the influence of temperature, SOC, reported power, and frequency regulation conditions on the negative potential distribution of the battery and the degree of lithium evolution from the perspective of simulation. The P2D model was built according to the dynamic and durability mechanisms of lithium-ion batteries. The orthogonal test was also used to simplify the number of simulation groups; the negative electrode potential distribution diagram under each group of simulations and the qualitative results were obtained. Then, the battery thickness and simulation time are integrated with the negative electrode potential, and the integral value obtained is analyzed to obtain certain quantitative results.