A capacity model based on charging process for state of health estimation of lithium ion batteries

Applied Energy 177 (2016) 537–543

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A capacity model based on charging process for state of health estimation of lithium ion batteries Xue Li a,b,⇑, Jiuchun Jiang a,b, Le Yi Wang c, Dafen Chen a,b, Yanru Zhang a,b, Caiping Zhang a,b a

National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University, Beijing 100044, China Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Jiaotong University, Beijing 100044, China c Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA b

h i g h l i g h t s
A capacity model based on charging process is proposed to estimate SOH.
The accuracy of the model is validated on commercial lithium ion batteries.
The universality of the model is verified on different batteries and statuses.

a r t i c l e

i n f o

Article history: Received 5 April 2016 Received in revised form 15 May 2016 Accepted 19 May 2016

Keywords: Lithium ion battery Capacity model Incremental capacity analysis State of health

a b s t r a c t The incremental capacity (IC) analysis method is widely used to analyze the aging origins and state of health (SOH) of lithium ion batteries. This paper analyzes the technical difficulties during the application of the IC analysis method at first. A universal capacity model based on charging curve is then proposed, which not only inherits the advantages of IC analysis method but also avoids the tedious data preprocessing procedure, to estimate SOH of lithium ion batteries. The feasibility and accuracy of the model are demonstrated. To verify the accuracy and flexibility of the proposed capacity model, it is applied on different types of lithium ion batteries including LiFePO4 ; LiNi1=3 Co1=3 Mn1=3 O2 , and Li4=3 Ti5=3 O4 . Furthermore, the proposed capacity model is applied on the aged cells to validate the model accuracy during the whole life span of lithium ion batteries. The results show that the model error is less than 4% of the nominal capacity for each case. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Energy crisis and environmental concerns are urgent problems to be solved for world’s sustainable development [1–3]. Lithium ion batteries (LIBs) can be used both on static energy storage and transportation energy storage [4,5] thanks to their remarkable advantages such as high specific energy, high efficiency, and long life [6,7]. The two key tasks in battery management system (BMS) are to estimate state of charge (SOC) [8,9] and state of health (SOH) [10–12] to avoid battery abuse and prolong its life span [13]. SOC is the ratio of the remaining capacity to the nominal capacity of the battery [14,15], and SOH reflects the ability of the battery to deliver the peak power and energy compared with the initial state

⇑ Corresponding author at: National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University, Beijing 100044, China. E-mail address: [email protected] (X. Li). http://dx.doi.org/10.1016/j.apenergy.2016.05.109 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

[16]. In recent years, many researchers focused on SOC and SOH estimations. Many robust and accurate estimation techniques to estimate SOC have been studied [17–20]. In contrast, the development of the SOH estimation methods is more challenging due to the complicated electrochemical mechanisms involved in the battery fading [21]. However, the accurate SOH estimation is as crucial as the accurate SOC estimation for the efficient energy management in energy storage systems [12,19]. To analyze SOH of LIBs, a differential transformation is usually executed on the charging curve to generate an incremental capacity (IC) curve [22,23]. The main idea of the IC analysis theory is to transform the voltage plateaus on the voltage curve into clearly identifiable dQ/dV peaks on the IC curve by differentiating the charged capacity (Q) with respect to the terminal voltage (V) [24]. The IC curve is associated with the phenomena of the phase þ transition during the Li intercalation/deintercalation process of the active material [25]. So SOH could be estimated based on the correlation between the maximum capacity and specific parame-

