A Single-Phase Multilevel Inverter With Battery Balancing - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 5, MAY 2013

A Single-Phase Multilevel Inverter With Battery Balancing Chung-Ming Young, Member, IEEE, Neng-Yi Chu, Student Member, IEEE, Liang-Rui Chen, Member, IEEE, Yu-Chih Hsiao, and Chia-Zer Li

Abstract—In this paper, a single-phase multilevel inverter with battery balancing is proposed. The input of each individual inverter is directly connected to a battery. The combination of batteries can be controlled according to the batteries’ voltages to implement the battery-balancing function. The operational principle of the proposed system is first described, and then, the design equation is derived. Experiments show that the battery-balancing discharge function is achieved. Finally, a prototype is designed and implemented to verify the feasibility and excellent performance. Index Terms—A multilevel inverter, battery balancing. Fig. 1.

Renewable energy systems.

I. I NTRODUCTION

I

N RECENT years, environmental concerns and the continuous depletion of fossil fuel reserves have spurred significant interest in renewable energy sources. However, renewable energy sources such as wind turbines and photovoltaics are intermittent in nature and produce fluctuating active power. Interconnecting these intermittent sources to the utility grid on a large scale could affect the voltage/frequency control of the grid and lead to severe power quality issues [1]–[6]. An energy storage system which contains a large capacity of the battery bank is indispensable for countering uneven compensation. To obtain better battery storage performances, many battery charging strategies have been presented [7]–[14]. In order to reduce energy loss in transmission lines and increase the overall battery capacity, the battery bank is series connected for a high-voltage dc power supply [1], [2], [7], [15]–[18]. Because of the manufacturing capacity, the internal impedance and the self-discharge rate are different in each battery, and individual batteries will overcharge or overdischarge in a series-connected battery pack, resulting in smaller storage. Therefore, the power conversion system requires a battery-balancing circuit, as shown in Fig. 1, to adjust each battery voltage to be equal. There have been some battery-balancing circuits made to control the battery capacity, and these can be classified as

Manuscript received October 16, 2011; revised April 3, 2012; accepted June 1, 2012. Date of publication July 10, 2012; date of current version January 30, 2013. C.-M. Young and N.-Y. Chu are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail: [email protected]). L.-R. Chen, Y.-C. Hsiao, and C.-Z. Li are with the Department of Electrical Engineering, National Changhua University of Education, Changhua 500, Taiwan (e-mail: [email protected]). 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.2012.2207656

dissipative battery-balancing circuits [19], [20] and nondissipative battery-balancing circuits [21]–[27]. The simplest dissipative battery-balancing circuit is made by shunting a resistor across each cell in the string to make the cell maximum voltage equal to prevent voltage unbalance. This dissipative circuit is not good for energy preservation. The nondissipative batterybalancing circuits approach is based on dc/dc converters, such as the flyback converter [21], [22], the buck–boost converter [21], [23], [24], the switch-capacitor converter [20], [21], [25]– [27], etc. The principle is to transfer energy from the higher voltage cell to the lower voltage cell or to the whole stack with less power loss; it is more energy efficient. However, an additional battery-balancing circuit not only increases circuit’s complexity and cost but also reduces efficiency. To solve this problem, a single-phase multilevel inverter with battery balancing is proposed. Additionally, the switch angle is controlled to contain the ac output voltage with minimal total harmonic distortion (THD). Finally, a prototype is realized to verify the feasibility and excellent performance.

II. S YSTEM D ESCRIPTIONS Among topologies of multilevel inverters, the cascaded multilevel inverter with separate dc sources is superior to the other multilevel structures in terms of its structure which is simple and modular. This modular structure makes it easily extensible for a higher number of output voltage levels without increasing in the power circuit complexity [3], [4], [28]–[36]. In this paper, the characteristics of a cascaded multilevel inverter are achieved. In addition, the battery-balancing function is implemented. Fig. 2 shows the conventional 2N + 1-level multilevel inverter composed of N individual full-bridge inverters and N batteries. The set of the batteries can be defined as

0278-0046/$31.00 © 2012 IEEE

B = {B1 , B2 , . . . , Bn , . . . , BN }.

