**A Method for the Combined Estimation of Battery State of Charge and State of Health Based on Artificial Neural Networks**

#### **Angelo Bonfitto**

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy; angelo.bonfitto@polito.it; Tel.: +39-011-090-6239

Received: 25 March 2020; Accepted: 17 May 2020; Published: 18 May 2020

**Abstract:** This paper proposes a method for the combined estimation of the state of charge (SOC) and state of health (SOH) of batteries in hybrid and full electric vehicles. The technique is based on a set of five artificial neural networks that are used to tackle a regression and a classification task. In the method, the estimation of the SOC relies on the identification of the ageing of the battery and the estimation of the SOH depends on the behavior of the SOC in a recursive closed-loop. The networks are designed by means of training datasets collected during the experimental characterizations conducted in a laboratory environment. The lithium battery pack adopted during the study is designed to supply and store energy in a mild hybrid electric vehicle. The validation of the estimation method is performed by using real driving profiles acquired on-board of a vehicle. The obtained accuracy of the combined SOC and SOH estimator is around 97%, in line with the industrial requirements in the automotive sector. The promising results in terms of accuracy encourage to deepen the experimental validation with a deployment on a vehicle battery management system.

**Keywords:** battery; state of charge; state of health; artificial intelligence; artificial neural networks; hybrid vehicles; electric vehicles; estimation

#### **1. Introduction**

The automotive industry is recently dedicating increasing attention to sustainability, with the objective of mitigating the negative effects of vehicular mobility on the environment. Carmakers cope with the always more stringent regulations about CO2 emissions, focusing their efforts on the development of advanced powertrain architectures [1,2]. Solutions based on the adoption of full electric (battery electric vehicles (BEVs)) powertrains or on the combination of an internal combustion engine (ICE) and electric traction (hybrid/plug-in hybrid electric vehicles (HEVs/PHEVs)) are now established as reliable alternatives to conventional powertrains [3,4]. They exploit batteries as the primary energy source in BEVs or as an auxiliary source in HEVs and PHEVs [5]. In the automotive industry, the most common battery technology exploits lithium because of its remarkable advantages in terms of the energy density, fast charging, low maintenance, and long lifetime allowances. Moreover, lithium-based solutions allow for obtaining powerful, compact, and light configurations together with satisfactory levels of autonomy, which is currently settled in the order of a few hundreds of kilometers [6]. However, the reliability and performance of these type of batteries are strongly influenced by the management of the charging and discharging phases. It is indeed well known that an appropriate handling of these operations is mandatory to avoid the occurrence of overcharging or deep discharging, that would lead to permanent or hardly reversible damages of the pack. A continuous and accurate monitoring of the battery state takes on significant importance to extend the battery lifetime, effectively plan the trip route and charging stops, optimize the energy flow management of HEVs [7,8], and mitigate psychological effects, such as the range anxiety that is commonly experienced by a large

number of BEV drivers [6]. The main parameters to be assessed for a correct battery monitoring are the residual available energy in the pack, known as state of charge (SOC), and the degradation suffered by the battery, indicated by the state of health (SOH) [9]. As is well known, these two states cannot be directly measured, since the technology to make a sensor that plays the equivalent role of a fuel gauge is not available. Therefore, the adoption of some estimation techniques becomes mandatory [10,11]. Typically, carmakers exploit look-up tables (LUTs), where the SOC and SOH behavior is mapped during the preliminary experimental characterizations conducted in a laboratory environment. These tests are done following the so-called direct methods, which are based on ampere-hour counting or the measurement of the internal impedance and open circuit voltage of the battery [10,12]. However, the adoption of LUTs may have a high computational cost and imposes the storage of a huge amount of data in the electronic control unit memory, particularly in the case of the SOH estimation. A further class of methods exploits model-based techniques for the real-time assessment of both the SOC and SOH [13]. The most common are the Kalman filter [14] and its derivations, namely the extended (EKF) [15] and unscented Kalman filters (UKF) [16,17], the adaptive particle filter (APF) [18], and the smooth variable structure filter (SVSF) [19]. Although these solutions can be implemented in real time on a vehicle, they may suffer problems of inaccuracies if the reference model is not completely and accurately tuned in all the possible operating conditions. An alternative and promising approach to overcome this limitation is represented by artificial intelligence (AI). In most cases, these solutions adopt artificial neural networks (ANNs) and allow getting rid of the model while obtaining satisfactory levels of accuracy and reliability, provided that the networks are properly trained. An extensive literature is dedicated to the methods for the estimation of the SOC [20–23] or SOH [24–27] with AI. Nevertheless, to the best of the author's knowledge, very few works deal with the combined estimation of the SOC and SOH and most of them describe model-based techniques [28–30].

This paper proposes a technique for the combined estimation of the SOC and SOH with a set of five ANNs: four regression networks dedicated to the SOC estimation and one classification network for the SOH identification. The method is independent by the battery model and is designed with a training phase conducted with datasets obtained from the preliminary laboratory experimental characterizations. The SOC estimation exploits four nonlinear autoregressive neural networks with exogenous input. Each of them is associated with a specific class of ageing (SOH) of the battery. The correct estimation among the four outputs is selected according to the SOH identification, which is obtained separately by a classifier that is done with a pattern recognition neural network. The SOH estimator provides a class of ageing among four possibilities, ranging from 80% to 100% with a step of 5%. A further class is associated to exhausted batteries and covers the range from 0% to 80% of the SOH, where 80% is the degradation threshold in the automotive sector. The output of the SOH classifier is used to select the correct SOC estimation among the four outputs of the regression ANNs, while the SOC estimation is used as an input for the SOH classifier in a closed-loop recursive architecture. The SOH estimator is an algorithm which is triggered only when a specific battery load condition in terms of the mean charging/discharging capacity request in a predefined time window is detected. This procedure allows reducing the training dataset of the SOH neural classifier to only one specific case. This aspect represents a relevant advantage in terms of a size reduction of the training dataset and a consequent time saving during the dataset collection and learning procedures. Additionally, the size of the network is smaller with a consequent reduction of the memory occupation when deployed on the battery management system (BMS).

The paper describes the design of the two estimators and the validation phase is conducted with the adoption of driving cycles acquired on a mild hybrid electric vehicle. The performance of the SOC estimator is evaluated by comparing the temporal evolution of the expected and estimated state of charge, whereas the SOH classifier accuracy is measured by using a confusion matrix, a common evaluation tool of classification algorithms.

The novel contributions of this work are as follows: a) the proposal of a combined estimation of the SOC and SOH with ANNs, allowing to make the method independent from the model and valid for every operating condition, provided that the network training dataset is complete and accurate; and b) the proposal of an SOH estimation method that is triggered only when a specific load condition corresponding to a predefined charging/discharging current profile is detected: this results in a compact algorithm that can be trained with a dataset that is smaller with respect to what would be needed in the case of a reproduction of the whole set of ageing conditions.

#### **2. Method**

The proposed method aims to provide a combined estimation of both the SOC and SOH of a battery. The approach is equally valid for a battery pack, module, or for the single cell.

Figure 1 illustrates the overall layout of the method that is composed of two subsystems: the SOC estimator, consisting of four regression ANNs, that is illustrated in the top left dashed box, and the SOH estimator, that exploits a neural classifier, that is reported in the bottom right dotted box. As is well known, the behavior of the two parameters is connected: the SOC of a battery is strongly influenced by the ageing, as well as the SOH estimation needing the information of the SOC variation during the charging/discharging operations. This motivates the adoption of a recursive loop architecture, where the SOC output is provided as an input to the SOH classifier and vice-versa. Both algorithms were trained on the basis of the preliminary experimental characterizations conducted in a laboratory. The two subsystems are described in detail in the following sections.

**Figure 1.** Overall method architecture. Dashed box: state of charge (SOC) estimation. Dotted box: state of health (SOH) estimation. *i*(*t*): charging/discharging current. *v*(*t*): voltage at battery terminals. *T*(*t*): battery temperature. *E*(*t*): energy request. SOH classes: 1: (100 ÷ 95)%; 2: (95 ÷ 90)%; 3: (90 ÷ 85)%; 4: (85 ÷ 80)%.

The battery pack considered for the study is composed of 168 cells (the cell model is Kokam SLPB 11543140H5, its characteristics are reported in Table 1) in the configuration 12p14s (p: parallel, s: series). The pack has a nominal voltage of 48 V, a nominal capacity of 60 Ah, and is designed for a mild hybrid electric vehicle with a peak electric power of around 20 kW, obtained considering a discharge rate of around 7C in nominal conditions.


**Table 1.** Main characteristics of the battery cell.

#### *2.1. SOC Estimation*

The SOC estimator consists of four parallel regression ANNs (dashed box in Figure 1) working on the same inputs. Each network is associated with a specific ageing condition: SOH class 1 (from 100% to 95%), SOH class 2 (from 95% to 90%), SOH class 3 (from 90% to 85%), and SOH class 4 (from 85% to 80%). The threshold of 80% was decided considering that in the automotive sector, a battery has to be considered exhausted when the capacity or power fading is higher than 20%. The step of 5% is aligned with the typical precision that can be reached when dealing with the SOH estimation problem [31,32].

Each of the four regression ANNs receive, simultaneously, the following signals as inputs: charging/discharging current (*i*(*t*) [*A*]), voltage at battery terminals (*v*(*t*) [*V*]), and temperature (*T*(*t*) [C]). They provide four different outputs: *SOC*ˆ <sup>1</sup>(*t*), *SOC*ˆ <sup>2</sup>(*t*), *SOC*ˆ <sup>3</sup>(*t*), and *SOC*ˆ <sup>4</sup>(*t*). The final SOC estimation (*SOC*ˆ (*t*)) is obtained with a downstream selector that is operated by a signal fed back from the SOH classifier output, that is running separately, as indicated in Figure 1.

The structure of the four SOC estimators is the nonlinear autoregressive neural network with exogenous input (NARX) architecture. Typically, this layout is adopted for prediction tasks and finds an application in industrial engineering fields as well as in other sectors, namely linguistic search engines or weather forecasting. However, its effectiveness has been demonstrated also for estimation tasks and has been presented as an effective solution to estimate the SOC of lithium batteries in [21], where an additional comparison with other ANN architectures in terms of the computational cost and estimation accuracy is provided. The scheme of the NARX is reported in Figure 2, where the two adopted configurations are illustrated: an open-loop configuration (a), often indicated also as the series–parallel (SP) mode, that is adopted during the training procedure, and a closed-loop configuration (b), or equivalently the parallel (P) mode, that is the final architecture adopted for the estimation when the network is deployed on the vehicle for the real-time execution.

The output of the regression is defined as

$$y(n) = \varphi\left[y(n-1), y(n-2), \dots, y(n-d\_y); \mathbf{x}(n-1), \mathbf{x}(n-2), \dots, \mathbf{x}(n-d\_x)\right] \tag{1}$$

where *<sup>y</sup>*(*n*) <sup>∈</sup> <sup>R</sup> and *<sup>x</sup>*(*n*) <sup>∈</sup> <sup>R</sup> denote the output (state of charge) and inputs (current, voltage, and temperature) of the NARX model at the discrete timestep *n*, respectively, *dx* and *dy* are the input and output memory delays used in the model, respectively, and ϕ is the function, generally non-linear, represented by the ANN. During the regression computation, the next value of the dependent output

signal *y*(*n*) is regressed on the previous *dy* values of the output signal and previous *dx* values of the independent (exogenous) input signal. In the open-loop configuration, the output regressor is

$$y(n) = q \left[ \overline{y}(n-1), \overline{y}(n-2), \dots, \overline{y}(n-d\_y); \mathbf{x}(n-1), \mathbf{x}(n-2), \dots, \mathbf{x}(n-d\_x) \right] \tag{2}$$

A supervised training procedure is conducted using the measured output as the target. This approach allows for enriching the information to be processed by the network and permits using a common static backpropagation algorithm, the Levenberg–Marquardt in this case, for the training process, since the resulting network has a purely feedforward architecture.

**Figure 2.** Nonlinear autoregressive neural network with exogenous input (NARX) architecture. (**a**) Series–parallel (SP) mode (open-loop configuration) adopted during the training. (**b**) Parallel (P) mode (closed-loop configuration) adopted for the estimation when the network is deployed. HAF: hidden activation function. OAF: output activation function. *w*: weight. *b*: bias.

In the first second of computation, the value of the algorithm output is not stable and is unpredictable. Therefore, if this value is fed back and provided as input to the ANN, it generates an estimation divergence over time. To avoid the occurrence of this irremediable condition, during the first second of estimation the feedback of the estimated SOC is replaced by the last estimation value (*SOCINIT* in Figure 2b) recorded on a non-volatile memory at the previous shut down of the vehicle. After 1 second, when the output has become stable, the SOC input of the network switches from the previously recorded value to the real feedback of the estimation so that the regular operation of the algorithm can start.

Referring to Figure 2b and indicating with *n* = *n*<sup>0</sup> the time instant when the feedback signal switches from *SOCINIT* to the estimated output, the characteristic equations of the model are written as

$$\varphi(n) = \varphi\left[\text{SOC}\_{\text{INT}}; \mathbf{x}(n-1, \mathbf{x}(n-2), \dots, \mathbf{x}(n-d\_{\mathbf{x}})) \right], n < n\_0 \tag{3}$$

and

$$y(n) = \varphi\left[y(n-1), y(n-2), \dots, y(n-d\_y); \mathbf{x}(n-1), \mathbf{x}(n-2), \dots, \mathbf{x}(n-d\_x)\right], n \ge n\_0 \tag{4}$$

The four networks have the same size in terms of layers, neurons, and delays and adopts the same activation functions. All these parameters have been designed with a trial and error approach aimed to maximize the estimation accuracy and avoid the risk of overfitting. Specifically, each network has one layer with eight neurons, the delays *dx* and *dy* are equal to two, the activation function in the hidden layer (*HAF*) and output layer (*OAF*) are the hyperbolic tangent and linear functions respectively, and the training function is the Levenberg–Marquardt function.

During the design phase, the training precision is evaluated by computing the mean square error (MSE) that reached a value of 1 <sup>×</sup> 10−<sup>13</sup> as indicated in the small box embedded in Figure 3, and the estimation accuracy is measured with the maximum relative error (MRE), that is computed as

$$\text{MRE}\left[\%\right] = \max\_{1 \le i \le n} \left( \left| \frac{\text{SOC}\_{\text{exp}}(\text{i}) - \text{SOC}\_{\text{est}}(\text{i})}{\text{SOC}\_{\text{exp}, \text{max}} = 1} \right| \right) \times 100 \tag{5}$$

**Figure 3.** Comparison performance between the estimation (dashed line) and expected values (solid line) of the SOC in the case of an SOH = 100%. The obtained maximum relative error (MRE) is equal to 0.35%. The small box in the bottom left indicates the trend of the mean square error during the training phase.

This parameter reached the value of 0.35% as indicated in Figure 3, where the comparison between the estimation (dashed line) and the expected value (solid line) of the state of charge is reported in the case of a new battery (SOH = 100%). This plot wants to represent an indication of the training evaluation during the design phase.

The time length of the training dataset for the four regression ANNs is 13 h.

A more detailed description of the overall method results is reported in the final section of the paper.

#### *2.2. SOH Estimation*

The degradation of the battery is estimated with an algorithm reproducing a pattern recognition classifier with an ANN. Since the algorithm is proposed for the automotive sector, the method considers 20% as the maximum admitted capacity fading. Therefore, the considered life cycle of the battery ranges from an SOH of 100% when the battery is new to an SOH of 80% when the battery has to be considered exhausted. The proposed solution aims at quantifying the degradation suffered by the battery by identifying the five different levels of ageing which correspond to the five classes provided as an output by the classification algorithm. The first class covers the interval of ageing below the level of 80% (assumed as the threshold of the maximum degradation of the battery) of the SOH. The other four classes are equally distributed between 80% and 100% with four intervals of 5%, a percentage that is considered as consistent with the reasonable level of accuracy that can be reached when dealing with the problem of the SOH estimation.

As in the case of the SOC network design, the proposed algorithm for the SOH estimation exploits a preliminary experimental characterization phase conducted on the battery in a laboratory environment. The obtained results are used to build the training dataset to be adopted for the learning phase of the neural classifier. Specifically, the data of interest are recorded in a specific battery load condition corresponding to a mean request of 12 Ah in an interval of time of 120 s. This condition was selected because it can be detected quite frequently during a common driving cycle of an electric or hybrid vehicle. Afterwards, the network is trained with the dataset corresponding to this specific operating condition obtained at different values of temperature. Therefore, when the algorithm is deployed on the vehicle, it is called to estimate the level of ageing whenever the same condition is detected during the real driving cycle. This implies that when driving the vehicle, consecutive buffers of 120 s are analyzed back-to-back by a control logic that is implemented in the "Triggering load detection" block in Figure 1. As soon as the specific load condition of interest (mean capacity request of 12 Ah in 120 s) is detected, the classifier is triggered and provides the SOH classification as an output. Therefore, the estimation rate is not continuous over time, but it is produced in a discrete and not time deterministic way, only in correspondence with the detection of the predefined known load condition. The output of the estimator is kept equal to the last SOH estimation if the triggering condition is not occurring.