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ters of IC curve. Dubarry et al. [26] analyzed the cell degradation mechanisms of LiFePO4 (LFP) such as loss of Li inventory and loss of active materials from the intensity, area, and position of IC peaks. Weng et al. [24] established the relationship between SOH and IC peak value through proposing a unified SOC–OCV model to get IC curve. However, the parameters in proposed SOC–OCV model have less relations with the electrochemical phenomena. To make the parameters used to indicate SOH associate with the phenomena of the phase transition, Torai et al. [25] estimated SOH of LFP/graphite by establishing dQ/dV model. The dQ/dV model of the full-cell for the SOH estimation was calculated from the halfcell models by subtracting the anode from the cathode. The differential capacity property of the LFP electrode for a half cell during the oxidation reaction was expressed using a single peak function, and the differential capacity property of the graphite electrode for a half-cell under the reduction reaction was expressed using four peak functions. However, a great quantity of parameters increase the load of parameters identification. In addition, these models are usually built for a particular type of battery that has specific anode and cathode materials. Therefore, it is extremely difficult to apply the model of one battery with specific electrode materials on another battery with different electrode materials. However, variety of cathode and anode materials are used for their unique merits. Graphite is the most commonly used anode material because of its low charging voltage and wide range of lithium insertion [27]. Lithium titanium oxide (LTO) has been accepted as a novel anode material due to its high power density and long life [28,29]. From the view of cathode materials, LiNi0:8 Co0:15 Al0:05 O2 (NCA), and LiCoO2 (LCO) have high energy density; LiNi1=3 Co1=3 Mn1=3 O2 (NCM) and LiMn2 O4 (LMO) are less expensive; LiFePO4 (LFP) is the safest [6]. A universal model for SOH analysis needs to be proposed, which could be easily adapted to all types of batteries comprised of different cathode and anode materials. This paper analyzes the technical difficulties during the application of the IC analysis method in the commercial BMS, which include the data distortion during the data preprocessing, the selection of voltage interval, and the fitting error of IC curve. To solve these issues by identifying the IC characteristic parameters from the experimental data directly, a universal capacity model based on charging process is proposed to estimate SOH. The proposed capacity model establishes the correlation between SOH and the phenomena of the phase transition. In addition, compared with Ref. [25], the number of model parameters depending on the number of IC peaks of full cell has been reduced. The versatility and flexibility of the proposed capacity model on different chemistries are validated by different type of LIBs including graphitekLFP, graphitekNCM + LMO, and LTOkLCO cells. Moreover, to illustrate the capability of the proposed capacity model to capture the changes during the whole life span of the battery, the proposed capacity model is also applied on two cells at different aging statuses. The main contribution of this paper is to propose a universal capacity model based on charging process of LIBs. The proposed universal capacity model is capable to be applied on LIBs with different chemistries due to the flexibility of the model parameter n. Parameters of the proposed model can be used to estimate SOH thanks to their explicit meanings corresponding to the realistic phase transition behavior of the active material. Not only that, but the satisfied accuracy of the proposed universal capacity model during the whole life span of LIBs provides the potential to be applied to estimate SOH accurately. The remainder of this paper is organized as follow. Section 2 illustrates the modeling process. Then, the experiments are introduced in Section 3. The versatility and flexibility of the proposed model are discussed in Section 4. Then the conclusions are summarized in Section 5.

2. Modeling 2.1. Theory The working mechanism of LIBs is that lithium ions swing between two electrodes after intercalating to or de-intercalating from cathode and anode materials. The average intercalation potential of each electrode can be calculated by Eq. (1) [30],

