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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011 2743

A Universal Selective Harmonic Elimination Methodfor High-Power Inverters

Damoun Ahmadi, Student Member, IEEE, Ke Zou, Student Member, IEEE, Cong Li, Student Member, IEEE,Yi Huang, Member, IEEE, and Jin Wang, Member, IEEE

Abstract—In medium-/high-power inverters, optimal pulse-width modulation (OPWM) is often used to reduce the switchingfrequency and at the same time, realize selective harmonic elim-ination (SHE). For both two-level and multilevel inverters, mostselective harmonic elimination (SHE) studies are based on solvingmultiple variable high-order nonlinear equations. Furthermore,for multilevel inverters, SHE has been often studied based on theassumption of balanced dc levels and single switching per level. Inthis paper, the authors further developed harmonics injection andequal area criteria-based four-equation method to realize OPWMfor two-level inverters and multilevel inverters with unbalanced dcsources. For the cases, where only small number of voltage levelsare available, weight oriented junction point distribution is utilizedto enhance the performance of the four-equation method. A casestudy of multilevel inverter at low-modulation index is used as anexample. Compared with existing methods, the proposed methoddoes not involve complex equation groups and is much easier to beutilized in the case of large number of switching angles, or multipleswitching angles per voltage level in multilevel inverters.

Index Terms—Equal area criteria, modulation index, multi-level inverters, optimal pulsewidth modulation, selective harmonicselimination, total harmonic distortion.

I. INTRODUCTION

THE developments of flexible ac transmission system de-vices, medium voltage drives, and different types of dis-

tributed generations, have provided great opportunities forthe implementations of medium- and high-power inverters. Inthese applications, the frequency of the pulse-width modulation(PWM) is often limited by switching losses and electromagneticinterferences caused by high dv/dt. Thus, to overcome theseproblems, selective harmonic elimination (SHE)-based optimalpulsewidth modulation (OPWM) are often utilized in both two-level inverters and multilevel inverters to reduce the switchingfrequency and the total harmonic distortion [1]–[12].

A typical multilevel inverter utilizes voltage levels from mul-tiple dc sources. These dc sources can be interconnected or iso-lated depending on circuit topologies. Because of the complexity

Manuscript received June 16, 2010; revised September 30, 2010 andDecember 22, 2010; accepted February 1, 2011. Date of current version Septem-ber 21, 2011. Recommended for publication by Associate Editor V. G. Agelidis.

The authors are with the Department of Electrical and Computer Engineering,Ohio State University, Columbus, OH 43210 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2011.2116042

of the problem, most studies on SHE methods for multilevel in-verters are based on the assumptions that the dc voltage sourcesare balanced (equal to each other) and there is only one switch-ing angle per voltage level. But in real applications, dependingon the nature of the dc sources and operation conditions of thecircuits, the dc sources could be unbalanced [13], [14]. Also, atlow-modulation index ranges of multilevel inverters [15]–[18],where very limited voltage levels, e.g., three or five, are involved,the one switching per level scheme will result in high-harmonicsdistortion.

Thus, in this paper, the author’s four-equation-based method[40]–[43] is further developed to solve the following threeproblems:

1) SHE-based optimal switching angle calculations for two-level inverters;

2) SHE for multilevel inverter with unbalanced dc sources;3) Multiple switching angles per level in multilevel inverters

at low-modulation indices, which is equivalent to high-modulation indices in inverters with low number of voltagelevels.

Case studies and related experimental results are presented tovalidate the proposed methods.

The paper is organized in the following way. Section II pro-vides a brief review of different OPWM and SHE methods.Section III presents the detailed description of the improvedfour-equation-based method for 1) OPWM in two-level invert-ers and 2) weight oriented junction distribution for multilevelinverters with unbalanced dc sources. Case studies of the pro-posed methods are shown in Section IV, whereas the simulationand experimental verifications are shown in Section V.

II. OPWM METHODS FOR SELECTED HARMONICS

ELIMINATION

PWM method was proposed for inverters in 1960 s and dig-italized in 1970 s [19], [20]. Soon after the birth of the basicPWM method, in 1964, Turnbull proposed the SHE idea [21].In this method, harmonic components are described as func-tions of the switching angles in trigonometric terms. If N is thetotal number of switching transitions, as shown in Fig. 1, theFourier series expansion of the symmetric PWM waveform canbe expressed as

V (ωt) =∞∑

m=1,3,5,...

