IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011
2743
A Universal Selective Harmonic Elimination Method
for 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 pulsewidth modulation (OPWM) is often used to reduce the switching
frequency and at the same time, realize selective harmonic elimination (SHE). For both two-level and multilevel inverters, most
selective harmonic elimination (SHE) studies are based on solving
multiple variable high-order nonlinear equations. Furthermore,
for multilevel inverters, SHE has been often studied based on the
assumption of balanced dc levels and single switching per level. In
this paper, the authors further developed harmonics injection and
equal area criteria-based four-equation method to realize OPWM
for two-level inverters and multilevel inverters with unbalanced dc
sources. For the cases, where only small number of voltage levels
are available, weight oriented junction point distribution is utilized
to enhance the performance of the four-equation method. A case
study of multilevel inverter at low-modulation index is used as an
example. Compared with existing methods, the proposed method
does not involve complex equation groups and is much easier to be
utilized in the case of large number of switching angles, or multiple
switching angles per voltage level in multilevel inverters.
Index Terms—Equal area criteria, modulation index, multilevel inverters, optimal pulsewidth modulation, selective harmonics
elimination, total harmonic distortion.
I. INTRODUCTION
HE developments of flexible ac transmission system devices, medium voltage drives, and different types of distributed generations, have provided great opportunities for
the implementations of medium- and high-power inverters. In
these applications, the frequency of the pulse-width modulation
(PWM) is often limited by switching losses and electromagnetic
interferences caused by high dv/dt. Thus, to overcome these
problems, selective harmonic elimination (SHE)-based optimal
pulsewidth modulation (OPWM) are often utilized in both twolevel inverters and multilevel inverters to reduce the switching
frequency and the total harmonic distortion [1]–[12].
A typical multilevel inverter utilizes voltage levels from multiple dc sources. These dc sources can be interconnected or isolated depending on circuit topologies. Because of the complexity
T
Manuscript received June 16, 2010; revised September 30, 2010 and
December 22, 2010; accepted February 1, 2011. Date of current version September 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: ahmadi-khatir.1@
buckeyemail.osu.edu; zou.35@buckeyemail.osu.edu; li.1012@buckeyemail.
osu.edu; hyinwh@gmail.com; wang@ece.osu.edu).
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/TPEL.2011.2116042
of the problem, most studies on SHE methods for multilevel inverters are based on the assumptions that the dc voltage sources
are balanced (equal to each other) and there is only one switching angle per voltage level. But in real applications, depending
on the nature of the dc sources and operation conditions of the
circuits, the dc sources could be unbalanced [13], [14]. Also, at
low-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-harmonics
distortion.
Thus, in this paper, the author’s four-equation-based method
[40]–[43] is further developed to solve the following three
problems:
1) SHE-based optimal switching angle calculations for twolevel 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 highmodulation indices in inverters with low number of voltage
levels.
Case studies and related experimental results are presented to
validate the proposed methods.
The paper is organized in the following way. Section II provides a brief review of different OPWM and SHE methods.
Section III presents the detailed description of the improved
four-equation-based method for 1) OPWM in two-level inverters and 2) weight oriented junction distribution for multilevel
inverters with unbalanced dc sources. Case studies of the proposed methods are shown in Section IV, whereas the simulation
and experimental verifications are shown in Section V.
II. OPWM METHODS FOR SELECTED HARMONICS
ELIMINATION
PWM method was proposed for inverters in 1960 s and digitalized in 1970 s [19], [20]. Soon after the birth of the basic
PWM method, in 1964, Turnbull proposed the SHE idea [21].
In this method, harmonic components are described as functions of the switching angles in trigonometric terms. If N is the
total number of switching transitions, as shown in Fig. 1, the
Fourier series expansion of the symmetric PWM waveform can
be expressed as
V (ωt) =
0885-8993/$26.00 © 2011 IEEE
∞
m =1,3,5,...
4Vdc
(cos(mθ1 ) − cos(mθ2 ) . . .
mπ
+ cos(mθN )) sin(mωt)
(1)
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Fig. 1.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011
Multiple switching angles in OPWM.
where m is the order of the harmonic, and θk are the kth switching angle. Based on (1), the following group of polynomial
equations can be utilized to calculate the N switching angles
and realize the selective harmonic elimination up to mth order.
Please note that the value of “m” could be much higher than
“N.”