Figure 4 reports a part of the ANN training dataset obtained by the preliminary experimental characterization conducted on the battery. Subplot "a)" illustrates the behaviour of the degradation of the battery as a function of the number of discharging cycles at different values of temperature [33]. The discharging is conducted with the predefined load above-mentioned. Subplot "b)" reports the coupling effects between the SOH, capacity, SOC, and battery voltage. In this test, the temperature is set to 25 ◦C and the variation of the capacity is motivated by the difference in the time needed to discharge the battery at the different levels of ageing.

The time length of the training dataset covering all the considered levels of ageing is equal to 916 h obtained from 27,494 buffers with a duration of 120 s.

The SOH classifier works on discrete inputs, the so-called predictors, that are extracted in the "Feature extraction" block in Figure 1 from the time histories of the following signals: current, voltage, temperature, SOC, and energy. The latter is obtained from the "Energy computation" block in Figure 1 and is defined as

$$E = \int\_{t\_0}^{t\_0 + t\_b} v(t)i(t)dt\tag{6}$$

where *t*<sup>0</sup> is the initial time of the buffer and *tb* is the time length of the processed buffer that is set equal to 120 s.

The list of the extracted predictors is state of charge variation (-) (Δ*SOC*), voltage variation (V) (Δ*V*), requested energy (Wh) (*E*), and mean temperature (◦C) (*T*).

The architecture of the classifier is illustrated in Figure 5. The training phase of the neural classifier is performed exploiting the scaled conjugate gradient (SCG) backpropagation training function [27]. This algorithm is designed to minimize the cost function including the difference between the estimated and expected outputs. This approach gives a good performance over a large number of pattern recognition problems that may include numerous parameters and guarantees a low performance degradation while reducing the training error. Additionally, this function is characterized by a relatively low computational cost and memory requirements [21], and its ability to provide well-separated classes in data mining and classification problems has been proven in many research works [34].

**Figure 4.** Battery experimental characterization for the SOH estimation. (**a**) SOH as a function of the number of discharging cycles and of the temperature. (**b**) Behavior of the SOH as a function of the voltage, capacity, and SOC. The temperature in this case is set equal to 25 ◦C.

**Figure 5.** Pattern recognition a feed-forward artificial neural network (ANN) architecture for the SOH classification. HAF: hidden activation function. OAF: output activation function. *w*: weight. *b*: bias.

The classifier is composed of one input, two hidden and one output layer. As in the case of the SOC network design, the number and size of the hidden layers is defined heuristically, by means of a trial and error procedure. Specifically, the hidden layers consist of ten neurons each, HAF is a hyperbolic tangent sigmoid, and OAF is a normalized exponential function. The performance of the training process is evaluated by means of the cross-entropy cost function, that at the end of the training process is equal to 1 <sup>×</sup> <sup>10</sup><sup>−</sup>3, after around 3000 training epochs.

#### **3. Results and Discussion**

The validation of the method is conducted in two separate phases: (a) an analysis of the performance of the SOH identifier and (b) an evaluation of the accuracy of the overall SOC estimation that includes the ageing classification.

#### *3.1. SOH Classification*

As is described above, the classification algorithm is called to identify the class of degradation only when a specific load condition is detected during the driving operations. To evaluate the effectiveness of the method, a profile corresponding to the specific charging/discharging profile was created artificially to have an exhaustive number of occurrences in the different operating conditions to test.

The profile is reported in Figure 6, where it has a duration of 5000 s and includes 42 different consecutive buffers with the time length of 120 s and a mean capacity request of 12 Ah. The profile was cycled until reaching a total duration of 50 h, to sweep the range of the SOC of the battery, corresponding to 1500 buffers of 120 s, for each class of ageing. The resulting timeseries was provided to the LUT representing the battery. This LUT was tuned after the preliminary laboratory experimental characterization and allows for extracting the predictors provided to the classifier in the five ageing conditions.

**Figure 6.** Current profile created to validate the SOH classifier. The profile is replicated until reaching the total duration of 50 h and a number of buffers of 1500 for each class of ageing.

The resulting validation dataset is therefore composed of 7500 different buffers with a time length of 120 s each. The resulting profile represents the different operating conditions at different degradation levels and is given as an input to the classifier.

The tool adopted to evaluate the accuracy of the SOH estimation is the confusion matrix reported in Figure 7. The classified and actual ageing condition instances are reported in the rows and columns, respectively. The values contained in the main diagonal cells indicate the correct classifications, whereas the off-diagonal cells report the number of the misclassifications. The overall obtained estimation accuracy is equal to 2.4%, which is equal to the number of misclassifications (178 buffers) over the total number of tested occurrences (7500 buffers). This result is aligned with the expected accuracy.


**Figure 7.** Evaluation of the SOH classification performance. Confusion matrix obtained for the ANN trained with the scaled conjugate gradient (SCG) algorithm. The cell in the grey background indicates the overall accuracy of the method.

#### *3.2. SOC Estimation*

The second part of the validation is dedicated to the evaluation of the accuracy of the SOC estimation. To this end, the profiles illustrated in Figure 8 have been adopted as validation timeseries. The subplot "a)" reports the current profile, and the subplot "b)" illustrates the behavior of the battery terminal voltage at different levels of ageing. The voltage is only an occurrence of the many possibilities that are associated to a class of degradation. The plots in the right part of the figure are zoomed-in areas with a time length of 2000 s. When providing these timeseries to the SOC estimation block (dashed box in Figure 1), the regression ANNs will provide four different outputs. The one corresponding to the correct ageing level of the battery is then selected according to the output of the SOH classifier (dotted box in Figure 1).

**Figure 8.** ANN validation datasets recorded from a real mild hybrid vehicle. (**a**) Current *i*(*t*). (**b**) Voltage *v*(*t*) at four different degradation levels corresponding to the four SOH classes.

The results obtained in the five ageing levels are illustrated in Figure 9, where for each SOH class, the estimated SOC, on the blue line, is compared with the expected value, on the red line. The expected value is the one obtained from the preliminary experimental characterization conducted in the laboratory. The estimation error is reported in the lower subplot for each case. The accuracy of the estimation is demonstrated by the error that is limited to a maximum value of 3%. The results obtained for the class of ageing going from 0% to 80% (subplot "e") demonstrate that the algorithm keeps being valid also under the threshold of 80%. The reported test has been conducted at a temperature of around 25 ◦C. A more exhaustive validation of the method should be conducted in a climatic test chamber to evaluate the accuracy of the estimation at different environmental conditions.

**Figure 9.** SOC estimation at different degradation levels. Red line: expected value. Blue line: estimation. Error indicates the difference between the estimated and expected values. (**a**): ageing class 1 (SOH: 95 ÷ 100%); (**b**): ageing class 2 (SOH: 90 ÷ 95%); (**c**): ageing class 3 (SOH: 85 ÷ 90%); (**d**): ageing class 4 (SOH: 80 ÷ 85%); (**e**): ageing class 5 (SOH: 0 ÷ 80%).

#### **4. Conclusions**

This paper presented a method for the combined estimation of the state of charge and state of health of batteries with artificial intelligence. The technique is valid at the cell, module, and pack levels and is suitable for adoption in the automotive sector in the case of hybrid and full electric vehicles. The design procedure of the algorithm and specifically the training phase of the artificial neural networks were presented. The method was demonstrated to be effective in terms of the estimation accuracy when tested on real driving cycles extracted from the acquisition on-board of an electric vehicle. The estimation error of the combined method is around 3%. The good potential and the promising results encourage the adoption of the proposed method for deployment in a vehicle battery management system for a real-time battery monitoring.

**Funding:** This research received no external funding.

**Acknowledgments:** This work was developed in the framework of the activities of the Interdepartmental Center for Automotive Research and Sustainable Mobility (CARS) of Politecnico di Torino (www.cars.polito.it).

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery**

#### **Davide Clerici †, Francesco Mocera \*,† and Aurelio Somà †**

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso duca degli Abruzzi 24, 10129 Torino, Italy; davide.clerici@polito.it (D.C.); aurelio.soma@polito.it (A.S.)

**\*** Correspondence: francesco.mocera@polito.it

† These authors contributed equally to this work.

Received: 17 January 2020; Accepted: 31 March 2020; Published: 4 April 2020

**Abstract:** Electric cycling is one of the major damage sources in lithium-ion batteries and extensive work has been produced to understand and to slow down this phenomenon. The damage is related to the insertion and extraction of lithium ions in the active material. These processes cause mechanical stresses which in turn generate crack propagation, material loss and pulverization of the active material. In this work, the principles of diffusion induced stress theory are applied to predict concentration and stress field in the active material particles. Coupled and uncoupled models are derived, depending on whether the effect of hydrostatic stress on concentration is considered or neglected. The analytical solution of the coupled model is proposed in this work, in addition to the analytical solution of the uncoupled model already described in the literature. The analytical solution is a faster and simpler way to deal with the problem which otherwise should be solved in a numerical way with finite difference method or a finite element model. The results of the coupled and uncoupled models for three different state of charge levels are compared assuming the physical parameters of anode and cathode active material. Finally, the effects of tensile and compressive stress are analysed.

**Keywords:** diffusion induced stress; hydrostatic stress influence on diffusion; electrode particle model; battery mechanical aging; li-ion battery

#### **1. Introduction**

Lithium-ion batteries are actually one of the most widespread rechargeable energy-storage systems [1]. They have a large field of application from small electronic systems up to electric vehicles in automotive and industrial applications [2,3]. Indeed, they can span a great capacity and power range with a good energy density and long lifetime.

Safety and batteries performance have been analysed through modelling and experimental tests in the last decades [4,5]. Progressive damage with charge/discharge cycles is the major weak point of lithium ion cells, since it affects the lifetime considerably [6]. The lithium ions are stored/withdrawn in the active material of the electrodes through insertion/extraction processes. These processes must be studied at a micrometre scale, at which active material of both electrodes appears as a particulate matter, as depicted in Figure 1a. Insertion/extraction processes induce expansion/contraction of the active material particles, and in turn mechanical stress which damage the electrode structure. The electrode damage causes indirectly the increase of solid electrolyte interface (SEI) growth which in turn affects the battery performance and the available capacity [7]. Stress and strain due to insertion/extraction processes are recently investigated via in-situ measurements in battery electrodes [8–10]. However, the lack of experimental stress measurements in active material particles does not allow to validate the results derived in this work.

**Figure 1.** Battery scheme at micrometer scale and focus on the lithium intercalation mechanism in anode particles (**a**). Stress and deformation of the active material particles during lithium insertion (**b**) and extraction (**c**). Blue shadows depict the lithium concentration (blue means high concentration, white means low concentration). Concentration level affects tension (arrows pointing toward each other) and compression (arrows pointing away from each other) of radial and hoop stress. The concentric lines show expansion or shrinking of the particle: they are evenly spaced in the undeformed configuration.

These type of stresses are described originally by Prussin [11] as chemical stress or diffusion induced stress (DIS), which manages the interaction between chemical and mechanical problem. Later, Larché and Cahn [12,13] and Chu and Lee [14,15] studied the interaction between thermodynamic of diffusion and stress.

Several continuum models of diffusion induced stress were proposed in the last decade, each of them highlights some particular features. The models mainly divide in two groups: the coupled models consider the influence of the hydrostatic stress on the lithium ions diffusion, namely "pressure diffusion effect," and the uncoupled models neglect this effect.

Cheng and Verbrugge presented an uncoupled model for stress evolution in spherical particle in Reference [16] and they studied the effect of surface mechanics in nanometre particles, showing that tensile stress may be significantly reduced in magnitude or even be reverted to a state of compression with small particle radius [17].

Christensen and Newman were among the first to study DIS models applied to lithium ions cell [18–20] deriving a stand-alone electrode particle model. Meanwhile, Zhang et al. performed a numerical implementation of coupled DIS problem, and studied the influence of the aspect ratio of an ellipsoidal particle of lithium manganese oxide (LMO) on stress [21]. Later they studied the stresses which arise both from concentration gradient and heat generation in cathode particles, assumed as ellipsoidal with varying aspect ratio [22]. The basis of DIS theory applied to lithium-ion cells are clearly explained in Reference [23–25] for different geometry domain. Recently Bagheri et al. presented the numerical results of coupled DIS problem for galvanostatic and potentiostatic insertion in spherical

LMO particle [26]. Eshghinejad et al. presented a continuum model which couples diffusion and mechanics of ions intercalation for non-dilute solutions [27], according to Haftbaradaran et al. [28], and solved it with a finite elements (FE) model. Eshghinejad et al. highlighted that compressive stress results in lower lithium ions solubility and thus lower achievable capacity. Recently Wu et al. extended the study of diffusion induced stress to the interaction with other particles. Indeed, they developed a three-dimensional particle network model in a FE platform and a multiscale model which considers the stress in the particle as the superposition of the concentration gradient induced stress and the stress which comes from the interaction with other particles [29].

Tensile hoop stress due to insertion/extraction processes is the driving force for the analytical crack propagation model described by Deshpande et al. [30]. The authors described the capacity reduction rate due to electrolyte decomposition on the new free surfaces created by the cracks. Other works performed numerical analysis to predict crack propagation in active material with a stochastic approach [31] and considering the effect of current rate [32]. Grantab et al. developed a numerical method for studying lithiation-induced crack propagation in silicon nanowires that accounts for the effects of pressure-diffusion on the stress, and compared the results with an uncoupled model [33].

A continuum model of diffusion-mechanical problem in spherical geometry is presented in this paper. The model described in Section 2 gives a tool to estimate the stresses and strains in active material particles during lithiation/delithiation on the basis of particle size and mechanical properties with specific assumptions. Furthermore the model takes into account the hydrostatic stress influence on lithium diffusion, namely the "pressure diffusion effect", which couples mechanical and diffusive problem. The hydrostatic stress effect is highlighted comparing the results of the coupled and uncoupled model, which considers or neglects the stress influence, respectively. The definition of an equivalent diffusion coefficient which accounts for the hydrostatic stress effect allows to derive an analytical solution even for the coupled model, still not available in literature, as far as the authors know. The results of the analytical model are compared with numerical results in literature in Section 3. Furthermore, lithium concentration and stress are derived in galvanostatic insertion and extraction with different state of charge (SOC) for anode and cathode insertion material in Section 3. It is highlighted that tensile stresses are the driving force for crack propagation, and thus solid electrolyte interface (SEI) growth and capacity fade. On the other hand, compressive stresses induce a reduction of lithium flux which in turn affects the achievable capacity.

#### **2. Problem Formulation**

The mechanical stresses which arise in the active material particles are directly linked to lithium intercalation/de-intercalation phenomena which occur over charge/discharge cycling. For this reason, this model works just for intercalation materials, and not for conversion material, such as Silicon, since lithium ions would interact with host material differently. The particle is assumed spherical, isotropic and linear elastic, and the current density is assumed uniform all over the particle surface. These assumptions make the problem axisymmetric, leading to a one-dimensional problem in the radial coordinate. A couple of boundary conditions are given: traction-free condition is applied on the outer surface of the particle, thus neglecting the interaction with surroundings, and a fixed central point is imposed to prevent rigid body motion.

The lithium ions diffuse gradually in the particle during insertion and extraction. The ions diffusion makes the lithium concentration inhomogeneous along the particle radius, as shown in Figure 1b,c.

The concentration gradient causes a mechanical stress state in analogy to temperature gradient. Therefore, the areas with greater concentration gradient are affected by larger deformation compared to the areas where the gradient is lower. Therefore, a diffusion-elastic problem must be studied, since the stress state described by the elastic problem depends on the concentration level which is described by the diffusive problem.

The concentration level in insertion and extraction affects the sign of the stresses. Referring to insertion in Figure 1b, the greater concentration of the outer layers causes a tensile radial stress all over the particle because the surface expands more than the core. The hoop stress is compressive in the outer layers and tensile in the core because the greater deformation of the surface is prevented by the core. In extraction (Figure 1c) the particle shrinks, and the radial stress is compressive because the concentration level decreases along the radius. The hoop stress is tensile in the surface and compressive in the core because the greater expansion of the core is prevented by outer layers which are characterized by a lower concentration level.

#### *2.1. Mechanical Problem*

Strains are characterized by an elastic and a chemical contribution, which is expressed according to Prussin [11] in Equation (1).

$$
\varepsilon\_{\rm ch} = \frac{\Omega}{3} \mathcal{C}(r),
\tag{1}
$$

where Ω is the partial molar volume, which describes the volume variation of the solution host material and intercalated lithium. *C* is the lithium concentration field within the particle. The total strain is expressed as the sum of elastic strain and chemical strain [11], so the constitutive equations are expressed in spherical coordinates in Equations (2) and (3).

$$
\varepsilon\_{\tau} = \frac{1}{E} \left( \sigma\_{\tau} - 2\nu \sigma\_{c} \right) + \frac{\Omega C}{3} \,\prime \tag{2}
$$

$$
\varepsilon\_{\varepsilon} = \frac{1}{E} \left[ (1 - \nu) \sigma\_{\varepsilon} - \nu \sigma\_{r} \right] + \frac{\Omega \mathcal{C}}{3} \,\prime \tag{3}
$$

where *E* and *ν* are the Young modulus and Poisson ratio. The last term in Equations (2) and (3) couples the mechanical and chemical aspects. It is worth noting that this expression is written in analogy to an elastic-thermal problem, so the diffusivity part of the equation is totally equivalent to a thermal problem if the concentration field is replaced by the temperature and the partial molar volume is replaced by thermal expansion coefficient.

