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INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2016; 40:1869–1883 Published online 27 June 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3576

An alternating current heating method for lithium-ion batteries from subzero temperatures Jiangong Zhu, Zechang Sun, Xuezhe Wei and Haifeng Dai*,† Clean Energy Automotive Engineering Center, School of Automotive Engineering, Tongji University, Shanghai, 201804, China

SUMMARY An alternating current (AC) heating method for lithium-ion batteries is proposed in the paper. Effects of current frequency, amplitudes and waveforms on the temperature evolution and battery performance degradation are respectively investigated. First, a thermal model is established to depict the heat generation rate and temperature status, whose parameters are calibrated from the AC impedance measurements under different current amplitudes and considering battery safe operating voltage limits. Further experiments with different current amplitudes, frequencies and waveforms on the 18650 batteries are conducted to validate the effectiveness of the AC heating. The experimental data recorded by appropriate measurement instrument are of great consistence with simulation results from the thermal model. At high frequency, the temperature rises prominently as the current increases, and high frequency serves as a good innovation to reduce the battery degradation. However, efficient temperature rise can be obtained from high impedance at low frequencies. Typically, 600 s is needed to heat up the battery from 24 °C to 7.79 °C with sinusoidal waveform and approximately from 24 °C to 25.6 °C with rectangular pulse waveform at 10A and 30 Hz. The model and experiments presented have shown potential value in battery thermal management studies for electric vehicle (EV)/hybrid electric vehicle (HEV) applications at subzero temperatures. Copyright © 2016 John Wiley & Sons, Ltd. KEY WORDS lithium-ion battery; low temperature; alternating current; heating method; impedance; electric vehicle Correspondence *Haifeng Dai, Clean Energy Automotive Engineering Center, School of Automotive, Engineering, Tongji University, Shanghai 201804, China. † E-mail: [email protected] Received 28 March 2016; Revised 4 May 2016; Accepted 22 May 2016

1. INTRODUCTION Currently lithium-ion batteries are considered as excellent energy storage system for electric vehicle (EV) and hybrid electric vehicle (HEV) because of their high energy density, low maintenance, less toxic, good cycle life and capable of accepting high charging rate [1]. However, the problems of security and thermal behavior of the power lithium-ion battery remain obstacles to the deployment of EV and HEV [2,3]. Evidently, the remarkable deterioration in the performance of battery power and energy density at subzero temperatures is also hampering their practice applications [4–6]. Generally, the limiting factors associated with the poor performance of lithium-ion cells at low temperatures are composed of poor electrolyte conductivity [7], sluggish kinetics of charge transfer [8,9], increased resistance of solid electrolyte interphase (SEI) [10,11] and slow lithium ions diffusion in graphite [12,13]. During charging at sub-ambient temperature, the aforementioned diffusion of

Copyright © 2016 John Wiley & Sons, Ltd.

lithium ions is hindered, which leads to a low intercalation rate and thus favors lithium plating at the graphite surface [14]. Also, lithium intercalation can be impeded by the limitation of charge transfer kinetics which occurs at smaller time constants than the diffusion limitation [15]. Deposited lithium is a major reason of battery energy density fading. In the worst case scenario, lithium dendrites may pierce the separator and cause an internal short circuit leading to thermal runaway and battery explosion [16]. To guarantee batteries in a normal operation temperature range, especially for the EV/HEV road and highway applications which would result in a temperature increase that accelerates cell aging, efficient thermal management systems for the energy storage are highly required [17]. Rao et al. [18] discussed the traditional air and liquid battery thermal energy management, and proposed that pulsating heat pipe method may be effective to heat/cool batteries with well designed. They considered that phase change materials for battery thermal management were a

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Heating method for lithium-ion batteries