4Vdc

mπ(cos(mθ1) − cos(mθ2) . . .

+ cos(mθN )) sin(mωt) (1)

0885-8993/$26.00 © 2011 IEEE

2744 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011

Fig. 1. Multiple switching angles in OPWM.

where m is the order of the harmonic, and θk are the kth switch-ing angle. Based on (1), the following group of polynomialequations can be utilized to calculate the N switching anglesand realize the selective harmonic elimination up to mth order.Please note that the value of “m” could be much higher than“N.”

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

4Vdc

π(cos(θ1) − cos(θ2) · · · + cos(θN )) = VF

cos(5θ1) − cos(5θ2) · · · + cos(5θN ) = 0cos(7θ1) − cos(7θ2) · · · + cos(7θN ) = 0.......cos(mθ1) − cos(mθ2) · · · + cos(mθN ) = 0

(2)

In this equation group, the first equation is used to guar-antee the amplitude of the fundamental component (VF ) andthe other equations are utilized to ensure the elimination of se-lected harmonics. Thus, by calculating the N switching angles,N-1 number of harmonics can be eliminated [22], [39]. In ear-lier days, algorithms like quarter symmetric polynomials andNewton-Raphson method with multiple variables or lineariza-tion had been utilized to solve this equation group [23], [24].

Recently, various control theory orientated algorithms are uti-lized to solve this group of equations. For instance, in [25], aclonal selection algorithm is introduced to find optimum so-lution with a random disturbance selection operation; in [26],sliding mode variable structure control is proposed based onclosed loop algorithm for better performance in harmonics elim-ination; in [27], Homotopic fixed-point approach is utilized tofind the initial values of the roots and conduct cubic iterationsto refine the roots; and in [28], a feed forward artificial neuralnetwork is applied for selected harmonics elimination. In [29],m dimensional space is introduced to eliminate m harmonics.However, this method is practical to eliminate three harmoniccomponents.

For multilevel inverters, harmonics elimination follows thesimilar equation group as (2). Multiple methods, such as fuzzyproportional integral controller [30], resultants theory-basedalgorithm [31], adaptive control algorithm [32], genetic algo-rithm [33], [38] etc., have been proposed. Online calculationsof the switching angels for both two-level inverters and multi-level inverters have also been reported [34], [35].

However, all the aforementioned methods are eventuallybased on solving complex groups of equations. Therefore, forhigher number of switching transients, it is quite difficult or timeconsuming to solve these nonlinear equations with current com-putation methods [36], [37]. Thus, based on harmonics injec-tion and equal area criteria, the authors have recently proposeda simple and fast four-equation method for multilevel inverters.In this method, regardless the number of voltage levels, only

Fig. 2. Different approaches for harmonics elimination.

Fig. 3. The illustration of equal area criteria.

four simple equations are needed for switching angle calcula-tions [40]–[43]. For easy referencing, different PWM strategiesfor high-power two-level inverters and multilevel inverters arecategorized in Fig. 2.

III. PROPOSED METHODS FOR SELECTED HARMONIC

ELIMINATION

A. OPWM Method for Two-Level Inverters

The basic idea is that, if a sinusoidal reference waveform isutilized to generate a series of switching angles with equal areacriteria, the resulting PWM waveform would have both funda-mental component and harmonics. Therefore, if selected neg-ative harmonics are injected into the original pure sinusoidalreference waveform, because of the nature of the equal areacriteria, the injected harmonics may cancel out the harmonicsgenerated by the original pure sinusoidal reference. The follow-ing is the detailed illustration of the proposed method. For thesimple case shown in Fig. 3, the harmonics content of the PWMwaveform can be described from

hm =N∑

k=1,2,..,N

2Vdc

mπ(cos(mθk ) − cos(mσk )) (3)

where “N” is the total number of the switching angles and “m”is the order of the harmonics. Starting from this equation, thefour-equation method includes the following basic steps:

1) Use a pure sinusoidal waveform and equal area criteriato decide initial switching angles of θk with predefinedinitial values of σk ;

2) Find the lower harmonics content in the resulting PWMwaveform with (3);

AHMADI et al.: UNIVERSAL SELECTIVE HARMONIC ELIMINATION METHOD FOR HIGH-POWER INVERTERS 2745

Fig. 4. The diagram showing four-equation method.

