IN RECENT years, owing to the renowned features, such as

5620 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 Improvement of Li-ion Battery Discharging Performance by Pulse and Sinusoidal Current Strategies Liang-Rui Chen, Member, IEEE, Jin-Jia Chen, Chun-Min Ho, Shing-Lih Wu, Student Member, IEEE, and Deng-Tswen Shieh Abstract In this paper, the ac impedance analysis is used to explore the optimal discharging frequency for a Li-ion battery. Experiments indicate that the optimal discharging frequency is at the minimum ac impedance frequency f Zmin for a conventional pulse-current (PC) discharging. In addition, a sinusoidal current (SC) discharging strategy is also proposed to achieve better performances. This SC discharging strategy improves the discharging capacity, discharging efficiency, and rising temperature of the Li-ion battery by about 1.3%, 1.32%, and 41.9%, respectively, as compared with the traditional constant-current discharging. Index Terms Li-ion battery, minimum ac impedance, sinusoidal current (SC) discharging. I. INTRODUCTION IN RECENT years, owing to the renowned features, such as high dense power, low self-discharge rate, high operating voltage, and light weight of Li-ion batteries, the development of portable electronic apparatus, electric vehicles, and renewable energies has aggressively proliferated. In addition, many battery charging technologies [1] [15] were presented and showed that the battery charging performances, such as speed, efficiency, rising temperature, and life cycle, can be greatly improved. It seems that these advanced charging methods can reach the ultimate performance of the battery-powered system. However, the performance still increases through the consideration of the battery discharging process. In fact, many battery management methods such as integer linear programming [16], weighted-k round-robin scheduling [17], energy management algorithm method [18], [19], and fuzzy logic control [20], [21] were proposed. These methods are capable of optimizing the voltage source and then prolonging the run time and life cycle. Meanwhile, some researchers focused their discharge performance study on the effect of the pulse current (PC) [22] [28]. Manuscript received April 2, 2012; revised July 6, 2012; accepted August 11, 2012. Date of publication November 29, 2012; date of current version June 21, 2013. L.-R. Chen, J.-J. Chen, C.-M. Ho, and S.-L. Wu are with the Department of Electrical Engineering, National Changhua University of Education, Changhua 500, Taiwan (e-mail: lrchen@cc.ncue.edu.tw; jjchen@cc.ncue. edu.tw; gtomichaelho@yahoo.com.tw; D96621001@cc.ncue.edu.tw). D.-T. Shieh is with the Material and Chemical Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan (e-mail: dts@itri.org.tw). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2012.2230599 Fig. 1. Complete Li-ion battery ac impedance model. The PC charging/discharging provides the battery pulsed current, instead of the constant current (CC); therefore, it can provide a rest period for ions to diffuse and also distribute the electrolyte s ions more evenly to improve charging/discharging performance. In addition, other discharging waveforms, such as triangle, sawtooth, and trapezoidal waveforms, were also used [29]. This kind of non-cc discharging technologies seems to increase the battery discharging performance, and thus, it is very potential to be widely used in the future [30] [33]. However, until present, there is no such method exploring the optimal frequency for PC discharging. Recently, owing to the wide use of ac impedance analysis in the research of electrochemistry, it can also be used to explore the battery performance [34] [36]. Thus, the optimal discharging frequency is assessed by using ac impedance analysis in this paper. Additionally, sinusoidal current (SC) discharging is also presented with significant performance. The experiments show that, when the discharging frequency is chosen as the minimum ac impedance frequency, the rising temperature can be improved about 41.9%. II. AC IMPEDANCE MODEL Fig. 1 shows the Li-ion battery ac impedance model. This model consists of two charge transfer resistances R ct1 and R ct2, two Warburg impedances Z w1 and Z w2, two double-layer capacitances C d1, and C d2, an ohmic resistance R o, and two inductances L d1 and L d2 [37] [40]. The Warburg impedance Z w influences the ac impedance only when the charging frequency is below 1 Hz [41]. In the non-cc discharging study, the Warburg impedance Z w can be neglected, and the simplified Li-ion battery equivalent circuit model is shown as Fig. 2. At the viewpoint of electrical circuit, different discharging frequencies will result in different battery ac impedances. In order to obtain the maximum energy transfer efficiency during 0278-0046/$31.00 2012 IEEE