better selection. Nevertheless, the conflict between large heat storage capacity and low thermal conductivity of traditional materials must be solved and investigated experimentally. To achieve desired battery performance in cold climates, Pesaran et al. [19] compared several approaches including internal core heating, external jacket electric heating, internal jacket electric heating and internal jacket fluid heating, and suggested the battery core heating being the most effective method to warm battery quickly with least amount of energy. The heating efficiency and temperature non-uniformity are two main considerations. Zhao et al. [20] proposed a new charging mode, in which the batteries were excited by current pulses, and the results demonstrated the surface temperature ascended to 3 °C from 10 °C. Stuart and Hande [21,22] studied the alternating current (AC) heating method experimentally for lead acid batteries and nickel metal hydride batteries respectively. Based on a thermal-electrochemical model, Yan et al. [23] put forward three heating strategies, namely self-internal heating, convective heating and mutual pulse heating, and compared the advantages and disadvantages from the aspects of capacity loss, heating time and system durability. From the perspective of heating efficiency and energy conversion efficiency, AC heating method is feasible way to heat the battery core [21–23]. However, these studies do not offer scientific explanations for the AC impedance corresponding to large current nor have they systematically studied the heating temperature variations considering battery operating voltage limits. And to our best knowledge, the influence of the AC heating on battery performance degradation has never been investigated with detailed experiments in previous literatures. To address the above issues, an electro-thermal model, which is derived from Arrhenius empirical equation, Butler–Volmer equation (BVE) and the AC impedance spectra and considers the charge/discharge (charge means that lithium ions move from positive electrode to negative electrode, and discharge is contrary) voltage limits, is established to understand the battery AC heating operating mechanism. Moreover, a comprehensive investigation of the effects of current frequency, amplitudes and waveforms on temperature evolution and battery performance degradation during AC heating is implemented with experiments. The heat generation resistance in the model is associated with frequency, current amplitude and temperature, while the relationships are derived and calibrated based on AC impedance measurements and battery electrochemical equations. The current correction equations are established in the model for the purpose to make the battery operate within the scope of safe operating voltage. AC heating experiments consist of two parts: (i) the current amplitudes vary from 1.5A (0.65C) to 10A (4.35C) at 300 Hz, the symbol C means the current magnitude in terms of cell capacity (1C = 2.3A); (ii) 8A (3.5C) and 10A (4.35C) are selected and excitation frequencies include 600 Hz, 300 Hz, 80 Hz, 30 Hz, 10 Hz and 1 Hz. The sinusoidal waveform (sin) and rectangular pulse (rect) are considered in depth to verify the feasibility of the

method. The experimental measurements are also under normal operating voltage limit conditions (the upper limit voltage is set to 4.2 V, and the lower limit voltage is set to 2.7 V according to the battery specifications shown in Table I. Both limitations are controlled by a bipolar power source), that propagation of damage arising from overvoltage/under-voltage inside the battery can be avoided. The simulation results and experimental data show good concordance. The temperature rise is determined by both current amplitude and excitation frequency. The high frequency zone would witness a steeper rise in the temperature when the current amplitude becomes larger. When at low frequencies, the deterioration of the heating results can be ascribed to the calibrated current with the voltage limit protection. At 10A and 30 Hz, the sine and rectangular excitations experience the maximum temperature rise from 24 °C to 7.79 °C and 25.6 °C respectively. The experimental verifications are conducted to validate the effect of AC heating method to the battery life at the end of the paper.

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Int. J. Energy Res. 2016; 40:1869–1883 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/er

2. EXPERIMENTS The cells adopted in the experiments are commercial 18650 Lithium-ion batteries with a nominal capacity of 2.3 Ah, as shown in Figure 1. The specifications of the cell are listed in Table I. Generally, the overall heat generation of battery is determined by the impedance and current amplitude. In our previous work [25], a shrinking of semi-circle diameter of the impedance arc at medium-frequency part of measured spectrum was distinctly observed with rising current amplitude for lithium iron phosphate (LiFePO4) and lithium ion manganese (LiMn2O4) cells. The conclusion indicates that the charge transfer resistance reduces as the current amplitude increases, which fundamentally dominates the shrinking of the semi-circle at medium frequencies. In this study, The AC impedance measurements are also completed for 18650 (LiMnNiCoO2) battery, and detailed test method is as follows. The AC heating experimental procedures are

Table I. Specifications of the Li-ion battery used. Battery type Anode material Cathode material Electrolyte Nominal voltage Charge voltage Discharge ending voltage Capacity Battery mass (m) Battery length Battery diameter Specific heat capacity (Cp) Battery surface area (Scell)

18650 Graphite Lithium cobalt manganese nickel oxide (LiMnNiCoO2) Solution of lithium hexafluorophosphate (LiPF6) 3.6 V 4.2 V 2.7 V 2.3 Ah 45.0 g 0.065 m 0.018 m 1 1 1.72 J g K [24] 3 2 4.263 × 10 m

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Figure 1. Equivalent electrical circuit model and the 18650 battery.