It is useful to rearrange the constitutive equations in terms of stresses for later purposes:

$$\sigma\_{\tau} = \frac{E\left[ \left( \varepsilon\_{\tau} - \frac{\Omega \zeta}{3} \right) (1 - \nu) + 2\nu \left( \varepsilon\_{\varepsilon} - \frac{\Omega \zeta}{3} \right) \right]}{(1 + \nu)(1 - 2\nu)},\tag{4}$$

$$\sigma\_{\varepsilon} = \frac{E\left[\left(\varepsilon\_{\varepsilon} - \frac{\Omega \mathbb{C}}{3}\right) + \nu \left(\varepsilon\_{r} - \frac{\Omega \mathbb{C}}{3}\right)\right]}{(1+\nu)(1-2\nu)}.\tag{5}$$

The congruency equations, which relate strain and displacement are:

$$
\varepsilon\_r = \frac{du}{dr} \tag{6}
$$

$$
\varepsilon\_c = \frac{u}{r}.\tag{7}
$$

The characteristic time of solid elastic deformation is much smaller than the diffusion of atoms in solids, for this reason the mechanical equilibrium is reached much faster than the diffusive one, and the elastic problem is treated as a quasi-static problem: the transient is not considered, and the equilibrium is assumed to be reached instantaneously.

The mechanical equilibrium equation over a spherical domain is given by Equation (8) according to References [16,17,26,34].

$$\frac{d\sigma\_r}{dr} + \frac{2}{r} \left(\sigma\_r - \sigma\_\varepsilon\right) = 0.\tag{8}$$

The mechanical stress state within a spherical particle is completely described by the set of Equations (4)–(8). The elastic problem is solved for the displacement replacing the congruency equations (Equations (6) and (7)) in the constitutive ones (Equations (4) and (5)), and the latter in the equilibrium equation (Equation (8)).

This leads to a second order differential equation (Equation (9)) depending on displacement and concentration field.

$$\frac{d^2u}{dr^2} + \frac{2}{r}\frac{du}{dr} - \frac{2u}{r^2} = \frac{1+\nu}{1-\nu}\frac{\Omega}{3}\frac{d\mathbb{C}}{dr}.\tag{9}$$

Equation (9) is solved for the displacement integrating it twice. A first integration leads to:

$$\frac{du}{dr} + \frac{2u}{r} + \int\_0^r \frac{2u}{r^2} \, dr - \int\_0^r \frac{2u}{r^2} \, dr = \frac{1+\nu}{1-\nu} \frac{\Omega}{3} \mathcal{C}(r) + \mathcal{C}\_1. \tag{10}$$

The displacement field is got in Equation (11) multiplying Equation (10) for *r*2, integrating another time and rearranging the terms.

$$
\mu(r) = \frac{1+\nu}{1-\nu} \frac{\Omega}{3} \frac{1}{r^2} \int\_0^r \mathbb{C}(r) r^2 dr + \frac{\mathbb{C}\_1}{3} r + \frac{\mathbb{C}\_2}{r^2}.\tag{11}
$$

The constants *C*<sup>1</sup> and *C*<sup>2</sup> are obtained imposing the boundary condition for *r* = 0 and *r* = *R*. The first boundary condition is null displacement at the center of the sphere which leads to *C*<sup>2</sup> = 0. This result is obtained solving lim*r*→<sup>0</sup> *u*(*r*), since Equation (11) is not defined for *r* = 0.

The second boundary condition is derived from the behaviour on the surface. When free expansion is considered, the radial stress must vanish on the surface. This condition is got solving Equation (12) according to the constitutive equation (Equation (4)).

$$\nu \left( \frac{du}{dr} \Big|\_{r=R} - \frac{1}{3} \Omega \mathcal{C}(R) \right) (1 - \nu) + 2\nu \left( \frac{u(R)}{R} - \frac{1}{3} \Omega \mathcal{C}(R) \right) = 0. \tag{12}$$

The displacement and its derivative valued for *r* = *R* are replaced in Equation (12). Then Equation (12) is solved for *C*1, leading to:

$$\mathcal{C}\_1 = 2 \frac{1 - 2\nu}{1 - \nu} \frac{\Omega}{R^3} \int\_0^R \mathcal{C}(r) r^2 dr. \tag{13}$$

At this stage all the boundary conditions are set, and the displacement field is expressed in Equation (14).

$$u(r) = \frac{\Omega}{3(1-\nu)} \left[ (1+\nu)\frac{1}{r^2} \int\_0^r \mathbb{C}(r)r^2 \, dr + 2(1-2\nu)\frac{r}{R^3} \int\_0^R \mathbb{C}(r)r^2 \, dr \right]. \tag{14}$$

Therefore Equation (14) is replaced in the congruency equations (Equations (6) and (7)) and radial and hoop strains are obtained in Equation (15).

$$\begin{cases} \varepsilon\_{r}(r) = \frac{1+\nu}{1-\nu} \frac{\Omega}{\mathbb{S}} \left[ -\frac{2}{r^{3}} \int\_{0}^{r} \mathbb{C}(r) r^{2} \, dr + \mathbb{C}(r) \right] + \frac{2\Omega}{3} \frac{1-2\nu}{1-\nu} \frac{1}{R^{3}} \int\_{0}^{R} \mathbb{C}(r) r^{2} \, dr\\ \varepsilon\_{\varepsilon}(r) = \frac{1+\nu}{1-\nu} \frac{\Omega}{\mathbb{S}} \frac{1}{r^{3}} \int\_{0}^{r} \mathbb{C}(r) r^{2} \, dr + \frac{2}{3} \Omega \frac{1-2\nu}{1-\nu} \frac{1}{R^{3}} \int\_{0}^{R} \mathbb{C}(r) r^{2} \, dr \end{cases} . \tag{15}$$

*Energies* **2020**, *13*, 1717

Then, the stresses are derived replacing the strain equations (Equation (15)) in the constitutive ones (Equations (4) and (5)).

$$\begin{cases} \sigma\_r(r) = \frac{2\Omega}{3} \frac{E}{1-\nu} \left[ \frac{1}{R^3} \int\_0^R \mathbb{C}(r) r^2 \, dr - \frac{1}{r^3} \int\_0^r \mathbb{C}(r) r^2 \, dr \right] \\\\ \sigma\_\mathbf{c}(r) = \frac{\Omega}{3} \frac{E}{1-\nu} \left[ \frac{2}{R^3} \int\_0^R \mathbb{C}(r) r^2 \, dr + \frac{1}{r^3} \int\_0^r \mathbb{C}(r) r^2 \, dr - \mathbb{C}(r) \right]. \end{cases} \tag{16}$$

Finally, the hydrostatic stress, defined according to Equation (17), is obtained. The value of hydrostatic stress is the coupling factor between elastic and diffusion in the diffusive problem.

$$\sigma\_h(r) = \frac{\sigma\_1 + \sigma\_2 + \sigma\_3}{3} = \frac{\sigma\_r + 2\sigma\_c}{3} = \frac{2\Omega E}{9(1 - \nu)} \left[ \frac{3}{R^3} \int\_0^R \mathbb{C}(r) r^2 \, dr - \mathbb{C}(r) \right]. \tag{17}$$

The results of the mechanical problem, namely the displacement, the strains and the stresses in Equations (14)–(17) depend on the concentration field, that is solved in the diffusion problem.

#### *2.2. Diffusive Problem*

The diffusive equation is derived with the thermodynamic approach described by Chu and Lee [15] and later adopted by most of the works concerning stress in intercalation materials [21–26]. Chemical potential gradient is the driving force for mass transport. The chemical potential of a solute in an ideal solution subjected to stress is written in Equation (18) according to Chu and Lee [15].

$$
\mu = \mu\_0 + R\_{\mathbb{S}} T \ln(\mathbb{C}) - \sigma\_h \Omega,\tag{18}
$$

where *μ*<sup>0</sup> is a constant, *Rg* the universal constant of gasses, *C* the concentration field, *T* the temperature, *σ<sup>h</sup>* the hydrostatic stress experienced by the particle and Ω the partial molar volume. The expression of chemical potential in Equation (18) is formulated for dilute solution and does not take into account non ideality: namely the lithium migrates among interstitial sites and the structure of the host material is not modified by the intercalation process. The flux of lithium ions inside the particle due to the chemical potential is expressed in Equation (19) according to Reference [15].

$$J = -M\mathbb{C}\frac{\partial\mu}{\partial r},\tag{19}$$

where *M* is the mobility of the solute.

The mass conservation law of lithium ions in radial coordinate is introduced in Equation (20) [15].

$$\frac{\partial \mathbb{C}}{\partial t} + \frac{1}{r^2} \frac{\partial (r^2 f)}{\partial r} = 0 \tag{20}$$

#### *2.3. Uncoupled Problem*

At first the uncoupled problem is solved, so the hydrostatic stress term in the chemical potential expression in Equation (18) is neglected, allowing to decouple the elastic problem from the diffusive one.

This simplified version of chemical potential is replaced in Equation (19). Therefore, the lithium ions flux is expressed as Equation (21).

$$J = -D \frac{\partial \mathcal{C}}{\partial r} \tag{21}$$

where *D* is the diffusion coefficient, defined as *D* = *MRgT*.

*Energies* **2020**, *13*, 1717

Finally Equation (21) is replaced in the mass conservation law (Equation (20)), and the diffusion equation in radial coordinate is derived in Equation (22).

$$\frac{\partial \mathcal{C}}{\partial t} = \frac{D}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \mathcal{C}}{\partial r} \right) \tag{22}$$

Diffusion Equation (22) is written in perfect analogy with thermal diffusion, if concentration field is replaced by the temperature one.

Equation (22) is associated to a couple of boundary conditions which describe two possible cell operations: constant voltage (potentiostatic operation, Equation (23)) or constant current (galvanostatic operation, Equation (24)).

A constant lithium concentration equal to *CR* is imposed at the cell boundary over time with potentiostatic operation. The diffusion Equation (22) has a singularity for *r* = 0, so the second boundary condition prescribes a finite concentration value at the centre of the sphere. Finally, a constant initial concentration value *C*<sup>0</sup> is prescribed for *t* = 0 across the domain.

$$\begin{cases} \frac{\partial \mathcal{C}}{\partial t} = \frac{D}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \mathcal{C}}{\partial r} \right) \\ \mathcal{C}(r, 0) = \mathcal{C}\_{0\prime} & \text{for } 0 \le \mathbf{r} \le \mathbf{R} \\ \mathcal{C}(\mathcal{R}, t) = \mathcal{C}\_{\mathcal{R}\prime} & \text{for } t \ge 0 \\ \mathcal{C}(0, t) = finite, \qquad \text{for } \mathbf{t} \ge \mathbf{0} \end{cases} \tag{23}$$

A constant lithium flux, proportional to the current density, is applied on the external surface of the particle over time in galvanostatic operation. The lithium flux goes from the particle surface radially toward the centre, so the flux must be zero for *r* = 0. An initial concentration value *C*<sup>0</sup> is present all over the particle, as defined before.

$$\begin{cases} \frac{\partial \mathcal{C}}{\partial t} = \frac{D}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \mathcal{C}}{\partial r} \right) \\\\ \mathcal{C}(r, 0) = \mathcal{C}\_{0'} & \text{for } 0 \le \mathbf{r} \le \mathbf{R} \\\\ \frac{\partial \mathcal{C}(r, t)}{\partial r} \bigg|\_{r=R} = \frac{I}{FD'} & \text{for } t \ge 0 \\\\ \frac{\partial \mathcal{C}(r, t)}{\partial r} \bigg|\_{r=0} = 0, & \text{for } t \ge 0 \end{cases} \tag{24}$$

The solutions of the problem in Equations (23) and (24) are derived analytically by variable separation. However the solutions are well known in the literature [16] and are reported in Equation (25) for potentiostatic operation and in Equation (26) for galvanostatic operation.

$$\frac{\mathbb{C}(r,t) - \mathbb{C}\_R}{\mathbb{C}\_0 - \mathbb{C}\_R} = -2\sum\_{n=1}^{\infty} \frac{(-1)^{n+1}}{\pi n \mathbf{x}} \sin(n\pi \mathbf{x}) \, e^{-n^2 \pi^2 \tau},\tag{25}$$

$$\mathcal{L}(r,t) = \mathcal{C}\_0 + \frac{IR}{FD} \left[ 3\pi + \frac{\mathbf{x}^2}{2} - \frac{3}{10} - \frac{2}{\mathbf{x}} \sum\_{n=1}^{\infty} \left( \frac{\sin(\lambda\_n \mathbf{x})}{\lambda\_n^2 \sin(\lambda\_n)} e^{-\lambda\_n^2 \tau} \right) \right]. \tag{26}$$

The solutions are normalized according to the dimensionless characteristic time expressed as *τ* = *Dt*/*R*<sup>2</sup> and to the radial position *x* = *r*/*R*. *λ<sup>n</sup>* are the positive roots of the transcendent equation *λ<sup>n</sup>* = *tan*(*λn*). *CR* is the concentration value on the particle surface, *C*<sup>0</sup> is the initial concentration, *F* is the Faraday constant, *I* is the current density and *R* is the radius of the particle.

The concentration solutions in Equations (25) and (26) are replaced in Equations (14)–(17) to get displacement, strains and stress expressions for the uncoupled model.

#### *2.4. Coupled Problem*

The lithium ion flux for the coupled problem reported in Equation (27) is obtained by replacing the chemical potential (Equation (18)) in lithium flux (Equation (19)).

$$J = -D\left(\frac{\partial \mathcal{C}}{\partial r} - \frac{\Omega \mathcal{C}}{RT} \frac{\partial \sigma\_h}{\partial r}\right). \tag{27}$$

Finally, the concentration equation for the coupled problem is derived in Equation (28) replacing Equation (27) in the mass conservation law (Equation (20)).

$$\frac{\partial \mathcal{C}}{\partial t} = D \left[ \frac{\partial^2 \mathcal{C}}{\partial r^2} + \frac{2}{r} \frac{\partial \mathcal{C}}{\partial r} - \frac{\Omega}{R\_\mathcal{\mathbb{S}}} \frac{\partial \mathcal{C}}{\partial r} \frac{\partial \sigma\_h}{\partial r} - \frac{\Omega \mathcal{C}}{R\_\mathcal{\mathbb{S}}} \left( \frac{\partial^2 \sigma\_h}{\partial r^2} + \frac{2}{r} \frac{\partial \sigma\_h}{\partial r} \right) \right]. \tag{28}$$

Equation (28) cannot be solved analytically as Equation (22), so the flux expression in Equation (27) is rearranged in order to obtain an expression similar to Equation (21) which brings back to a concentration equation analogue to Equation (22), whose analytical solution is already known.

The term *∂σ<sup>h</sup> <sup>∂</sup><sup>r</sup>* in Equation (27) is written according to the chain rule method as: *∂σ<sup>h</sup> <sup>∂</sup><sup>r</sup>* <sup>=</sup> *∂σ<sup>h</sup> <sup>∂</sup><sup>C</sup> <sup>∂</sup><sup>C</sup> ∂r* . Then the hydrostatic stress in Equation (17) is differentiated with respect to the concentration: *∂σ<sup>h</sup> <sup>∂</sup><sup>C</sup>* = <sup>−</sup> <sup>2</sup>Ω*<sup>E</sup>* <sup>9</sup>(1−*ν*). Finally, the lithium flux is expressed in Equation (29) factoring the term *<sup>∂</sup><sup>C</sup> ∂r* .

$$J = -D\left(1 + \frac{2\Omega^2 EC}{9R\_\circ T(1-\nu)}\right)\frac{\partial C}{\partial r} \tag{29}$$

Equation (29) is similar to the expression of lithium ions flux derived for the uncoupled problem (Equation (21)), but the diffusion coefficient is multiplied by a new factor. So, the equivalent diffusion coefficient for the coupled problem is introduced in Equation (30), in accordance with Chu and Lee [15].

$$D\_{eqvn}(r) = D\left(1 + \frac{2\Omega^2 EC}{\theta R\_\mathcal{S} T(1 - \nu)}\right) = D(1 + k \cdot C). \tag{30}$$

The equivalent diffusion coefficient is composed by the physical diffusion coefficient *D* and by an artificial contribution *k* · *C* due to the hydrostatic stress effect. This factor is always greater than one, both for material with positive and negative fraction molar volume. Thus, hydrostatic stress effect always enhances lithium diffusion decreasing the concentration gradient within the particle.

This result can be derived even with general boundary conditions on the surface, that is, a general form of *C*1. The displacement in Equation (11) as a function of *C*<sup>1</sup> (*C*<sup>2</sup> = 0) is replaced in the expression of the radial and hoop stress, and the hydrostatic stress is calculated according to Equation (17). After some calculations it gives:

$$\sigma\_h(r) = \frac{2\Omega E}{\Re(1-\nu)} \left[ \mathbb{C}(r) + \mathbb{C}\_1 \frac{\Im(1-\nu)}{2(1-\nu)\Omega} \right] \tag{31}$$

Even in this condition the derivative of the hydrostatic stress with respect to the concentration has the same value computed before, leading to the same artificial diffusion contribution.