CHEN et al.: IMPROVEMENT OF Li-ion BATTERY DISCHARGING PERFORMANCE BY PC AND SC STRATEGIES 5621 Fig. 2. Simplified Li-ion battery ac impedance model. discharging, we need to select the minimum ac impedance Z min which corresponds to the optimal discharging frequency f Zmin. That means that the energy loss in chemical energy transferring to electrical energy is minimized. In other words, the maximum energy transfer efficiency (i.e., the best electrochemical reaction) is obtained in the battery. In fact, it has been shown that a smaller charge transfer resistance means a better electrochemical reaction [41], [42], and the minimum ac impedance frequency f Zmin corresponding to the minimum ac impedance Z min is obtained and shown in [43]. The mathematical expression is given as where f Zmin = 1 2πR ct C d k 1 (1) K = 2Ro R 3 ctc 2 d +2L dr 2 ctc d + R 4 ctc 2 d L d. (2) III. EXPERIMENT PROCESS AND TEST PLATFORM Fig. 3 shows the flowchart of the battery discharging test. First, a CC of 1 C is used to charge a Li-ion battery for a constant time. The battery charging capacity Q IN is calculated as Q IN = I IN t IN (3) where I IN is the charging current and t IN is the charging time. Next, the ac impedance spectrum of the Li-ion battery is obtained by using an ac impedance analyzer. According to the ac impedance spectrum, the minimum ac impedance frequency f Zmin can be obtained. Then, the Li-ion battery is discharged by different strategies. While in the battery discharging process, the discharging time, the discharging capacity, and the rising temperature are measured and recorded simultaneously. When the open-circuit voltage of the Li-ion battery reaches to the fully discharging voltage, i.e., 3.0 V, the Li-ion battery is regarded as fully discharged and then rested for 1 hour. The total discharging capacity Q OUT can be calculated as Q OUT = I OUT t OUT (4) where I OUT is the average discharging current and t OUT is the discharging time. Finally, the battery discharging efficiency η is Fig. 3. Experiment flowchart. calculated according to η = Q OUT 100%. (5) Q IN Fig. 4 shows the battery discharging test platform that consists of a digital oscilloscope, a voltage meter, a function generator, a temperature recorder, and a voltage/current converter which includes a MOSFET and an operational amplifier. First, the function generator is used to produce sinusoidal ripple signals V S (t) shown as follows: V S (t) =V m + V m sin 2πf s t (6)

5622 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 Fig. 4. Block diagram of the discharge test platform. in which V m is the maximum voltage and f s is the discharging frequency. The sinusoidal current for discharging the Li-ion battery can be generated by the voltage/current converter and shown as I C (t) = V S(t) R = V m + V m sin 2πf s t R where R is a current set resistor. When the battery is discharging, the digital oscilloscope is used to get the wave of the discharging current and the discharging voltage. Meanwhile, the discharging time, the discharging capacity, and the rising temperature are also measured and recorded. Fig. 5 shows the actual picture of the battery discharge test platform, and the adopted apparatus are listed in Table I. (7) Fig. 5. Pictures of (a) the battery discharge test platform and (b) the ac impedance analyzer. TABLE I APPARATUS IV. EXPERIMENTAL RESULTS Three brand-new high-power Li-ion batteries, named Batteries A, B, and C, are used. The specifications of the high-power Li-ion batteries used are listed as Table II. In order to verify the PC discharging performance, five discharging frequencies, 1 Hz, 10 Hz, 100 Hz, 10 khz, and f Zmin, are tested. In addition, the performance of the CC discharging is also included. Fig. 6 shows the ac impedance spectrum of Battery A measured by the ac impedance analyzer Solartron 1280B. The ac impedance spectrum indicates that the minimum ac impedance frequency f Zmin and the minimum ac impedance Z min are about 1055 Hz and 0.0384 Ω, respectively. Fig. 7 shows the generated PC of the proposed battery discharge