(1)

YOUNG et al.: SINGLE-PHASE MULTILEVEL INVERTER WITH BATTERY BALANCING

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Clearly, a sine wave can be generated by programming a suitable M sequence with a positive/negative polarity control [29]– [35]. If the characteristics of all of the batteries are equal, the switching pattern-swapping scheme can be adopted to achieve battery balancing [34]. Unfortunately, any two batteries are different. In order to solve this problem, this paper proposes a new battery-balancing method for a cascaded multilevel inverter. First, the battery set B is sorted, and the sorted battery set Bsort can be shown as ∗ Bsort = {B1∗ , B2∗ , . . . , Bn∗ , . . . , BN }

(4)

∗ in which the relation of battery voltages is VBn∗ ≤ VBn−1 , n = 1, 2, . . . , N . This means that the battery with the highest voltage is denoted as B1∗ , the battery with the second highest voltage is denoted as B2∗ , and the battery with the lowest voltage is ∗ . Using the Fourier series analysis, the rootdenoted as BN mean-square (rms) voltage and the hth harmonic H(h) of the quasi-sinusoidal wave can be expressed as [34]–[36] ∗ vh,rms αB1∗ , αB2∗ , . . . , αBN 4 VB1∗ cosh α1 +VB1∗ cosh α2 +· · ·+VB1∗ cosh αN , =√ 2hπ h = 1, 3, 5, 7. (5)

Fig. 2. 2N + 1-level inverter with battery balancing.

According to (5), the switching angles α1 , α2 , . . . , αN can be found such that the THD is minimized and the rms of the fundamental frequency is close to the reference voltage v1,rms_ref . After that, M batteries for output voltage are decided according to the switching angles α1 , α2 , . . . , αN . Finally, these M batteries with higher voltage are chosen and shown as

TABLE I R ELATIONSHIPS OF THE O UTPUT VOLTAGES OF I NDIVIDUAL F ULL -B RIDGE I NVERTERS AND T HEIR S WITCH S TATES

∗ BM = {B1∗ , B2∗ , . . . , BM }.

(6)

The output voltage of the multilevel inverter can be expressed as vo =

M

∗ . VBi∗ = VB1∗ + VB2∗ + · · · + VBM

(7)

i=1

Each individual full-bridge inverter has a separate battery source Bn . Thus, the individual full-bridge inverter can provide three different voltage outputs +VBn , 0, and −VBn by different combinations of the four switches Sn,A+ , Sn,A− , Sn,B+ , and Sn,B− as shown in Table I. The output voltage vo of the multilevel inverter is equal to the sum of the voltages of the individual full-bridge inverters, shown as vo =

N

V Bn

(2)

n=1

where Vbn is the voltage of battery Bn . The set of the batteries providing the output voltage in the multilevel inverter can be defined as Bsel = {B1 , B2 , . . . , Bn , . . . , BM },

M ≤ N.

(3)

As shown in Fig. 3, a quasi-sinusoidal wave can be generated. Assume that the load current IL is constant during a half-cycle of a sinusoidal wave; the discharge capacities QBn of battery Bn can be expressed as QBn = IL · (π − 2αn )

(8)

where αn is the nth switch angle and αn ≤ αn+1 . Clearly, the discharging capacity of a battery with higher voltage is greater than that of a battery with lower voltage. Thus, the batterybalancing function is achieved. III. D ESIGN E XAMPLE In order to verify the performance of the proposed singlephase multilevel inverter with battery balancing, a seven-level inverter for providing a 110-V ac source is designed and implemented. The circuit specifications are listed in Table II. Fig. 4 shows the block diagram of the realized seven-level inverter that comprises three individual full-bridge inverters and a controller.