E ¼ DG=nF

ð1Þ

where DG is the difference of the Gibbs free energy for the intercalation reaction, n is the number of electrons intercalated in each unit cell, and F is the Faraday constant. Therefore, different electrodes have their specific potential ranges and plateaus because the DG is unique for different materials. The open circuit voltage (OCV) of the full cell is the differential voltage between cathode and anode, that is OCV full ¼ Ecathode  Eanode . To meet requirements of different applications, cells with different combinations of cathodes and anodes, such as graphitekLFP cells, graphitekNCM cells,and LTOkNCM cells, are designed and manufactured. As a result, all those cells have distinct OCV curves. In addition, the OCV curve of a cell is changing gradually with the aging of the cell because of different aging origins, such as the active material loss in cathode and anode. In other words, the OCV curve is a reflection of the electrode materials and contains the aging information. As the terminal voltage of LIBs during charging and discharging is determined by the OCV and resistance, the terminal voltage curve inherits the information contained in OCV curve and can be used for SOH diagnostic. To eliminate the influence of resistance, the terminal voltage under 0.05 C charging or discharging is suggested by researchers as a trade-off between test time and accuracy. The left plot in Fig. 1 shows the terminal voltage curve of cell No. 1 (as shown in Table 2) during 0.05 C charging from SOC = 0% to SOC = 100% before cycling. As shown in Fig. 1, the measured voltage is a monotonous function of the charged capacity. The voltage increases rapidly at the two ends, while the voltage increases tardily at the middle of the curve with several voltage plateaus. The plateau represents the two phase co-existence state of Lipoor phase and Li-rich phase during the charge/discharge process, thus it is the most important characteristic to analyze the performance of the battery. While, as shown in the middle plot of Fig. 1, more than 90% of the capacity is charged from 3.2 V to 3.4 V, which only accounts for less than 20% of whole voltage range. Furthermore, all the voltage plateaus also appear during this voltage range. Thus, it is hard to analyze the statuses and characteristics of cells from the voltage curve directly. In order to dig out the implicit battery information from the terminal voltage curve, a well known technique – incremental capacity analysis is usually used. The basic theory is: transform the voltage (V) vs. charged capacity (Q) curve into dQ =dV vs. voltage (V) curve. The right plot of Fig. 1 shows the IC transformation results from the terminal curve of cell No. 1 at its fresh status. Several peaks appear in IC curve with each peak corresponding to one voltage plateau in the curve. These peaks in IC curve make the associated phase transition inside the cathode and anode become much more intuitive and sensitive. The area below the IC peak is the capacity between a specific voltage range, and the peak center of IC curve reveals the voltage value of voltage plateau. From the change of peak parameters (those are the peak intensity, width, and center location), the aging origins, such as the loss of active material, the loss of usable lithium-ion, and the increase of the internal resistance, can be analyzed, and then the SOH can be calculated [22].

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Fig. 1. OCV and IC curve of cell NO. 1 at fresh status.

2.2. The technical difficulties during IC analysis method application

dQ ¼ dV

rffiffiffiffi n X 2 Ai i¼1

p xi

 2 ! ðV  V 0i Þ exp 2

xi

n dQ X 2Ai xi ¼ 2 dV p x þ ð2V  2V 0i Þ2 i¼1 i

ð2Þ

dV=1mV dV=5mV dV=10mV dV=15mV dV=25mV

40

dQ/dV(Ah/V)

The IC curves are derived from correlating the amount of incremental capacity associated with a successive voltage step in the charging curve to cell voltage [23]. While the voltage and capacity data are usually logged per second in the commercial BMS. Numerical derivative is usually applied to obtain the IC curve. The disadvantages of numerical derivative are obvious. Firstly, the BMS data needs to be preprocessed to transform the equal time interval data to equal voltage interval data. It is sensitive to the resolution of the BMS acquisition system. Errors are introduced to the IC curve because of data preprocessing. Secondly, the shape of the IC curve is dependent on voltage interval (dV) as shown in Fig. 2. The intensity of each peak in the IC curve decreases with the increase of voltage interval. If voltage interval is too small, the IC curve appears to be very noisy(the red curve). If voltage interval is too large, the boundary of each peak becomes fuzzy and even disappears(the blue curve). No related reports are found on how to choose the voltage interval. To obtain the IC peak indicators for quantitative analysis, the peak fitting functions, such as Gaussian function and Lorentzian function, could be adopted to fit IC curve. Then, the dQ =dV vs. voltage curve thus can be expressed by Gaussian function and Lorentzian function respectively, as shown in Eqs. (2) and (3).

50

30

20

10

0 3.2

3.25

3.3

3.35

3.4

Volatge(V) Fig. 2. dQ =dV vs. voltage under different voltage intervals.