test platform. Clearly, the PC discharging waveform can be excellently generated as desired. In the PC discharging strategy, the duty cycle and average current are 50% and 1.5 A (i.e., 1 C), respectively. The discharging voltage and temperature curves of Battery A discharged with the PC strategy for different frequencies and those with the CC strategy in a fully discharging cycle are shown in Fig. 8(a) and (b). More detailed experiment results are listed in Table III. It is interesting that different discharging frequencies have different ac impedances and then result in different discharging losses. Therefore, same capacity batteries have different discharging times when discharged with different frequencies. From Fig. 8(a) and (b) and Table III, we can find different discharging performances with different discharging frequencies. This means that the discharging frequency for the Li-ion batteries is an important variable. It is clear that the PC discharging with f Zmin has

CHEN et al.: IMPROVEMENT OF Li-ion BATTERY DISCHARGING PERFORMANCE BY PC AND SC STRATEGIES 5623 TABLE II SPECIFICATIONS OF THE LI-ION BATTERIES USED Fig. 6. ac impedance spectrum of Battery A. Fig. 8. (a) Discharging voltage curves and (b) temperature curves of Battery A. TABLE III EXPERIMENTAL RESULTS OF BATTERY ADISCHARGED WITH THE PC AND CC STRATEGIES Fig. 7. PC discharging waveforms. the maximum discharging capacity, maximum discharging efficiency, and minimum rising temperature. Figs. 9 and 10 show the ac impedance spectrum of Batteries B and C, respectively. The minimum ac impedance frequencies f Zmin for Batteries B and C are about 1062 and 1065 Hz, respectively. The minimum ac impedances Z min of Batteries B and C are about 0.0383 and 0.0386 Ω, respectively. Clearly, the minimum ac impedance frequencies f Zmin are varied for different Li-ion batteries. Tables IV and V show the experiment results of Batteries B and C discharged with PC and CC strategies. We can see that Batteries B and C discharged with the PC strategy for f Zmin have the best performance, with the same result as that of Battery A. Table VI shows the averaging experimental values of Batteries A, B, and C. It is interesting that the discharging efficiency and rising temperature of the PC discharging with 100 Hz and f Zmin are better than those of the CC discharging. However, the rising temperature of the CC discharging is smaller than that of the PC discharging with 1 Hz, 10 Hz, and 10 khz. This indicates that the PC discharging without suitable frequency is not better than the CC one. However, Batteries A, B, and C discharged with f Zmin have the best discharging performance. We can therefore conclude that the optimal discharging frequency of the conventional PC discharging is f Zmin.The averaging discharging time, averaging efficiency, and averaging rising temperature of the conventional PC strategy with f Zmin are 3200 s, 98.74%, and 3.8 C, respectively. As compared with the CC discharging, the discharging capacity, discharging

5624 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 TABLE V EXPERIMENTAL RESULTS OF BATTERY CDISCHARGED WITH THE PC AND CC STRATEGIES Fig. 9. ac impedance spectrum of Battery B. TABLE VI AVERAGING EXPERIMENTAL VALUES OF THESE THREE LI-ION BATTERIES DISCHARGED WITH THE PC AND CC STRATEGIES Fig. 10. ac impedance spectrum of Battery C. TABLE IV EXPERIMENTAL RESULTS OF BATTERY BDISCHARGED WITH THE PC AND CC STRATEGIES efficiency, and rising temperature are improved by about 0.9%, 0.9%, and 15.8%, respectively. Since the waveform of the PC discharging consists of 45% total harmonic distortion, much electrochemical reaction is not at the minimum ac impedance frequency f Zmin.Inthis paper, the SC discharging strategy is presented to achieve better performances. In fact, the SC charging was verified and showed good performance [43]. Fig. 11 shows the voltage and current waveforms of Battery A discharged with the SC strategy. The average discharging current is 1.5 A (i.e., 1 C), which is the same current as that used in the PC and the CC discharging. In order to verify the discharging performance of the SC strategy, five discharging frequencies, 1 Hz, 10 Hz, 100 Hz, Fig. 11. SC waveforms of Battery A with frequency of 1055 Hz. 10 khz, and f Zmin, are tested. The voltage and temperature curves of Battery A discharged with SC, CC, and PC strategies in a fully discharging cycle are shown in Fig. 12(a) and (b). Clearly, the proposed SC strategy with f Zmin is not only better than the CC one but also better than the PC one with f Zmin. More detailed experiment results are listed in Table VII. We can find different discharging performances for the SC discharging with different frequencies. However, the performances of Battery A discharged with the SC strategy for 1 Hz,