3) Form a new reference waveform which is defined by

Vref = VF sin(ωt) − hms sin(mωt) (4)

where hms is the sum of hm

hms =iter∑

i=1,2,...

hm (i) (5)

4) Use the new reference waveform and equal area criteria toform a new set of σk and θk .

5) Repeat step 1) to 4) until the selected harmonics is elimi-nated. The general equation to calculate θk based on equalarea criteria is

θk = σk − VF (cos(σk−1) − cos(σk ))Vdc

− h5s(cos(5σk−1) − cos(5σk ))5Vdc

· · · − hms(cos(mσk−1) − cos(mσk ))mVdc

(6)

This four-equation procedure is illustrated in Fig. 4.From this basic procedure, it is clear that the proposed method

is an iteration-based method. So, there should be some initialstarting point for σk . A simple start point is to evenly distributeinitial σk s in the region of 0 to π/2.

Equation (6) also shows that in this method, there is a de-fined relationship between σk and θk . Thus, when comparedwith methods that are based off solving high-order nonlinearequations, theoretically, the four-equation method will have lessfreedoms in eliminating the switching angles. But, because ofthe simplicity of proposed method, when eliminating the samenumber of harmonics, the four-equation method shall have fasterresults.

To clarify the advantages and simplicity of the proposedmethod, in Table I, this method is compared with other methodsthat normally use the polynomial equations. Solving high-ordernonlinear equations is no longer needed, thus, advanced algo-rithms are also no longer required. In the traditional methods,the number of equations grows with the number of switchingangles in nonlinear way. Thus, it is very difficult to calculate theswitching angles when the total number of the switching anglesis high. Conversely, in the four-equation method, the four ba-sic equations are used repeatedly, the total number of equationsgrows linearly with the number of switching angles. As a result,this method would be more suitable for cases with high num-

bers of switching angles or complex scenarios such as multipleswitching angles per voltage level in multilevel inverters.

B. Compensation of Fundamental Component

With the basic procedure described above, it was found thatthe resulting fundamental component is usually different fromthe desired fundamental component. This is because of possibleover modulation caused by the harmonics injection or overlap ofswitching angles at high-modulation indices. Thus, fundamentalvoltage compensation is needed for the proposed method. Thebasic solution starts with the comparison between the resultingfundamental component and the reference. Then, based on thisdifference, a Δθ is calculated to modify the last switching anglethat is the nearest to π/2. However, this Δθ will result in moreharmonics. So, the resulting additional harmonics are calculatedand added to the total harmonics injection to improve SHE. This“adjustment” angle can be calculated by inverse cosine in thefollowing equation

Δθ = arccos(

π

2Vdc(VF − V1N )

)(7)

where V1N is the total fundamental voltage generated switchingangles from θ1 to θN . This “adjustment” angle is used to modifythe last switching angle

θN (modified) = arccos(cos(θN ) + cos(Δθ)). (8)

Therefore, based on the switching angle adjustment, the de-sired voltage magnitude in the fundamental frequency can beachieved. The total process of this modified method is illustratedin Fig. 5.

C. OPWM in Multilevel Inverters at Low-Modulation IndexWith Unbalanced DC Sources

For multilevel inverters, the harmonics selected for elimina-tion are limited by the number of available dc levels. To over-come this problem, in each dc level, the number of switchingangles can be increased to eliminate more harmonic compo-nents, as shown in Fig. 6. This is very helpful, especially for1) low-modulation indices, where limited dc levels are avail-able in multilevel inverters with high number of total dc voltagelevels or 2) high-modulation index in inverters with limitedvoltage levels. In theory, there is no limitation for the number ofswitching angles used for each level. But, generally the numberof switching angles is limited by the switching losses. In thissection, as an example, the four-equation method is adapted toachieve SHE for multilevel inverters at low-modulation indexwith unbalanced dc sources, as shown in Fig. 6.