Lithium ion flux of the coupled problem in Equation (32) is formally similar to the flux of the uncoupled problem in Equation (21): namely it is equal to a coefficient multiplied for the derivative of the concentration with respect to the radius.

$$J = -D\_{\text{eq:v}} \frac{\partial \mathcal{C}}{\partial r} \tag{32}$$

This observation allows to derive the same diffusion equation of the uncoupled problem (Equation (22)) introducing the new diffusion coefficient *Deqv* instead of the physical diffusion coefficient. Therefore, the same solutions derived for the uncoupled problem can be used also for the coupled one replacing the physical diffusion coefficient with the equivalent diffusivity.

The concentration solutions reported in Equations (25) and (26) become non-linear because the equivalent diffusion coefficient depends itself on concentration. Thus, an iterative calculation, described in Figure 2 must be performed as follows:


The iterations go on until the maximum difference between the concentration computed in the *k*th iteration and *k* − 1th is below a certain threshold. This iterative computation converges in few iterations to a stable value.

**Figure 2.** Iterative calculation procedure.

Once the concentration field is obtained, it is replaced in Equations (14)–(17) to get displacement, strains and stresses expressions for the coupled model.

#### **3. Results and Discussion**

In this section, the numerical results derived with the model explained in Section 2 are presented. The concentration functions for galvanostatic and potentiostatic insertion are compared with the results available in literature derived through numerical simulation. Then, concentration and stress function computed with the analytical model are presented in case of galvanostatic operation. The comparison between the coupled and uncoupled model highlights the hydrostatic stress influence on lithium diffusion. The results are derived according to the physical parameters reported in Tables 1 and 2, referring to anode and cathode materials.


**Table 1.** Graphite properties (anode).


**Table 2.** LixMn2O4 (LMO) properties (cathode).

#### *3.1. Compatibility between Model Assumptions and Real Material*

Graphite and lithium manganese oxide (LMO) are chosen as case study for anode and cathode intercalation materials respectively. The compatibility between the assumptions of the analytical model and real active materials is discussed in this section. The linear elastic assumption is respected for all the insertion materials, because they show slight deformation. There are two aspects to discuss: geometry and homogeneity assumptions.

About the geometry assumption, it is necessary to understand how a sphere is capable to represent the random geometry of the active material particles. For some materials, such as NMC or graphite the real particle geometry is close to a sphere, as showed by SEM images in Reference [37–39], but for other materials, such as LMO or LCO, particles shape is more elongated and irregular. However, a modelling approach must overcome the statistical variation of the samples and give reasonable and general results which can be valid for the entire samples population. For this reason, an ideal geometry which can be extended and representative of all the other particles is adopted in this work, according the following reasoning. Simulations confirm that greater particle size results in higher stress, because of longer diffusion path. Hence, the radius is chosen so that the ideal spherical particle adopted in simulation circumscribes the mean real particle, once the statistical distribution of the particle size of a powder is known. In this manner, it is possible to give a safe estimation of the stress in the powder particles based on their size, overcoming the limit of the random distribution of the particles shapes. The results of the simulation at least overestimate the real stress in the particles of a powder, since a bigger spherical equivalent particle is used to simulate all the different particles shapes present in a powder.

For what concerns different ideal geometries, Zhang et al. studied the influence of the aspect ratio of an ellipsoidal LMO particle on the stress [21,22]. The results show that the stresses computed with aspect ratios different from one (one corresponds to the sphere) are ±10% of the stress computed with spherical geometry. Hence, spherical geometry minimizes the error due to the statistical distribution of the particle shape [21].

Some works analysed the stress over a realistic particle geometry extracted from SEM images [40–43]. The results show that the main difference between realistic particle and ideal spherical particle resides in the stress concentrations in notches. In future works, it is meaningful to study a generalized notch factor, based on the statistical analysis of powder samples, which can be representative of the notching effect of different active material particles. Indeed, stress concentration due to notching effect causes cracks propagation: the main reason for electrode damage and capacity fade.

Moreover, a recent work [44] demonstrated how the assumptions of spherical geometry and isotropic and linear elastic material are accurate for LCO and graphite, since they found a good agreement between the macroscopic deformation predicted by their numerical model and the experimental measurements conducted on pouch cell. Finally, spherical assumption is widely accepted among several works [20–22,26,45].

The second aspect concerns the homogeneity assumption. This aspect can be still divided in two issues: phase transition during Li insertion and inhomogeneity of primary particles. Phase transition occurs in some materials when lithium content exceeds the equilibrium concentration. Lithium ions begin to intercalate in different type of interstices above the equilibrium concentration, modifying the crystallographic structure: this leads to a stress and concentration jump between the two phases because they are characterized by different physical parameters. Christensen et al. pointed out that LMO shows a single phase in the 4V plateau, and the transformation in cubic-tetragonal phase occurs with deep discharge [20]. In LCO, which has a negative partial molar volume, Li poor phase has a larger partial molar volume than the lithium rich phase [46]. Therefore, as the second phase starts to form during the discharge process, the magnitude of stress starts to decrease—phase change leads to a safer condition in this case.

However, a simple general approach which considers phase transition in our model is the following: it is necessary to change the physical parameters according to the concentration level with a moving boundary concept. When the concentration level exceeds the equilibrium concentration of a phase in a certain radial position, equilibrium concentration and physical parameters (Young modulus, Poisson ratio and especially partial molar volume) must be changed with the physical parameters of the new phase. During insertion the "boundary" between the two phases moves towards the core, and the physical parameters must be changed accordingly. So, phase transition can be implemented in the model in Section 2 tuning the input parameters, but the framework of the model remains unchanged.

The particles of some materials, such as NMC, are synthesized from primary particles [39]. However, it is hard to model the influence of randomly distributed primary particles which compose secondary particle, and because of the random orientation of primary particles, secondary particles are usually assumed as a continuum material [47,48]. However, Wu et al. [49] tried to consider the influence of primary particle on the stress.

#### *3.2. Comparison with the Results of Numerical Models in Literature*

The analytical solution of DIS problem was proposed by Cheng et al. [16] according the uncoupled formulation. As far as the authors know, analytical solution of the coupled problem are still not available in literature. Generally, the finite difference method [18,20,21,23,24] or FE simulations [16,21,27,33] in commercial codes were adopted in order to solve the DIS problem in the coupled formulation. Following the procedure explained in Section 2, the analytical solutions of the standard diffusion problem are used to get the solution of the DIS coupled problem via an iterative computation, which is a much simpler way compared to solve the whole coupled equation (Equation (28)) with finite difference method or building up a FE analysis.

The concentration function computed with the analytical model in galvanostatic and potentiostatic insertion are compared with the results derived via finite different method by Bagheri et al. [26] in Figure 3. A good agreement is achieved between the analytical model proposed in this work and Reference [26] derived via numerical computation. Furthermore the concentration trend with and without "stress effect" matches with the results of Zhang et al. [21] and Christensen et al. [19]. Moreover the results of the uncoupled model matches with the model derived by Cheng et al. [16]. Even the stress functions fits faithfully the numerical results available in the literature, since they depend uniquely on concentration.

**Figure 3.** Concentration level as a function of dimensionless radial position for different time constants *τ* in galvanostatic (**a**) and potentiostatic (**b**) insertion. The analytical model is reported with solid (coupled) and dashed (uncoupled) lines. The solution of the numerical model [26] is reported in discrete radial coordinates with dots (coupled) and crosses (uncoupled).

The lack of stress measurements in insertion material particles makes the results in this work impossible to be validated experimentally, as pointed out even by other authors [26], and mathematical modelling is the only way to make these computations.

#### *3.3. Insertion under Galvanostatic Control*

Concentration level and the stress functions in galvanostatic insertion are computed with the analytical model proposed in Section 2 assuming null initial concentration. The results are derived for three different SOC levels: 25%, 50%, 75%. The SOC level is calculated according to Zhang [26,50] as:

$$\text{SOC} = \frac{\int\_0^{\mathbb{R}} c(r) r^2 dr}{\int\_0^{\mathbb{R}} c\_{\text{max}} r^2 dr} \cdot 100. \tag{33}$$

The current density over the particle surface is 3 A/m2, which corresponds roughly to 2C. The temperature is assumed to be constant at 298 K. The results for anode and cathode particles whose physical parameters are listed in Tables 1 and 2 are reported in Figures 4 and 5.

The concentration level normalized with the maximum concentration value which can be stored in the active material particles is reported in Figure 4a. So, when the normalized concentration is equal to the unity all the available sites in the particle are occupied by lithium ions. Radial, hoop and Von Mises stress are reported in Figure 4b–d for graphite particles. The same data are reported in Figure 5 for LMO particles.

The pressure diffusion dependence determines a greater equivalent diffusion coefficient which allows a faster lithium diffusion within the particle. In particular enhances mass transport from areas subjected to compression to areas subjected to tensile stress. This fact makes the lithium concentration gradient predicted by the coupled model lower if compared to the uncoupled model, as shown in Figures 4a and 5a. Remembering the thermal analogy, lower gradient means lower stress, so the coupled model predicts a lower stress state, as highlighted in Figures 4b–d and 5b–d; the differences between the two model are up to 40%. The differences between the stresses computed with the three SOC levels are small (the maximum is 15% for graphite and 7% for LMO), this suggests that the active material particles experience similar stresses during almost the whole SOC range.

The comparison between the results obtained for anode (Figure 4) and cathode (Figure 5) shows the influence of the diffusion coefficient. Indeed, the slight difference in the diffusion coefficient between LMO and graphite produces an important increase of the concentration gradient in the cathode particles, which in turn causes a serious increase of the stress. Consequently, a greater equivalent stress makes the coupling between mechanical and diffusion aspect stronger.

**Figure 4.** Lithium concentration (**a**), radial stress (**b**), hoop stress (**c**) and Von Mises stress (**d**) for different SOC levels in galvanostatic insertion in anode material. Dashed lines refer to the uncoupled model and solid lines refer to the coupled model.

**Figure 5.** Lithium concentration (**a**), radial stress (**b**), hoop stress (**c**) and Von Mises stress (**d**) for different SOC levels in galvanostatic insertion in cathode material. Dashed lines refer to the uncoupled model and solid lines refer to the coupled model

This results in a greater difference between the concentration computed with the coupled model or the uncoupled one in LMO because the mechanical component in the chemical potential (Equation (18)) becomes greater.

#### *3.4. Extraction under Galvanostatic Control*

The galvanostatic extraction is modelled assuming an initial concentration within the particle equal to *Cmax*, namely SOC 100%, and surface current density equal to −3 A/m2. The extraction determines a reduction of the SOC level, and the result for SOC equal to 75%, 50% and 25% are reported in Figures 6 and 7 for anode and cathode material, respectively. Concentration is reported in Figure 6a, radial, hoop and Von Mises stress are reported in Figure 6b–d for graphite. The same data are reported in Figure 7 for LMO.

**Figure 6.** Lithium concentration (**a**), radial stress (**b**), hoop stress (**c**) and Von Mises stress (**d**) for different SOC levels in galvanostatic extraction in anode material. Dashed lines refer to the uncoupled model and solid lines refer to the coupled model.

The same conclusions made for insertion about the differences of concentration and stress state between the coupled and uncoupled model can be made also for extraction. The differences between the stress computed with the coupled and uncoupled model are up to 35%. In Figures 6c and 7c it is highlighted that the particle experiences tensile hoop stress on its surface during galvanostatic extraction, which is supposed to be the driving force for crack propagation in active material [30].

**Figure 7.** Lithium concentration (**a**), radial stress (**b**), hoop stress (**c**) and Von Mises stress (**d**) for different SOC levels in galvanostatic extraction in cathode cathode. Dashed lines refer to the uncoupled model and solid lines refer to the coupled model.

#### *3.5. Evolution of Von Mises Stress in Time*

The continuous evolution in time of the Von Mises stress is shown in Figure 8. The hydrostatic stress effect homogenizes the lithium concentration within the particle, so the stress values computed by the coupled model are lower than the uncoupled one, in accordance with Reference [21]. On the contrary, for high extraction time the stress predicted by the coupled model tends to the uncoupled one.

**Figure 8.** Von Mises stress as a function of insertion (**a**) and extraction (**b**) time. The results are derived with physical parameters of Table 2.

#### *3.6. Influence of Hydrostatic Stress on Concentration*

Hydrostatic stress influence always enhances lithium diffusion. This assertion is justified from a quantitative point of view by the artificial contribution to the equivalent diffusion coefficient in Equation (30). This contribution is always positive regardless of the insertion or extraction operation, time constant or radial position, so the coupled model is always characterized by a greater diffusion coefficient which decreases the concentration gradient within the particle, as showed in Figures 4a–7a.

This concept is qualitatively explained in Figure 9. Indeed, the chemical potential in Equation (18) can be split in the concentration contribution (*μ<sup>C</sup>* = *RgT* ln (*C*)) and the hydrostatic stress contribution (*μσ* = −Ω*σh*) as follow: *μ* = *μ<sup>C</sup>* + *μσ*. In case of insertion, referring to Figure 9a, the concentration *C*<sup>2</sup> at *r* + *dr* is greater than the concentration *C*<sup>1</sup> at *r* − *dr* for a generic radial coordinate *r*, resulting in a positive concentration contribution. In the same way the hydrostatic stress *σh*,2 at *r* + *dr* is lower than the hydrostatic stress *σh*,1 at *r* − *dr*, resulting in a positive hydrostatic stress contribution. This analysis can be extended to all the radial coordinates from zero to *R* because both concentration and hydrostatic stress are monotonic. Therefore, both the contributions are concordant due to the shape of concentration and hydrostatic stress functions showed in Figure 9a, and concur to the incoming flux. This analysis is also valid for extraction, as explained in Figure 9b. In this case, concentration, hydrostatic stress and thus chemical potential contributions are the opposite, resulting in an outgoing flux.

**Figure 9.** Hydrostatic stress influence on lithium diffusion for insertion and extraction operation. The qualitative trend of the lithium concentration (red) and the hydrostatic stress (green) for insertion (**a**) and extraction (**b**) are reported in the graphics. The chemical potential is split in concentration contribution and hydrostatic stress contribution whose increments are valued for a general radial position *r*. The stress and concentration contributions for a general radial coordinate are graphically reported with green and red arrows which goes from the lower to the higher value (**c**). The lithium flux due to the chemical potential difference is reported with the blue arrows (**c**).

On the other hand, hydrostatic stress influences the concentration level in the particle. Tensile hydrostatic stress allows to store a greater amount of lithium ions, on the contrary compressive hydrostatic stress determines a reduction of the storable lithium ions. These differences are highlighted comparing the results with the uncoupled model, which neglects the influence of the hydrostatic stress on the lithium concentration. Referring to Figure 10a, black arrows mark the border between positive

and negative hydrostatic stress. This trend matches with the differences in concentration function computed with the two models in Figure 10b: where the hydrostatic stress is positive the concentration level of the coupled model is higher than the uncoupled one, where the hydrostatic stress is negative the coupled model predicts a lower concentration level compared to the uncoupled model. About this issue it is worth noting that the model in this work assumes free expansion of the particle surface, neglecting the interaction with its surroundings.

**Figure 10.** Hydrostatic stress (**a**) and concentration (**b**) in cathode material. Black arrows show the points where the hydrostatic stress changes sign which partially reflect the turnaround of the concentration function. Dashed lines refer to the uncoupled model and solid lines refer to the coupled model.

A more accurate model should consider the surface constraints of the particle which are supposed to generate an increase in the compressive stress and in turn lower achievable concentration values. Future works should be carried out in order to confirm this hypothesis.

#### **4. Conclusions**

The stress state within active material particle of graphitic anode and LMO cathode are computed with coupled and uncoupled model according to DIS theory, assuming no constraints on the external surface. The analytical solution of the coupled model is proposed in this work defining an equivalent diffusion coefficient composed by a physical term and by an artificial contribution connected to the hydrostatic stress. This definition allows to exploit the analytical solutions of the uncoupled model even for the coupled one with an iterative calculation, since the equivalent diffusion coefficient depends itself on concentration.

The results derived with the analytical solution of the coupled model are compared with the solutions derived with numerical methods in literature and show a good agreement. The analytical solution proposed in this work is easier and requires a lower computing time if compared to strongly non-linear FE method or finite difference method. The concentration function and the stress state within the particle are computed for three SOC levels: 25%, 50%, 75%. The differences between the stresses computed with the different SOC levels are small: this fact suggests that particles experience almost the same stress state during about the whole SOC window. The differences between the stress state in LMO and graphite is mainly due to diffusion: a smaller diffusion coefficient causes higher lithium concentration gradient, and higher stress consequently (up to 40%), according to thermal analogy concept. Thus, the coupling factor Ω*σ<sup>h</sup>* in chemical potential becomes higher and the differences between coupled and uncoupled model are not negligible.

Finally, it is pointed out that tensile stress, in particular tensile hoop stress which occurs on the particle surface during extraction, is the driving force for crack propagation, which in turn damages the active material and accelerates the SEI growth. On the other hand, compressive hydrostatic stress influences the lithium solubility decreasing the achievable capacity, namely the lithium ions which can be stored in the host material. An increase of compressive stress is expected if surface constraints are considered, because the particle expansion is prevented. Future works should analyse this issue which can result in a not negligible achievable capacity reduction.