⎧
4Vdc
⎪
⎪
(cos(θ1 ) − cos(θ2 ) · · · + cos(θN )) = VF
⎪
⎪
π
⎪
⎨ cos(5θ
1 ) − cos(5θ2 ) · · · + cos(5θN ) = 0
(2)
cos(7θ
1 ) − cos(7θ2 ) · · · + cos(7θN ) = 0
⎪
⎪
⎪
⎪
.......
⎪
⎩
cos(mθ1 ) − cos(mθ2 ) · · · + cos(mθN ) = 0
In this equation group, the first equation is used to guarantee the amplitude of the fundamental component (VF ) and
the other equations are utilized to ensure the elimination of selected harmonics. Thus, by calculating the N switching angles,
N-1 number of harmonics can be eliminated [22], [39]. In earlier days, algorithms like quarter symmetric polynomials and
Newton-Raphson method with multiple variables or linearization had been utilized to solve this equation group [23], [24].
Recently, various control theory orientated algorithms are utilized to solve this group of equations. For instance, in [25], a
clonal selection algorithm is introduced to find optimum solution with a random disturbance selection operation; in [26],
sliding mode variable structure control is proposed based on
closed loop algorithm for better performance in harmonics elimination; in [27], Homotopic fixed-point approach is utilized to
find the initial values of the roots and conduct cubic iterations
to refine the roots; and in [28], a feed forward artificial neural
network 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 harmonic
components.
For multilevel inverters, harmonics elimination follows the
similar equation group as (2). Multiple methods, such as fuzzy
proportional integral controller [30], resultants theory-based
algorithm [31], adaptive control algorithm [32], genetic algorithm [33], [38] etc., have been proposed. Online calculations
of the switching angels for both two-level inverters and multilevel inverters have also been reported [34], [35].
However, all the aforementioned methods are eventually
based on solving complex groups of equations. Therefore, for
higher number of switching transients, it is quite difficult or time
consuming to solve these nonlinear equations with current computation methods [36], [37]. Thus, based on harmonics injection and equal area criteria, the authors have recently proposed
a 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 calculations [40]–[43]. For easy referencing, different PWM strategies
for high-power two-level inverters and multilevel inverters are
categorized 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 is
utilized to generate a series of switching angles with equal area
criteria, the resulting PWM waveform would have both fundamental component and harmonics. Therefore, if selected negative harmonics are injected into the original pure sinusoidal
reference waveform, because of the nature of the equal area
criteria, the injected harmonics may cancel out the harmonics
generated by the original pure sinusoidal reference. The following is the detailed illustration of the proposed method. For the
simple case shown in Fig. 3, the harmonics content of the PWM
waveform can be described from
hm =
N
k =1,2,..,N
2Vdc
(cos(mθk ) − cos(mσk ))
mπ
(3)
where “N” is the total number of the switching angles and “m”
is the order of the harmonics. Starting from this equation, the
four-equation method includes the following basic steps:
1) Use a pure sinusoidal waveform and equal area criteria
to decide initial switching angles of θk with predefined
initial values of σk ;
2) Find the lower harmonics content in the resulting PWM
waveform with (3);
AHMADI et al.: UNIVERSAL SELECTIVE HARMONIC ELIMINATION METHOD FOR HIGH-POWER INVERTERS
2745
bers of switching angles or complex scenarios such as multiple
switching angles per voltage level in multilevel inverters.
B. Compensation of Fundamental Component
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
hm (i)
(5)
i=1,2,...
4) Use the new reference waveform and equal area criteria to
form a new set of σk and θk .
5) Repeat step 1) to 4) until the selected harmonics is eliminated. The general equation to calculate θk based on equal
area criteria is
θk = σk −
−
VF (cos(σk −1 ) − cos(σk ))
Vdc
hms (cos(mσk −1 ) − cos(mσk ))
mVdc
where V1N is the total fundamental voltage generated switching
angles from θ1 to θN . This “adjustment” angle is used to modify
the last switching angle
θN (m o dified) = arccos(cos(θN ) + cos(Δθ)).
h5s (cos(5σk −1 ) − cos(5σk ))
5Vdc
··· −
With the basic procedure described above, it was found that
the resulting fundamental component is usually different from
the desired fundamental component. This is because of possible
over modulation caused by the harmonics injection or overlap of
switching angles at high-modulation indices. Thus, fundamental
voltage compensation is needed for the proposed method. The
basic solution starts with the comparison between the resulting
fundamental component and the reference. Then, based on this
difference, a Δθ is calculated to modify the last switching angle
that is the nearest to π/2. However, this Δθ will result in more
harmonics. So, the resulting additional harmonics are calculated
and added to the total harmonics injection to improve SHE. This
“adjustment” angle can be calculated by inverse cosine in the
following equation
π
(VF − V1N )
(7)
Δθ = arccos
2Vdc
(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 initial
starting point for σk . A simple start point is to evenly distribute
initial σk s in the region of 0 to π/2.