Based on equal area criteria, the switching angles are deter-mined through the following equation

θk = 1/Vdc(k)

( k∑

i=1

Vdc(i)δk −k−1∑

i=1

Vdc(i)δk−1

+ VF (cos(δk ) − cos(δk−1)) −h5

5(cos(5δk )

− cos(5δk−1)) · · · −hm

m(cos(mδk )− cos(mδk−1))

)(9)


TABLE INUMBER OF FIRST-ORDER EQUATIONS SHOULD BE SOLVED FOR HARMONICS ELIMINATION IN DIFFERENT METHODS

Fig. 5. Modified method with “adjustment” for the switching angle in optimal PWM based on four-equation method.

Fig. 6. Optimal PWM with four-equation-based method on multilevel invert-ers with unbalanced dc sources.

where δk−1 and δk are the two subjunction points per eachsubarea as shown in Fig. 7. The effectiveness of OPWM reliesheavily on the values of δk−1 and δk .

D. Weight Orientated Junction Point Distribution

To define the values of δk−1 and δk , one possible solution isto equally divide the total area based on number of switchingangles, as shown in Fig. 7(a). However, this strategy does notwork well for low-modulation indices. This is simply becausethat with less voltage levels, larger area per level is needed inthe compensation of harmonics. Thus, the distribution of thearea becomes more crucial. However, it is also observed thatmagnitudes of harmonic contents decrease as the order of theharmonics increases

hm =N∑

k=1,2,..,N

4Vdc(k)

mπ(cos(mθk ) − cos(mδk ). (10)

This means that the corresponded area needed for the com-pensation of higher order harmonics also decreases. Based onthis observation, in the adapted four-equation method, the areadivision for low-modulation indices can be determined by the

Fig. 7. Two methodologies for area division in OPWM and four-equationcombined method; (a) Symmetric method in medium and high- modulationindex, and (b) Weight oriented method in low-modulation index.

weight of the harmonics, which is shown in Fig. 7(b). In thisweight orientated solution, larger area is made available forlower order harmonic components. Thus, better accuracy ofharmonics elimination can be achieved. The procedure for thismethod is illustrated in Fig. 8.

If λk is defined by the difference between two subjunc-tion points, δk−1 , and δk , then based on weight orientateddistribution

λk = δk − δk−1 (11)

λk+1

λk=

k + 1k

(12)

In this case, for a symmetric waveform, the summation of thesubareas shall be π/2

π/2 =m∑

k=1

λk = λ1

m∑

k=1

k = λ1m(m + 1)

2(13)

thus,

λ1 =π

m(m + 1). (14)

With (13) and (14), all the subjunction points δk can be de-termined easily.


Fig. 8. Block diagram for weight oriented solution in low-modulation indices.

TABLE IISAMPLE POINTS WITH PROPOSED METHOD

IV. CASE STUDIES

Two case studies of the proposed SHE are shown in thissection: 1) two-level inverter and 2) multilevel inverter at low-modulation indices.

A. Two-Level Inverter

In this case study of two-level inverter, ten switching anglesare utilized. The modulation index is defined as

MI =πVF

4(15)

where VF is the fundamental ac voltage in the output. Table IIshows some sample points achieved with this method. In thiscase, δk s are simply fixed at points k · π/20. Fundamental com-ponent compensation shown in Fig. 5 is adapted for these samplepoints. The switching angles vs. modulation indices are shownin Fig. 9. Harmonics analysis in Table II shows that the selectedharmonics are precisely eliminated.

B. OPWM in Multilevel Inverters at Low-Modulation IndexWith Unbalanced DC Sources

To verify the effectiveness of the four-equation method inmultilevel inverters with unbalanced dc sources, the method

Fig. 9. The overall switching angles for different modulation indices.

is used to calculate switching angles of 11-level waveformswith five unbalanced dc sources. The modulation indices of thewaveform are defined as

MI =VF

4π

∑P

i=1Vdc(i)

(16)


TABLE IIISAMPLE POINTS BASED ON THE FOUR-EQUATION AND OPWM COMBINED METHOD FOR LOW-MODULATION INDICES

Fig. 10. Simulated line-line voltage based on four-equation OPWM at three different modulation indices; (a) MI = 0.8286, (b)MI = 0.6748, (c) MI = 0.2672.

TABLE IVHARMONIC COMPONENTS FOR THE SIMULATED- MODULATION INDICES

Fig. 11. Experimental results for OPWM with ten switching angles for MI = 0.6748; (a) No load test voltage with ten switching angles, and (b) Load test voltageand current waveforms for MI = 0.6748.