also designed in the paper, and a brief introduction is presented in accordance with the orders of their appearance respectively. 2.1. AC impedance measurements Considering that current amplitude is one of the most important factors in the AC heating method and to reveal the influence of large current amplitude on battery performance, the AC impedance experiments with various AC amplitudes are proposed to investigate the AC impedance behaviors. The experiments are conducted over the frequency ranging from 100 kHz to 0.1 Hz, with sine signals of 1.5A, 2A, 4A, 6A, 8A and 10A using an electrochemical workstation (Solartron SI 1287, 1255B) and a power booster (PBI250-10) as illustrated in Figure 2. The temperature is controlled and monitored by a Votsch C4-180 environmental chamber. Measurements are made over the range of 25 °C to 40 °C, and a sufficient time period, e.g. 3 h, is allowed for the temperature of the battery to equilibrate with the chamber temperature. The results for 20%SOC (state of charge) are shown which are representative for the observations at other SOC. 2.2. AC heating experiments To investigate the impact of current amplitudes on the battery AC thermogenesis, the current amplitude changes from 1.5A to 10A at a fixed frequency (300 Hz). Then, the heating effects of various frequencies are analyzed at 8A and 10A, in which frequencies contain 600 Hz, 300 Hz, 80 Hz, 30 Hz, 10 Hz and 1 Hz. Sinusoidal excitation and rectangular pulse are all from the bipolar power (KIKUSUI PBZ20-80, Figure 2), while the calibrated current waveforms are monitored and displayed in a digital oscilloscope (Tektronix DPO 3054). To prevent irreversible damage in the working of battery, the over-voltage and under-voltage should be avoided. The decomposition of SEI layer resulting from Int. J. Energy Res. 2016; 40:1869–1883 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/er

over-voltage and under-voltage leads to exothermic reactions, gassing and thermal runaway of the battery [26,27]. Therefore, the voltage limit protection needs serious considerations in the AC heating model and experiments design. According to empirical values used in battery tests and the specifications in Table I, the upper limit voltage is set to 4.2 V, while 2.7 V is for the lower counterpart in all tests. The SOCs are adjusted to 20% before AC heating experiments in this study. The cells are placed inside a sealed box during the AC heating process and the equivalent heat transfer coefficient from battery to environment is 16 W m2 K1 (Appendix A) with calibration. Every cell is separately prepared with three thermocouples to measure the temperature on the surface during the testing process along the axial direction uniformly. The experimental temperature is calculated as the average value of the three thermocouples, because it is observed that the temperature differences along the cell surface are no higher than 2 °C even for the tests at high current rates. Temperatures from thermocouples are measured using a HIOKI temperature unit (LR8510) and recorded by a HIOKI wireless logging station (LR8410-30). The MACCOR in Figure 2 serves the functionality of calibrating the battery capacity and direct current (DC) impedance at room temperature (25 °C) after every 20 times heating.

3. MATHEMATIC MODEL 3.1. Energy balance Because all of the electrode component layers are thermally conductive, the heat fluxes in the jelly-roll are continuous in all three directions. And for the 18650 cells, even under high current excitation, the internal and surface temperatures are quite close [28,29]. The energy balance equation inside the cell can be written as mC p ∂T =∂t ¼ qn þ q

(1)

where m is the mass of the battery, Cp is the specific heat capacity, t is time, T is the battery temperature, qn is the heat flux transferred to the outside of the battery and q is the battery heat generation rate. Considering that Equation (1) is a lumped energy conversion equation, the surface convective heat dissipation which is dependent on the convective heat transfer is defined qn ¼ hS cell ðT T 0 Þ

(2)

where h is the equivalent heat transfer coefficient (16 W m2 K1, Appendix A), Scell is the battery surface area and, T0 is the ambient temperature. 1871

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Figure 2. Experimental device.

3.2. Heat source For the reproduction of the electric-thermal cell behavior, an equivalent circuit model (ECM) is employed as shown in Figure 1. The model chosen for the described investigation consists of a serial resistance in combination with two RC (resistance and capacitance) circuits in series [30,31]. The elements are parameterized as a function of T. The charge transfer resistance is also current dependent and described as Rct(T, I). Detailed discussions about the relationship between charge transfer resistance Rct and current are conducted in section 3.3. The heat generation rate for the cell is defined by q ¼ qohm þ qact þ qrev :

(3)

The overall heat generation of battery charge/discharge is consisted of ohmic heat qohm, active polarization heat qact and electrochemical reaction heat qrev [29,32,33]. qrev can be obtained from qrev

ΔS ¼ IT nF

conductance of contacts, which is composed of electrode and electrolyte resistance. RSEI(T) represents the impedance of solid electrolyte interface. R0(T) and RSEI(T) are all temperature dependent in the model. The active polarization which occurs at both electrodes can be generally expressed by BVE. Rct(T, I) represents the electrochemical polarization resistance, and describes the coupling relationship with temperature and current. The diffusion impedance is neglected because it is quite small in the frequency range (>1 Hz) used in this study. This paper concentrates on the high-frequency and medium-frequency impedance arc. During the AC heating process, heat generation rate is related to the real part of impedance. Combined with the ECM, the real part of the impedance can be expressed as

RQ ðT ; I; f Þ ¼ Ro ðT Þ þ þ

(4)

RSEI ðT Þ 1 þ ð2πf Þ2 R2SEI ðT ÞC 2SEI Rct ðT; I Þ 1 þ ð2πf Þ2 R2ct ðT ; I ÞC 2dl