**Author Contributions:** Conceptualization, D.C., F.M. and A.S.; methodology, D.C., F.M. and A.S.; formal analysis, D.C.; investigation, D.C., F.M.; Writing—Original draft preparation, D.C.; Writing—review and editing, F.M. and A.S.; supervision, F.M. and A.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Butyronitrile-Based Electrolytes for Fast Charging of Lithium-Ion Batteries**

#### **Peter Hilbig 1, Lukas Ibing 1, Martin Winter 1,2 and Isidora Cekic-Laskovic 2,\***


Received: 19 June 2019; Accepted: 18 July 2019; Published: 25 July 2019

**Abstract:** After determining the optimum composition of the butyronitrile: ethylene carbonate: fluoroethylene carbonate (BN:EC:FEC) solvent/co-solvent/additive mixture, the resulting electrolyte formulation (1M LiPF6 in BN:EC (9:1) + 3% FEC) was evaluated in terms of ionic conductivity and the electrochemical stability window, as well as galvanostatic cycling performance in NMC/graphite cells. This cell chemistry results in remarkable fast charging, required, for instance, for automotive applications. In addition, a good long-term cycling behavior lasts for 1000 charge/discharge cycles and improved ionic conductivity compared to the benchmark counterpart was achieved. XPS sputter depth profiling analysis proved the beneficial behavior of the tuned BN-based electrolyte on the graphite surface, by confirming the formation of an effective solid electrolyte interphase (SEI).

**Keywords:** lithium-ion batteries; non-aqueous electrolyte; nitrile-based solvents; butyronitrile; SEI forming additives; fast charging

#### **1. Introduction**

Thanks to their excellent performance characteristics, lithium ion battery (LIB) cells find application in a broad spectrum of different fields, comprising the consumer and automotive industries as well as application in small portable devices, like mobile phones or laptops [1–4]. The main reason behind the broad field of application relates, among other reasons, to the high specific energy and energy density of LIBs [5–7] and the numerous cell materials, that can be employed [8].

In standard LIBs, organic carbonate-based non aqueous aprotic electrolytes are employed. Although given as state of the art electrolytes, they display several disadvantages (e.g., moderate ionic conductivity and low flash points) [9–12]. To further advance state of the art battery electrolytes, many solvent classes were comprehensively investigated to replace organic carbonates [9,13–24]. Nitriles and other cyano-compounds display high ionic conductivity as well as low temperature cycling performance [25–34]. Nevertheless, many examples of this class of compounds are known for being incompatible with metallic lithium and not able to form an effective solid electrolyte interphase (SEI) on graphite [35–40]. For this reason, the presence of SEI forming electrolyte additive(s) is inevitably required to enable their application in graphite based LIBs [41].

In the case of organic carbonate-based electrolytes, ethylene carbonate (EC) is typically involved in the formation of the SEI on graphite in the first charge/discharge cycles [42]. In addition to EC [43,44], other SEI forming agents on graphite were reported in the literature, e.g., lithium difluoro-(oxalate)borate (LiDFOB), vinylene carbonate (VC) or fluoroethylene carbonate (FEC) [45–53] and many more. Among them, VC and FEC are preferred as SEI additives on graphite anodes for organic carbonate-based electrolytes [9,13].

In this contribution, butyronitrile (BN)-based electrolytes containing EC, FEC or both as co-solvents/functional additives are considered for fast charging application in lithium-nickelmanganese-cobalt-oxide (NMC)/graphite cells. The investigations were mainly performed in full cell setup. The optimum BN:EC:FEC solvent/co-solvent-functional additive ratio was investigated in terms of long-term cycling and C-rate performance in NMC/graphite cells. The obtained electrochemical results were correlated to the surface analysis of the graphite electrodes via XPS measurements.

#### **2. Experimental Section**

#### *2.1. Electrolyte Formulation*

All considered electrolytes were formulated using volume percent (vol.%) in an argon-filled glovebox (MBRAUN, Garching, Germany) with a water and oxygen content below 0.1 ppm. BN 99% (MERCK, Darmstadt, Germany), lithium hexafluorophosphate (LiPF6, BASF, battery grade, Ludwigshafen, Germany), FEC (BASF, battery grade, Ludwigshafen, Germany) and EC 99.8% anhydrous (MERCK, Darmstadt, Germany) were used as received. As reference electrolyte, 1M LiPF6 in EC:DMC (1:1 wt.%) (LP30, BASF, battery grade, Ludwigshafen, Germany) was used.

#### *2.2. Preparation of T44 Graphite and Lithium Manganese Oxide Electrodes*

The composition of graphite electrodes was as follows: 87 wt.% T44 graphite (Imerys, Paris, France) 8 wt.% polyvinylidene difluoride (PVdF, Arkema, Colombes, France) and 5 wt.% conductive additive Super C65 (Imerys, Paris, France). T44 graphite was used as the active material due to its high BET surface area, leading to a pronounced reduction of the electrolyte [54] The LiMn2O4 (LMO) electrodes were composed of 80 wt.% LMO (Toda, Hiroshima, Japan), 10 wt.% PVdF and 10 wt.% Super C65. In the fabrication process of the electrodes, PVdF was dissolved in *N, N*-dimethylformamide 99.8% anhydrous (DMF, Alfa Aesar, Haverhill, MA, USA). Subsequently, conductive additive (Super C65) and active material (T44 or LMO) were added to the solution and mixed with a dissolver. The suspension was thereafter coated with a special film applicator, on a copper foil (negative electrodes; T44; 120 μm wet thickness) and on aluminum foil (positive electrodes; LMO; 100 μm wet thickness). The coated foils were dried in an oven (Binder, Tuttlingen, Germany) at 80 ◦C overnight. The obtained electrodes were cut with a punching tool (Hohsen Corp. Osaka, Japan) into a diameter of 12 mm and thereafter dried at 120 ◦C in vacuum for 24 h in a Buchi Glass Oven 585 with a rotary vane pump vacuum (Büchi, Flawil, Switzerland). After weighting (Sartorius laboratory balance; Sartorius, Göttingen, Germany), the resulting electrodes had an active mass loading between 2.5 and 3 mg cm−<sup>2</sup> [53]. For the investigations in the full-cell setup, balanced NMC111 (Litarion, Kamenz, Germany) and graphite electrodes (Litarion, Kamenz, Germany) both 12 mm diameter, were used.

#### *2.3. Electrochemical Measurements*

#### 2.3.1. Cell Set-Up

The electrochemical measurements were performed in a two electrode, coin cell (2032) (Hohsen Corp. Osaka, Japan), setup as well as in three-electrode T-cell setup (Swagelok® Solon, OH, USA). The NMC was used as the working electrode (WE), graphite as the counter electrode (CE), whereas lithium foil (Albemarle, Charlotte, NC, USA) was taken as the reference electrode (RE).

#### 2.3.2. Linear Sweep Voltammetry Measurements

The electrochemical stability window of the considered BN-based electrolytes was determined by means of linear sweep voltammetry (LSV) using a VMP3 potentiostat (Bio-Logic, Seyssinet-Pariset, France). A lithium manganese oxide (LMO) based electrode was used as WE, whereas lithium foil was used as the CE and RE. The measurements were performed in the potential range between the

open circuit potential (OCP) and 5.0 V vs. Li/Li <sup>+</sup>, using a scan rate of 100 μV s−<sup>1</sup> at room temperature (20 ◦C).

#### 2.3.3. Cyclic Voltammetry Measurements

Cyclic voltammetry (CV) measurements were carried out at room temperature, using a Bio-Logic VMP3 potentiostat, in the potential range from 0.02–2.00 V vs. Li/Li+. The cells were cycled with a scan rate of 20 μV s<sup>−</sup>1. T44 graphite was used as WE. Lithium foil was used as the CE and RE.

#### 2.3.4. Galvanostatic Measurements

Measurements were carried out at 20 ◦C by means of battery cycler (MACCOR Series 4000, Tulsa, OK, USA). The cathode limited NMC/graphite cells (20% capacity-oversized anode) were cycled for five formation cycles at 0.1C in a voltage range between 3.00–4.30 V. After the formation sequence, cells were cycled with a charge and discharge rate of 372 mA g−<sup>1</sup> (1C). For the C-rate evaluation, C-rate of the charge step, the discharge step and of both the charge and the discharge steps was always altered after five cycles in the following manner: five cycles with a C-rate of 1C followed by a C-rate of 0.2C, 1C, 2C, 5C, 10C, 15C, 20C followed by 30 cycles with a C-rate of 1C. During the performance assessment of the charge behavior, the C-rate of the charge step was altered, and the C-rate of the discharge step was set to 1C. The performance assessment was based on the discharge capacity. In the discharge performance evaluation, the C-rate of the discharge step was altered, and the C-rate of the charge step was set to 1C. In the charge/discharge performance rating, the C-rate of the charge step as well as the C-rate of the discharge step were altered in afore mentioned way. During the 5C performance evaluation, the C-rate was set to 1C after the formation sequence for 10 cycles followed by 95 charge/discharge cycles with 5C for each charge and discharge step. During the long-time cycling evaluation, the C-rate of the charge and discharge step was set to 1C after the formation procedure. Furthermore, a current-limited CV step of 0.05C was introduced to the galvanostatic cycling procedure, for the 1000 cycle measurement.

#### *2.4. Conductivity Measurements*

AC impedance measurements were used to determine the conductivity of the considered BN-based electrolyte formulations. All measurements were carried out on a Solartron 1260A (AMETEK, Berwyn, PA, USA) impedance gain phase analyzer, connected to a Solartron 1287A (AMETEK, Berwyn, PA, USA) potentiostat using a customized cell having two stainless steel disk-electrodes. A frequency range from 1 kHz to 1 MHz using an AC amplitude of 20 mV was applied to the cell for each temperature (−40 to 60 ◦C), which was regulated via a climate chamber.

#### *2.5. X-ray Photoelectron Spectroscopy (XPS) Analysis*

For the XPS measurements, an AXIS Ultra DLD (Kratos, Shimadzu Corporation, Kyoto, Japan) was used. An area of 300 μm × 700 μm was irradiated using a filament voltage of 12 kV, an emission current of 10 mA and a pass energy of 20 eV. The obtained spectra were calibrated against the adventitious carbon signal at 284.5 eV. For the XPS sputter depth profiling measurements a sputter crater diameter of 1.1 mm, an emission current of 8 mA, and a filament voltage of 0.5 kV as well as a pass energy of 40 eV and a 110 μm aperture were applied. The fitting of the resulted spectra was performed with the help of CasaXPS.

#### **3. Results and Discussion**

Nitrile-based electrolytes are known to deliver higher ionic conductivity values compared to the state of the art organic carbonate-based counterparts (Figure 1) [55]. This solvent class is particularly interesting when it comes to fast charging behavior of LIBs. Having in mind that BN is not stable against metallic lithium or graphite, a SEI-forming co-solvent was added to the BN-based electrolyte. With this in line, 1M LiPF6 in BN:EC (1:1) as well as 1M LiPF6 in BN:FEC (1:1) electrolyte formulations were compared with the 1M LiPF6 in EC:DMC (1:1) electrolyte, taken as reference.

**Figure 1.** Temperature dependent conductivity measurements of 1M LiPF6 in EC:DMC (1:1), 1M LiPF6 in BN:FEC (1:1) and 1M LiPF6 in BN:EC (1:1), in the temperature range from −40 to 60 ◦C.

When using EC as co-solvent, the BN-based electrolyte delivers higher conductivity values compared to the 1M LiPF6 in EC:DMC (1:1) electrolyte (Figure 1). Especially at low temperature (0 ◦C), the conductivity of the considered BN:EC-based electrolyte is at least 32% higher (7.69 mS/cm) compared to the organic carbonate-based counterpart (5.83 mS/cm). Substitution of EC with FEC leads to a decreased conductivity (from 11.80 mS/cm to 9.16 mS/cm) at 20 ◦C. In the temperature range of 20 ◦C to 60 ◦C, the conductivity of 1M LiPF6 in EC:DMC (1:1) is equal to the conductivity values of the 1M LiPF6 in BN:FEC (1:1) electrolyte. In contrast to the high conductivity of the BN:EC mixture, the conductivity of the BN:FEC mixture was shown to be quite poor. The high conductivity of the BN:EC mixture-based electrolytes makes them suitable for fast charging (>1C).

The conductivity values of the investigated electrolytes can be explained by means of relevant physicochemical properties of the used solvents. The conductivity is related to the viscosity and to the relative permittivity of the electrolyte formulation. The ion mobility is linked to the viscosity whereas the salt dissociation capability is related to the relative permittivity. To obtain a high conductivity, the viscosity of the electrolyte formulation should be low, and the relative permittivity must be high enough to ensure a sufficient dissolution of the conducting salt.

To determine the oxidative stability of the BN-based electrolytes, compared to the reference electrolyte, corresponding voltammograms were recorded using LMO as WE (Figure 2). A content of 50% of FEC was chosen to overcome the instability of nitriles towards metallic lithium and to ensure the passivation of the metallic lithium [13,61]. Whereas with organic carbonate-based electrolyte Li metal is stable, [62] with an EC content of only 50%, in the mixture the degradation of the electrolyte could not be inhibited. Therefore, EC:BN mixtures could not be investigated in combination with lithium metal. Nevertheless, this mixture should display the same oxidative stability (as confirmed by later full cell experiments). With 1M LiPF6 in EC:DMC (1:1) as reference electrolyte, the maxima of the de-insertion peaks of LMO are positioned at. 4.05 V vs. Li/Li<sup>+</sup> and 4.16 V vs. Li/Li<sup>+</sup> [63]. In this setup, the reference electrolyte was found to be electrochemically stable up to 4.90 V vs. Li/Li<sup>+</sup> [64].

Compared to the reference electrolyte, the voltammogram of the cell containing 1M LiPF6 in BN:FEC (1:1) displays de-insertion peak maxima of LMO at 4.05 V vs. Li/Li<sup>+</sup> and 4.19 V vs. Li/Li+. This electrolyte formulation shows electrochemical stability up to 4.50 V vs. Li/Li+, which is much higher compared to other literature known nitriles [65]. Furthermore, this result fits well with literature showing known density functional theory (DFT) calculations [55]. This behavior makes the combination of BN-based electrolytes with cathode materials, such as lithium nickel cobalt aluminum oxide (NCA) and NMC possible.

**Figure 2.** Linear sweep voltammograms of cells containing 1M LiPF6 in BN:FEC (1:1) and 1M LiPF6 in EC:DMC (1:1) (wt.%), LMO as WE, and Li as CE and RE, at scan rate of 100 μV s−<sup>1</sup> at room temperature.

Cyclic voltammetry measurements in T44 graphite/lithium cells containing 1M LiPF6 in various BN:FEC solvent/co-solvent ratios were performed to determine the reductive stability of the considered electrolyte formulations vs. the anode (Figure 3).

The decomposition of FEC starts at a potential of 1.60 V vs. Li/Li+, reaching the peak maximum at a potential value of 1.50 V vs. Li/Li<sup>+</sup> (Figure 3a–d). Due to the SEI formation in presence of FEC, the decomposition of the 1M LiPF6 in BN:FEC (1:1) (Figure 3a), 1M LiPF6 in BN:FEC (6:4) (Figure 3b), 1M LiPF6 in BN:FEC (7:3) (Figure 3c), 1M LiPF6 in BN:FEC (8:2) (Figure 3d) electrolyte formulations are inhibited, thus leading to the reversible intercalation and deintercalation of lithium ions into the graphite host structure, as indicated by the presence of the corresponding peaks (starting at a potential of 0.30 V vs. Li/Li<sup>+</sup>). Compared to the aforementioned electrolyte formulations, 1M LiPF6 in BN:FEC (9:1) electrolyte (Figure 3e) is not able to form an effective SEI on graphite and results in a severe decomposition. As a consequence, no intercalation/deintercalation steps take place. The amount of FEC seems not to be enough to protect the BN against decomposition on both T44 graphite and lithium electrode. Compared to FEC, the decomposition of in the 1M LiPF6 in EC:DMC (1:1) (Figure 3f) mixture starts at 0.9 V vs. Li/Li<sup>+</sup> and the peak maximum is reached at 0.80 V vs. Li/Li+.