Equation (6) also shows that in this method, there is a defined relationship between σk and θk . Thus, when compared
with methods that are based off solving high-order nonlinear
equations, theoretically, the four-equation method will have less
freedoms in eliminating the switching angles. But, because of
the simplicity of proposed method, when eliminating the same
number of harmonics, the four-equation method shall have faster
results.
To clarify the advantages and simplicity of the proposed
method, in Table I, this method is compared with other methods
that normally use the polynomial equations. Solving high-order
nonlinear equations is no longer needed, thus, advanced algorithms are also no longer required. In the traditional methods,
the number of equations grows with the number of switching
angles in nonlinear way. Thus, it is very difficult to calculate the
switching angles when the total number of the switching angles
is high. Conversely, in the four-equation method, the four basic equations are used repeatedly, the total number of equations
grows linearly with the number of switching angles. As a result,
this method would be more suitable for cases with high num-
(8)
Therefore, based on the switching angle adjustment, the desired voltage magnitude in the fundamental frequency can be
achieved. The total process of this modified method is illustrated
in Fig. 5.
C. OPWM in Multilevel Inverters at Low-Modulation Index
With Unbalanced DC Sources
For multilevel inverters, the harmonics selected for elimination are limited by the number of available dc levels. To overcome this problem, in each dc level, the number of switching
angles can be increased to eliminate more harmonic components, as shown in Fig. 6. This is very helpful, especially for
1) low-modulation indices, where limited dc levels are available in multilevel inverters with high number of total dc voltage
levels or 2) high-modulation index in inverters with limited
voltage levels. In theory, there is no limitation for the number of
switching angles used for each level. But, generally the number
of switching angles is limited by the switching losses. In this
section, as an example, the four-equation method is adapted to
achieve SHE for multilevel inverters at low-modulation index
with unbalanced dc sources, as shown in Fig. 6.
Based on equal area criteria, the switching angles are determined through the following equation
k
k −1
Vdc(i) δk −
Vdc(i) δk −1
θk = 1/Vdc(k )
i=1
i=1
+ VF (cos(δk ) − cos(δk −1 )) −
h5
(cos(5δk )
5
hm
(cos(mδk ) − cos(mδk −1 )) (9)
− cos(5δk −1 )) · · · −
m
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011
TABLE I
NUMBER 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 inverters with unbalanced dc sources.
where δk −1 and δk are the two subjunction points per each
subarea as shown in Fig. 7. The effectiveness of OPWM relies
heavily 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 is
to equally divide the total area based on number of switching
angles, as shown in Fig. 7(a). However, this strategy does not
work well for low-modulation indices. This is simply because
that with less voltage levels, larger area per level is needed in
the compensation of harmonics. Thus, the distribution of the
area becomes more crucial. However, it is also observed that
magnitudes of harmonic contents decrease as the order of the
harmonics increases
hm =
N
k =1,2,..,N
4Vdc(k )
(cos(mθk ) − cos(mδk ).
mπ
Fig. 7. Two methodologies for area division in OPWM and four-equation
combined method; (a) Symmetric method in medium and high- modulation
index, and (b) Weight oriented method in low-modulation index.
weight of the harmonics, which is shown in Fig. 7(b). In this
weight orientated solution, larger area is made available for
lower order harmonic components. Thus, better accuracy of
harmonics elimination can be achieved. The procedure for this
method is illustrated in Fig. 8.
If λk is defined by the difference between two subjunction points, δk −1 , and δk , then based on weight orientated
distribution
λk = δk − δk −1
λk +1
k+1
=
λk
k
(12)
In this case, for a symmetric waveform, the summation of the
subareas shall be π/2
π/2 =
m
λk = λ1
k =1
(10)
This means that the corresponded area needed for the compensation of higher order harmonics also decreases. Based on
this observation, in the adapted four-equation method, the area
division for low-modulation indices can be determined by the
(11)
m
k = λ1
k =1
m(m + 1)
2
(13)
thus,
λ1 =
π
.
m(m + 1)
(14)
With (13) and (14), all the subjunction points δk can be determined easily.
AHMADI et al.: UNIVERSAL SELECTIVE HARMONIC ELIMINATION METHOD FOR HIGH-POWER INVERTERS
Fig. 8.
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Block diagram for weight oriented solution in low-modulation indices.