(5)

where ΔS/n is the entropy change of the cell reaction, which is associated with SOC. I is current and represents Root Mean Square (RMS) current in the follows. F is Faraday constant. During the AC heating process, the SOC is unchanged with one period, so the electrochemical reaction reversible heat can be ignored in the AC heating model. In the ECM illustrated in Figure 1a, R0(T) is mainly influenced by the active material, electrolyte and

where f is signal frequency. The overall impedance RQ affecting heat generation rate is associated with signal frequency. CSEI is the capacitance of SEI and Cdl is electric double-layer capacitance. According to the analysis above, the total heat generation rate can be given as

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q ¼ qohm þ qact ¼ I 2 RQ ðT ; I; f Þ:

(6)

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3.3. Determinations of model parameters 3.3.1. AC impedance results and calibration of RQ (T, I, f) The impedance spectra obtained with different current amplitudes (1.5A, 2A, 4A, 6A, 8A, 10A) at 20%SOC are shown in Figure 3, which are consistent with previous work [25]. It can be concluded that the impedance arc in medium-frequency range shrinks regularly with the increase of current amplitude. Also, as the operation temperature falls below 10 °C, the impedance undergoes a sharp rise, which will result in the deteriorating effect on the battery performance. Based on the analysis of BVE and Arrhenius empirical equation, we measured the impedance response under large current for LiFePO4 and LiMn2O4 cells, and have proved that the shrinking phenomenon in the medium-frequency region does not result from battery SOC, internal pressure and temperature rise during the high-rate short-time charge/discharge process [25]. During the AC impedance measurements for 18650 batteries, the shrinking of the semi-circle diameters at medium-frequency part is considered to be mainly ascribed to the variation of current amplitude. The ECM elements at different T and I can be fitted using the data in Figure 3. The effects of T and I are further illustrated in Figure 4, where distinct variations can also be demonstrated. All three resistances (R0, RSEI, Rct) decrease with increasing temperature T, and Rct decreases much faster than R0 and RSEI, and appears to dominate the total resistance at low temperatures. Low temperatures lead to high electrolyte viscosity and poor lithium ion transport, which is consistent with the study of Zhang et al. [6–8,11]. A certain number of previous relevant researches on the relationship between (R0, RSEI, Rct) and temperature T of Lithium-ion battery, as illustrated in Figure 4, has been accomplished [34–36], which provide abundant evidence to the conclusion that the Arrhenius equation is reliable to describe the relations [34,37]. Note that the charge transfer resistance Rct in Figure 4c is also current dependent.

According to Arrhenius equation, the Rct can be given as Ea Rct ðT Þ ¼ Aexp T

(7)

where Ea is the activation energy, and A is a preexponential constant. The electrode reaction current can be calculated from the BVE [38] and the over-potential of the intercalation reaction [39]. αa Fη αc Fη I F ¼ Si0 exp exp RT RT

(8)

η ¼ ϕ s ϕ l E eq ðSOC Þ

(9)

where IF is the transfer current, S is the active surface of the electrode, αa and αc are anodic and cathodic transfer coefficient, i0 is exchange current density, R is the gas constant and η is the over-potential of the intercalation reaction, and the over-potential of the intercalation reaction can be obtained [39], ϕ s is the solid phase potential and ϕ l is the electrolyte phase potential. Eeq(SOC) is the opencircuit potential, which is dependent on SOC. Fleischer et al. [40,41] have proposed an approximation of the BVE first, and utilized the equation for on-line adaptive battery impedance parameter and state estimation. The dependency of the charge transfer resistance Rct(IF) on the current can be described by [40]: Rct ðI F Þ ¼ η=I F :

(10)

According to porous electrode theory [38,39,42], i0 in Equation (8) is independent from battery current, and can be given as:

Figure 3. Impedance spectra at various temperatures and current amplitudes at 20%SOC for 18650 battery. Int. J. Energy Res. 2016; 40:1869–1883 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/er

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Therefore, combined with the equations above, the description can be obtained: Rct ðT ; I F Þ ( 1 2SA′ BF

ln

exp

¼ A

Ea T

I F þ

1 2SA′ BF

1 2SA′ BF

exp

Ea T

I F

2

1=2 ) þ1 :

I F

(12) When the AC frequency is located at the junction of medium-frequency arc and low-frequency slop, the imaginary part of the impedance is closed to zero, so the current IF flowing through the Rct is approximately considered be equal to the battery terminal current I. Then the charge transfer resistance calculated from the impedance spectra can be given as [25]: Rct ðT ; I Þ

(

ln ¼ A

1 2SA′ BF

1=2 ) Ea 2 1 I þ I exp Ea exp þ 1 ′ T T 2SA BF 1 2SA′ BF

I

:

(13) Based on the derivation of BVE and Arrhenius empirical equation, the reduced charge transfer resistance (Rct) with the increasing current amplitude contributes to the observed shrinking of medium-frequency impedance arc. The Equation (13) can express the laws in Figure 4 c. Through the analysis above, and combined with Equation (5), the relationships between heat generation resistance RQ and T, f, I can be established in the AC heating model.