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Fig. 3. Output voltage waveform of the proposed multilevel inverter. TABLE II C IRCUIT S PECIFICATIONS

The controller is meant to achieve battery balancing and selective harmonic elimination by using (5) and to decide the suitable switching angles α1 , α2 , and α3 . The controller includes a battery-balancing algorithm, a harmonic-reducing algorithm, and a MOSFET state control algorithm. In this prototype, a microprocessor HT46R24 is adopted as the controller. Fig. 5 shows the program flowchart of the realized prototype. First, battery voltages VB1 , VB2 , and VB3 are measured at ωt = 0 and π and then sorted as Bsort = {B1∗ , B2∗ , B3∗ }. For example, if the battery voltage relationships are VB2 ≥ VB1 ≥ VB3 , the sorting result is B1∗ = B2 , B2∗ = B1 , and B3∗ = B3 . Next, the rms voltage of the fundamental frequency, the third-, and the fifth-order harmonic equations can be expressed as the following according to (5): 4 VB1∗ cos(α1 ) + VB2∗ cos(α2 ) v1,rms (α1 , α2 , α3 ) = √ 2π + VB3∗ cos(α3 ) (9) 4 VB1∗ cos(3α1 ) + VB2∗ cos(3α2 ) v3,rms (α1 , α2 , α3 ) = √ 3 2π + VB3∗ cos(3α3 ) (10) 4 VB1∗ cos(5α1 ) + VB2∗ cos(5α2 ) v5,rms (α1 , α2 , α3 ) = √ 5 2π + VB3∗ cos(5α3 ) . (11)

Fig. 4.

System block diagram of the realized prototype.

Fig. 5.

Output voltage waveform of the proposed seven-level inverter.

By using the Newton–Raphson method, we can find a set of switching angles α1 , α2 , and α3 to meet (9)–(11). If the switching angles α1 , α2 , and α3 cannot meet all of (9)–(11), then (9) will be the priority. Since finding a set of switching angles α1 , α2 , and α3 by using the Newton–Raphson method requires complex computing, the real-time decision and control are difficult to be realized. In this paper, a lookup table is built for the controller to solve this problem. Then, M batteries for output voltage is decided according to α1 , α2 , and α3 . That is, M = 1, M = 2, and M = 3 when 0 < ωt ≤ α1 or (π − α1 ) < ωt ≤ π, α1 < ωt ≤ α2 or (π − α2 ) < ωt ≤ (π − α1 ), α2 < ωt ≤ α3 or (π − α3 ) < ωt ≤ (π − α2 ), and α3 < ωt ≤ (π − α3 ) as shown in Fig. 6. After that, all switch states can be obtained according to α1 , α2 , α3 , M , and Table I. According to this algorithm, the relation of battery discharge capacities is QB1 < QB2 < QB3 . Finally, functions of the battery balancing and the harmonic reduction in the realized seven-level inverter can be achieved.


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Fig. 7 Picture of the 1-kW prototype.

Fig. 6.

Program flowchart of the realized prototype. TABLE III BATTERY PACK S PECIFICATIONS

Fig. 8. Battery discharging voltages and currents of the realized prototype.

IV. E XPERIMENT R ESULTS In this paper, a prototype is designed and implemented to verify the feasibility and excellent performance. The battery pack specifications are listed in Table III. Fig. 7 shows a picture of the realized 1-kW prototype. Fig. 8 shows the battery discharging voltage and current curves in a fully discharging period. The discharging voltage of the battery pack begins at 52 V and stops at 44 V. The total discharging time is 13 690 s. The discharging capacities of batteries B1 , B2 , and B3 are 5.7, 6.0, and 6.3 Ah, respectively. It is interesting that batteries B1 , B2 , and B3 have different discharging capacities to make their voltage be almost equalized. This indicates that the battery balancing is achieved. Figs. 9–11 shows the zoom views of Fig. 8 at times A, B, and C. In time A (i.e., during 991–1000 s), the relation of the battery voltages is

Fig. 9. Battery discharging voltages and currents during 991–1000 s.

VB1 < VB3 < VB2 , so Bsort = {B1 , B3 , B2 }, and the battery discharge current is IB1 < IB3 < IB2 as shown in Fig. 9. In time B (i.e., during 7002–7011 s), the relation of the battery voltages is VB1 < VB3 < VB2 , so Bsort = {B1 , B3 , B2 }, and the battery discharge current is IB1 < IB3 < IB2 as shown in Fig. 10. Noteworthily, during 7008–7011 s, the relation

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Fig. 10. Battery discharging voltages and currents during 7002–7011 s. Fig. 13.