TABLE VHARMONICS CONTENT IN THE EXPERIMENTAL VOLTAGE AND CURRENT FOR MI = 0.6748


Fig. 12. Frequency spectrum of experimental results for OPWM with ten switching angles in MI = 0.6748; (a) Harmonics analysis for output voltage in loadtesting, and (b) Harmonics analysis for output current in load testing.

TABLE VISIMULATION RESULTS FOR OUTPUT VOLTAGE AND SELECTED HARMONIC COMPONENTS ON DIFFERENT MODULATION INDICES

Fig. 13. OPWM for multilevel inverters with unbalanced dc Voltage and weight orientated junction point distribution; (a) Three-level phase voltage waveformwith MI = 0.1414, and (b) Five-level phase voltage waveform with MI = 0.2545.

where P is the number of dc levels and Vdc(i) is the dc magnitudefor each voltage level in multilevel inverter output waveform.One possible application of this study is cascade multilevel in-verters for Photovoltaic (PV). For PV modules with differentirradiations or temperatures, the dc voltage magnitudes at max-imum power point are close to each other. The typical variationis less than 15%. Therefore, in this case study, the voltage dif-ferences between two dc sources are chosen as ± 15%.

The switching angles and calculated harmonics content forlow-modulation indices are shown in Table III. At these low-modulation indices, only one or two dc sources are utilized. Butfor each voltage level, there are multiple switching angles. Inthe five-level waveform, θ1 and θ2 are applied at voltage levelone; θ3 , θ4 , and θ5 are applied at voltage level two.

V. SIMULATION AND EXPERIMENTAL VERIFICATION

To verify the proposed method, simulations and experimentshave been carried out for the two case studies aforementioned.

Fig. 14. Experimental setup for multilevel inverter with unbalanced dcsources.

For no load conditions, dc voltage is increased up to 200 V. Forload test, the dc-link voltage is increased up to 100 V. The loadimpedance are R = 3.2 ohm and L = 6 mH. A TI TMS320F2812


Fig. 15. Experimental results for multilevel inverter with unbalanced dc sources at low-modulation indices; (a) Three-level phase voltage waveform with MI =0.1414, and (b) Five-level phase voltage waveform with MI = 0.2545.

TABLE VIIHARMONICS ANALYSIS FOR THE EXPERIMENTAL RESULTS WITH LOW-MODULATION INDICES (FIG. 15)

DSP board is used to control the inverters. During the exper-iments, offline procedure is utilized. The switching angles areprecalculated, and then programmed via the TI DSP. Thoughthere are voltage and current sensors integrated in the inverters,they are not utilized in the tests. The voltage and current probesare used to read the numbers.

A. OPWM With Ten Switching Angles for Two-Level Inverter

To show the performance of the four-equation-based methodOPWM for two-level inverter, three different modulationindices, 0.8286, 0.6748, and 0.2672, are simulated andtested. The simulated line-line output voltages are shown inFig. 10(a)–(c).

The harmonics analysis of the above waveforms is summa-rized in Table IV. The results show that the magnitudes of theselected harmonics for each modulation index are minimizedsuccessfully. However, in the proposed method, number of it-eration for the steps can be increased resulting in completeharmonic elimination.

Experiments were carried out for the case that modulationindex equals to 0.6748. Fig. 11 shows the waveforms fromboth no load and inductive load cases. As a comparison toTable IV, the harmonics analysis for the voltage and load currentare shown in Table V. The spectrum analysis is shown in Fig. 12.It is noted that there are slight difference between Tables IVand V in terms of voltage harmonics content. The difference ismainly due to the 1.5 us dead time and dc voltage fluctuationcaused by the oscillation between the load inductor and thedc-link capacitor.

B. Low-Modulation Indices in Multilevel Inverters

For weight oriented solution, two cases of low-modulationindices with unbalanced dc levels are simulated. Table VI showsthe switching angles and selected harmonic components forthese two-modulation indices. Correspondent waveforms areshown in Fig. 13. As described in Section III(c) and III(d), theangles in Table VI are switch turn-on points. The switch turn-off points are the subjunction points that are calculated with theweighted area distributions. It is shown in Table VI that whenmore voltage levels are involved, because of the complexity ofthe problem, the performance of the proposed method degradeda little bit, but the concerned harmonics are still minimizedeffectively.