Figure 4. Variation of the resistance at different temperatures and current amplitudes: (a) effect of temperature and current amplitudes on R0; (b) effect of temperature and current amplitudes on RSEI; (c) effect of temperature and current amplitudes on Rct.

i0 ¼ BFk 0

(11)

3.3.2. Calibration of I considering voltage limiting Over-voltage and under-voltage will lead to exothermic reactions, gassing and thermal runaway of the battery [26,27]. To prevent irreversible damage in the working of battery, the battery voltage should be monitored and battery over-voltage should be averted at large current amplitude during the AC heating process. Thus, it is necessary to add current correction equations to the model. When the battery reaches the upper or lower voltage limits, the current is corrected to satisfy the voltage limit condition. To improve the model, the mathematical derivations are conducted for both sine and rectangular under the condition of over-voltage. When RQ is obtained, according to ohm’s law, the upper limit current can be given as (14) I upper_ limit ¼ U upper_ limit U OCV =RQ I lower_ limit ¼ ðU OCV U lower_ limit Þ=RQ

(15)

where B is the function of the concentration of lithium ion in the battery, k0 is the electrochemical reaction rate constant and can be described as [42] k 0 ¼ A′ exp Ea T and A′ is pre-exponential factor.

where Uupper_ limit is the upper voltage limit, Ulower_ limit is the lower voltage limit and UOCV is open-circuit voltage, which is related to SOC in the model. Iupper_ limit and Ilower_ limit are the limiting current amplitudes as shown in

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Figure 5. Sine and rectangular pulse waveforms.

Figure 5. Ipk is the input current amplitude. The selected frequencies in this study are within the range (>1 Hz) of which the imaginary part is quite small. RQ can be used to replace the modulus of total impedance approximately. (1) When the current is sinusoidal input, pffiffiffi If Iupper_ limit ≥ Ipk and Ilower_ limit ≥ Ipk, then, I ¼ I pk = 2 If Iupper_ limit < Ipk and Ilower_ limit ≥ Ipk, then,

If Iupper_ limit ≥ Ipk and Ilower_ limit < Ipk, then, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I 2pk þI 2lower_ limit I¼ 2 If Iupper_ limit < Ipk and Ilower_ limit < Ipk, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I 2upper_ limit þ I 2lower_ limit I¼ 2

(17)

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 uI 2 2 2 I I I upper_ limit I upper_ limit I upper_ limit 5 I upper_ limit u pk pk 4 upper_ limit I ¼t þ 1 arcsin π 2arcsin þ 4 2π I pk I pk I pk 2π I pk

If Iupper_ limit ≥ Ipk and Ilower_ limit < Ipk, then, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 uI 2 2 2 I I lower_ limit I lower_ limit I lower_ limit 5 I lower_ limit I lower_ limit u pk pk 4 I ¼t þ 1 arcsin π 2arcsin þ 4 2π I pk I pk I pk 2π I pk

If Iupper_ limit < Ipk and Ilower_ limit < Ipk, then, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 u I2 I lower_ limit I lower_ limit I lower_ limit 2 5 I 2lower_ limit I lower_ limit u pk 4 þ 1 arcsin π 2arcsin þ u u 2π I pk I pk I pk 2π I pk u 3 I ¼u 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u 2 I 2upper_ limit u I pk I I I I upper_ limit upper_ limit upper_ limit upper_ limit 5 t 4arcsin 1 π 2arcsin þ 2π I pk I pk I pk 2π I pk

(2) When selecting the rectangular pulse current, If Iupper_ limit ≥ Ipk and Ilower_ limit ≥ Ipk, then, I = Ipk If Iupper_ limit < Ipk and Ilower_ limit ≥ Ipk, I ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 I upper_ limit þI pk 2


(16)

Fundamentally, battery voltage limit is a complex nonlinear control process during battery AC charge/discharge process. In order to simplify the thermal model in the paper, the input RMS current in the simulation is calculated, and iterative calculation method is adopted according to the above formulas. 1875

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The methodology of the determination of the thermal model parameters and the working flowchart is shown in Figure 6. After the initialization of variables, and according to the impedance spectra results, Equations (5) and (13) derived from BVE and Arrhenius empirical equation, the overall heat generation resistance RQ can be calculated. Equations (16) and (17) are used to correct the current amplitude I because of the voltage limit condition. Considering the total resistance and battery current, total heat generation rate can be calculated. The temperature T can be obtained from the lumped energy balance equation. Because of the complex correlations between the values of the ECM elements and the temperature/current/frequency, numerical solutions are obtained with MATLAB programming.