Generated ac 110-V waveform at 13 200 s.

TABLE IV BATTERY S PECIFICATIONS FOR THE D IFFERENT BATTERY C APACITIES

Fig. 11. Battery discharging voltages and currents during 13 008–13 017 s.

Fig. 12. Generated ac 110-V waveform at 6500 s.

of the battery voltages is changed to VB2 < VB3 < VB1 , so Bsort = {B2 , B3 , B1 }, and the relation of the battery discharge currents is changed to IB2 < IB3 < IB1 . In time C (i.e., during 13 008-13 017 s), the relation of the battery voltages is IB2 < IB3 < IB1 , so Bsort = {B2 , B3 , B1 }, and the battery discharge current is IB2 < IB3 < IB1 as shown in Fig. 11. From Figs. 8–11, we can see that the discharging current of a battery with higher voltage is greater than that of a battery with lower voltage. Thus, battery-balancing discharging is implemented. Figs. 12 and 13 show the generated ac 110-V waveforms at times 6500 and 1320 s, respectively. At 6500 s, VB1 = 48.77 V,

VB2 = 48.79 V, and VB3 = 48.77 V, and the switch angles are α1 = 27.3◦ , α2 = 7.75◦ , and α3 = 53.41◦ . The rms, the third-, and the fifth-order harmonics are 108.7 V, 1.6%, and 0.03%, respectively. At 13 200 s, VB1 = 44.02 V, VB2 = 44.02 V, and VB3 = 44.03 V, and the switch angles are α1 = 21.93◦ , α2 = 47.03◦ , and α3 = 4.07◦ . The rms, the third-, and the fifth-order harmonics are 103.3 V, 7.8%, and 0.23%, respectively. We can see that the third-order harmonic is obviously larger. The reason for this is that the switching angles α1 , α2 , and α3 cannot meet all of (9)–(11), so only (9) is the priority matched, and then, the third- and fifth-order harmonics are not equal to zero. Furthermore, battery packs with different capacities are used to verify the battery-balancing performance. The capacities of the three battery packs are 7, 7, and 4.2 Ah, as listed in Table IV, in which the 4.2-Ah battery can be regarded as the aged battery. Fig. 14 shows the battery voltage curves of a conventional inverter without battery balancing for powering a constant 50Ω load. Since the three batteries’ discharge currents are the same, the aged battery (i.e., the 4.2-Ah battery) is first fully discharged, and the discharge time is 5692 s. Fig. 15 shows the battery voltage and current curves. As shown in Fig. 15, the battery B3 (i.e., the 4.2-Ah battery) has the lowest voltage, and then, the discharging current is the smallest. Thus, the discharging time can be prolonged to 13 690 s. The discharging time is dramatically improved by about 58.4% compared with that of an inverter without battery balancing. Table V lists the discharging capacities of batteries B1 , B2 , and B3 with and without the battery-balancing function. Clearly, batteries B1 ,


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R EFERENCES

Fig. 14. Battery discharging voltage curves of a conventional inverter without battery balancing.

Fig. 15. Battery discharging voltage and current curves of the realized prototype. TABLE V D ISCHARGING C APACITIES OF BATTERIES W ITH AND W ITHOUT THE BATTERY-BALANCING F UNCTION

B2 , and B3 discharging with battery-balancing function can obtain a greater discharging capacity to proving to load. V. C ONCLUSION In this paper, a single-phase multilevel inverter with battery balancing has been proposed and proved successful. The input of each individual inverter is directly connected to a battery. The combination of batteries can be controlled according to the batteries’ voltages to implement the battery-balancing function. A prototype was designed and implemented to verify the feasibility and excellent performance. Experiments show that the battery-balancing discharge function was achieved as we wanted. Additionally, the switch angle is controlled to contain the ac output voltage with minimal THD.