Table 1 Peak parameters of cell No. 1 (fresh). i

Ai

V 0i

xi

1 2 3 4

0.420264 0.436317 0.310032 0.077451

3.370009 3.330456 3.294571 3.24488

0.010316 0.006265 0.091547 0.009974

ð3Þ

where n is the number of peaks, Ai is the area below the ith peak, xi is the peak width at half height of ith peak, V 0i is the symmetry center of ith peak. The IC curve fitting error cannot be avoided to be introduced to the results when we identify the IC function parameters (such as the intensity, width and center location) by choosing any function to fit IC curve. As a result, the identification accuracy of the IC function parameters is affected by data preprocessing and IC curve fitting process. 2.3. Charged capacity (Q) vs. voltage (V) function Assuming that the IC function parameters could be identified from BMS logged data (capacity and voltage) directly, the error of the parameters caused by the data preprocessing can be avoided. The easiest way to realize that purpose is to apply the integral to Eqs. (2) and (3). Lorentzian function is chosen to use in this paper due to its own simplicity and the relatively simple integral form, which is of great importance for building a capacity model dependent on voltage.

Therefore, the relationship between charged capacity and voltage can be derived from Eq. (3) by integral:

Q¼

n X Ai i¼1

p

  V  V 0i þC arctan 2

xi

ð4Þ

where C is a constant produced by integral, the remaining parameters, Ai ; xi , and V 0i inherit the same meanings in Eq. (3). There are totally 3  n þ 1 parameters in this equation, n is the number of peaks found in IC curve which is determined by the electrode materials of LIBs. The expected analytical function of charged capacity (Q) vs. voltage (V) is thus constructed successfully. Moreover, the maximum available capacity of the cell Q cell can be calculated as:

Q cell ¼ QðV e Þ  Q ðV b Þ

ð5Þ

where Q ðV e Þ and Q ðV b Þ is the charged capacity calculated by Eq. (4) using the voltage at the end of charging and at the begin of charging, respectively. The parameters used in these functions are associated with the realistic phase transition behavior of the active material, where xi is the full width at half maximum derived from the interaction of

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2

1.4 1.2

experimental fitted

Capacity error (%)

1

Capacity (Ah)

1 0.8 0.6 0.4

0

-1

-2 0.2 0 2.6

2.8

3

3.2

3.4

3.6

Voltage (V)

-3 2.6

2.8

3

3.2

3.4

3.6

Voltage(V)

Fig. 3. Comparison of experimental and modeling results of cell No. 1 at fresh status.

the active material, Ai is the peak area which represents the total charged/discharged capacity in the phase transition derived from the usable active material, V 0i is the peak potential derived from the redox potential of the phase transition. Here, Q is defined as the charged capacity of the battery cell, which is different for the notation of Q cell , being defined as the maximum available capacity of the cell. The proposed capacity model (4) has several obvious advantages: a. The parameters in proposed capacity model can be identified from experimental data directly, whose accuracy doesn’t depend on the data preprocessing. No additional error is introduced to the parameters except the fitting error of the charged capacity curve. b. The value of the parameter n in Eq. (4) can be flexibly adjusted according to the electrode materials of LIBs, so it is capable to be applied on different battery chemistries easily. c. The parameters in proposed capacity model are associated with the realistic phase transition behavior of the active material and independent to the selection of dV, which can be used to analyze the SOH quantitatively. This part will be emphasized in our further work. 2.4. Parameters identification and model validation The experimental data of cell No. 1 at fresh status is used here to validate the modeling accuracy. As shown in Table 2, cell No. 1 is a LFP-based battery whose cathode is LFP and anode is graphite. LFP is well-known for its two-phase structure, characterized by only one flat voltage plateau [31]. As a result, the IC curve is dominated by the anode material—graphite. Graphite usually has four obvious voltage plateaus [32]. So n ¼ 4 is used in Eq. (4) for cell No. 1. The nonlinear least square method is used to identify the parameters in the proposed capacity model. Reasonable value ranges of parameters need to be constrained in the nonlinear least square identification process. According to the characteristics of cell No. 1, the following restricts are applied:

8 ði ¼ 1; 2; 3; 4Þ > < Ai 2 ½0; 1:1 V 0i 2 ½3:2; 3; 4 ði ¼ 1; 2; 3; 4Þ > : xi 2 ½0; 0:2 ði ¼ 1; 2; 3; 4Þ