4. RESULTS AND DISCUSSION 4.1. Varying current amplitudes at 300 Hz Respectively, the experimental and simulated temperature rise curves of various current amplitudes at 300 Hz are illustrated in Figures 7 and 8. The temperature increases significantly as the current increases. Although the resistance reduces during the temperature rise, the heat generation rate is more sensitive to current because of the squared relationship in Equation (6), which gives rise to a dramatic temperature growth inside the cell with the increment of current. The results show that 600 s are needed to heat the battery from 24 °C to 3 °C with sinusoidal waveform (10A, 300 Hz). Rectangular pulse heating harbors more obvious effect on the temperature evolution. It takes 10 min to warm up the cell from 24 °C to 21.1 °C. No over-voltage is observed through the surveillance of the oscilloscope because of the low impedance at 300 Hz. In terms of AC heating effect, rectangular pulse is better than sine waveform, and the main reason is that the RMS current of which is greater than the sine at the same current amplitude.

Figure 7. Effect of different current amplitudes on temperature evolution during AC heating at 300 Hz with sinusoidal waveform, simulations (continuous) and experimental measurements (dotted).

which can be illustrated from impedance spectra in Figure 3. The selected frequencies are 600 Hz, 300 Hz, 80 Hz, 30 Hz, 10 Hz and 1 Hz. The frequency effect on heating time is demonstrated in Figures 9 and 10, which show the temperature evolution in various AC signal frequencies. The temperature differences primarily result from the variation of impedance. At low frequencies (eg. 1 Hz), temperature curves in Figures 9 and 10 can be divided into two parts: the first part of the temperature evolution pointed by arrow A rises slowly, while the second portion enjoys a more rapid increase indicated by arrow B. The alternative interpretation is that the low temperature and low frequency result in the increase of impedance, and according to the descriptions in Equations (16) and (17), the heat generation rate decreases because the current amplitude is corrected as the result of voltage limit condition. Because of the combined effects of current amplitude and frequency, both the sine and rectangular excitations obtain

4.2. Varying frequencies at 8A and 10A The battery AC impedance is associated with the excitation frequency corresponding to different electrode processes,

Figure 6. Working flowchart of the thermal battery model.

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Figure 8. Effect of different current amplitudes on temperature evolution during AC heating at 300 Hz with rectangular pulse waveform, simulations (continuous) and experimental measurements (dotted). Int. J. Energy Res. 2016; 40:1869–1883 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/er


Figure 9. Effect of different frequencies on temperature evolution during AC heating at 8A and 10A with sinusoidal waveform, simulations (continuous) and experimental measurements (dotted).

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Figure 10. Effect of different frequencies on temperature evolution during AC heating at 8A and 10A with rectangular pulse waveform, simulations (continuous) and experimental measurements (dotted).

the maximum temperature rise at 10A and 30 Hz, from 24 °C to 7.79 °C for the former waveform and from 24 °C to 25.6 °C for the later one. Figure 11 describes the maximum temperature under different frequencies within 600 s. The coupling relationship can be expressed distinctly. With the reduction of frequency and the increase of current amplitude, temperature rises faster, but when frequency is too low, the temperature evolution becomes poor because of the influence of voltage limit protection. To better analyze and validate the temperature evolutions, the calibrated current waveforms are collected and displayed in Figure 12. It is apparent that the correction of current is obvious as the reduction of frequency. The data is in accordance with temperatures in Figures 9 and 10. The calibration of current begins from 30 Hz at 8A, and specifically, from 80 Hz for rectangular pulse waveform when the excitation current is 10A. During the battery charge and discharge process, current flows through the battery and battery voltage is larger or less than opencircuit potential because of the fact that electrode potential deviates from balance potential. This phenomenon is called polarization. It can be observed that simulation model results and experimental results differ slightly larger at

1 Hz. The explanation for this phenomenon is that the existence of electrochemical polarization corresponding to slow charge transfer reaction and mass transfer ionic diffusion in the electrolyte and electrodes inside the battery


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Figure 11. Maximum temperatures under different frequencies in 600 s.

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Figure 12. Calibrated current waveform from oscilloscope.

at low frequencies results in the irregular waveforms in Figure 12, which is not in accordance with the corrected waveforms based on Equations (16) and (17) in the simulation model.

4.3. The verification of battery performance degradation in AC heating Overall, the AC heating strategy affords us an easier access to heat a battery uniformly using external power. To verify if the AC heating method influences the battery performance degradation of the battery, the capacity calibration and DC impedance analysis are conducted after 20 and 40 times heating process at room temperature. When the frequency exceeds 10 Hz, the capacity and impedance would barely experience any attenuation. The irreversible impacts of rectangular pulse waveform at 1 Hz and 10A are illustrated in Table II. After 20 and 40 times heating, 3.7% and 6.6% capacity fading are observed, and the DC resistance increases by 1.2% and 2.2%, respectively.