CHEN et al.: IMPROVEMENT OF Li-ion BATTERY DISCHARGING PERFORMANCE BY PC AND SC STRATEGIES 5625 TABLE VIII EXPERIMENTAL RESULTS OF BATTERY BDISCHARGED WITH THE PROPOSED SC AND CC STRATEGIES Fig. 12. (a) SC voltage curves and (b) temperature curves of Battery A. TABLE IX EXPERIMENTAL RESULTS OF BATTERY CDISCHARGED WITH THE PROPOSED SC AND CC STRATEGIES TABLE VII EXPERIMENTAL RESULTS OF BATTERY ADISCHARGED WITH THE PROPOSED SC AND CC STRATEGIES TABLE X AVERAGING EXPERIMENTAL VALUES OF THESE THREE LI-ION BATTERIES DISCHARGED WITH THE PROPOSED SC AND CC STRATEGIES 10 Hz, 100 Hz, f Zmin, and 10 khz are all better than or equal to those with the CC strategy. The SC discharging with f Zmin has the best performance as predicted. The experimental results of Batteries B and C discharged with the SC strategy for 1 Hz, 10 Hz, 100 Hz, f Zmin, and 10 khz and with the CC strategy are also listed in Tables VIII and IX. Obviously, the performances, including the discharging capacity, discharging efficiency, and rising temperature of the SC strategy, are all better than or equal to those of the CC strategy. Table X shows the averaging experimental values of these three Li-ion batteries discharged using SC and CC strategies. It

5626 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 TABLE XI AVERAGING EXPERIMENTAL VALUES OF THESE THREE LI-ION BATTERIES DISCHARGED WITH THE CC STRATEGY, THE PC STRATEGY WITH f Zmin, AND THE PROPOSED SC STRATEGY WITH f Zmin Fig. 13. Charge/discharge cycle experimental results. (a) Z min and (b) f Zmin. is clear that the proposed SC strategy with f Zmin is the best one among these three strategies. The averaging discharging capacity, averaging efficiency, and averaging rising temperature of the proposed SC strategy with f Zmin are 3212 s, 99.11%, and 3.1 C, respectively. The discharging capacity, discharging efficiency, and rising temperature are improved by about 1.3%, 1.32%, and 41.9%, respectively, as compared with those of the conventional CC strategy. Comparing Tables VI and X, we can also see that the discharging capacity, discharging efficiency, and rising temperature of the battery discharged with the SC strategy are also all better than those with the PC strategy. As compared with the performance of the PC strategy, the discharging capacity, efficiency, and rising temperature are improved by about 0.37%, 0.36%, and 22.6%, respectively, by using the SC strategy. Table XI listed the averaging experimental values of these three Li-ion batteries discharged with the CC strategy, the PC strategy with f Zmin, and the proposed SC strategy with f Zmin. The aforementioned experiment results indicate that the discharging frequency for the Li-ion batteries is an important parameter. In particular, Li-ion battery discharging frequency selected at the minimum ac impedance frequency f Zmin, larger discharging capacity, higher discharging efficiency, and lower rising temperature can be obtained. We can also find that the proposed SC strategy with f Zmin has the best discharging performance, particularly in rising temperature. In a Li-ion battery, the rising temperature obviously affects the life cycle. The life cycle will be reduced by 50% if the rising temperature increases by 10 C [44], [45]. This means that a battery life cycle can be effectively enlarged by selecting suitable discharging frequency and using the presented SC strategy. The curves of Z min and f Zmin for different charge/ discharge cycles are plotted in Fig. 13(a) and (b). We can see that the minimum ac impedance frequencies f Zmin are within (1000 Hz, 1100 Hz). This means that a fixed frequency can be set in a practical discharger to obtain a near optimal charging performance. However, developing an online adaptive tuning algorithm to find f Zmin is necessary and worth to study in the future. V. C ONCLUSION In this paper, the ac impedance spectrum is used to explore the optimal discharging frequency. Experiments show that the