ð6Þ

The estimated parameters of four peaks are shown in Table 1. The experimental data and fitted results are shown in Fig. 3(a). The fitted results show a great consistence to the experimental data. And the voltage plateaus are also well captured by the proposed capacity model. The maximum error of charged capacity

Fig. 4. ICA curve of cell No. 1 at fresh status.

during the whole charging process is less than 3% of the nominal capacity as shown in Fig. 3(b). These verify the accuracy of the proposed capacity model on describing the relationship between voltage (V) and charged capacity (Q). To validate the capability of the proposed capacity model for SOH prognostic, the IC curves are further calculated as shown in Fig. 4.1 The IC curve (blue solid line) derived from the proposed capacity model captures all the four peaks. Compared to the IC curve (red dashed line) obtained using numerical derivation under dV ¼ 2:5 mV from the voltage vs. charged capacity curve, it is much smoother. The robustness of the proposed model during the whole life span of LIBs can also be guaranteed by applying the same constrains during the parameters estimation. Another advantage of using the proposed capacity model to analyze SOH is that each peak can be analyzed independently. As shown in Fig. 4, four peaks are exhibited separately. Moreover, the characteristics of peaks are explicitly contained in the model parameters, which can be deduced easily. The subplot in Fig. 4 illustrates the relationships between the peak characteristics and the parameters in the proposed capacity model visually by taking the peak 2 as an example. A2 is area of peak 2, which can be used to indicate the total charged/discharged capacity in the phase transition derived from the usable active material between the voltage range from 3.23 V to 3.34 V approximatively. V 02 is the center of peak 2, which represents peak potential derived from the redox

1 For interpretation of color in Figs. 4–6, the reader is referred to the web version of this article.

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potential of the phase transition. x2 is the full width at half maximum of peak 2 derived from the interaction of the active material. The peak intensity can be calculated as h ¼ 2A2 =ðpx2 Þ. These make the quantitative analysis of IC curve become practicable and easy.

4. Results and discussion As shown in Section 2, the proposed capacity model performs very well when it is applied on the fresh LFP cell. The universality of the proposed capacity model needs to be verified further on different types of LIBs and at different aging statuses.

3. Experimental

4.1. Application on different types of LIBs

Three kinds of commercial LIBs were tested at room temperature to acquire the data used in this paper. As shown in Table 2, the tested cells have different shapes and materials. No. 1 is a 1.1 Ah 18650 cylindrical graphitekLFP cell; No. 2 is a 35 Ah pouched graphitekNCM + LMO cell; No. 3 is a 20 Ah prismatic LTOkLCO cell. In practical use of the electric vehicles, the charging process was more controlled, whereas the discharging process included complex operating patterns. Therefore, the constant current charging process was chosen. The 0.05 C current magnitude is the tradeoff between test time and OCV accuracy. So the terminal voltages of those cells during 0.05 C constant current charging process were recorded to develop the model. Cell No. 1 was cycled using 0.5 C constant current charging and discharging at room temperature from SOC = 10% to SOC = 90%. Cell No. 2 was cycled using 2 C constant current full charging and discharging at 45  C. The 0.05 C constant current charging tests were taken every 200 cycles for cell No. 1 and 100 cycles for cell No. 2. All experiments were executed using Arbin BT2000. The data logging frequency was 1 Hz.

4.1.1. LTO-based cell Similar to LFP cathode material, LTO anode has only one voltage plateau. Thus the IC curve is dominated by cathode material in cell whose anode is LTO. The cathode material of cell No. 3 is mainly LCO. Three peaks appear in its IC curve, so n in Eq. (4) is set to be 3 in this case. The comparison of experimental data and fitted result is shown in Fig. 5(a), and the error of charged capacity during the whole charging process is less than 2% of its nominal capacity as shown in Fig. 5(b). To validate the capability of the proposed capacity model for SOH prognostic, the IC curves are further calculated as shown in Fig. 5(c). The IC curve (red dashed line) is obtained using numerical derivation under dV ¼ 2:5 mV from the voltage vs. charged capacity curve. The IC curve (blue solid line) is derived from the proposed capacity model. Compared to the calculated IC curve, the IC curve gotten by the proposed capacity model could capture peaks of IC curve. These indicate that the model is also accurate and suitable for LTO cell.