The possible rate-limiting factors in the low temperature, such as charge-transfer resistance, lithium ion diffusion in the graphite particles and SEI layer on the negative, have been investigated by Fan et al. [5] and Tippmann et al. [43] for lithium-ion battery. No final conclusion about the battery degradation during the AC process at low temperature was obtained. We here propose a possible model during the AC heating process to support the theoretical considerations, as illustrated in Figure 13. Lithium ions and electronics reciprocate in the electrolyte, separator and active electrodes, and electrochemical reaction and diffusion processes are performed alternately in the AC process. At high frequencies, the excitation duration becomes short and the obstacle inside the battery only results from the electrolyte, electrode and the separator. As shown in Figure 13a, there is no lithium plating in the graphite material. As the excitation frequency decreases, the internal lithium-ion charge transfer process and the diffusion process would occur and the embedded lithium ions in the first charging half are delithiated in the coming

Table II. Capacity fading and resistance increase of rectangular pulse waveform at 1 Hz and 10A.

Battery capacity Ohmic resistance Polarized resistance Total DC resistance

1878

Before heating

After 20 times heating

After 40 times heating

100% 100% 100% 100%

96.3% 100.9% 102.5% 101.2%

93.4% 101.6% 104.6% 102.2%


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Figure 13. Schematic illustration of low-temperature aging behavior with AC heating method.

discharge part. So it does not produce dead lithium from Figure 13b. When the current becomes large in Figure 13 c, because of the complexity of nonlinear electrochemical reaction, the produced lithium has not been delithiated completely in the AC process. With some other side effects the created dead lithium causes the battery capacity fading and reduction of power characteristics. The irreversible lithium significantly affects chemical reaction and lithium ion diffusion process, which can be proven from increased polarization resistance in Table II. The discharge curves illustrated in Figure 14 are consistent with the hypothesis above. After 20 and 40 times heating, there is no existence of capacity fading and impedance growth. Because of the same variation trend, only the results for 10 Hz and 10A are shown which are representative for the observations at other frequencies and currents. Therefore, large current amplitudes arouse remarkable temperature rise, while signal frequency exerts more influence on the cell degradation. High frequency pulse serves as a good innovation to reduce the risk. However, efficient temperature rise can be obtained from high impedance at low frequencies. We present Figure 15 to describe the coupling relationships between current amplitudes, frequencies, impedance and total heat generation rate. The blue curve represents the AC impedance spectroscopy, and the green lines express the RMS current, which will be calibrated from the over-voltage limits. The bold black line stands for the battery age degradation boundary, and no lithium plating occurs below the line. The heating temperature evolution is indicated by the purple trend line. At the same current amplitude, rectangular

pulse performs better than sin waveform, and the main reason is that the RMS current of the pulse is greater than the sine excitation. The impedance increases with the reduction of frequency, and a critical point comprehensively depended on current and frequency will be generated. We speculate that there will be a degradation boundary line (may be not straight), and when the point is located over the degradation boundary line, such the yellow dot as shown in Figure 15, it is easier to produce lithium plating, which also shows conformance with the experiments. The degradation boundary line is comprehensively determined by current and frequency and varies at different temperature presumably. And one potential approach is to carry out the orthogonal experiments to obtain more information about the line. A reasonable as well as cautious selection of current and frequency (optimal point) is necessary in the practical application.

5. CONCLUSION The paper verifies the reliability and validity of the AC heating method based on establishment of the thermal model and experiments. The battery thermal model considers the coupling relationship between heat generation resistance and temperature, frequency and current amplitude, particularly the description through the derivation of Arrhenius empirical equation and BVE from the impedance spectra. To avoid the possibility of forever damage caused by over-voltage and under-voltage in AC heating, continuous correction of currents is performed to satisfy

Figure 14. Calibration of battery capacity and DC impedance at 10A and 10 Hz. Int. J. Energy Res. 2016; 40:1869–1883 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/er

1879

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Figure 15. Diagram of coupling relationships between current amplitudes, frequencies, impedance and total heat generation rate.

helps to improve the understanding of battery AC heating operating mechanism, but also will improve the efficiency of the design process. The study in the paper could serve the function as guidance to the design and development of the battery thermal management systems for EV/HEV.