To prove the fast charging ability of the NMC/graphite cells containing afore mentioned BN-based electrolyte formulations, a C-rate evaluation up to 5C was performed, starting with five formation cycles at 0.1C. After the formation, 10 cycles at 1.0C were conducted, followed by 95 charge/discharge cycles with a C-rate of 5C. The obtained results are shown in Figure 4. As depicted in Figure 4a, the NMC/graphite cell containing 1M LiPF6 in BN:EC (1:1) electrolyte, reaches a Coulombic efficiency of 87% in the first cycle (see Meister et al. for the meanings of efficiencies) [66]. The specific discharge capacity amounts to 176 mAh/g with a C-rate of 0.1 C in the first five cycles, whereas in the consecutive 10 charge/discharge cycles, a specific discharge capacity of 153 mAh/g with a Coulombic efficiency of 99% is achieved. After 15 cycles, the C-rate evaluation was started with a C-rate of 5C for each charge and discharge step for the consecutive 95 charge/discharge cycles. The specific discharge capacity displays a negligible fading and drops from 76 mAh/g in the 30th cycle to 68 mAh/g in the 110th cycle. The Coulombic efficiency drop in the 6th and 16th cycle is related to the change of the C-rate and observed in each chart in Figure 4. The cell containing 1M LiPF6 in BN:EC (7:3) + 1% FEC electrolyte formulation displays a first cycle Coulombic efficiency of 87%, as illustrated in Figure 4b. The specific discharge capacity amounts to 177 mAh/g for each cycle with a C-rate of 0.1C. A specific discharge capacity of 155 mAh/g with a Coulombic efficiency of 99% is reached in the following 10 charge/discharge cycles. In the C-rate evaluation, the specific discharge capacity shows a notable fading and drops from 93 mAh/g in cycle 30 to 68 mAh/g in cycle 110. The cell chemistry outlined in Figure 4c comprises of 1M LiPF6 in BN:EC (9:1) + 3% FEC electrolyte. The specific discharge capacity amounts to 176 mAh/g in the first five cycles using a C-rate of 0.1C, whereas the first cycle

Coulombic efficiency amounts to 86%. Unlike other considered electrolyte formulations displayed in Figure 4, 99% Coulombic efficiency is not reached in the second but in the third cycle. The specific discharge capacity in the consecutive 10 charge/discharge cycles amounts to 155 mAh/g. During the 5C sequence, the capacity drops down to 105 mAh/g in the 30th cycle and decreases to 100 mAh/g in the 110th cycle, without a substantial fading. The cell containing 1M LiPF6 in EC:DMC (1:1) electrolyte formulation, (Figure 4d) displays a first Coulombic efficiency of 87%. The specific discharge capacity amounts to 176 mAh/g for each cycle with a C-rate of 0.1 C. The following 10 charge/discharge cycles display a specific discharge capacity of 155 mAh/g with a Coulombic efficiency of 99%. In the C-rate evaluation the specific discharge capacity drops from 67 mAh/g in the 30th cycle to 64 mAh/g in the 110th cycle. A comparison between the 1M LiPF6 in BN:EC (9:1) + 3% FEC and the reference electrolyte indicates a similar cycling performance at C-rates up to 1C and a superior higher performance of BN-based electrolyte at 5C. During cycling at 5C, the specific discharge capacity is decreased by 5% from 105 mAh/g to 100 mAh/g comparable to 4% with the reference electrolyte. In addition, the average specific discharge capacity at 5C is ≈ 103 mAh/g compared to ≈ 66 mAh/g for the reference electrolyte. The deviation amounts to 37 mAh/g (56%).

**Figure 3.** Cyclic voltammograms of T44 graphite/lithium cells containing 1M LiPF6 in (**a**) BN:FEC (1:1), (**b**) BN:FEC (6:4), (**c**) BN:FEC (7:3), (**d**) BN:FEC (8:2), (**e**) BN:FEC (9:1) and (**f**) EC:DMC (1:1) as electrolyte formulation, in the potential range between 0.02–2.00 V vs. Li/Li+, at scan rate of 20 μV s<sup>−</sup>1; insert shows the magnification of the reductive decomposition peak of fluoroethylene carbonate (FEC) at 1.5 V vs. Li/Li+.

**Figure 4.** C-rate evaluation of the NMC/graphite cells containing (**a**) 1M LiPF6 in BN:EC (1:1), (**b**) 1M LiPF6 in BN:EC (7:3) + 1% FEC, (**c**) 1M LiPF6 in BN:EC (9:1) + 3% FEC and (**d**) 1M LiPF6 in EC:DMC (1:1) in the voltage range of 3.00–4.30 V.

The obtained results show, that NMC/graphite cells containing 1M LiPF6 in BN:EC (9:1) + 3% FEC electrolyte display a remarkably stable cycling behavior at 5C. In addition, a C-rate evaluation, in NMC/graphite cells, up to 20C was carried out. Figure 5 shows the C-rate evaluation of 1M LiPF6 in BN:EC (9:1) + 3% FEC compared to the reference organic carbonate-based 1M LiPF6 in EC:DMC (1:1) electrolyte. Two types of C-rate evaluations were performed to determine whether the C-rate for charge (Figure 5a,b) or the C-rate for discharge (Figure 5c,d) has a more pronounced impact on the cycling stability of the NMC/graphite cells. In the first C-rate evaluation, the charge current is altered from 0.1C to 20C, whereas the C-rate of the discharge step was kept constant. In the second C-rate evaluation, the C-rate of the charge step remained constant while the C-rate of the discharge step was changed. The C-rate evaluation started with five formation cycles at 0.1C followed by five cycles at 1C.

When comparing the overall performance of the considered NMC/graphite cells with 1M LiPF6 in BN:EC (9:1) + 3% FEC and the 1M LiPF6 in EC:DMC (1:1) electrolytes, a better C-rate performance is achieved for the BN-based electrolyte containing cells, as depicted in in Figure 5a. Especially at a C-rate (charge step) of 5C and 10C, the specific discharge capacity is much higher for the BN-based electrolyte containing cell. At low C-rates (charge step), the specific discharge capacities of both electrolyte containing cells are quite similar. At 0.1C and 0.2C, the specific discharge capacity of the BN-based electrolyte containing cell has a value of 174 mAh/g and 160 mAh/g, respectively. On the other hand, the organic carbonate-based electrolyte containing cell delivers a specific discharge capacity of 172 mAh/g at 0.1 C and 154 mAh/g at 0.2C, which is nearly similar to the cell containing 1M LiPF6 in BN:EC (9:1) + 3% FEC. At 5C and 10C, the better electrochemical performance of the BN-based electrolyte containing cell becomes clear, as a discharge capacity of 125 mAh/g is reached, compared to the 82 mAh/g for the organic carbonate-based counterpart. Even though the specific discharge capacity of the BN-based cell is not constant at 10C, the specific discharge capacity value is 62 mAh/g, is higher compared to the 21 mAh/g obtained in the cell with the organic carbonate-based electrolyte. At a C-rate (charge step) of 20C, the BN-based electrolyte containing cell delivers a specific capacity of 8 mAh/g. The decrease of C-rate to 1C results in a stable cycling performance for both considered

cell chemistries. Nevertheless, the cell containing BN-based formulation has a slightly higher specific discharge capacity. The corresponding Coulombic efficiency values are depicted in Figure 5b.

**Figure 5.** Cycling profiles and Coulombic efficiencies of the NMC/graphite cells containing 1M LiPF6 in BN:EC (9:1) + 3% FEC and 1M LiPF6 in EC:DMC (1:1) electrolyte formulations cycled in a voltage range of 3.00–4.30 V using a C-rate procedure (**a**,**b**) the C-rate of the charge step is increasing while the C-rate of discharge step stays constant at 1C and a C-rate procedure (**c**,**d**) where the C-rate of the discharge step is increasing whereas the C-rate of the charge step stays constant at 1C.

For the C-rate (of the discharge step) performance, a similar behavior can be observed (Figure 5c). At low C-rates (of the discharge step), the electrochemical performance of both cells is nearly similar, whereas with increasing C-rate (discharge step), the cell with the BN-based electrolyte shows a much better performance. At 5C, a specific discharge capacity of 135 mAh/g is achieved. Increasing the discharge rate up to 10C, a value of 67 mAh/g is reached for the BN-based electrolyte containing cell. On the other side, the specific discharge capacity is much lower (101 mAh/g and 29 mAh/g, respectively) for the organic carbonate-based electrolyte containing cell. The decrease of the C-rate (discharge step) to 1C, results in stable cycling performance for both cell chemistries. Nevertheless, the cell containing BN-based electrolyte shows a higher specific discharge capacity (155 mAh/g vs. 144 mAh/g) at a C-rate (charge and discharge step) of one 1C after the 100th cycle. The corresponding Coulombic efficiency values are depicted in Figure 5d.

For both C-rate (both the charge and the discharge step) evaluations, it was shown that the cells containing a BN-based electrolyte outperform the organic carbonate-based counterpart. This is especially observed, at 5C and 10C. Even at higher C-rates (15C and 20C), a cell containing 1M LiPF6 in BN:EC (9:1) + 3% FEC electrolyte shows better electrochemical performance compared to the reference organic carbonate-based electrolyte counterpart. The simultaneous charge/discharge behavior of the considered BN-based cell and organic carbonate-based cell at different C-rates was evaluated further. As depicted in Figure 6, a similar behavior in terms of specific discharge capacity can be observed. An increase in the C-rate (of the charge and discharge step) results in higher difference between the specific discharge capacities of the cells containing BN-based electrolyte and the ones with the organic carbonate-based electrolyte. The cell containing BN as solvent shows much better cycling performance at higher C-rates (both charge and discharge), compared to the state-of-the-art electrolyte containing counterpart. At 1C, a specific discharge capacity of 154 mAh/g and 150 mAh/g for the cell containing organic carbonate-based electrolyte is achieved. By increasing the C-rate (both the charge and the discharge step) to 2C, the specific discharge capacity reach values of 140 mAh/g and 129 mAh/g, respectively, whereas an increase in the C-rate (both the charge and the discharge step to 10C results in a specific capacity value of 42 mAh/g and 22 mAh/g, respectively. After increasing the C-rate (both the charge and the discharge step) to 20C, the BN-based electrolyte containing cell reaches a specific capacity of 9 mAh/g in contrast to 1 mAh/g for the state-of-the-art electrolyte containing counterpart. After the C-rate (both the charge and the discharge step) is decreased to 1C again, both electrolyte containing cells exhibit a stable cycling behavior (for both Coulombic efficiency as well as specific discharge capacity). During cycling with a C-rate (both the charge and the discharge step) of 1C, the cells deliver specific discharge capacity of 151 mAh/g in case of the BN-based electrolyte and 148 mAh/g for the organic carbonate-based electrolyte. The corresponding Coulombic efficiency values are depicted in Figure 6b. Table 1 summarizes the results obtained from graphs presented in Figures 5 and 6 for the NMC/graphite cells cycled with 1M LiPF6 in BN:EC (9:1) + 3% FEC and 1M LiPF6 in EC:DMC (1:1) electrolytes, respectively.

**Figure 6.** Cycling profiles (**a**) and Coulombic efficiencies (**b**) of NMC/graphite cells containing 1M LiPF6 in BN:EC (9:1) + 3% FEC as well as 1M LiPF6 in EC:DMC (1:1), respectively as electrolyte, cycled in the voltage range of 3.00–4.30 V.


**Table 1.** Summary of solvents used in this work. Physical properties are reported at 25 ◦C if not stated otherwise [55].

<sup>a</sup> Viscosity (η) and relative permittivity (εr) values for EC are determined at 40 ◦C.

As data listed in Table 2 show, the cells containing BN-based electrolytes deliver higher specific capacity values at higher C-rate compared to their state-of-the-art electrolyte counterparts. The C-rate (discharge step) evaluation setup leads to higher specific discharge capacities compared to the other two C-rate evaluations. This might be explained on the basis of the intercalation and deintercalation steps on graphite: the deintercalation process for graphite is always favored therefore, higher discharge capacities can be reached for both electrolytes [57]. Based on the obtained results, the main use for the BN-based electrolyte formulation would be in applications with high demands to power, fast charge ability or even both.



As BN:EC (9:1) + 3% FEC electrolyte containing cells show remarkable C-rate performance, long-time cycling experiments were conducted to enable deeper characterization of the electrochemical behavior of the considered cell chemistry. In Figure 7, two different long-term cycling measurements (1000 charge/discharge cycles) were performed for the BN-based electrolyte containing NMC/graphite cell as well as the state-of-the-art electrolyte containing counterpart.

The afore mentioned C-rate evaluation was performed without using a constant voltage (CV) step after the charge step. A CV step is typically used to enhance the capacity of the graphite slightly, making sure, that the graphite is fully lithiated [67].

The long-time cycling measurements depicted in Figure 7 show that, without CV step, the long term cycling performance of the 1M LiPF6 in BN:EC (9:1) + 3% FEC containing cells (Figure 7c) is comparable to the state of the art electrolyte based on 1M LiPF6 in EC:DMC (1:1) cell counterparts, as depicted in Figure 7a. The 1st cycle Coulombic efficiency of the cell containing 1M LiPF6 in EC:DMC (1:1) electrolyte (87%) matches the Coulombic efficiency resulting with the 1M LiPF6 in BN:EC (9:1) + 3% FEC electrolyte (87% Coulombic efficiency). Ninety-nine percent Coulombic efficiency is reached in the second cycle for the state-of-the-art electrolyte as well as for the BN-based counterpart. From this point onwards, the Coulombic efficiency values of both cells containing considered electrolytes are nearly similar, amounting to ≈99% during the long-term cycling performance. In the initial cycles, in which SEI formation takes place, a specific discharge capacity of 177 mAh/g is reached for the cell containing BN-based electrolyte, whereas the one with the EC:DMC-based electrolyte shows a specific discharge capacity of 173 mAh/g. After the initial cycles (five cycles with 0.1C), the cells were cycled with 1C until the 1000th charge/discharge cycle. For both cell chemistries, a stable long-term cycling is observed, with an absence of strong fading in capacity. In the 10th cycle, a specific discharge capacity of 155 mAh/g is reached and decreases slightly to 129 mAh/g in the last (1000th) cycle, for the cell with 1M LiPF6 in BN:EC (9:1) + 3% FEC as electrolyte. For the cell containing 1M LiPF6 in EC:DMC (1:1) as electrolyte, a specific discharge capacity of 145 mAh/g in the 10th cycle and 135 mAh/g in the 1000th cycle is reached. Comparing the 10th cycle with the 1000th cycle, both electrolytes reach over 80% of the initial capacity, meeting the automotive requirements (80% state of health after 1000 charge/discharge cycles).

**Figure 7.** Long-term cycling profiles of the NMC/T44graphite cells containing electrolyte formulations: (**a**) 1M LiPF6 in EC:DMC (1:1) without cyclic voltammetry (CV) step (cell a), (**b**) 1M LiPF6 in EC:DMC (1:1) including CV step (cell b), (**c**) 1M LiPF6 in BN:EC (9:1) + 3% FEC without CV step (cell c), (**d**) 1M LiPF6 in BN:EC (9:1) + 3% FEC including CV step (cell d) in the voltage range of 3.00–4.30 V.

For the long-term evaluations comprising a current-limited constant voltage step the results are different. The long-term cycling performance of the 1M LiPF6 in BN:EC (9:1) + 3% FEC (Figure 7d) is decreased compared to the state-of-the-art electrolyte-based cell depicted in Figure 7b. The 1st cycle Coulombic efficiency of the 1M LiPF6 in EC:DMC (1:1) electrolyte (87%) containing cell is similar to the Coulombic efficiency obtained for the 1M LiPF6 in BN:EC (9:1) + 3% FEC electrolyte (86% Coulombic efficiency) based counterpart. The Coulombic efficiency of 99% for the state-of-the-art electrolyte containing cell is reached in the second cycle. For the BN-based electrolyte containing cell, a Coulombic efficiency amounts to o 99% only in the 4th cycle. From this point onwards, the Coulombic efficiency values of both electrolyte containing cells are nearly similar, >99% prolong the long-term cycling. During the initial cycles, a specific discharge capacity of 174 mAh/g is reached for the BN-based electrolyte containing cell, whereas the one with the EC:DMC-based electrolytes displays a specific discharge capacity of 175 mAh/g. After the initial cycles (five charge/discharge cycles with 0.1C), the cells were cycled at 1C until the 1000th cycle. Both cells passed the long-term cycling procedure, thus indicating a good cycling performance. However, a slight fading of the cell with the BN-based electrolyte (Figure 7d) is noticeable. In the 10th cycle, a specific discharge capacity of 161 mAh/g is reached and decreases to 100 mAh/g in the 1000th cycle, for the cell with 1M LiPF6 in BN:EC (9:1) + 3% FEC as electrolyte. For the cell containing 1M LiPF6 in EC:DMC (1:1) as electrolyte, a specific discharge capacity of 159 mAh/g in the 10th cycle and 139 mAh/g in the 1000th cycle is reached. Comparing the 10th cycle with the 1000th cycle only the state of the art electrolyte has reached over 80% of the initial capacity, meeting the automotive requirements [68]. Table 3 summarizes afore mentioned cycling performance and comperes both cycling procedures (with and without CV step).

The capacity retention values show, that a CV step deteriorates the electrochemical performance of the NMC/graphite cells. The same effect is observed with the reference electrolyte containing cell however, the effect is less pronounced. This outcome is explained by the time at which the cells remain at the cut-off voltage. For the cells cycled with a CV step, this duration is much larger and is leading to a pronounced degradation (shorter lifespan) of these cells. To correlate the obtained results with the surface chemistry of electrodes containing BN-based electrolyte, XPS sputter depth profiling of graphite electrodes was performed, to prove the stability of the electrolyte towards graphite. The electrochemical decomposition of considered BN-based electrolyte formulations on the graphite surface was analyzed by means of XPS (see Figure 8).

**Table 3.** 1st Coulombic efficiency, discharge capacity as well as capacity retention between the 10th and 1000th cycle for the reference electrolyte (cells a/b) and the nitrile-based electrolyte formulation (cells c/d) containing cells.


**Figure 8.** F 1s and N 1s core spectra of graphite electrodes, after five charge/discharge cycles at 0.1C in a NMC/graphite cells with different amounts of FEC in the electrolyte: (**a**,**b**) 1M LiPF6 in BN, (**c**,**d**) 1M LiPF6 in BN + 5% FEC, (**e**,**f**) 1M LiPF6 in BN:EC (9:1) + 2% FEC, (**g**,**h**), 1M LiPF6 in BN:EC (9:1) + 3% FEC and (**i**,**j**) pristine electrode.