TABLE II
SAMPLE POINTS WITH PROPOSED METHOD
IV. CASE STUDIES
Two case studies of the proposed SHE are shown in this
section: 1) two-level inverter and 2) multilevel inverter at lowmodulation indices.
A. Two-Level Inverter
In this case study of two-level inverter, ten switching angles
are utilized. The modulation index is defined as
πVF
(15)
MI =
4
where VF is the fundamental ac voltage in the output. Table II
shows some sample points achieved with this method. In this
case, δk s are simply fixed at points k · π/20. Fundamental component compensation shown in Fig. 5 is adapted for these sample
points. The switching angles vs. modulation indices are shown
in Fig. 9. Harmonics analysis in Table II shows that the selected
harmonics are precisely eliminated.
B. OPWM in Multilevel Inverters at Low-Modulation Index
With Unbalanced DC Sources
To verify the effectiveness of the four-equation method in
multilevel 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 waveforms
with five unbalanced dc sources. The modulation indices of the
waveform are defined as
MI =
VF
4 P
Vdc(i)
i=1
π
(16)
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011
TABLE III
SAMPLE 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 IV
HARMONIC 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 voltage
and current waveforms for MI = 0.6748.
TABLE V
HARMONICS CONTENT IN THE EXPERIMENTAL VOLTAGE AND CURRENT FOR MI = 0.6748
AHMADI et al.: UNIVERSAL SELECTIVE HARMONIC ELIMINATION METHOD FOR HIGH-POWER INVERTERS
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Fig. 12. Frequency spectrum of experimental results for OPWM with ten switching angles in MI = 0.6748; (a) Harmonics analysis for output voltage in load
testing, and (b) Harmonics analysis for output current in load testing.
TABLE VI
SIMULATION 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 waveform
with 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 magnitude
for each voltage level in multilevel inverter output waveform.
One possible application of this study is cascade multilevel inverters for Photovoltaic (PV). For PV modules with different
irradiations or temperatures, the dc voltage magnitudes at maximum power point are close to each other. The typical variation
is less than 15%. Therefore, in this case study, the voltage differences between two dc sources are chosen as ± 15%.
The switching angles and calculated harmonics content for
low-modulation indices are shown in Table III. At these lowmodulation indices, only one or two dc sources are utilized. But
for each voltage level, there are multiple switching angles. In
the five-level waveform, θ1 and θ2 are applied at voltage level
one; θ3 , θ4 , and θ5 are applied at voltage level two.
V. SIMULATION AND EXPERIMENTAL VERIFICATION
To verify the proposed method, simulations and experiments
have been carried out for the two case studies aforementioned.
Fig. 14.
sources.
Experimental setup for multilevel inverter with unbalanced dc
For no load conditions, dc voltage is increased up to 200 V. For
load test, the dc-link voltage is increased up to 100 V. The load
impedance are R = 3.2 ohm and L = 6 mH. A TI TMS320F2812
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 10, OCTOBER 2011
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 VII
HARMONICS ANALYSIS FOR THE EXPERIMENTAL RESULTS WITH LOW-MODULATION INDICES (FIG. 15)
DSP board is used to control the inverters. During the experiments, offline procedure is utilized. The switching angles are
precalculated, and then programmed via the TI DSP. Though
there are voltage and current sensors integrated in the inverters,
they are not utilized in the tests. The voltage and current probes
are used to read the numbers.
A. OPWM With Ten Switching Angles for Two-Level Inverter
To show the performance of the four-equation-based method
OPWM for two-level inverter, three different modulation
indices, 0.8286, 0.6748, and 0.2672, are simulated and
tested. The simulated line-line output voltages are shown in
Fig. 10(a)–(c).
The harmonics analysis of the above waveforms is summarized in Table IV. The results show that the magnitudes of the
selected harmonics for each modulation index are minimized
successfully. However, in the proposed method, number of iteration for the steps can be increased resulting in complete
harmonic elimination.
Experiments were carried out for the case that modulation
index equals to 0.6748. Fig. 11 shows the waveforms from
both no load and inductive load cases. As a comparison to
Table IV, the harmonics analysis for the voltage and load current
are shown in Table V. The spectrum analysis is shown in Fig. 12.
It is noted that there are slight difference between Tables IV
and V in terms of voltage harmonics content. The difference is
mainly due to the 1.5 us dead time and dc voltage fluctuation
caused by the oscillation between the load inductor and the
dc-link capacitor.