NOMENCLATURE °C A C

Figure 16. Battery temperature cooling curves.

the voltage limit condition, which plays a very important role in the AC heating process. The experiments are conducted to investigate the effects of signal frequency and current amplitudes on temperature evolution. The temperature variations obtained from the simulation show good concordance with the experimental results. Then comprehensive analysis and explanation are presented. The temperature rise is determined by the current amplitude and excitation frequency comprehensively. Both the sine and rectangular excitations obtain the maximum temperature rise at 10A and 30 Hz in 600 s, from 24 °C to 7.79 °C for sine and from 24 °C to 25.6 °C for rectangular pulse. Although the AC heating method has prominent heating efficiency, it should be cautious to consider the possible battery performance degradation. Efficient temperature rise can be obtained from high impedance at low frequencies, but high frequency pulse serves as a good innovation to reduce the risk. From the capacity and impedance calibration, the irreversible damage is observed only at 1 Hz and 10A with rectangular pulse. The thermal model not only 1880

Hz s V W K m Cp t T qn q h Scell T0 Rct qohm qact qrev ΔS I F

= degree Centigrade = ampere = current magnitude in terms of cell capacity (1C = 2.3A) = hertz = seconds = volt = watt = Kelvin = mass of the battery (g) or the unit meter (m) = specific heat capacity (J g1 K1) = time (s) = battery temperature (°C) = heat flux transferred to the outside of the battery (W m2) = battery heat generation rate (W m2) = equivalent heat transfer coefficient (W m2 K1) = battery surface area (m2) = ambient temperature (°C) = charge transfer resistance (ohm) = ohmic heat (W m2) = active polarization heat (W m2) = electrochemical reaction heat (W m2) = entropy change of the cell reaction = current and represents RMS current (A) = Faraday constant (C mol1)


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R0 RSEI f RQ CSEI Cdl Ea A IF S i0 R Eeq(SOC) B k0 A′ Uupper_ limit Ulower_ limit UOCV Iupper_ limit Ilower_ limit Ipk c

= electrode and electrolyte resistance (ohm) = solid electrolyte interface impedance (ohm) = frequency (Hz) = battery overall impedance (ohm) = capacitance of solid electrolyte interphase (F m2) = electric double-layer capacitance (F m2) = activation energy (J mol1) = pre-exponential constant = transfer current (A) = active surface of the electrode (m2) = exchange current density (A m2) = the gas constant (J mol1 K) = open-circuit potential (V) = function of the concentration of lithium ion in the battery = electrochemical reaction rate constant = pre-exponential factor = upper voltage limit (V) = lower voltage limit (V) = open-circuit voltage (V) = upper limiting current amplitudes (A) = lower limiting current amplitudes (A) = the input current amplitude (A) = constant

Acronyms EV HEV LiFePO4 LiMn2O4 LiMnNiCoO2

= = = = =

LiPF6

=

SEI AC sin rect SOC DC ECM OCV RC RMS BVE

= = = = = = = = = = =

electric vehicle hybrid electric vehicle lithium iron phosphate lithium ion manganese lithium cobalt manganese nickel oxide solution of lithium hexafluorophosphate solid electrolyte interphase alternating current sinusoidal waveform rectangular pulse state of charge direct current equivalent circuit model open-circuit voltage resistance and capacitance Root Mean Square Butler–Volmer equation

Greek letters αa αc

η ϕs ϕl

= over-potential (V) = solid phase potential (V) = electrolyte phase potential (V)

Subscripts/superscripts cell ct ohm act rev dl eq upper_ limit lower_ limit pk s l

= = = = = = = = = = = =

battery charge transfer ohmic active polarization electrochemical reaction double-layer equivalent upper limit lower limit peak amplitude solid electrolyte

APPENDIX A: CALIBRATION OF THE EQUIVALENT HEAT TRANSFER COEFFICIENT The utilization of equivalent heat transfer coefficient permits to incorporate the effect ambient cooling conditions in thermal model. The heat generation rate q is equal to zero in the battery cooling process; thus, the equivalent heat transfer coefficient can be calculated according to Equations (1) and (2). The thermal parameters used for the thermal modeling are listed in Table I. Battery density and heat capacity of the cell are assumed to be uniform throughout the battery and to remain constant within a known range of temperature. Following Equations (1) and (2), the ambient temperature is 24 °C, other parameters can be found in Table I. A simplified equation can be derived as follows: ∂T =∂t ¼ 5:5507810-5 hT þ 0:013763h

(A:1)

Also, the general solution of Equation (A.1) can be given by T ¼ 248:9 þ cexp 5:55078105 ht

(A:2)

where c is a constant. Through the high quality of fit between the experimental data and simulation as shown in Figure 16, the h can be calculated as follows according to Equation (A.2) h ¼ 16:02W m-2 K-1 :

(A:3)

ACKNOWLEDGEMENTS = anodic transfer coefficient = cathodic transfer coefficient


This work is financially supported by the National Natural Science Foundation of China (NSFC, Grant 1881

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No.51576142) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP, Grant No.20130072110055).

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