[1] T. Hirose and H. Matsuo, “Standalone hybrid wind–solar power generation system applying dump power control without dump load,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 988–997, Feb. 2012. [2] H. Kanchev, D. Lu, F. Colas, V. Lazarov, and B. Francois, “Energy management and operational planning of a microgrid with a PV-based active generator for smart grid applications,” IEEE Trans. Ind. Electron., vol. 58, no. 10, pp. 4583–4592, Oct. 2012. [3] Z. Haihua, T. Bhattacharya, T. Duong, T. S. T. Siew, and A. M. Khambadkone, “Composite energy storage system involving battery and ultracapacitor with dynamic energy management in microgrid applications,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 923–930, Mar. 2011. [4] H. Qian, J. Zhang, J. S. Lai, and W. Yu, “A high-efficiency grid-tie battery energy storage system,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 886–896, Mar. 2011. [5] S. Kouro, M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B. Wu, J. Rodriguez, M. A. Pérez, and J. I. Leon, “Recent advances and industrial applications of multilevel converters,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2553–2580, Aug. 2010. [6] C. Abbey and G. Joos, “Supercapacitor energy storage for wind energy applications,” IEEE Trans. Ind. Appl., vol. 43, no. 3, pp. 769–776, May/Jun. 2007. [7] B. Y. Chen and Y. S. Lai, “New digital-controlled technique for battery charger with constant current and voltage control without current feedback,” IEEE Trans. Ind. Electron., vol. 59, no. 3, pp. 1545–1553, Mar. 2012. [8] 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. [9] 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. [10] 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. [11] 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. [12] 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. [13] L. R. Chen, R. C. Hsu, and C. S. Liu, “A design of a grey-predicted Li-ion battery charge system,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3692–3701, Oct. 2008. [14] 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. [15] M. Pahlevaninezhad, J. Drobnik, P. K. Jain, and A. Bakhshai, “A load adaptive control approach for a zero-voltage-switching dc/dc converter used for electric vehicles,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 920–933, Feb. 2012. [16] H. Fakham, D. Lu, and B. Francois, “Power control design of a battery charger in a hybrid active PV generator for load-following applications,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 85–94, Jan. 2011. [17] S. Vazquez, S. M. Lukic, E. Galvan, L. G. Franquelo, and J. M. Carrasco, “Energy storage systems for transport and grid applications,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3881–3895, Dec. 2010. [18] K. Jin, M. Yang, X. Ruan, and M. Xu, “Three-level bidirectional converter for fuel-cell/battery hybrid power system,” IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 1976–1986, Jun. 2010. [19] A. Xu, S. Xie, and X. Liu, “Dynamic voltage equalization for seriesconnected ultracapacitors in EV/HEV applications,” IEEE Trans. Veh. Technol., vol. 58, no. 8, pp. 3981–3987, Oct. 2009. [20] Y. Yuanmao, K. W. E. Cheng, and Y. P. B. Yeung, “Zero-current switching switched-capacitor zero-voltage-gap automatic equalization system for series battery string,” IEEE Trans. Power Electron., vol. 27, no. 7, pp. 3234–3242, Jul. 2012. [21] S. H. Park, K. B. Park, H. S. Kim, G. W. Moon, and M. J. Youn, “Singlemagnetic cell-to-cell charge equalization converter with reduced number of transformer windings,” IEEE Trans. Power Electron., vol. 27, no. 6, pp. 2900–2911, Jun. 2012. [22] H. S. Park, C. E. Kim, C. H. Kim, G. W. Moon, and J. H. Lee, “A modularized charge equalizer for an HEV lithium-ion battery string,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1464–1476, May 2009.