CHEN et al.: IMPROVEMENT OF Li-ion BATTERY DISCHARGING PERFORMANCE BY PC AND SC STRATEGIES 5627 discharging frequency for the Li-ion batteries is an important variable, and the optimal discharging frequency is at the minimum ac impedance frequency f Zmin. As compared with the performance of the CC strategy, the discharging capacity, discharging efficiency, and rising temperature of the PC discharging with f Zmin are improved by about 0.9%, 0.9%, and 15.8%, respectively. The SC discharging strategy was also presented in this paper. Experiments show that the proposed SC strategy is not only better than the CC strategy but also better than the PC strategy. As compared with the discharging performance of the CC strategy, the discharging capacity, discharging efficiency, and rising temperature are improved by about 1.3%, 1.32%, and 41.9%, respectively, by using the proposed SC strategy. REFERENCES [1] L. R. Chen, Design of duty-varied voltage pulse charger for improving Li-ion battery-charging response, IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 480 487, Feb. 2009. [2] L. R. Chen, N. Y. Chu, C. S. Wang, and R. H. Liang, Design of a reflexbased bidirectional converter with the energy recovery function, IEEE Trans. Ind. Electron., vol. 55, no. 8, pp. 3022 3029, Aug. 2008. [3] C. H. Lin, C. Y. Hsie, and K. H. Chen, A Li-ion battery charger with smooth control circuit and built-in resistance compensator for achieving stable and fast charging, IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 2, pp. 506 517, Feb. 2010. [4] Y. H. Liu and Y. F. Luo, Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi approach, IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3963 3971, Dec. 2010. [5] Y. H. Liu, C. H. Hsieh, and Y. F. Luo, Search for an optimal five-step charging pattern for Li-ion batteries using consecutive orthogonal arrays, IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 654 661, Jun. 2011. [6] H. Qian, J. Zhang, J. S. Lai, and W. S. Yu, A high-efficiency grid-tie battery energy storage system, IEEE Trans. Power Electron., vol. 26, no. 3, pp. 886 896, Mar. 2011. [7] Y. C. Chuang, High-efficiency ZCS buck converter for rechargeable batteries, IEEE Trans. Ind. Electron., vol. 57, no. 7, pp. 2463 2472, Jul. 2010. [8] J. J. Chen, F. C. Yang, C. C. Lai, Y. S. Hwang, and R. G. Lee, A high-efficiency multimode Li-ion battery charger with variable current source and controlling previous-stage supply voltage, IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2469 2478, Jul. 2009. [9] L. R. Chen, J. J. Chen, N. Y. Chu, and G. Y. Han, Current-pumped battery charger, IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2482 2488, Jun. 2008. [10] L. R. Chen, R. C. Hsu, and C. S. Liu, A design of a grey-predicted Liion battery charge system, IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3692 3701, Oct. 2008. [11] L. R. Chen, C. S. Liu, and J. J. Chen, Improving phase-locked battery charger speed by using resistance-compensated technique, IEEE Trans. Ind. Electron., vol. 56, no. 4, pp. 1205 1211, Apr. 2009. [12] L. R. Chen, A design of optimal pulse charge system by variable frequency technique, IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 398 405, Feb. 2007. [13] A. A.-H. Hussein and I. Batarseh, A review of charging algorithms for nickel and lithium battery chargers, IEEE Trans. Veh. Technol., vol. 60, no. 3, pp. 830 838, Mar. 2011. [14] L. R. Chen, C. M. Young, N. Y. Chu, and C. S. Liu, Phase-locked bidirectional converter with pulse charge function for 42-V/14-V dualvoltage powernet, IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 2045 2048, May 2011. [15] J. Zhang, J. Yu, C. Cha, and H. Yang, The effects of pulse charging on inner pressure and cycling characteristics of sealed Ni/MH batteries, J. Power Sources, vol. 136, no. 1, pp. 180 185, Sep. 2004. [16] Z. Ren, B. H. Krogh, and R. Marculescu, Hierarchical adaptive dynamic power management, IEEE Trans. Comput., vol. 54, no. 4, pp. 409 420, Apr. 2005. [17] H. Kim and K. G. Shin, Scheduling of battery charge, discharge, and rest, in Proc. IEEE RTSS, Washington, DC, Dec. 2009, pp. 13 22. [18] A. Manenti, A. Abba, A. Merati, S. M. Savaresi, and A. Geraci, A new BMS architecture based on cell redundancy, IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 4314 4322, Sep. 2011. [19] Z. Amjadi and S. S. Williamson, Power-electronics-based solutions for plug-in hybrid electric vehicle energy storage and management systems, IEEE Trans. Ind. Electron., vol. 57, no. 2, pp. 608 616, Feb. 2010. [20] S. G. Li, S. M. Sharkh, F. C. Walsh, and