Figure 8 depicts the XPS F 1s and N 1s core spectra of graphite electrode-based cells cycled in presence of a,b) 1M LiPF6 in BN; c,d) 1M LiPF6 in BN with 5% FEC; e,f) 1M LiPF6 in BN:EC (9:1) + 2% FEC; as well as g,h) 1M LiPF6 in BN:EC (9:1) + 3% FEC as electrolyte. As reference spectra, the XPS F 1s and N 1s core spectra of a pristine graphite electrode (Figure 8i,j) are shown. In the F 1s spectra (Figure 8i), a signal located at 687 eV is observable, which can be attributed to the polyvinylidene difluoride (PVdF) binder [69]. The decrease of the peak intensity during sputtering is related to the decomposition of the binder during XPS measurement [70]. On the other hand, no nitrogen

signal was observed on the pristine electrode surface (Figure 8j). In the F 1s spectra of the cycled electrodes (Figure 8a,c,e,g), an additional signal attributed to lithium fluoride (LiF), formed due to the decomposition of the conducting salt LiPF6, occurs at 685 eV. As depicted in Figure 8a,c the amount of LiF remains unaffected relatively to the intensity of the PVdF peak with increasing the sputter time. This could be explained by a limited degradation of LiPF6 in the BN-based electrolytes without EC. Due to the severe decomposition of BN, the corresponding peaks overlap the peaks assigned to the decomposition of LiPF6. In addition, in the N1s core spectra of the electrodes containing pure BN-based electrolyte (Figure 8b,d) a signal at 399 eV is observed, attributed to the decomposition of the nitrile during cycling. In the absence of BN decomposition, the peak of LiF increases relatively to the PVdF peak with increasing the sputter time (Figure 8e,g), as LiF is the main component of the inorganic part of the SEI [70]. The increase of the LiF peak indicates absence of decomposition, meaning that a SEI was formed on graphite surface. Nevertheless, the N 1s core spectra of the graphite electrode cycled with 1M LiPF6 in BN:EC (9:1) + 2% FEC, exhibit a peak 399 eV related to BN decomposition, thus indicating that the formed SEI does not fully prevent the decomposition of the nitrile. By adding 3% FEC to the BN:EC (9:1) electrolyte formulation, the peak in the corresponding N1s core spectrum at 399 eV disappears (Figure 8h), thus indicating an effective SEI formation, which prevents BN against decomposition. Table 4 lists the corresponding surface concentration given in arbitrary units (a.u.).

**Table 4.** Surface concentration on graphite in arbitrary unit (a.u.) of the performed XPS measurements using different BN-based electrolytes.


For the electrodes with pure BN-based electrolyte, as well as for the electrolyte formulation containing 5% FEC, only small amounts of LiF were detected. The origin of the spectra can be dedicated to the decomposition of small amounts of the conducting salt LiPF6. The N 1s surface concentration for both electrolytes indicates a severe decomposition of BN. Without formation of an effective SEI, an ongoing decomposition of the solvent (BN) takes place. For the electrolyte formulations BN:EC (9:1) with addition of 2% and 3% FEC respectively, the amount of LiF increases during sputtering [70,71]. The intensity of the N 1s signal decreases for both electrolytes corresponding to a less pronounced

decomposition of the BN-solvent. However, regarding the N 1s surface concentration, the addition of 2% FEC is not enough for the formation of an effective SEI on graphite. The N 1s surface concentration of the formulation containing 3% FEC is comparable to the N 1s surface concentration of the reference electrode, however, both do not show a significant signal.

#### **4. Conclusions**

With two successfully tuned BN-based electrolyte formulations (one used in half-cell and the other in full-cell configuration), the decomposition on both lithium metal and graphite, could be prevented. Both electrolytes were comparable or even better compared to the state-of-the-art organic carbonate-based electrolyte. In half cell experiments, 1M LiPF6 in BN:FEC (1:1) containing cell showed the most promising results. EC was compared to FEC, due to its lower passivation capability towards metallic lithium, not suitable to protect BN against decomposition. Nevertheless, 1M LiPF6 in BN:FEC formulation showed lower ion conductivity values compared to BN:EC counterparts. Especially at low temperatures around 0 ◦C, the conductivity of the BN:EC-based electrolytes was at least 32% higher (7.69 mS/cm) compared to the BN:FEC-based and the organic carbonate-based electrolyte (5.83 mS/cm). Since the main focus of this paper is related to the possible the automotive applicability of BN, investigations in NMC/graphite cells containing BN:EC-based electrolytes were studied in detail. In each investigation, the cell containing 1M LiPF6 in BN:EC (9:1) + 3% FEC showed a superior high performance compared to the organic-carbonate-based counterpart. To match automotive requirements, a C-rate evaluation of 5C was performed. It was shown, that the average specific discharge capacity at 5C amounted to ≈103 mAh/g for the investigated BN-based electrolyte containing cell, which was nearly twice the capacity of the cell with the reference electrolyte (≈66 mAh/g). Further, a C-rate evaluation up to 20C was performed. The cells containing investigated BN-based electrolyte formulation showed a superior C-rate performance compared to the organic state of the art counterpart. In addition, the CV step in the CCCV measurements, typically used in case of organic carbonate-based electrolyte containing cells, was investigated. It was found out, that a CV step increases the charge/discharge capacity at the beginning of the cycling procedure so that more lithium ions can be intercalated into graphite. Nevertheless, the CV step reduces the overall cycle-life of the cell as well, due to the pronounced electrolyte degradation. In the long-term cycling experiment (Figure 7c,d) the advantage of the CV step is lost after the 150th cycle. From the 150th cycle onwards the capacity of the cell cycled without CV step is higher compared to the cell cycled with CV step.

XPS analysis of the NMC electrodes complements well to the electrochemical characterization of the BN-based electrolytes, showing that a minimum amount of 3% FEC is needed to prevent the BN-based electrolyte formulation of 1M LiPF6 in BN:EC (9:1) from decomposition on graphite in NMC/graphite cell setup.

**Author Contributions:** P.H., I.C.-L. and M.W. conceived and designed theexperiments; P.H. and L.I. performed the experiments; P.H., L.I., I.C.-L. and M.W. analyzed the data; P.H. and I.C.-L. wrote the paper.

**Funding:** Financial support by the German Federal Ministry for Education and Research (BMBF) within the project Electrolyte Lab 4E (project reference 03X4632) is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Overview and Comparative Assessment of Single-Phase Power Converter Topologies of Inductive Wireless Charging Systems**

#### **Phuoc Sang Huynh \*, Deepak Ronanki, Deepa Vincent and Sheldon S. Williamson \***

Smart Transportation Electrification and Energy Research (STEER) Group, Department of Electrical, Faculty of Engineering and Applied Science, Computer and Software Engineering, University of Ontario Institute of Technology (Ontario Tech University), Oshawa, ON L1G 0C5, Canada; dronanki@ieee.org (D.R.); deepa.vincent@ontariotechu.net (D.V.)

**\*** Correspondence: phuoc.huynh@ontariotechu.net (P.S.H.); sheldon.williamson@uoit.ca (S.S.W.)

Received: 22 March 2020; Accepted: 22 April 2020; Published: 1 May 2020

**Abstract:** The acquisition of inductive power transfer (IPT) technology in commercial electric vehicles (EVs) alleviates the inherent burdens of high cost, limited driving range, and long charging time. In EV wireless charging systems using IPT, power electronic converters play a vital role to reduce the size and cost, as well as to maximize the efficiency of the overall system. Over the past years, significant research studies have been conducted by researchers to improve the performance of power conversion systems including the power converter topologies and control schemes. This paper aims to provide an overview of the existing state-of-the-art of power converter topologies for IPT systems in EV charging applications. In this paper, the widely adopted power conversion topologies for IPT systems are selected and their performance is compared in terms of input power factor, input current distortion, current stress, voltage stress, power losses on the converter, and cost. The single-stage matrix converter based IPT systems advantageously adopt the sinusoidal ripple current (SRC) charging technique to remove the intermediate DC-link capacitors, which improves system efficiency, power density and reduces cost. Finally, technical considerations and future opportunities of power converters in EV wireless charging applications are discussed.

**Keywords:** AC–AC converters; battery chargers; electric vehicles; power conversion harmonics; wireless power transmission

#### **1. Introduction**

The electrification of transportation has been considered as a promising solution to tackle greenhouse gas emissions and fossil fuel depletion. To boost the market share of electric vehicles (EVs), their inherent issues such as limited driving range, long charging time, and costly and cumbersome energy storage systems should be resolved. Wireless charging technology can mitigate the aforementioned issues [1–10]. Wireless power transfer (WPT) enabling transferring energy from a source to a load without electrical contact has been extensively studied and successfully demonstrated using various techniques, namely, acoustic power transfer (APT) [11,12], radio frequency power transfer (RFPT) [13,14], optical power transfer (OPT) [15,16], capacitive power transfer (CPT) [17], and inductive power transfer (IPT) [18]. However, it is well demonstrated from the literature that the IPT technology is the most suitable for EV charging applications where the power requirement is form few to several kW, and the air gap varies from a few centimeters to a few meters [5]. Particularly, researchers and engineers have fitted the outcomes of the IPT to EV battery charging applications with various commercial products and standards [19]. The IPT chargers offer with several benefits such as safety, convenience, flexibility, weather immunity, and the possibility of range extension and battery volume reduction [1,8,10,20,21]. The wireless chargers can be deployed in residential garages, and office/service/shopping center parking lots for static wireless charging [22], or they can be placed at bus stops, taxi ranks, and traffic lights to implement quasi-dynamic wireless charging [23]. Moreover, dynamic wireless charging systems can be installed on the roads to constantly charge the EVs, in turn, to extend the driving range and reduce the battery volume of the vehicles [24–26].

Essentially, an IPT charging system comprises an inductive coupling coil pair, compensation networks, primary converters to generate high-frequency inputs, and a secondary rectifier to convert AC to DC current to charge the battery. In the IPT charging systems, power electronic converters make a significant contribution to the size and cost, and efficiency of the overall system. Typically, dual-stage conversion (AC–DC–AC) systems have been employed to excite the IPT systems, as shown in Figure 1a. The dual-stage converter topologies are intensively studied and widely used in industry [27–29]. The main advantage of these topologies is that each conversion stage can be separately designed and controlled to optimize specific performance indices. However, the presence of multiple conversion stages and a bulk DC-link capacitor increases the cost, size, and weight of the system. In recent years, the use of matrix converters (MCs) for feeding the IPT systems has drawn increasing attention [30–38]. MCs enable direct conversion of low-frequency AC inputs (50–60 Hz) to high-frequency outputs (up to 85 kHz) without any intermediate conversion stage; therefore, they enhance the system performance in terms of power density, reliability, and cost [32,39]. The single-phase matrix converter-based IPT systems remove the DC-link energy storage elements in the primary side to absorb double line frequency ripple, thus it appears on the battery side. Sinusoidal ripple current (SRC) charging technique reported in [40–45] allows batteries to be charged by double line frequency (100 or 120 Hz) current with minor side effects on their performance. Therefore, matrix converter-based IPT systems can use the sinusoidal charging technique advantageously and remove the intermediate DC-link capacitor. The single-stage EV IPT charging system using MCs is illustrated in Figure 1b.

**Figure 1.** Configuration of electric vehicle (EV) inductive power transfer (IPT) systems with (**a**) dual-stage power conversion and (**b**) single-stage power conversion. PFC, power factor correction; EMI, electromagnetic interference.

This paper aims to provide an extensive overview of single-phase power conversion topologies employed in static wireless charging. Then, a comprehensive performance comparison between the conventional dual-stage (power factor correction (PFC) and full-bridge voltage source inverter (VSI)) and single-stage topologies including the buck-derived full-bridge (FB)MC and boost-derived FBMC

in the IPT EV charging application is presented. The comparison involves the input power factor, input current distortion, power losses, switching stress, and normalized cost, while taking into account the requirements of Standard J2954 [19] established by the Society of Automotive Engineers (SAE). The Standard SAE J2954 defines acceptable criteria for interoperability, electromagnetic compatibility, electromagnetic field (EMF), minimum performance, safety, and testing for wireless charging of light-duty electric vehicles. Table 1 shows the power classes, operating frequency, and efficiency performance targets of the WPT systems defined in the SAE J2954. As can been seen, four wireless power transfer (WPT) classes are defined based on the maximum input volt-amp (VA) drawn from the grid by the primary side or ground assembly (GA) electronics. The input real power depends on the input power factor, while the output power depends on the efficiency of the system. The SAE J2954 specifies that WPT systems should be operated at a single nominal frequency of 85 kHz. However, for WPT systems using frequency control to compensate operating variations, their operating frequency must be tuned in the band of 81.38 to 90.00 kHz. Finally, the improvement opportunities for each of the IPT charging topologies are discussed in this paper.

**Table 1.** Wireless power transfer (WPT) power classification for light-duty electric vehicles—SAE J2954.


#### **2. Power Converter Topologies for Inductive Wireless Charging**

In this section, an overview of front-end converter topologies for WPT applications is provided. They can be classified into two groups, namely dual-stage and single-stage based on the power conversion stages. The classification of single-phase converter topologies for IPT systems is shown in Figure 2.

**Figure 2.** Classification of front-end converter topologies for IPT applications. FB, full-bridge; WPT, wireless power transfer.

#### *2.1. Dual-Stage Power Conversion*

A front-end AC–DC converter is used to convert the supply AC voltage to an intermediate DC-link voltage and to shape the input current for both PFC and harmonic reduction. A comprehensive review for the PFC rectifiers is presented in [46,47]. For the inversion stage, a current-source inverter (CSI) or a VSI can be employed.

Two CSI topologies commonly used in IPT systems are push-pull, half-bridge [48–53], and full-bridge [54,55]. Figure 3a–c shows the configuration of CSIs. The requirement of blocking diodes and bulky inductors that increases the size and cost of the whole IPT system is one of the major drawbacks of the CSIs. A single parallel compensating capacitor in the primary circuit is normally used with CSIs; however, the inverter switches suffer high voltage stress in high-power applications [48,50,52,54]. In order to overcome this drawback, a parallel-series *CC* compensation circuit is introduced in [53,55]. The CSIs combined with the parallel-series *CC* compensation circuit mitigates current and voltage stress on inverter switches and harmonic contents in primary coil current.

**Figure 3.** Inverter topologies: (**a**) push-pull, (**b**) half-bridge CSI, (**c**) full-bridge CSI, (**d**) buck, (**e**) half-bridge VSI, and (**f**) full-bridge VSI.

For VSI topologies, buck, half-bridge, and full-bridge topologies shown in Figure 3d–f can be used in the IPT systems, and they are compatible with single capacitor series, *LCL*, and *LCCL* compensation networks [1,21,56–66]. The series compensation is simple and cost-effective. However, under light load conditions or in the absence of the receiver, the system experiences severe instability [67,68]. *LCL* or *LCCL* tanks overcome these issues and have a high tolerance to coil misalignments [68]. However, a significant amount of lower-order harmonics in the output current of the VSIs connected with *LCL* and *LCCL* compensation circuits deviates zero-phase-angle operation of the inverters, increasing their switching losses [69]. Moreover, the inductors in *LCL* and *LCCL* compensation circuits must be designed precisely as the effective power transfer capability is highly sensitive to the inductance value [57,61]. Figure 4 shows the compatibility of the inverter types and primary compensation circuits of the IPT systems. Table 2 shows the comparison of the inverter topologies regarding the component requirement. It can be seen that the CSIs require more components than the VSIs.

**Figure 4.** Compatibility between inverter types and primary compensation circuits in IPT systems. (**a**) Series *C,* (**b**) *LCL,* (**c**) *LCCL,* (**d**) parallel *C,* and (**e**) parallel-series *CC*.

**Figure 5.** Single-stage conversion topologies: (**a**) buck matrix converter, (**b**) half-bridge matrix converter, (**c**) full-bridge matrix converter, (**d**) boost-derived matrix converter, and (**e**) bridgeless boost converter.



#### *2.2. Single-Stage AC–AC Conversion*

Matrix converters (MCs) are considered as a prominent candidate for powering the WPT systems with only single-stage power conversion. Several MCs including buck [36,37], half-bridge [30,31], and full-bridge [35] have been introduced to IPT applications in the literature. All MCs reported in [30,31,35–37] have a buck-derived configuration, as shown in Figure 5a–c, thus line-current regulation is compromised. In EV charging application, if a highly nonlinear diode-bridge rectifier is used at the battery side, there will be severe line current distortion and power factor deterioration, as explained in [70]. In [35], a secondary active full-bridge rectifier whose phase shift angle follows the line-voltage waveform is used to shape the line current. In this topology, the primary and secondary converters must be controlled synchronously in every switching cycle, which increases the implementation complexity.

In order to overcome the above issue, a boost-derived full-bridge MC (FBMC) compatible with a primary parallel-series *CC* compensation network is proposed in [38]. The proposed converter topology is able to shape the line current and regulate power flow through two control loops, which are similar to those of a conventional boost converter. In [39], a single-stage topology integrating bridgeless boost PFC converter and full-bridge VSI is proposed for IPT applications. The converter is operated in discontinuous conduction mode, thereby, the line current control loop is eliminated. However, in discontinuous conduction mode (DCM), the converter incurs more current stress, losses, and electromagnetic interference (EMI) problems, which is not suitable for high-power applications. Figure 5d and e show the configuration of boost-derived FBMC and bridgeless boost PFC converter in IPT systems.