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[23] P. A. Cassani and S. S. Williamson, “Design, testing, and validation of a simplified control scheme for a novel plug-in hybrid electric vehicle battery cell equalizer,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3958– 3962, Dec. 2010. [24] Y. S. Lee and G. T. Cheng, “Quasi-resonant zero-current switching bidirectional converter for battery equalization applications,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1213–1224, Sep. 2006. [25] M. Uno and K. Tanaka, “Influence of high-frequency charge–discharge cycling induced by cell voltage equalizers on the life performance of lithium-ion cells,” IEEE Trans. Veh. Technol., vol. 60, no. 4, pp. 1505– 1515, May 2011. [26] A. Shukla, A. Ghosh, and A. Joshi, “Flying-capacitor-based chopper circuit for DC capacitor voltage balancing in diode-clamped multilevel inverter,” IEEE Trans. Ind. Electron., vol. 57, no. 7, pp. 2249–2261, Jul. 2010. [27] A. C. Baughman and M. Ferdowsi, “Double-tiered switched-capacitor battery charge equalization technique,” IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2277–2285, Jun. 2008. [28] J. Pereda and J. Dixon, “High-frequency link: A solution for using only one DC source in asymmetric cascaded multilevel inverters,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3884–3892, Sep. 2011. [29] S. Mekhilef and M. N. A. Kadir, “Novel vector control method for threestage hybrid cascaded multilevel inverter,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1339–1349, Apr. 2011. [30] J. Rodriguez, J. S. Lai, and F. Z. Peng, “Multilevel inverters: A survey of topologies, controls, and applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 724–738, Aug. 2002. [31] J. Rodriguez, S. Bernet, B. Wu, J. O. Pontt, and S. Kouro, “Multilevel voltage-source-converter topologies for industrial medium-voltage drives,” IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 2930–2945, Dec. 2007. [32] P. Lezana, J. Rodríguez, M. A. Pérez, and J. Espinoza, “Input current harmonics in a regenerative multicell inverter with single-phase PWM rectifiers,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 408–417, Feb. 2009. [33] P. Lezana, J. Rodríguez, and D. A. Oyarzún, “Cascaded multilevel inverter with regeneration capability and reduced number of switches,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1059–1066, Mar. 2008. [34] L. M. Tolbert, Z. P. Fang, and T. G. Habetler, “Multilevel converters for large electric drives,” IEEE Trans. Ind. Appl., vol. 35, no. 1, pp. 36–44, Jan./Feb. 1999. [35] H. Taghizadeh and M. T. Hagh, “Harmonic elimination of cascade multilevel inverters with nonequal DC sources using particle swarm optimization,” IEEE Trans. Ind. Electron., vol. 57, no. 11, pp. 3678–3684, Nov. 2010. [36] L. M. Tolbert, J. N. Chiasson, D. Zhong, and K. J. McKenzie, “Elimination of harmonics in a multilevel converter with nonequal DC sources,” IEEE Trans. Ind. Appl., vol. 41, no. 1, pp. 75–82, Jan./Feb. 2005.

Chung-Ming Young (M’09) received the B.S. and M.S. degrees in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 1983 and 1987, respectively, and the Ph.D. degree from National Taiwan University, Taipei, in 1996. He is currently an Associate Professor with the Department of Electrical Engineering, National Taiwan University of Science and Technology. His research interests include power electronic converters, analog circuit design, and DSP applications.

Neng-Yi Chu (S’11) was born in Taoyuan, Taiwan, in 1984. He received the M.S. degree from the Department of Electrical Engineering, National Yunlin University of Science and Technology, Douliu, Taiwan, in 2008. He is currently working toward the Ph.D. degree in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan. His research interests include microcontroller control applications, multilevel inverter, and battery charging systems.

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 the National Taiwan University of Science and Technology, Taipei, Taiwan, in 1994, 1996, and 2001, respectively. Since 2006, he has been with the faculty of the Department of Electrical Engineering, National Changhua University of Education, Changhua, where he is currently a Professor. His major research interests are power electronics, battery-powered circuit design, and renewable energy.

Yu-Chih Hsiao was born in Chiayi, Taiwan, in 1986. He received the M.S. degree in electrical engineering from the National Changhua University of Education, Changhua, Taiwan, in 2010. His research interests include microcontroller control, bidirectional converter design, fluorescent lamp electronic ballast, and control applications.

Chia-Zer Li was born in Chiayi, Taiwan, in 1986. He received the M.S. degree in electrical engineering from the National Changhua University of Education, Changhua, Taiwan, in 2011. His research interests include microcontroller control, battery charger, and multilevel inverter.