Since low-modulation indices tests only request two dcsources, during the tests, two H-Bridge modules are cascaded toachieve five-level waveforms. The test setup is shown in Fig. 14.The experimental waveforms are shown in Fig. 15.

As a comparison to Table VI, the harmonics analysis for theexperimental results in two-modulation indices with weight ori-ented solution are shown in Table VII. From both the simulationand experimental results, it can be seen that the selected har-monics contents are eliminated effectively with the proposedmethod.

VI. CONCLUSIONS

In this paper, a modified four-equation method is proposed forselected harmonics elimination for both two-level inverters andmultilevel inverters with unbalanced dc sources. For this casewith fairly low number of switching angles and unbalanced


multiple voltage levels, the weight orientated junction point dis-tribution is applied to enhance the performance of the proposedmethod. Both the simulation and experimental results validatethe proposed methods. Compared with existing methods, thefour-equation method does not involve high-order polynomialequations, thus is friendlier toward the cases, like large numberof switching angles or multiple switching angles per dc source.Earlier papers by the authors have demonstrated the effective-ness of the four-equation method for multilevel inverters withsingle switch angle per level. In this paper, it is demonstratedthat the same method can be adopted for optimal PWM in bothtwo-level inverters and multilevel inverters with unbalanced dcsources at low-modulation indices. Thus, it is fair to claim thatthe four-equation-based method is a simple and universal SHEmethod for all types of high-power inverters.

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Damoun Ahmadi (S’09) was born in Iran in 1981.He received the M.S. degree from Sharif Universityof Technology, Tehran, Iran, in 2005. He is currentlyworking toward the Ph.D. degree in Power Electron-ics at the Ohio State University, Columbus, OH.

During that time, he worked on different controlstrategies for ac motor drives and applying flexibleac transmission system (FACT’s) devices for reactivepower compensation. His research interests includemultilevel inverters, real time simulation of renew-able energies for smart grid, intelligent and optimized

power tracking for automotive battery charging, power electronic circuits, hard-ware in the loop, and DSP applications for high power systems and distributedgenerations.

Ke Zou (S’09) received the B.S. and M.S. degreesin electrical engineering from Xi’an Jiaotong Uni-versity, China, in 2005, and 2008, respectively. Heis currently working toward the Ph.D. degree in theOhio State University, Columbus, OH.

His current research interests include switchedcapacitor dc/dc converter and dc/ac multilevel in-verter, battery model in high-frequency application,and hardware in the loop (HIL) systems for powerelectronics and power systems.

Cong Li (S’10) received the B.S. and M.S. degreesin electrical engineering from the Wuhan University,Wuhan, China, in 2007, and 2009, respectively. He iscurrently working toward the Ph.D. degree in electri-cal engineering at The Ohio State University, Colum-bus, OH.

His research interests include power electronic cir-cuits and applications, and renewable energy, thermo-electric cooling application, low-voltage high- cur-rent dc/dc converter design, and circuit analysis ofMW PV power plant.

Yi Huang (S’05–M’10) received the B.S. and M.S.degrees in electrical engineering from the WuhanUniversity, China, in 1998, and 2001, respectively.She received the Ph.D. degree in electrical engineer-ing from the Michigan State University, East Lansing,in 2009.

She is currently a Postdoctoral Researcher at theOhio State University, Columbus, OH,. Her researchinterests include dc-ac inverter, dc-dc converter, ad-vanced digital control technique, and Photovoltaicinverter systems.

Jin Wang (S’02–M’05) received the B.S. degreefrom Xi’an Jiaotong University, in 1998, M.S. de-gree from the Wuhan University, in 2001, and thePh.D. degree from Michigan State University, EastLansing, in 2005, all in electrical engineering.

He is currently an Assistant Professor in the en-ergy/power area at The Ohio State University (OSU),Columbus, OH. His Teaching Position is cospon-sored by American Electric Power, Duke/Synergy,and FirstEnergy. Before joining OSU, he worked atFord Motor Company as a Core Power Electronics

Engineer for two years. His research interests include high-voltage and high-power converter/inverters, integration of renewable energy sources, and electri-fication of transportations.

Dr. Wang received the National Science Foundation’s CAREER Award in2011. He has been an Associate Editor for IEEE Transactions on Industry Ap-plication from March 2008.

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