B. Low-Modulation Indices in Multilevel Inverters
For weight oriented solution, two cases of low-modulation
indices with unbalanced dc levels are simulated. Table VI shows
the switching angles and selected harmonic components for
these two-modulation indices. Correspondent waveforms are
shown in Fig. 13. As described in Section III(c) and III(d), the
angles in Table VI are switch turn-on points. The switch turnoff points are the subjunction points that are calculated with the
weighted area distributions. It is shown in Table VI that when
more voltage levels are involved, because of the complexity of
the problem, the performance of the proposed method degraded
a little bit, but the concerned harmonics are still minimized
effectively.
Since low-modulation indices tests only request two dc
sources, during the tests, two H-Bridge modules are cascaded to
achieve 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 the
experimental results in two-modulation indices with weight oriented solution are shown in Table VII. From both the simulation
and experimental results, it can be seen that the selected harmonics contents are eliminated effectively with the proposed
method.
VI. CONCLUSIONS
In this paper, a modified four-equation method is proposed for
selected harmonics elimination for both two-level inverters and
multilevel inverters with unbalanced dc sources. For this case
with fairly low number of switching angles and unbalanced
AHMADI et al.: UNIVERSAL SELECTIVE HARMONIC ELIMINATION METHOD FOR HIGH-POWER INVERTERS
multiple voltage levels, the weight orientated junction point distribution is applied to enhance the performance of the proposed
method. Both the simulation and experimental results validate
the proposed methods. Compared with existing methods, the
four-equation method does not involve high-order polynomial
equations, thus is friendlier toward the cases, like large number
of switching angles or multiple switching angles per dc source.
Earlier papers by the authors have demonstrated the effectiveness of the four-equation method for multilevel inverters with
single switch angle per level. In this paper, it is demonstrated
that the same method can be adopted for optimal PWM in both
two-level inverters and multilevel inverters with unbalanced dc
sources at low-modulation indices. Thus, it is fair to claim that
the four-equation-based method is a simple and universal SHE
method 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 University
of Technology, Tehran, Iran, in 2005. He is currently
working toward the Ph.D. degree in Power Electronics at the Ohio State University, Columbus, OH.
During that time, he worked on different control
strategies for ac motor drives and applying flexible
ac transmission system (FACT’s) devices for reactive
power compensation. His research interests include
multilevel inverters, real time simulation of renewable energies for smart grid, intelligent and optimized
power tracking for automotive battery charging, power electronic circuits, hardware in the loop, and DSP applications for high power systems and distributed
generations.
Ke Zou (S’09) received the B.S. and M.S. degrees
in electrical engineering from Xi’an Jiaotong University, China, in 2005, and 2008, respectively. He
is currently working toward the Ph.D. degree in the
Ohio State University, Columbus, OH.
His current research interests include switched
capacitor dc/dc converter and dc/ac multilevel inverter, battery model in high-frequency application,
and hardware in the loop (HIL) systems for power
electronics and power systems.
Cong Li (S’10) received the B.S. and M.S. degrees
in electrical engineering from the Wuhan University,
Wuhan, China, in 2007, and 2009, respectively. He is
currently working toward the Ph.D. degree in electrical engineering at The Ohio State University, Columbus, OH.
His research interests include power electronic circuits and applications, and renewable energy, thermoelectric cooling application, low-voltage high- current dc/dc converter design, and circuit analysis of
MW PV power plant.
Yi Huang (S’05–M’10) received the B.S. and M.S.
degrees in electrical engineering from the Wuhan
University, China, in 1998, and 2001, respectively.
She received the Ph.D. degree in electrical engineering from the Michigan State University, East Lansing,
in 2009.
She is currently a Postdoctoral Researcher at the
Ohio State University, Columbus, OH,. Her research
interests include dc-ac inverter, dc-dc converter, advanced digital control technique, and Photovoltaic
inverter systems.
Jin Wang (S’02–M’05) received the B.S. degree
from Xi’an Jiaotong University, in 1998, M.S. degree from the Wuhan University, in 2001, and the
Ph.D. degree from Michigan State University, East
Lansing, in 2005, all in electrical engineering.
He is currently an Assistant Professor in the energy/power area at The Ohio State University (OSU),
Columbus, OH. His Teaching Position is cosponsored by American Electric Power, Duke/Synergy,
and FirstEnergy. Before joining OSU, he worked at
Ford Motor Company as a Core Power Electronics
Engineer for two years. His research interests include high-voltage and highpower converter/inverters, integration of renewable energy sources, and electrification of transportations.
Dr. Wang received the National Science Foundation’s CAREER Award in
2011. He has been an Associate Editor for IEEE Transactions on Industry Application from March 2008.