C. N. Zhang, Energy and battery management of a plug-in series hybrid electric vehicle using fuzzy logic, IEEE Trans. Veh. Technol., vol. 60, no. 8, pp. 3571 3585, Oct. 2011. [21] M. Zandi, A. Payman, J. P. Martin, S. Pierfederici, B. Davat, and F. M. Tabar, Energy management of a fuel cell/supercapacitor/battery power source for electric vehicular applications, IEEE Trans. Veh. Technol., vol. 60, no. 2, pp. 433 443, Feb. 2011. [22] Y. C. Hsieh, C. S. Moo, T. J. Tsai, and K. S. Ng, Investigation on intermittent discharging for lead-acid batteries, in Proc. IEEE PESC, Rhodes, Greece, Jun. 2008, pp. 4683 4688. [23] K. S. Ng, C. S. Moo, Y. C. Lin, Y. C. Hsieh, and Y. L. Tsai, Intermittent discharging for lead-acid batteries, in Proc. IEEE PCC, Nagoya, Japan, Apr. 2007, pp. 216 220. [24] J. Zhang, S. Ci, H. Sharif, and M. Alahmad, Modeling discharge behavior of multicell battery, IEEE Trans. Energy Convers., vol. 25, no. 4, pp. 1133 1141, Dec. 2010. [25] J. Wang, K. Zou, C. C. Chen, and L. H. Chen, A high frequency battery model for current ripple analysis, in Proc. IEEE APEC, Palm Springs, CA, Feb. 2010, pp. 676 680. [26] M. Chen and G. A. Rincón-Mora, Accurate electrical battery model capable of predicting runtime and I-V performance, IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 504 511, Jun. 2006. [27] C. C. Hua and Z. W. Syue, Charge and discharge characteristics of lead-acid battery and LiFePO 4 battery, in Proc. IEEE PEC, Jun. 2010, pp. 1478 1483. [28] K. Zou, S. Nawrocki, R. X. Wang, and J. Wang, High current battery impedance testing for power electronics circuit design, in Proc. IEEE VPPC, Dearborn, MI, Sep. 2009, pp. 531 535. [29] Y. C. Hsieh, C. S. Moo, T. J. Tsai, and K. S. Ng, High-frequency discharging characteristics of LiFePO 4 battery, in Proc. IEEE ICIEA, Jun. 2011, pp. 953 957. [30] X. M. Xiang, Y. B. Liu, Z. Y. Luo, and P. W. Tu, Study of a battery gridconnected discharging system which based on boost converter, in Proc. IEEE ICECE, Yichang, China, Sep. 2011, pp. 4980 4983. [31] L. R. Yue, Y. Q. Tang, and S. D. Zhu, The research on detection method of battery discharge, in Proc. IEEE ICDMA, Zhangjiajie, Hunan, China, Aug. 2011, pp. 1324 1327. [32] K. A. Smith, C. D. Rahn, and C. Y. Wang, Model-based electrochemical estimation and constraint management for pulse operation of lithium ion batteries, IEEE Trans. Control Syst. Technol.,vol.18,no.3,pp.654 663, May 2010. [33] A. Hammar, P. Venet, R. Lallemand, G. Coquery, and G. Rojat, Study of accelerated aging of supercapacitors for transport applications, IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3972 3979, Dec. 2010. [34] F. Huet, A review of impedance measurements for determination of the state-of-charge or state-of-health of secondary batteries, J. Power Sources, vol. 70, no. 1, pp. 59 69, Jan. 1998. [35] S. Buller, M. Thele, R. W. A. A. De Doncker, and E. Karden, Impedancebased simulation models of supercapacitors and Li-ion batteries for power electronic applications, IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 742 747, May/Jun. 2005. [36] M. Coleman, C. K. Lee, C. Zhu, and W. G. Hurley, State-of-charge determination from EMF voltage estimation: Using impedance, terminal voltage, and current for lead-acid and lithium-ion batteries, IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2550 2557, Oct. 2007. [37] S. M. R. Niya, M. Hejabi, and F. Goba, Estimation of the kinetic parameters of processes at the negative plate of lead-acid batteries by impedance studies, J. Power Sources, vol. 195, no. 17, pp. 5789 5793, Sep. 2010. [38] R. Li, J. F. Wu, H. Y. Wang, and G. C. Li, Prediction of state of charge of lithium-ion rechargeable battery with electrochemical impedance spectroscopy theory, in Proc. IEEE ICIEA, Taichung, Taiwan, Jun. 2010, pp. 684 688. [39] F. Croce, F. Nobili, A. Deptula, W. Lada, R. Tossici, A. D Epifanio, B. Scrosati, and R. Marassi, An electrochemical impedance spectroscopic study of the transport properties of LiNi 0.75 Co 0.25 O 2, Electrochem. Commun., vol. 1, no. 12, pp. 605 608, Dec. 1999. [40] S. Rodrigues, N. Munichandriah, and A. K. Shukla, AC impedance and state-of-charge analysis of a sealed lithium-ion rechargeable battery, J. Solid State Electrochem., vol. 3, no. 7/8, pp. 397 405, Sep. 1999. [41] D. Qu, The ac impedance studies for porous MnO 2 cathode by means of modified transmission line model, J. Power Sources, vol. 102, no. 1/2, pp. 270 276, Dec. 2001.