Table 2 Experimental cells and schedules. No.

Shape

Cathode

Anode

Nominal capacity (Ah)

Nominal voltage (V)

Cycling current

1 2 3

Cylindrical Pouched Prismatic

LFP LMO + NCM LCO-based

Graphite Graphite LTO

1.1 35 20

3.2 3.6 2.3

0.5 C 2C –

25

1.5 experimental fitted

1

15 10 5 0 -5

0.5

dQ/dV(Ah/V)

Capacity error (%)

Capacity (Ah)

20

0 -0.5 -1 -1.5 -2

2

2.2

2.4

-2.5

2.6

2

2.2

2.4

2.6

200 180 160 140 120 100 80 60 40 20 0

calculated derivative

1.8

2

2.2

Voltage (V)

Voltage (V)

2.4

2.6

2.8

4

4.2

Voltage

Fig. 5. Comparison of experimental and modeling results of cell No. 3 at fresh status.

experimental fitted

120

30 25 20 15 10

0.5

dQ/dV(Ah/V)

Capacity error (%)

35

Capacity(Ah)

140

1

40

0 -0.5

100 80 60 40 20

5 0

calculated derivative

3.2

3.4

3.6

3.8

Voltage (V)

4

4.2

-1

3.2

3.4

3.6

3.8

4

4.2

0

3.2

3.4

Voltage (V)

Fig. 6. Comparison of experimental and modeling results of cell No. 2 at fresh status.

3.6

3.8

Voltage

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X. Li et al. / Applied Energy 177 (2016) 537–543

capture peaks of IC curve. So the model is accurate and suitable for this kind of LIBs, too.

Capacity Retention (%)

100

95

4.2. Application on different aging statuses

90

Guaranteeing the model accuracy during the whole life span of LIBs is crucial when the proposed model is used for SOH diagnostic. As mentioned before, cell No. 1 and cell No. 2 were cycled under different cycling profiles and ambient temperatures. The capacity retention curves of these two cells shown in Fig. 7 indicate that the degradation rates of the two cells are different and these two cells arrive at different aging statuses after cycling. The comparison results shown in Fig. 8 depict that the proposed capacity model can fit the voltage vs. charged capacity curve accurately for both cell No. 1 and cell No. 2 at different aging statuses along the whole life span. The errors of charged capacity during the whole charging process are less than 4% in all conditions. Thus the universality and accuracy of the proposed capacity model during the whole life span of LIBs are demonstrated. The results above indicate that the proposed capacity model is not only universal for different types of LIBs, but also very accurate during the whole life span of LIBs. The highly accurate model provide reliable parameters which could be used to calculate the SOH of LIBs. For example, the reduction of Ai of aged cell represents the capacity fading corresponding to the ith phase transition process of LIBs; the shift of V 0i indicates the variation of power performance corresponding to the ith phase transition process of LIBs. As SOH of LIBs is usually estimated by the combination of remaining capacity and power capability, SOH containing abundant details could be obtained by the model parameters.

85

80

75

70

cell 1 cell 2 0

200

400

600

800

Cycles Fig. 7. The capacity fading curves.

4.1.2. NCM-based cell Cell No. 2 is comprised of graphite anode and LMO + NCM cathode. The phase transitions of cell No. 2 are more complicated than that of two types of cells which are modeled above. Three obvious voltage plateaus are observed, so the number of peak functions is set to be 3. The comparison of experimental data and fitted result is shown in Fig. 6(a), and the error of charged capacity during the whole charging process is less than 1% of its nominal capacity as shown in Fig. 6(b). To validate the capability of the proposed capacity model for SOH prognostic, the IC curves are further calculated as shown in Fig. 6(c). The IC curve (red dashed line) is obtained using numerical derivation under dV ¼ 2:5 mV from the voltage vs. charged capacity curve. The IC curve (blue solid line) is derived from the proposed capacity model. Compared to the calculated IC curve, the IC curve gotten by the proposed capacity model could