#### **3. Power Control Schemes**

Figure 6 shows the classification of power control schemes for IPT systems. Power control in IPT systems can be implemented on the primary side, secondary side, or both sides. The secondary side control is suitable for the IPT applications where multiple secondary coils are coupled to a single primary coil. In these applications, the frequency and the magnitude of primary current are fixed, and the power flow is controlled on the secondary side by an active rectifier or a back-end DC–DC converter illustrated in Figure 6 for each secondary coil [30,58,59,71–74]. These topologies are normally employed in long-power track systems where a constant track current is required to power independent secondary coils.

**Figure 6.** Classification of power control schemes for IPT applications.

However, in charging applications where only one a secondary coil is coupled to a primary coil and keeping the secondary-side configuration as simple as possible is a priority, the primary side control is selected. The primary side control can be divided into three groups: fixed frequency, variable frequency, and discrete energy injection. In fixed frequency control, the switching frequency of the inverter is kept at a constant value, which is slightly different from the primary resonant frequency to offer soft-switching operation. In order to control the power flow, the phase (phase shift control) or the duty cycle of the inverter switches is varied [75,76]. This allows the inverters to produce output voltage/current with variable pulse width. The other way to regulate the power flow with the fixed switching frequency is controlling the input DC voltage of the inverter using a front-end DC–DC converter [48]. For the variable switching frequency control scheme, the duty cycle of the gating signals is maintained constant at 50% and the switching frequency is varied to regulate the output power [49]. However, if the operating frequency is largely different from the resonant frequency, the resonant tank will incur a large circulating current, causing an efficiency drop in the overall system owing to large losses in switches and the coils. Moreover, the bifurcation phenomenon must be carefully considered in this control technique [77]. In [36], a discrete energy injection control is used for the matrix buck converter in order to control the magnitude of the primary current. The control technique reduces the switching frequency and enables soft switching. However, the zero-crossing detection of primary high-frequency current that is required to ensure the converter to be operated in zero current switching (ZCS) conditions is an implementation challenge. Moreover, current sag occurs during the zero-crossing of its single-phase input voltage, which degrades the average power transferred. The dual-side control is suitable for bidirectional IPT systems where power flow can be regulated in both directions by controlling the duty cycle of the primary and secondary converters and the phase-shift between them [56,57,78]. Table 2 shows the compatibility of power conversion topologies and control schemes of the IPT applications.

#### **4. Performance Comparison and Discussion**

In this section, the performance of a conventional dual-stage topology and two potential single-stage topologies including buck- and boost-derived FBMCs are compared regarding input power quality, current stress, voltage stress, power losses, and cost.

#### *4.1. Design Considerations*

The conventional dual-stage IPT charging system is illustrated in Figure 7a. At the front end, a conventional boost rectifier is used to shape the grid current and maintain a constant DC voltage *Vdc* across DC-link capacitor *Ci*. As a bulky and costly inductor is required for the CSIs, an FBVSI is the most common choice at the primary side to generate a high-frequency voltage (*vp*) feeding the primary coil. A series-series (SS) compensation topology is used because it is simple and cost-effective, and its primary compensation is independent of the coupling coefficient and load. Moreover, the efficiency of SS compensation is high even at a low coupling coefficient [68,79]. In order to maximize the power transfer capabilities and minimize the VA rating of the primary inverter, the resonant circuits at both sides of the coupling are usually tuned to the same resonant frequency (ω0) equal to the switching frequency of the inverter.

$$
\omega\_0 = \frac{1}{\sqrt{L\_p \mathbb{C}\_p}} = \frac{1}{\sqrt{L\_s \mathbb{C}\_s}} \tag{1}
$$

where *Lp* and *Ls* are primary and secondary coil self-inductances, respectively, and *Cp* and *Cs* are primary and secondary tuning capacitors, respectively.

Power regulation is conducted using the phase-shift control at the primary inverter side. Considering an ideal IPT system operating at the resonance frequency (ω0), power transferred from the primary to the secondary side can be given by

$$P\_o = \frac{8V\_{dc}V\_b}{\pi^2 a v\_0 M} \sin \pi D\_p \tag{2}$$

where *Dp* is the duty cycle of the primary voltage (*vp*) and *M* is the mutual inductance and can be calculated as

$$
\Delta M = k \sqrt{\mathcal{L}\_p \mathcal{L}\_s} \tag{3}
$$

**Figure 7.** IPT charging system fed by (**a**) dual-stage power converter (PFC and full-bridge VSI), (**b**) buck-derived FBMC, and (**c**) boost-derived FBMC.

In EV wireless charging applications, the coupling coefficient *k* may be in the range of 0.1–0.3. In a dual-stage topology, the major drawback is low power density owing to multiple conversion stages and a bulky DC-link capacitor. The reduction of the number of power conversion stages can be obtained using MCs. Figure 7b shows the IPT charging system using a buck-derived FBMC. The FBMC constituted by four bidirectional switches can directly convert low frequency (50–60 Hz) grid voltage to resonant frequency (85 kHz) voltage feeding the inductive coil. During the positive half cycle of the grid voltage *vg*, switches *Spnb* (*n* = 1, 2, 3, 4) are turned on and switches *Spna* are the phase-shift pulse-width modulation (PWM) strategy. Otherwise, during the negative half-cycle, the switches *Spna* are kept on and switches *Spnb* are controlled by the phase-shift PWM strategy.

An active rectifier is employed in the battery side for shaping the input current. The primary and secondary converters are synchronized in every switching cycle so that primary voltage *vp* is 90◦

lagging with secondary voltage *vs*, and the duty cycle of the secondary voltage is controlled following grid voltage waveform to correct input current, as shown in Figure 7b. The power transferred is controlled by adjusting the duty cycle of the primary voltage.

$$P\_o = \frac{4\sqrt{2}V\_{\frac{\nu}{\mathcal{S}}}V\_b}{\pi^2 \alpha\_0 M} \sin \pi D\_p \tag{4}$$

where *Vg* is the root mean square (RMS) value of the grid voltage.

Although the buck-derived FBMC-based IPT charging system removes the intermediate conversion stage, high-frequency communication is required to synchronize the PWM patterns of the primary and secondary converters in every switching cycle, which increases the control complexity. The boost-derived MC can solve the above issue. It is capable of correcting the grid current and regulating power flow through two control loops, which are similar to those of a conventional boost converter. Figure 7c shows an IPT topology fed by a boost-derived FBMC [38]. On the primary side, parallel-series *CC* compensation is used to reduce voltage stress on the MC switches. The tuning capacitor *Cps* is selected so as to limit the maximum peak of *vp* across the converter switches. It is desirable to restrict *vp* to 0.5~0.7 of the rating voltage of the switches [48]. The switching scheme and controller design for the boost-derived full-bridge matrix converter are described in [38]. Tables 3 and 4 show the passive component design and the switching stresses of the converter components.


**Table 3.** Passive component design. FB, full-bridge.


**Table 4.** Stress on switching devices.

#### *4.2. Performance Comparison*

In this section, the performance of IPT configurations is compared in terms of input power factor, input current distortion, current stress, voltage stress, power losses on converters, and normalized cost. The IPT charging systems are designed in compliance with the level 1 (WPT1) of static wireless charging standard for light-duty vehicles provided in SAE J2954 technical information report [19] with power rating *Po* = 3.3 kW, operating frequency *fs* = 85 kHz, grid voltage *Vg* = 208 V, and battery voltage *Vb* = 300–400 V. The parameters of the charging system with each type of power conversion configuration are shown in Table 5. All the components are designed based on Tables 3 and 4. The selection of components is based on their maximum current and voltage stresses. Note that available discrete Rohm SiC MOSFETs and Schottky diodes are considered for all power conversion topologies. Moreover, *LC* filters are used as interfaces between the grid and the charging systems to limit current harmonic injection owing to the switching power converters. The *LC* filters are designed based on the spectrum analysis of the input current waveforms (*ii*). The details of the selected components for different power conversion stages are listed in Table 6.

Figure 8 shows the typical waveforms of IPT charging systems with different power supply topologies. It can be seen that the absence of DC-link energy storage in MC-based topologies causes a double line frequency fluctuation in transferred power. This results in a fluctuating charging current as shown in Figure 8b and c. As reported in [40–44,83,84], batteries can be charged by double line frequency (100 or 120 Hz) current with negligible side effects on their performance.



**Table 6.** Main components of power conversion stages.


\* *n* = 1, 2, 3, 4.

**Figure 8.** Simulation waveforms of IPT charging systems fed by (**a**) dual-stage power converter (PFC and full-bridge VSI), (**b**) buck-derived FBMC, and (**c**) boost-derived FBMC.

#### 4.2.1. Input Power Factor and Input Current Distortion

An EV charger must ensure a good grid power quality with a high power factor and low current distortion. All three topologies provide sinusoidal grid currents with the power factor of 0.99. Figure 9a shows total harmonic distortion (THD) of the grid current under different load conditions (20%, 50%, and 100% of load). It can be seen that the three topologies can be preferred in order of boost-derived FBMC, dual-stage converter, and buck-derived FBMC, regarding grid current distortion. Despite having the identical input *LC* filter, the buck-derived FBMC injects higher current harmonics to the grid than dual-stage topology, because its input current is discontinuous. The boost-derived FBMC has

the continuous input current with ripple frequency at a twofold switching frequency, thereby gaining the significant harmonic reduction of grid current with a smaller input filter.

**Figure 9.** Performance comparison of three IPT charging systems: (**a**) grid current total harmonic distortion (THD), (**b**) switch current stress, (**c**) switch voltage stress, and (**d**) power-conversion-stage efficiency.

#### 4.2.2. Switching Stress

Figure 9b and c show the maximum current and voltage stress on the converter switches. Although the parallel-series *CC* compensation is used, the switches of boost-derived FBMC still suffer from high voltage stress. The buck-derived FBMC is characterized by low switch voltage stress (grid voltage peak) and high switch current stress. The dual-stage topology exhibits the lowest switch current stress in the primary inverter and secondary rectifier.

#### 4.2.3. Efficiency and Loss Distribution

The losses on the conversion stages of each system are simulated and analyzed using the thermal modules in PSIM simulation. The efficiency of the power conversion stages of each system versus various output power is illustrated in Figure 9d. It is clear that the efficiency of the buck-derived FBMC system is the highest (almost 98%) at full load conditions, but it decreases gradually to 93% at the light load conditions. In contrast, the efficiency of the boost-derived FBMC system steadily increases from 92.5% to 96% when the load decreases from 100% to 20%. The dual-stage system maintains fairly high efficiency (94~96.5%) in a wide load range.

The detailed loss distribution of the three systems is shown in Figure 10. It can be observed that the conduction losses of primary converters dominate the total losses of power conversion stages. In the dual-stage system, the conduction losses of the front-end rectifier and the primary inverter are the two major parts. For the single-stage systems, the conduction losses of matrix converters contribute to the largest proportions (>60%).

#### 4.2.4. Cost

Cost is also an important quantity to evaluate the performance of a power converter. The cost structure of each charging system excluding inductive coupling coils and compensation networks is illustrated in Figure 11. The costs of the power conversion stages are calculated based on the component cost provided in Table 7. In order to simplify the cost analysis, the auxiliary cost including printed circuit board (PCB) cost, cooling system cost, and housing cost is assumed to be 10% of the power converter cost. Note that MOSFETs are driven by isolated gate drivers, and MOSFETs having common-source connection utilize a common gate driver power supply to reduce the system cost. This shows that the cost of single-stage systems is lower than that of the dual-stage counterpart. The buck-derived FBMC system is the most cost-effective solution, as it presents 8.4% less cost than the dual-stage system. It is found that the costs of the passive components dominate in the dual-stage system, whereas the semiconductor devices of matrix converters occupy the largest portions in the total cost of the single-stage systems.

**Figure 11.** Component cost structure of the charging system excluding inductive coupling coils and compensation networks.


**Table 7.** Cost of components.

#### *4.3. Discussions*

From the above analysis, it can be observed that the three IPT charging systems have their own advantages and disadvantages. A comparison summary of the three IPT charging systems is shown in Figure 12, where performance indices are presented in a scale range from 1 (worst) to 3 (best). In order to evaluate the efficiencies of the three systems, their average values under all load conditions are considered. The switching stresses are assessed based on the product of the maximum current and voltage stresses. Figure 12 shows that the buck-derived FBMC surpasses the other counterparts with the advantages of high efficiency, cost reduction and possible power density improvement due to less component count, while the boost-derived FBMC has the greatest input current quality due to the feature of the continuous input current with ripple frequency at a twice switching frequency. The conventional dual-stage topology has the lowest stress on switching devices, and its efficiency maintains a comparable high level over wide load range. Moreover, the dual-stage converter topology is highly matured in terms of manufacturability and control as it has been developed by many manufacturers and widely used in the industry. Also, this topology allows each converter stage to be separately designed and optimized.

**Figure 12.** Comparison summary of the dual-stage and single-stage IPT charging systems.

#### **5. Future Trends and Opportunities**

Over the past decade, there have been significant developments in power converter topologies and control schemes for EV IPT charging. One of the important challenges is the design of high-frequency power converters for IPT to meet future requirements. Still, there is a lot of scope for further improvements to enhance the performance in terms of efficiency, power density, scalability, and reliability to promote the IPT-based systems for EV charging. Reducing power losses in power conversion from the source to the input of the coil is a vital factor in improving efficiency. One of such initiatives is to develop advanced soft-switching modulation techniques for the existing converter topologies and new reduced-switch-count converter topologies to reduce switching losses. This is expected to improve the thermal design and power density of the overall system. Several soft-switching control schemes have been reported in the literature. Generally, they can be divided into three groups: with auxiliary DC-DC converters [85–87], with variable resonant networks [88,89], and with active inverter/rectifier control [59,90–92]. However, the proposed control schemes require extra DC-DC converters or resonant components, or have an operation range limitation and high control complexity.

Direct power conversion topologies such as matrix converters can be one of the possible candidates with the elimination of life-limited bulky DC capacitors employing enhanced charging techniques like SRC charging. Another important performance enhancement is employing wide bandgap devices in the existing converter topologies or development of advanced topologies, which can operate at higher switching frequencies with low switching losses [93]. This can boost the performance of power converters in the wireless charging applications [94]. The application of gallium nitride (GaN) in IPT systems has opened up a new scope in improvement in power transfer and power density. These devices have a low voltage drop, ability to operate at the higher switching frequency, and comparatively lower thermal generation during operation, which allows for passive cooling to increase the converter power density and cost-effectiveness [95]. However, some challenges regarding the manufacturing process, packaging with higher current ratings, the gate driver design, device characterization, busbar

layout, thermal management, and reliability need to be addressed. Therefore, much more research initiatives in the aforementioned issues could decide the power density of the converter. In addition, employing the GaN devices allows an increase in switching frequencies even at higher current standards, which improves the performance of WPT, such as transfer distance extension, higher tolerance to coil misalignment, and passive component size reduction. Furthermore, the magnetic integration can be used to integrate magnetic components of power converters, compensation networks, and coupling coils, in turn, to enhance using higher flux density material to reduce the system size and losses. One of the possible ways is the utilization of advanced materials and nanotechnology to reduce the size and weight of passive components.

In the recent days, modular power converters with fault-tolerance are demanded due to industrial requirements such as flexibility in assembly, manufacturing process, scalability and reduced mean time to failure (MTTF). Some of the possible potential candidates are multiphase parallel inverter [96], modular multilevel converter [97], parallel IPT power supply topologies [98] and extreme fast charging architectures [99] to improve the output power capability and fault tolerance for WPT systems, which can open up more research in developing advanced power topologies and fault-tolerant control schemes. Other stimulating research areas for developing technology are bidirectional power flow, integration with hybrid energy storage systems and multiple energy sources [100]. However, these areas are still under research that further attention and investigation for developing advanced multi-port converter topologies and newly advanced control schemes must comply with future charging standards to promote IPT systems for EV charging applications.

#### **6. Conclusions**

This paper presents an extensive overview of power conversion topologies and control schemes for IPT-based EV charging applications. The design considerations and performance evaluation of the conventional dual-stage topology and two potential single-stage topologies including buck- and boost-derived FBMCs were discussed. It is concluded that the conventional dual-stage topology has the lowest stress on switching devices, and the boost-derived FBMC provides the greatest input current quality. On the other hand, the superiorities of the buck-derived FBMC over the other topologies are high efficiency, low component count and cost. However, further investigation on IPT-based charging systems is needed including scalability to higher power levels, adoption of soft-switching technology, fault-tolerability technology, active power decoupling methods, magnetic integration, green energy based-IPT systems, multi-mode operation systems, wide bandgap device technology, high-performance advanced and non-invasive control schemes. With the continual improvements and the aforementioned advancements, IPT-based systems will definitively increase the availability and economic viability of the EVs in the near future.

**Author Contributions:** Conceptualization, P.S.H. and S.S.W.; Software, P.S.H.; Validation, P.S.H.; Formal Analysis, P.S.H.; Investigation, P.S.H.; Resources, P.S.H. and D.R.; Data Curation, P.S.H.; Writing Original Draft Preparation, P.S.H. and D.R.; Writing Review & Editing, P.S.H, D.R., D.V., and S.S.W.; Visualization, P.S.H., D.R., and D.V.; Supervision, S.S.W.; Project Administration, S.S.W.; Funding Acquisition, S.S.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Natural Sciences and Engineering Research Council (NSERC), Canada.

**Conflicts of Interest:** The authors declare no conflict of interest.

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