5628 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 [42] R. M. Spotniz, AC impedance simulation for lithium-ion cells, in Proc. IEEE BCAA, Long Beach, CA, Jun. 2000, pp. 121 126. [43] L. R. Chen, S. L. Wu, D. T. Shieh, and T. R. Chen, Sinusoidal ripple current charging strategy and optimal charging frequency for Li-ion batteries, IEEE Trans. Ind. Electron., vol. 60, no. 1, pp. 88 97, Jan. 2013. [44] M. Uno and K. Tanaka, Accelerated charge-discharge cycling test and cycle life prediction model for supercapacitors in alternative battery applications, in Proc. IEEE INTELEC, Sagamihara, Japan, Oct. 2011, pp. 1 6. [45] X. Wang, Y. Sone, H. Naito, C. Yamada, G. Segami, and K. Kibe, Cyclelife testing of large-capacity lithium-ion cells in simulated satellite operation, J. Power Sources, vol. 161, no. 1, pp. 594 600, Oct. 2006. Chun-Min Ho was born in Kaohsiung, Taiwan, in 1977. He received the B.S. and M.S. degrees from the Department of Electrical Engineering, National Changhua University of Education, Changhua, Taiwan, in 2000 and 2007, respectively, where he is currently working toward the Ph.D. degree. His research interests include power electronics, battery chargers, renewable energy, and control applications. Liang-Rui Chen (M 04) was born in Changhua, Taiwan, in 1971. He received the B.S., M.S., and Ph.D. degrees in electronic engineering from National Taiwan University of Science and Technology, Taipei, Taiwan, in 1994, 1996, and 2001, respectively. He joined the faculty of the Department of Electrical Engineering, National Changhua University of Education, Changhua, in August 2006, where he is currently a Professor. His major research interests are power electronics, battery-powered circuit design, and renewable energy. Dr. Chen is a member of the IEEE Industrial Electronics Society. He was the recipient of the Young Researcher Award from the National Science Council, Taiwan, in 2005. Jin-Jia Chen received the B.Sc. degree in electrical engineering from Chung Yuan University, Chung Li, Taiwan, in 1980, the M.Sc. degree in electro-optic science from National Central University, Taoyuan, Taiwan, in 1985, and the Ph.D. degree in electrical engineering from Texas A&M University, College Station, in 1993. From 1985 to 1988, he was a Lecturer in electrical engineering with the Lee Ming Institute of Technology, Taipei, Taiwan. From 1993 to 2003, he was with the Department of Electro-Optics, National Formosa University, Yunlin, Taiwan. Since 2003, he has been with the Department of Electrical Engineering, National Changhua University of Education, Changhua, Taiwan, where he is currently a Professor of electro-optics. His main research interests are the modeling of optoelectronic devices, optic design for LED lighting, and power electronics. Shing-Lih Wu (S 09) was born in Taichung, Taiwan, in 1969. He received the B.S. degree from National Formosa University, Yunlin, Taiwan, in 2003, the M.S. degree from the Department of Electrical Engineering, Feng Chia University, Taichung, in 2005, and the Ph.D. degree from the Department of Electrical Engineering, National Changhua University of Education, Changhua, Taiwan, in 2012. He joined Toko University, Puzih City, Chiayi, Taiwan, in March 2013, where he is currently an Assistant Professor. His major research interests include microcontroller control, battery chargers, and control applications. Deng-Tswen Shieh was born in Tainan, Taiwan, in 1968. He received the B.S., M.S., and Ph.D. degrees in chemical engineering from National Taiwan University of Science and Technology, Taipei, Taiwan, in 1990, 1992, and 1995, respectively. He joined the Material and Chemical Research Laboratories of the Industrial Technology Research Institute, Hsinchu, Taiwan, in 2002, where he is currently a Researcher. His major research interests are safety and reliability of the lithium-ion battery/ module.