1.4

0.6

1 0.8 0.6

0.4

0.4

0.2

0.2 3

3.2

3.4

2.8

3

40

3.2

3.4

20 15

25 20 15 10

5

5

Voltage (V)

4

4.2

0

3.2

3.4

3.6

1

30

10

3.8

3

Voltage (V)

Capacity error (%)

Capacity (Ah)

25

3.6

2.8

experimental fitted

35

30

3.4

-2

-4 2.6

3.6

40 experimental fitted

3.2

0 -1

Voltage (V)

Voltage (V)

35

1

-3

0 2.6

3.6

fresh 400 cycles 800 cycles

2

Capacity error (%)

Capacity (Ah)

Capacity (Ah)

0.8

2.8

3 experimental fitted

1.2

1

0 2.6

Capacity (Ah)

In this paper, the incremental capacity analysis technology is introduced to transform the terminal voltage curve to the IC curve,

1.4 experimental fitted

1.2

0

5. Conclusion

3.2

3.4

3.6

3.8

Voltage (V)

4

4.2

0.5

0

-0.5

-1

fresh 300 cycles 600 cycles 3

3.2

3.4

3.6

3.8

Voltage (V)

Fig. 8. Comparison of experimental and modeling results of cell No. 1 and cell No. 2 at different aging statuses.

4

4.2

X. Li et al. / Applied Energy 177 (2016) 537–543

which makes the aging details of the cell more intuitive. To solve the issues during the application of IC analysis method, the charged capacity vs. voltage model is proposed based on the charging process. The universality and accuracy of the proposed model are validated using different types of LIBs (including graphitekLFP, graphitekNCM + LMO, and LTOkLCO cells) and different aged cells that degraded under different conditions. From this study, the following conclusions can be summarized:
The proposed capacity model could capture the voltage plateaus in the OCV curve as well as the peaks in the IC curve precisely, and the estimated charged capacity error is less than 4% of the nominal capacity in each case.
Model parameters have explicit meanings corresponding to the realistic phase transition behavior of the active material, which could be used in SOH diagnostic.
The parameters of the proposed model can be identified from the experimental data directly which avoids the error caused by data preprocessing.
The proposed capacity model could be widely applied on all types of LIBs that have different electrode materials.
The proposed capacity model is accurate during the whole life span of LIBs, which has the protential to be applied for SOH estimation. As this paper focuses on the deduction and validation of the charged capacity vs. voltage model, only the accuracy and capability of the proposed model are discussed. Our further work will focus on applying the proposed capacity model to analyze the SOH, which includes: (1) The evolution rules of the model parameters along different degradation paths. (2) SOH evaluation method based on the parameters of the proposed capacity model. (3) Model implementation into real battery management systems. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 51477009) and Fundamental Research Funds for the Central Universities (Grant No. 2016YJS144). References [1] Kong IM, Choi JW, Kim SI, Lee ES, Kim MS. Experimental study on the selfhumidification effect in proton exchange membrane fuel cells containing double gas diffusion backing layer. Appl Energy 2015;145:345–53. [2] Chatzizacharia K, Benekis V, Hatziavramidis D. A blueprint for an energy policy in Greece with considerations of climate change. Appl Energy 2016;162:382–9. [3] Fujimi T, Kajitani Y, Chang SE. Effective and persistent changes in household energy-saving behaviors: evidence from post-tsunami Japan. Appl Energy 2016;167:93–106. [4] Miranda D, Costa C, Almeida A, Lanceros-Méndez S. Computer simulations of the influence of geometry in the performance of conventional and unconventional lithium-ion batteries. Appl Energy 2016;165:318–28. [5] Capasso C, Veneri O. Experimental analysis on the performance of lithium based batteries for road full electric and hybrid vehicles. Appl Energy 2014;136:921–30. [6] Monem MA, Trad K, Omar N, Hegazy O, Mantels B, Mulder G, Van den Bossche P, Van Mierlo J. Lithium-ion batteries: evaluation study of different charging methodologies based on aging process. Appl Energy 2015;152:143–55.

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